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Managerial economics refers to those aspects of economics and its tools of analysis most relevant to the firm’s decision-making process. According to MeNair and Meriam, managerial economies consists of the the use use of econo economi micc mode models ls of thou thought ght to analy analyze ze busin busines esss situ situati ations ons.. Some Some writ writers ers consid consider er managerial economics as the integration of economic theory with business practice for the purpose of facilit facilitatin ating g decision decision-mak -making ing and forward forward plannin planning g by managem management ent.. The underly underlying ing idea of all these these definit definitions ions is that manage manageria riall economi economics cs means means economi economics cs applied applied in decision decision-mak -making. ing. So we may consider consider managerial managerial economics as a special special branch of economics bridging the gap between abstract theory and managerial practice. It may be pointed out here that effective decision-making at the firms’ level calls for a careful analysis of a choice between alternative courses of action. Economic theory offers a variety of concepts and analytic analytical al too tools ls which which can be of conside considerab rable le assistan assistance ce to the manage managerr in his his decision decision-mak -making ing process. In fact actual problem-solving may require many skills and tools which are not available in the traditional economist’s. For example, knowledge of accounting and of statistical concepts and methods, which are not taught in economics, can help the analyses to apply more effectively the economic tools in a concrete situation. The problems of industrial management do not neatly fall into one academic discipline or another. Rather they tend to out across different disciplines. Managerial economics is pragmatic, it is concerned with analytical tools that are useful, that have proven themselves in practice, or that promise to improve decision – making in the future. In the attempt to be practical it cuts through many of the refinements of theory. Managerial economies differs from other discipline in the field of economics in two important respects. First, it is that portion of economics which has to do specifically with managerial decision making. Therefore, it makes a selection from among all the theoretical tools available and those that are directly applicable, empirically based, and thus testable. These qualifications do not mean that these tools are either easier to work with or to comprehend or that they do not require atleast as high an order of economic know-how as the rest of economics. Haynes and others point out that y definition the scope of managerial economics does not extend to macro economic theory and the economics of public policy an understanding of which is who essential for the manager. This is because there is an important link between the two in so far as the decision at the firm level must take into account the trends in the economy and the impact of a host of environmental factors. Hence in our decision we extend its scope to macro economic theory also. The simplest way to calrify the scope of field of study is to discuss its relation to other subjects. In this connection it is easy to see that managerial economics has close connection with economics, the theory theory of decision decision-maki -making, ng, operati operation on research research,, statisti statistics cs and account accounting. ing. The fully fully trained trained manage managerial rial economist integrates concepts and methods form all of these disciplines, bringing them together to bear on managerial problems. Managerial economics has been defined as economics applied in decision-making. It is a special branch of economics bridging the gap between abstract economic theory and managerial practice. The primary source of concepts and analytical tools for managerial economics in micro-economic theory or what is popularly termed as Marshallian economics concepts such as the elasticity of demand, marginal cost, the short and long runs, market structures, etc. are all of great significance to managerial economics. Well-known model in price theory such as the models for the monopoly price, the kinked demand theory
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and the models of price discrimination are also made use of in managerial economics. Macro-economics aids managerial economics in the area of forecasting. Post-Keynesian theory of income and employment has direct implications for forecasting general business conditions. Since the prospects of an individual firm often depend greatly on business in general, individual firm forecasts depend on general business forecasts, which make use of models derived from theory. A survey conducted in the United Kingdom showed that business economists have found economic concepts concepts such as price elasticity elasticity of demand, income elasticity of demand, opportunity opportunity casts, the multiplier, multiplier, propensity propensity to consume, consume, marginal marginal revenue revenue products,. products,. Speculative Speculative motive, motive, production production function, function, balanced growth, growth, liquidity liquidity preferen preference ce etc., etc., quite quite useful useful and of frequen frequentt applic applicatio ation. n. They have have also found the following main areas of economics as useful in their works. 1) 2) 3) 4) 5) 6) 7) 8)
Demand Demand theory theory Theory of the the firm-price firm-price and output output Business Business financing financing Public Finance Finance and and Fiscal Fiscal Policy Policy Money Money and banking banking National National income income and Social Social accounting accounting Theory of internati international onal trade, trade, and Economics Economics of developing developing countrie countries. s.
To quote Haynes, et. Al. “The relation of managerial economics to economic theory (of either the micro micro or macr macro o varie varietie ties) s) is much much like like that that of engin enginee eerin ring g to physi physics cs,, or of medic medicin inee to biolo biology gy or bacte bacteri riolo ology. gy. It is the the relat relation ion of an appl applie ied d fiel field d to the the more more fundam fundament ental al but but more more abstr abstrac actt basic basic discipline from which it borrows concepts and analytical tools. The fundamental theoretical fields will no doubt on the long run make the greater contribution to the extension of human knowledge. But the applied fields involve the development of skills that are worthy of respect in themselves and that require specialized training. the practicing physician may not contribute much to the advance of biological theory but he plays an essential role in producing the fruits of progress in theory. The managerial economist stands in a similar relation to theory with perhaps the difference that the dichotomy between the pure and the “applied” is less clear in management than it is in medicine. The theory of decision-making ahs a significance to managerial economics. Much of economic theo theory ry is base based d on the the assu assump mpti tion on of a sin single gle goal goal-m -max axim imiz izat atio ion n of utili tility ty for for the the indi indivi vidu dual al or maximization of profit for the firm. It also rests on the assumption of certainty or perforce knowledge. The theory of decision – making, on the other hand, recognizes the multiplicity of goals and the existence of uncertainty in the realm of management. The theory of decision making invariably replaces the notion of a single optimum making invariably replaces the notion of a single optimum solution with the view what the objective is to find solution that “Satisfice” rather than maximize, It inquires into an analysis of motivation, of the relation of rewards and aspiration levels, of patterns of influence on human behaviour. The theory of decision-making, in short, is a reminder of the complexities of decision-making and the frequent needs to compromise “pure” models to make them useful in actual practice. Again, the theory of decision-making promise to contribute to the improvement of practice by focusing on new problems and suggesting new lines of attack. Managerial economics must take note of these developments. Operations research is very closely related to managerial economics. It is concerned with model building i.e. to the construction of theoretical models that aid in decision-making. Managerial economics applies these “models” of decision-making. Operations research is often concerned with optimization, econo0mics has long dealt with the consequences of the maximization of profits or minimization of costs.
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Oper Operati ation onss resea research rch,, as applie applied d to busin business ess,, gener general ally ly is conc concern erned ed with with the the broad broad,, Over Overall all operation of a company rather than with the details of a specific operation Viewing the business in its entire entirely, ly, studies studies are made made of he inter-re inter-relati lationsh onship ip and relativ relativee efficie efficienci ncies es of the various various aspect aspectss of a business in combination, such as sales production and financing. To find the most effective flow pattern, operations research may encompass the complete cycle of the flow of goods and services from suppliers to company plants, then to consumers. The primary purpose of operations research, as pointed out earlier, is to find the best (optimum) combination of factors to achieve a given objective, whether it be profit, reduction of costs, saving or time, or objectives. The resulting solution serves as a guide to company policy and decision-making. It is the “team approach” that makes operations research distinctive Operations research teams is usually usually compose composed d of persons persons from various various discipl discipline iness and professi professions. ons. Becaus Becausee of the company company wide approach approach to problem problems. s. Specia Specialist listss in such discipline discipliness as natur natural al science sciences, s, mathem mathematic atics, s, economi economics, cs, sociology, psychology, etc. are often included in the operations research team. This type of pooling of diverse talents seems to be its distinctive feature. Operations research relies heavily on mathematics and statisti statistics. cs. Most Most of the best known known operati operations ons researc research h techniqu techniques es are mathemat mathematica icall or statistic statistical al in character, as opposed to the more subjective and qualitative techniques usually used by management. Thus mathematical or statistical “techniques” such as linear programming, game theory, queuing theory, and related related methods methods are generally generally used used by operatio operations ns research researchers ers for analysi analysiss and evalu evaluation ation of the problem. As rightly pointed out by Haynes and others it is not important to determine where managerial economics begins and operations research ends. But it is important to recognize the closer relation of the two subjects and the contribution that each makes to the other. The student who \intends to do mover advanced work in managerial economics should obtain a through training in mathematics and statistics, for the models which are likely to be important, of the future will require considerable sophistication in the use of quantitative quantitative methods. Managerial economics and statistics are related in number of ways. Firstly it provides the basis for empirical testing of theory. Generalizations in economics, like generalizations in any other science, are subject to empirical test While deductive reasoning has make a central contribution to economics, the results of that reasoning can ever be fully accepted until they are verified against the data from the world of reality. Secondly, statistics is important in providing the individual firm with measures of the appropriate functional relationship involved in decision-making. Thirdly, the theory of probability, upon which many of the statistical studies are made, is also important in managerial economics. Managers generally do not have all or exact information about the vari variab able less affe affect ctin ing g deci decisi sion on,, they they must must deal deal with with the the unce uncert rtai ain nty of futu future re even events ts.. Unde Underr such such circumstances the theory of probability comes to the help of the managers in taking decisions. Fourthly, linear programming which is an important statistical technique for treating problems is used by managerial economists to find the best solution or the best alternative. Linear programming is the answer to the dilemmas of the business manager who may find it impossible to undertake personally the study of reports, figures trends and other data necessary in many decision programmes. Managerial economics is also related to accounting. Accounting is concerned with recording the financ financial ial operati operations ons of a busine business ss firm. firm. Accoun Accountin ting g informat information ion is one of he primary sources sources of data data required by a managerial economist for the decision-making purpose. For example, the profit and loss statement of a firm indicates how well or ill the firm has done and the informing it contains can be used by he managerial economist to throw some light on the future course of action – whether it should try to
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improve or close down. Managerial economics forms a part of normative economics. It tries to prescribe solutions. In other words it is concerned with what decisions ought to be made. The main body of economic theory confines itself to descriptive hypotheses attempting to generalize about the relations among variables, without judgm judgment entss about about what what is desir desirab able le or unde undesir sirab able le.. For insta instanc nce, e, the the law law of dimin diminish ishin ing g retur returns ns is a generalization about what happens to output when variable inputs are added to fixed inputs, involving no judgments about whether the results is good or bad. Normativ Normativee econom economics ics encompa encompasses sses those those branche branchess of economic economicss which which attempt attempt to combine combine descriptive economics with value judgments to arrive at policy conclusions. Public policy or the economic policy of the government is one form of normative economics and managerial economics is another. Ther Theree is one one inter interest estin ing g featu feature re of norma normati tive ve econ economi omics cs which which is of spec special ial sign signif ifica icanc ncee to managerial economics. Some of the main propositions of managerial Economics are heavily deductive. For instance, the statement that profits are at a maximum when marginal revenue is equal to marginal cost is entirely a matter of logic that does not require any check against the facts. A substantial part of economic analysis is of this character, providing a system of logic that is self-contained. But it must be pointed out that it is necessary to fit the correct data into the logical framework to reach specific conclusion about what should be done. And the question of whether a particular line of logic is useful is an empirical issue, requiring a check against the facts. Linear programming is an appropriate illustration. The logic of linear prog program rammin ming g is noth nothin ing g but but deduc deductio tion n of math mathema ematic tical al forms forms.. Given Given certa certain in assum assumptio ptions ns,, linea linearr programming denotes the logical consequences. But to use liner programming one must have he relevant data on items such as capacities, requirements, cost or whatever is involved. Economics is the science which studies human behaviour as a relationship between ends and scare means which have alternative uses. In other words, it is concerned with the study of the allocation of scar scarce ce resou resourc rces es among among compet competing ing ends. ends. Probl Problems ems of resou resource rce alloc allocat ation ionss are are cons constan tantl tlyy faced faced by individuals, enterprises and nations. During the curse of its development as a science, economics has developed a variety of concepts and analytical tools to deal with the resource allocation problems. The increasing increasing use of mathematica mathematicall reasoning reasoning and statistical statistical methodology methodology in recent years has introduce introduce a great deal of sophistication in this field. Managerial economics refers to those aspects of economics and its tool of analysis most relevant to the firm’s decision – making process. In other words, it is primarily an aid to analysis and decision making in the context of the firm and it stands firmly rooted in the foundation provided by economic theory. It has been been enric enriche hed d by the the grow growin ing g influ influen ence ce of quan quantit titat ative ive scien science cess espec especia ially lly throu through gh the the mediu medium m of operations research. The influence of and advances in management theory ahs strengthened its applied bias and is ability to be an aid in solving the practical problems faced by an enterprise.
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For most most purposes purposes economics economics can be divided divided into two broad categor categories ies.. Micro Micro Economic Economicss and Macr Macro o Econo Economi mics cs.. Macro Macro Econ Econom omics ics is the the study study of the the econom economic ic system system as a whole whole.. It inclu include dess the techniques of for determining the level and change in total exports and imports output total employment, the the consum consumer er pric pricee index index unemp unemploym loymen ent, t, rate rate and and expor exports ts and and import imports. s. Macro Macro Econ Econom omics ics addre address ss quest question ion about about the the effec effectt of employ employmen mentt and and price prices. s. Only Only aggr aggreg egate ate leve levels ls of these these vari variab ables les are considered. But concealed in the aggregate data are countless charges in the output levels of individuals firms, the consumption decisions of the individual consumers, and the prices of particular goods and services. Although macro economics issues and policies command much of the attention in the newspapers and television television the the micro micro dimension dimensionss of the economy economy also are important important end of ten are of most direct direct application of the day-to-day problems facing the manager. Micro Economics focuses on the behaviour of the individual actors on the economics stage. Firms and Individuals and their interactions in the markets. Mana Manage geria riall econo economic micss shoul should d be thoug thought ht of as applie applied d micro micro econ economi omics cs that that is manag manageri erial al economics is an application of that part of micro economics focusing on those topics of greatest interest and import importan ance ce to mana manage gers rs.. Those Those topic topicss inclu include de deman demand, d, produ producti ction on,, cost, cost, pricin pricing, g, and and marke markett structu structure re and government government regulatio regulation. n. A strong strong gaspin gasping g of the principl principles es that that govern governss the economic economic behaviours behaviours of the firms and individuals individuals as an important managerial managerial talent. In general, managerial economics can be used by the goal oriented manager in two ways. First given, an existing economic environment, the principles of managerial economics provides a frame work for evaluating whether resources are being allocated efficiently within a firm for example, economics can help the manager determine if profit could be increased by reallocating labour from a marketing activity to the production lien. Second, these principles help the managers respond to various economics signals. For example, given an increase in the price of output or the development of a new lower cost production techno technology logy,, the appropr appropriate iate mana manageri gerial al economic economicss respons responsee genera generally lly would would be to increas increasee output. output. Alternatively, an increase in the price of one output say labour, may be a signal to substitute other inputs for labour in the production process. The tools developed in the following chapters will increase the effectiveness of decision making by expan expandi ding ng and and sharpen sharpenin ing g the the anal analyt ytic ical al frame frame work work used used by Mana Manage gers rs to make make decisi decisions ons.. Thus, Thus, managerial economics can increase the value of both he firms and manager. Individuals own or control resources namely labour capital and natural resources which have value to firms because they are necessary inputs in the production process labour specialties vary from brain surgeons, to street sweepers, capital good range from electronic (Goods to) computers to brooms. Most people have labour resources to sell, and may own capital and or natural resources that are rented, loaned or sold to firms to be used as inputs in the production process. The money received by the individuals fro the sale of these pre sources can then he used to satisfy their consumption needs, demands for goods and services. The interaction between individuals and firms occurs in product market where goods and services are brought and sold and factors market where labour, capital and natural resources are traded.
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Product Markets
Product
Firms
Product
These interactions interactions are depicted depicted in Figure 1-1 In the product product Market, shown in the the top part of the figure, figure, individuals, individuals, demand goods and and service in order to satisfy their consumption desires. They make these demands known by bidding in the product marke markett for for these these goods goods and and servi service ces. s. Firms Firms anxio anxious us to earn earn profi profits ts respo respond nd to these these deman demands ds by supplying goods and services to the market. The production technology and input costs determine the supply conditions while consumer preference and income (i.e. the ability to pay) determines the price and quantity sold. In the product market, pressing power usually in the form of money purchasing flows, from cons consume umers rs,, to firms firms.. At the the someti sometime me,, goods goods and and servi service ce flow flow in opposi opposite te dire direct ction ions, s, from from firms firms to consumers. In the factor market shown at the bottom of figure 1-1 the flow are the reverse of those in the product. Individuals are the suppliers, in the tutor market and supply labour services capital, and natural services to firms that demand them to produce goods and services firms indicate their desire for these inputs by bidding for them in the market. The flow of money is from firms to individuals and factors of production, flow in opposite direction. The prices of these products are sets in this market. Prices and profits serve as the signals for regulation the flows of money and resources through the factor markets and the flows of money and goods through the product market. For example, relatively high price and profits in the personal computer industry in the 1990’s signaled producers to increase the production and more units of output to the production market. To produce more computer more laborers and capital were required Firms raised the prices they would pay for those resources. The factors market to signal resourced owners that higher returns were not available. The results was rapid growth in the personal computer industry as resources were bid away from the other sources. In the market economy individuals and firms are highly interdependent, each participant needs the others. For example, an individuals labour will have no value unless there is a firm that is willing to pay for it. Alternatively firms cannot justify production unless some consumers want to but their products. As a result, all participants have an incentive to provide what others want. All participate willingly because they have have somethin something g to gain by going going so firms firms earn profits, profits, the consumptio consumption n demand demandss of individu individuals als are satisfied, and resource owners receive wages, rent and interest payment of an individuals, does not benefit by buying and selling in these markets, he or she is not required to do so. Thus one can be sure that no individuals is made worse off by voluntary trade in these factor and product markets.
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Inside to earn profits, the firm organizes the factors of production to produce goods and services that will meet the demands of individuals consumers and other firms. The other concept of the firms plays a central role in the theory and practice of managerial economics. Thus a significant part of this text is focused on production cost and the organisation of firms in the Market place. These topics for the basis of what is in economics as the theory of the firm. An understanding of the reason for the existence of firms, their role in the economy and their objective provides a background for that theory. In a free free marke markett econo economy my the Orga Organis nisat ation ion and and inter interact action ion of produ producti ction on (ie.) (ie.) firms firms and and the consumers is accomplished through the price system. There is no need for any central direction by the Government, nor is such central control or planning thought to be desirable. Within the firm, however, transactions transactions and the organizations organizations of productive productive factors are generally accomplished accomplished by the t he general control of one one of more more manag manager ers. s. For examp example le,, work worker erss subje subjects cts thems themselv elves es to also also most most compl complete etely ly to a mana managem gemen entt durin during g the the work work perio period. d. Thus Thus there there is an appa apparen rentt dicho dichotom tomyy in the the organ organisa isatio tion n of production production in the market economy. The price system guides the decentralized interaction among consumers and firms while central planning and control intend to guide the interaction within the firms. Why does not the price system completely guide the production system) ie. Why do firms exist in a market economy? Essentially firms exist as organizations because the total cost of producing any level of output is lower than if the firms did not exist. Why these costs are lower? First, there is a cost using he price system to organize production. the cost of obtaining information on prices and the cost of the negotiating process would be very burden some firms often the hire labour for long periods of time under agreement that specify only that a wage rate per hour or day will be paid for the workers doing what they are asked. One Gener General al cont contra racts cts cove covers rs what what usua usually lly will will be a larg largee numb number er of trans transac actio tions ns betwe between en worke workers rs and entrepreneurs. The two parties do not have to negotiate a new contract every time the worker is given a new assignmen assignment. t. Such Negotia Negotiation tionss have have transact transaction ionss costs costs associated associated with them. them. Both Both Labour Labour and management voluntarily seek out such arrangement. Some Government interference in the market place, applied transaction among firms rather than within the firms. Sales tax, price controls, and rationing usually apply only to transactions between one firm and another. For example, in some area a construction company may have to pay sales tax on cabinet make makerr By hirin hiring g that that perso person n this this tax is avoid avoided ed and and the the cost cost of produ product ction ion outpu outputt is redu reduced ced.. By inte intern rnal aliza izati tion on of some some tran transa sact ction ionss with within in the the firm firm produ product ction ionss costs costs are are redu reduced ced.. Beca Becaus usee this this a secondary factors, firms would exist in the absence of such interference but it probably continues to their bring more and large firms. Given that production costs are reduced by organizing production factors in firms, why won’t this process continue until there is just one large firm such as a Giant Honda or Exxon that produce all goods and service for the entire economy? There were two reasons; first, the cost of organizing transaction within the firms tends to rose as the firm gets larger. Logic dictates the firms will internalize the lower cost transactions first and then the higher cost transactions at some point these internal transactions cost will level the cost of transacting in the market at that point the firm will cease to grow. For example all automobile producers in the work by their firms and companies that specialize in the production of rubber products. products. Hindustan Hindustan and General General parts manufacturers manufacturers must have considered considered bulgin b ulging g parts to produce their own own tyre tyres. s. The The cost cost of develo developin ping g the the new new manag manageme ement nt skill skillss requ requir ired ed for for such such a diffe differen rentt sort sort of production and the difficulty of managing an even larger and more complicated business must have been greater than the costs of continuing to buy tyres from the Good year, M.R.F., Modi and Srichakra Another example is legal services. Lawyers are not an integral parts of the production process and their services are contracted on a “When needed” basis the cost of which for most times is lower in
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contrast “large firms that have a continued need for legal service frequently have on “in house” legal staff. When When the entreprene entrepreneur ur organiz organizatio ationa nall skill skill is limited limited sources sources tithing tithing the company company may not be efficiently allocated if the firms size exceeds the managers ability to control the operation to over come this this probl problem, em, many many larg largee firms firms are are organ organize ized d into into a grou group p of divis division ion call called ed “Prof “Profit it cente centers” rs”.. The Management of each of these seeks to maximize that divisions profit by having a number of smaller organization organizationss each being managed somewhat independently. independently. The problem of limited li mited liability to control the large firm’s at least partially overcome. overcome. Both Both thes thesee reas reason onss for for a limi limitt on the the size size of the the firm firm fall fall unde underr “Dim “Dimin inish ishin ing g retu return rnss to management”. Production costs per unit of output will tend to rise as firms grow larger because of limited mana manager geria iall abil ability ity.. It shoul should d be the the probl problem em of excess excessive ive size. size. As a resul resultt of decent decentra raliz lizat ation ion by establishing a number of separate divisions or profit centers that act as individual firms. To be able to discuss efficient management of a business or other organisation, to discuss optimal decision decisionss making making requires requires that that a goal be establi established shed.. A managem management ent decision decision can only be evalua evaluated ted against the goal of the firm in attempting to achieve it. It is generally assumed that manager consistently make decisions in order to maximize profit. But profit in which period? This year? The next five year? Often manages are observed making decisions that reduce current year profits in an effort to increase the profits in future years. Expenditure for research and development, new capital equipment and major marketing programs programs are but few example exampless of activit activities ies that that reduce reduce profits profits initia initially lly but will will signific significant antly ly increa increase se profits in later year. Some managers who must report profit performance monthly or quarterly claim that the pressure for increased short term profits may cause them to make decision that increase the current profits at the expense of long terms profits.
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According to Robbins, “Economics is the science which studies human behaviour as a relationship between cads and scarce scarce means which have alternative alternative uses”. When When we analyz analyzee this this definition definition,, we find find out that it lays down down three three basic basic preposi preposition tionss which comprise comprise the main structu s tructure re of Economic Economic Science. These t hree are:
Ends here refer to human wants. Our wants are unlimited in number the satisfaction of one want immediately gives rise to another. In view of the multicipility of wants were never reach a stage when al the wants of a person are fully satisfied except after death. Since they are unlimited we have to choose between more urgent and less urgent wants.
The wants may be unlimited but the means which are available to satisfy these wants are strictly limited. The economic probe arise because most of the goods are scarce in relation to their demand. According to Prof. Milton Friedeman 66 if the means are not scarce there is no problems at all there is “NIRUNA” Here the ‘Scarcity’ is to be interpreted in a relative and not in our absolute manner. The mere existence of short supply does not lane a commodity scarce, if there is not demand for it. As Prof Robbin pointed out, the laid eggs though much smaller in number than good ones, are not scarce since in the economics sense, there is no demand whatsoever for laid eggs, which are not at all scarce in relation to their demand. On the other hand, food grains of the order of hundred of millions of tons may be available in the world market are yet food grains maybe scarce because their demand in much greater than the supply.
The Scarce means at our disposal should be capable of being put to alternative uses. A commodity with single use alone will not create any economic problem. After being used for a single purpose, the remainder of it becomes free commodity with little economic significance. In reality however, we find that a commodity can be put to several alternative uses, its aggregate demand becomes so large that its existing existing supply is insuff i nsufficient icient to meet it, and the commodity commodity concerned concerned acquires an economic economic significance. significance. The alternative uses ot which the commodity can be put should be of varying degree to importance. So that it becomes possible to select the use or the uses to which the commodity is to be put. It case, the various uses hold the same importance then it would become difficult if not impossible to choose the use to which it is to be put.
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It is evident that the economic problem. Would not arise unless all these conditions were fulfilled. An economic problem arises either to the manager of the firm or consumer only when ends, Scarce means and alternative applications of Scarce means are fulfilled simultaneously. The Scarcity concept helps us to distinguish clearly an economic form a non-economic problem. A country preparing for a war, has to make a choice between “GUNS” and “BUTTER”. The problem of choice arises because the means are scarce in relation to the unlimited ends. Time is Scarce and therefore on has to choose between competing ways of spending it. The greatest amount of choice occurs, however in the expenditure of one’s income. How much to spend on food, Clothing, rents etc., The managers have to decide the method of production they have to adopt, labour intensive or capital intensive technique. Thus, choice and cost are at the heart of economics. The “Opportunity Cost” (also known as Displacement Cost) is the direct outcome of Scarcity of measn in relation to ends. Since all the ends cannot be satisfied with the scarce means at our disposal, choice becomes inevitable. The choice of one alternative means that the other alternative is foregone. A person with a Fifty Rupees note can go to the movie or an One-Day-International Cricket Match because with a fifty rupee note he cannot see both. If he goes to the movie then the opportunity cost of the movie would be the cricket match. Bentham says the opportunity cost of a thing in the last resort is the thing which was most clearly chosen instead of the alternative alternative foregone. foregone. The problem of choice is universal as “Eric Roll puts it” It exists in the one man community of Robinson Crusoe in the patriarchal Crilo of Central Africa in medieval and feudalist Europe in modern capitalize U.S.A and in communist china. The laws of choice, like the laws of gravitation will be independ of the legal and political frame work. The problem of choice, thus arises in every society irrespective of its legal and political framework.
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“No “No war, war, no strike strike,, no depr depress ession ion,, no depre depressi ssion on,, can so comp complet letely ely destro destroyy an estab establis lishe hed d busi busin ness ess or its its prof profit its, s, as new and and bett better er meth method ods, s, equ equipme ipmen nt and and mate materi rial alss in the the hands ands of an enlightened competitor”
What What is enli enligh ghten tened ed busin business ess manag manageme ement nt?? How How can can it be ident identifi ified? ed? What What are the the metho methods ds followed by such management? The answers to these questions lead us to the heart of the management function-decision making. The quality of the decision made by management is the central clue to business success or failure. It is the ultimate test of good (enlightened) management. Let Let us, ther theref efor ore, e, exam examin inee the the proc proces esss of deci decisi sion on-m -mak akin ing g in some some deta detail il incl inclu udin ding the the fundamental concepts affecting or facilitating business decision – making.
A.R.C. Duncan defines a decision as “the appropriate response of an intelligent being to a situation which which deman demands ds actio action” n”.. W Jack Jack Dunc Duncan an defin defines es decis decision ion-ma -makin king g as “the “the act-ma act-makin king g as” as” the the act act of choosing from among alternatives. It is the way in which managers prescribe one course of action in view of the demands of a given situation. According to wheeler, decision-making is “the process of selecting a particular course of action from among a number of alternative ways of using resources to accomplish predetermined objectives”. Because a decision involves a choice that leads to some specific result the decision-maker must be aware of all the possible consequences that could result from choosing a specific course of action. In other words, the decision-maker decision-maker should evaluate the alternatives alternatives before taking taking the decision.
1) Decision-making Decision-making is a good-directed good-directed activity. Decisions Decisions are made to achieve specific specific objectives or goals. goals. When When the the goals goals or objec objectiv tives es are are simple simple,, decis decision ion,, makin making g also also becom becomes es simpl simple. e. But unfortunately, most decision situations are not that simple. Generally, the choice of an act does not lead to a single certain outcome. The consequence of selecting an act is usually uncertain. This is all the more true when the decision-maker is often forced to strike a balance between sometimes complimentary complimentary and sometimes sometimes confecting confecting goals. 2) Decis Decision ion-ma -makin king g is an inte integr gral al part part of manag managem ement ent.. Decis Decision ion-ma -makin king g and and manag managem emen entt are inseparable concepts. It embrances all the functions of management vix., planning, organizing, staffing, controlling and directing. 3) Decision-making Decision-making conscious conscious intellectual intellectual activity. Decision making making is a conscious conscious intellectual intellectual activity involving judgment evaluation and selection. Though ordinary day-to-day personal decisions are often often taken taken as a matt matter er of habit habit,, busin business ess decisi decision onss parti particu cula larly rly those those which which involv involvee huge huge inve investm stmen entt of reso resour urce cess are are take taken n afte afterr care carefu full anal analys ysis is.. They They are are subj subjec ecte ted d to rigo rigoro rous us conceptualization, deliberation, evaluation and verification. 4) Decision Decision-mak -making ing involves involves choice. choice. A decision decision is a choice choice.. More More precise precisely, ly, a decision decision is a choice choice among alternative course of action that lead to some pre-determined results. Without alternatives, there is only one course of action available, consequently, no choice can or need be made. However, if a problem can be solved in more than one ways, manages have to make conscious efforts to select the best possible course of action or alternative.
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Management Management decisions are classified under the following following head viz. i) ii) iii) iv) v)
Organization Organizational al and Personal Personal Decisions Decisions Basic and Routine Decisions Decisions Programmed Programmed and Unprogrammed Unprogrammed Decisions Decisions Individual Individual and Group Group Decisions Decisions Functio Functiona nall Decision Decisionss
Organiz Organizatio ationa nall and Persona Personall Decision Decision:: Organiz Organization ational al decision decisionss are taken taken by a person person in his capacity as a member of an organisation, whereas personal decisions are the individual decisions of a manager. Basic Basic and Routine Routine Decision Decisions: s: Accor Accordin ding g to McFarl McFarland and,, Basic Basic decision decisionss involve involve (1) long long range range commitments of relative permanence or duration (2) large investments or expenditures of funds and (3) a degree degree of importan importance ce such that a mistake mistake would serious seriously ly jeopar jeopardize dize the welfar welfaree of busine business ss “Basic “Basic decisions cover a longer time period and usually affect the entire organisation or a major segment of it. Such decisions decisions often determine determine the future direction of the company or organisation. organisation. Routine decisions on the other hand, are of, repetitive or recurring nature. They usually cover a shorter time period and affect only a small segment of the organization. Routine decisions are taken on the basis of well-established practices, techniques and precedents. Programmed and unprogrammed Decisions: Herbert A Simon groups decisions into programmed and unprogrammed categories programmed decisions refer to the routine and repetitive decision of an organ organis isati ation. on. Nove Novel, l, unstru unstructu cture red d and conse consequ quent entia iall decisi decision onss are group grouped ed unde underr unpr unprog ogram ramme med d decisions. decisions. Ingenuity Ingenuity and collective judgment play the most important role in unprogrammed unprogrammed decisions. decisions. Individu Individuals als and Group Group Decision Decisions: s: Decision Decisionss which which are made made by individu individuals als in their their capaci capacity ty as individual managers are known as individual decisions, Group decisions are taken usually on the basis of several several individuals, individuals, participation. participation. Group decision is also, therefore, known as participative participative decision. Functio Functiona nall Classif Classifica ication tion of Decision Decisions: s: Decision Decisionss are also also classif classified ied into function functional al catego categorie ries. s. Accordingly there can be as many classes of decisions as the number of functions to be performed in a business enterprise. Some examples of such functional decisions are (i) Production decisions (ii) Financial decisions decisions (iii) Marketing decisions, and (iv) Personal decisions.
As has already been point out, decision are generally taken on the basis of judgement, intuition, commonsense, commonsense, logic and/or scientific scientific analysis. Since the biggest problem in managerial managerial decision making is uncertainty no one approach can be considered best in all situations. According to Robert Albense, “The best approach depends in such factors, on the nature of the decision problem, time available, the state of techn technolo ology gy applic applicab able le to the the prob problem lems, s, skill skill and and knowl knowled edge ge of the the decis decision ion-ma -make kers rs,, costcost-ben benef efit it consideration considerationss and the degree degree of certainty in the problem situation. But, when we talk about decision-making process, we are concerned with the rational or scientific approach approach to decision decision-mak -making ing Rationa Rationall or scienti scientific fic approa approach ch involves involves a step-bystep-by-step step analysi analysiss of the problem and aims at findings out the most profitable solution. In such an approach, decision-making process is considered to be made up of a number of interrelated steps. Herbert A Simon conceptualizes three major steps in decision-making. decision-making. They are:
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i) Intelligence Intelligence activity activity i.e. searching searching the the environmental environmental conditions conditions calling calling for decision ii) Design activity activity i.e. inventing, inventing, developing developing and analyzing analyzing possible possible courses of action iii) Choice Choice activity i.e. i.e. selecting selecting a particular particular course course from those availabl available. e.
Newman, Summar and Warren classify decision-making decision-making process into the following following four steps: i) ii) iii) iv)
Makin Making g a diagn diagnos osis is Finding Finding alternative alternative solutions solutions Analyzing Analyzing and comparing comparing alternatives alternatives Selecting Selecting the the plan to flow
In the discussion that follows, the decision-making process is considered to be made up of the following steps. 1) 2) 3) 4) 5) 6)
Definition Definition and analysis analysis of of the problem Development Development of alternatives alternatives Evaluation Evaluation of alternatives alternatives Selection Selection of the best best alternativ alternativee Communicating Communicating and and implementing implementing the decision decision Follow-u Follow-up p action action
Definition and analysis of the problem. The first step in decision-making is to define and analyze the problem. Even the most complex decision problems can be solved in they are approached in a logical and consistent manner. Development of alternative solution. The second step in decision-making is the identification and listing of the complete set of viable alternative acts. There is hardly any problem which cannot be solved in more than one way. It is therefore essential for the decision maker to link for as many alternatives as possible. Evaluation Evaluation of alternative alternative solutions. The nest step in decision-making decision-making is the evaluation of alternative course of action. A large number of techniques have been developed for evaluating alternatives. Statistical decision theory theory or Bayesian decision decision theory is the foremost among them. But it may be said that judgment and common sense are the primary requirements for evaluating the alternatives. Selection of the best alternative. Evaluation of the different alternatives helps the decision-marker to form an idea of the relative importance of the various alternatives development by him. He has now to select the best alternative in the light of factors such as cost, feasibility and constraints of the critical or limiting factors. Most of the selections are made primarily on the basis of judgment and common sense. Commu Communic nicat atin ing g and and implem implemen entin ting g the the decis decision ion.. Decis Decision ion taken taken by manag manager erss are are gener general ally ly carrie carried-out d-out by their their subordin subordinates. ates. So, decisio decisions ns have have to be communic communicate ated d properly properly to those those who are expected to implement them. Hence communication assumes a significant role in the implementation of the decision taken. Follow-up action. Follow-up action, as a part of decision-making process, provides a basis for making future decisions or revising he past decisions, if required. So the development of a proper feed back system is a basic requirement for the realization of the objective. The process of decision-making in its simplest form is represented in Fig. 2.1 Definitio n of the Problem
Identificatio n of o f alternatives
Evaluation of Alternative
Selection of the best alternative
Communication and implementation
Follow up action
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The simplified model of decision – making represented in Fig. 2.1 assumes that only one course of action is selected. But in actual practice, the decision – maker may follow a multiple course of action. That is two or more alternatives may be used, or two more alternatives may be continued to form a combined course of action. But
Situation analysis Problem definition Setting up of objective Generating alternatives Evaluation of alternatives Deciding Deciding on optical optical choice Potential problem analysis Implementation Setting up feed back system Must objective objective Want objective objective The The vari variat ation ion in the the deci decisio sion n-mak -makin ing g to not in any any way way modi modify fy the the esse essent ntia iall natu ature of decision-making decision-making process. Only the laternatives laternatives are widened. widened. Two famous management experts Charles H Kepner and Benjamin B. Tregore have developed a step-by-step method which has been successfully taught to thousands of managers all over the world and used by renowned organizations such as General Electic. IBM, shell and so on F.G. 2.2 represents the flow diagram of the problem solving process developed by Charles H Kepner and Benjamin B. Tregore. If everything could be predicted accurately, then decision-making would become a fairly simple proc proces ess. s. But But when when the decis decision ion make makerr cann cannot ot contro controll comp complet letely ely then then outc outcom omee of his his deci decisio sions ns,, an element of uncertainty is introduced. In business were people are involved and can affect the outcome of decision, there are many circumstances under which the future may be wholly or partly unpredictable. Under such a situation and added burden is placed on the decision – maker and this results in three possi possibi bilit litie iess (1) (1) Compl Complete ete real realiza izati tion on of the the object objective ive (2) Parti Partial al real realiz izati ation on of the the objec objectiv tive, e, or (3) non-realizati non-realization on of the t he objective. These possibilities possibilities are illustrated below.
ALTERNATIVE COURSE OF ACTION
SELECTION OF A COURSE OF ACTION
Action A Action B Action C Action D
DECISOIN
ACTION CHOSEN
A CHOSEN PLAN OF ACTION
RESOL TO FACTION
COMPLETE REALIZATION OF OB ECTIVES PARTIAL
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Because of the presence of uncertainty, the decision-maker must be extremely careful about each step in the process of decision making. He may make use of feedback information system (a simple model of which is given below) for getting better results. FEEDBACK FEEDBACK INFORMATION SYSTEMS FOR DECISION DECISION MAKING
SOURCE
INITIAL DATA
PREDICTIONS AND INFERENCES
VALUE AND TARGET
INITIAL ACTION
COMPARE FEEDBACK DATA
SOURCE
PREDICTION AND INFERENCES
VALUES AND CHOICE
ACTION
With full realization that knowledge of the future in i n uncertain management management must nevertheless nevertheless make decision daily, and they must formulate plants for the future. There are various ways in which decision can be made made,, rangin ranging g from from off the the cuff cuff guessw guesswor ork k to fully fully info informe rmed d conclu conclusi sion onss comb combin ined ed with with good good judgem judgement ent.. Experi Experience ence has has shown shown that that the followin following g five five fundame fundament ntal al concept concepts. s. Viz the incremen incremental tal concept, the concept of time perspective, the discounting concept, the opportunity cost concept, and he equip marginal principal, help the management to take correct decisions. Here we propose to discuss each of the these concepts in some detail.
Increm Increment ental al reaso reasonin ning g invo involve lvess estima estimatin ting g the the impac impactt of decisi decision on altern alternat ative ivess on costs costs and revenues, stressing the changes in total cast and total revenue that result from changes in prices, products, procedures, investments, or whatever may be at stake in the decision. The two fundamental concepts in this analysis are incremental cost and incremental revenue. Incremental cost can be defined as the change in total cost consequent upon a decision. So also, incremental revenue can be defined as the change in
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total revenue resulting from a decision. decision. A decision is profitable if 1. It increase increase revenue revenue more than than costs costs 2. It decreases decreases some costs costs more than it increases increases others others 3. It increases increases some revenues revenues more more than it decreas decreases es others 4. It reduces reduces costs more than revenue revenue Some businessman hold the view that to make an overall profit they must make a profit on every job. Consequently, they often refuse orders that do not cover full cost (variable plus overhead) Plus some provision for profit. But incremental reasoning shows what such action from the side of management is inconsistent with profit maximization in the short run. It can be seen from the following illustration that a refusal to accept business below full cost means a rejection of a possibility of adding more to revenue than to cost.
Let us assume a case in which a new order will bring in Rs. 100,000/- additional revenue. The cost as estimated by the company accountant is as follows: Labour
30,000
Materials
40,000
Overhead (allocated at 12% of labour cost)
36,000
Selling Selling and administrative expense (allocated (allocated at 20% of labour and materials cost)
14,000
Full cost
1,20,000
From the cost estimates furnished by the accountant the above order appears to be unprofitable. But suppose that there exists idle capacity with which this order could be met. Also suppose that the acceptance of this order will add only Rs. 10,000/- of overhead (the incremental overhead limited to the added added use use of heat, heat, power power and and ligh light, t, the the added added wear and tear tear of the the machi machine nery, ry, the added added costs costs of supervision supervision etc.) The order in actually doesn’t doesn’t require any selling and administrative administrative expenses expenses as the only part of the labour cost in incremental, since some idle worker already on the pay-roll wil be put to work without without any additional pay. The incremental cost of accepting the above order is given below: Labour
20,000
Materials
40,000
Overhead
10,000
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Total incremental cost
70,000
From the accountant’s estimates of costs it appears that this order, if accepted with result in a loss of Rs. 20,000. But from the incremental cost, as it is given above, it appears that the order will result in an addition of Rs. 30,000 in profit. It may be point pointed ed out out here here ther theree is some some misun misunde derst rstan andin ding g about about incr increme ement ntal al reaso reasoni ning ng.. Incremental reasoning does not mean that the firm should price at cost or should accept all orders that cover cover merely merely their their increme incrementa ntall costs. costs. in fact, fact, “chang “changing ing what the market will bear” bear” is consiste consistent nt with instrumentalism for it implies increasing rates as long as the resultant revenues increase. The acceptance of he Rs. 100,000 order in our example depends upon (i) the existence of idle capacity which would otherwise go unused, and (ii) the absence of more profitable alternatives we would like to stress the fact that incremental concept wants to stress is that a decision is sound if it increases revenue more than costs, or reduces costs more than revenue.
Those Those who who know know the the elem element entary ary prin princi cipl ples es of Econ Economi omics cs will will at once once recogn recognize ize the the fact fact that that incremental reasoning is very much related to the marginal costs and marginal revenues of economic theory. theory. But it may be pointed pointed out here that there are similar similaries ies and differenc differences es between between incrementa incrementall reasoning reasoning and marginal marginal analysis, both of which demand attention. Firstly marginal costs and revenues are always defined in terms of unit changes in output whereas incremental costs and revenues are not necessarily restricted to unit changes. For example if one unit increase in output results in an increase in costs from Rs. 1000/- to Rs. 1010/- and an increase in revenue analysis (measurement of marginal costs and marginal revenues) enables one to have a micro scopic examination of such unit-by-unit changes. In fact, the decision maker may not be interested in such a microscopic analysis of the situation. His interest may be limited in the sense that he wants to know only whether the decision as a whole is profitable or not. To know this, he will be willing to look at the entire increase in revenue and costs. the defect of this approach is the possibility of ignoring some other change in output within the range that might be even more profitable. But it is often pointed bout that the cost of refinement in much more than the risk involved. Second Secondly, ly, incremen incremental tal concep concepts ts are more more flexibl flexiblee than margin marginal al concept concepts. s. As we have have already already noted, noted, margin marginal al costs costs and margin marginal al revenue revenue are restricte restricted d to the effects effects of unit unit change changess in put. put. But decision making, it may be noted, may not be concerned with changes in output at all. For example, the problem may be one of substuting one process for another to produce the same output. The problem is then one of comparing the cost of the first process with that of the alternative. The marginalist marginalist language is not particularly particularly suited to this kind of decision. decision. One One meth method od of compa comparin ring g marg margin inal al and and incr increme ement ntal al reaso reasoni ning ng is to draw draw a trad tradit ition ional al cost cost diagram. In the diagram marginal cost is depicted as a curve, rising over most of its range. Let us consider increasing output from 4,000 and 6,000 units what is the marginal cost of this change? It is dangerous to give any answer on the basis of the above diagram. In the range 3000 to 4000 units the marginal cost is comparatively low, but it rises rapidly afterwards. Even to speak of anything like an average marginal cost over this range is to oversimplify and to ignore the dramatic change over the range of output. But many studies of cost functions indicate the existence of constant marginal costs over a wide range of outputs. If this is the case, no error results from substituting a single marginal cost figure for the
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whole range. Let us consider that the total fixed costs of he firm illustrated below are Rs. 6000/- (per time period). The average variable cost is Rs. 2/- per unit. The marginal cost is also Rs. 2/- per unit. Imagine that that the the decis decision ion involve involvess a choic choicee betwe between en an outpu outputt of 3000 3000 units units and one one of 6000 units units.. In the language of marginal cost there is not doubt about how to express the change in cost. It is Rs. 2/- per unit. In the incremental language it is perfectly valid to speak of an addition to total cost of Rs. 6000/-. The question whether marginal costs are in fact constant may be asked at this juncture. If we could be certain of the universal linearity of short run costs, then the problem of decision-making would be greatly simplified. But the difficulty is that there is no consensus of opinion on this point. Stud Studie iess cond conduc ucted ted by Joel Joel Dean Dean Jonsto Jonston n and and Ynten Yntenia ia sugge suggest st that that cost cost curve curvess are linea linearr and marginal costs are constant in the short run. But studies conducted by Nordin failed to validate the cost linear linearity ity hypoth hypothesi esis. s. So it seems seems rather rather dangero dangerous us to assume assume that that the constan constancy cy of margina marginall cost in universal.
Short run and long run are widely known and popularly used economic concepts. The economics use these terms with the precision that is often missed in ordinary discussion. In economics short run refers to a period of time which is long enough to allow the variable factors of production to be used in different amounts in order to ensure that maximum profits are earned. But during which the fixed factors cann cannot ot be alter altered ed in amoun amount. t. For examp example le,, the the incr increas easee in the the output output of a depar departme tment nt that that requ require iress variation in the quantity of labour and materials but not the area of floor space or the number of machines. On the other hand long run refers to a period of time which is long enough to bring about possible, variations in all inputs. Building an entirely new plant is an example. Managerial Managerial economists economists are concerned concerned with the short run and long run effects of decisions decisions on costs as well as revenues. The line between short run of long run revenue (or demand) is even fuzzier than that for costs. the crucial problem in decision-making is to mai9ntain the right balance between the short run and long long run and and inte interme rmedi diate ate run persp perspect ective ives. s. In othe otherr words words,, the the mana managem gement ent shou should ld take take a long-range view of effects on costs and revenue rather than merely a “short-sighted” view. A decision may be made on the basis of short run considerations, but may, as time passes, have long run repercussions that make it more or less profitable than at first seemed. The following illustration may clarify this better. Assume a firm with some temporary idle capacity. A possible order for 15,000 units comes to management’s attention. The prospective e customer is willing to pay Rs. 3 per unit for Rs. 45,000 for the whole lot. The short run incremental cost (which ignores the fixed costs) is Re. 1/- per unit (for Rs. 150,0 150,000/ 00/- for the the whole whole lot). lot). In spite spite of this this favou favoura rable ble posit position ion,, befor beforee acce accepti pting ng this this order order,, the management must take in to consideration the long run repercussions viz. (1) What will happen if the management commits itself to a series of repeat orders at the same price (2) what will be the reaction of other customers if they come to know about the practice of accepting orders below full cost and (3) will this tarnish the image of the company? The above questions lead to the following conclusion A decision should take in to account the short run and long run effects on revenues and costs, customers reaction and company image etc., giving appropriate weight to the most relevant time periods. One of the fundamental principles in economics is that a rupee tomarrow is worth less than a rupee today. This means that a differentiation is to be made between cash received at different points in time. Even under conditions of certainty we cannot treat rupees received at different points in time as if they
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were equal equal since the earlier we receive receive a rupee, the earlier we can put ii to use to earn additional additional money. The underlying assumption there is that, in an economy in which interest and opportunities for investment exist exist a rupe rupeee recei received ved today today coul could d be invest invested ed to earn earn addit addition ional al money money immed immedia iatel tely. y. A rupee rupee to be received one year hence could not be invested until it is received. Therefore , it is less valuable than a rupee received today. In other words there is a premium for waiting to receive benefits, the longest we have to wait, the more return we should expect on out money. Stated in another way, where there is a time element there is a discounting problem. This demands the decisions-maker in business to use interest theory in the solution of a specific problem with numerical example. It may be pointed out here that discounting is nothing but the inverse of compounding. Both metho methods ds seek seek to demon demonstr strat atee the the fact fact that that a given given sum of money money in the the futur futuree diffe differs rs in terms terms of purchasing power from an identical sum today. Compounding implies that interest accruing in any one year is added to capital outstanding at the beginning of that year and interest is then charged on the total sum (interest plus capital) capital) during d uring the ensuring year. The following example will make clear the necessity of discounting. Suppose you are offered a choice between a gift of Rs. 100/- today or Rs. 100/- next year. Naturally you will select the Rs. 100/today. This is true even if there is certainty about the receipt of either gift, as today’s Rs. 100/- can be invested and can accumulate interest during the year. Suppose that you can earn 10 percent interest on any money you have at your disposal. If so, by the end of the year the gift will accumulate interest a to become a total of Rs. 110/In other words if a sum of Rs. X is invested in an interest rate or R per cent per annum, the capital will have accured by year end to Rs. X(1+) Interest on this amount is then charged during the second year at a rate of percent per annum so that at year and the capital has grown to Rs. X(1+) (1+) or Rs x(1+)². To generalize, we can say that the future worth of Rs. X at percent interest for years is Rs. X(1+) n. Another way of putting the matter that brings out the discounting principle more forcefully is to ask how much money today would be equivalent to Rs. 100 a year from now, Again assume a rate of interest of 10 percent. We must discount the Rs. 100/- at 10 percent, which means that we divide it by 1.10. thus
Rs. 100
Rs. 100
V = -----------------Rs. 90/90 1+
=
---------------------
=
1+ 0.10
Where v = Present value r = the rate of interest in other words, the present value of Rs. X, n years hence, at r percent interest is x ----------------------
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We have already noted that decisions require choices to be made among alternatives. Wherever one a alternative is chosen in preference to thers, an alternative, or opportunity cost, of some sort is incurred. Thus the decisions of company executives to accept a strike of union workers rather than pay higher wages involves costs to the company, in this case the loss of income resulting from a shut down. On the other hand, the decision to pay higher wages also entails a cost in the amount of the increased wage bill. The principle involved here is that the benefit which can be gained from any course of action is offset in part by the benefits or gains which might come from the selection of alternatives course of action. In reject rejectin ing g one one altern alternat ative ive in favou favourr of anoth another er,, the the poten potenti tial al benef benefits its avail availab able le from from the the rejec rejected ted alternative are an offset or cost to be selected alternative. It can be seen, therefore, that a net loss may occur to the decision maker if he chooses a form of action which has fewer benefits, than an alternative or better course of action. This possibility highlights the importance of careful study and evaluations of the comparative comparative advantage of the various available alternatives. alternatives. The skilful d ecision-maker ecision-maker recognizes recognizes this, so he attempts to fortify his decision by the collections and analysis of needed information to enable him to predict that course of action which will yield the best results in accomplishing an object. According to Harnes and others opportunity cost of a decision means the sacrifice of alternatives required required by that decision. The following following examples will clarify the meaning of opportunity opportunity cost concept. 1. The opportunity opportunity cost of the funds tied up in one’s own business business is the interest for profits profits corrected for differences in risk that could be carried on those funds in other ventures. 2. The opportunity opportunity cost of the time one puts into his own business business is the salary he could could earn in other occupations occupations (with a correction correction for the relative psychic income in the two occupations) occupations) 3. The The oppor opportun tunity ity cost of using using a mach machine ine to produc productt one one any other other purpo purpose se is nil, nil, since since its use requires requires no sacrifice of other opportunities. opportunities. From the above examples it can be seen that opportunity costs require the measurements of sacrifices. If a decision involved no sacrifices, it is cost free. The expenditure of cash (for the employment of labour, for example) involves a sacrifice of other possible expenditures, and so is an opportunity cost as defined here. Under this broad definition the costs that are relevant for decision – making are opportunity costs. In any discussion of opportunity cost, it is useful to make a distinction between explicit and implicit costs. explicit costs referred those costs which are recognized in the accounts. Examples are (i) Payments for raw materials, (ii) Payments for labour, and (iii) Payments for land. Implicit or imputed costs refer to sacrifices that are not recognized in the accounts. Examples are i) interest on the owner’s capital ii) rent to owner’s land and iii) salary to the owner. In our definition of opportunity cost both implicit as well as explicit sacrifices are included. It seems desirable to point out here that both incremental cost concept and discounting concept are special applications of opportunity cost concept. When excess capacity exists, it may be that the only sacrifice made in increasing a particular output is in employing variable units. Under such circumstances only part of the costs are reflected in incremental costs. Under conditions of full utilization of capacity or even even full full utiliza utilization tion of certain certain bottlene bottleneck ckss in productio production n the increment incremental al cost of any altern alternativ ativee must reflect the sacrifices of other alternative opportunities. An estimate of incremental costs thus requires the application application of opportunity opportunity cost reasoning. Fox example in the simple problem outlines earlier (in the discussion as incremental concept) on accepting the order, materials cost of Rs. 40,000/- labour costs or Rs. 20,000/- and incremental overhead of Rs. 10,000/- etc., are all opportunity costs because they all require a sacrifice in the form of payment for these factors. The other costs are excluded as they require no such sacrifices in view of the existence
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of excess capacity. If the entire capacity had been used, the estimate of incremental costs would have included estimates of sacrifices of other alternatives and would have been much higher than Rs. 70,000/Similarly the underlying reason for discounting is that when one ties his capital up in a particular project he sacrifices opportunities opportunities to earn profits on other alternatives. alternatives.
An important proposition of economics is that an input should be allocated in such a way that the valu valuee adde added d by the the last last unit unit is the the same same in all all uses uses.. This This prop propos osit itio ion n is popu popula larl rlyy know known n as the the equimarginal principal. Imagine a case in which a firm has 100 units of labour at its command. Also assume this amount to be fixed fixed so that that the tot total al payroll payroll is pre-det pre-determi ermined ned.. The firm is involved involved in four four activiti activitieses-act activity ivity.. A activity B, activity C and activity D. All these activities required the services of labour. The firm can increase any one of these activities by employing more labour, but only at cost of other activities. It is adds a unit of labour to activity. A an increase to output will result. The value of the added output may be termed as the value of the marginal product of labour in activity A. similarly the firm can estimate the value of the marginal product in activities B.C and D. If the firm finds that the value of the marginal product is greater inone activity than another, the firm must reaslise the fact that an optimum has not been achieved. This means that it would be profitable to shift laour from the low marginal value activity activity to the high high margin marginal al value value activit activityy and thereby thereby increas increasee the total value value of all product productss taken taken together. If, for example, the view value of the marginal product of labour in activity A is Rs. 20, while that in activity B is Rs. 30/- then it is profitable to shift labour from activity A to activity B. the optimum will be attained when the value of the marginal product is equal in all activities symbolically this is achieved when. We are of the view that several aspects of the equipmarginal principle need clarifications. i)
The value value of the margin marginal al products products in our formula formula are not of increme incrementa ntall costs. costs. for instance, instance, in activity A the addition of one unit of labour may result in an increase in physical output of 20 units. Each unit may sell at Rs. 1/- so that the 20 units will fetch Rs.20/-. But the increased production may also be the result of additional raw material, and/or other inputs and hence the variable costs in activity A (not counting the labour cost) are higher. Let us a assume that the incremental costs come to Rs. 10. This leaves a net addition of Rs. 10/- The value of the marginal product which is relevant for our purpose is thus only Rs. 10/-.
If there is any disparity in time in the realization of revenues that result from the addition of labour, it is necessary to discount these revenues before compressions in the alternative activities are made. For example activity B might not produce revenue almost immediately. In such a situation only the discounting of revenues will make them comparable. comparable. It may be pointed out here that the whole subject of capital budgeting discussed in chapter 9 is based on the above principle. In capital budgeting the resources to be allocated consists of the funds available to the firm. The objective is to allocate the funds where the discounted values of the marginal products are greatest, expanding the high-value activities and reducing the low-value activities until an equality equality of marginal values is achieved. achieved. The equimarginal principle holds good only in cases where the law of diminishing returns operates. To return to our earlier.
22 Value of margina
Example, as more labour is added to activity A, we except the value of the marginal product of labour to decline as shown in the above figures. We would also expect the operation of the law in other activities too in the same way, though each marginal product curve, depending.
V.M.P.A.
V.M.P.B.
V.M.P.C.
V.M.P.D.
On technology and other relevant factors, will take different shape figure 2.8 shows four marginal product curves having different shapes. Suppose that our firm allocated 25 units of labour to each activities, as shown in the above figure. Clearly the firm has not equated the values of the marginal products. The value of marginal product in activity d is much higher than the value of marginal product in other activities This means that it is profitable to transfer labour to D, from activities A,B, and C . By reshuffling labour in this way the firm can attain optimum under which the value of marginal products is equal in all activities. The optimum situation is represented in Fig 2.9 But when the values of marginal products are constant (horizontal marginal value product curves) We need an alternative form of the principle, making use of inequalities rather equalities. This form of the principle may be stated as follows – “Inputs should be applied first to activities with higher marginal product values before moving to lower values”. We would point out there that in addition to the five fundamental concepts discussed above there are certain other relevant relevant techniques techniques viz. Linear Programming, Programming, Game theory Queuing Queuing theory theory Brain storming method and concepts such as demand, elasticity of demand, cost concepts, market structure etc. Which
23
aid decision making making These T hese concepts concepts are discussed in the subsequent chapters. chapters.
24
3.2 The concept concept of Demand Function Function What will be the factors that determine the demand for a commodity? In the case of consumption, the willingness to buy a commodity, that is the demand for that, depends on the factors such as: i)
The income income of the consume consumerr
ii) The price price of the the commodity commodity iii) Prices Prices of other ot her goods and services services on which the consumer consumer spends his income iv) Tastes Tastes and prefere preference ncess of the consumer, consumer, size size of his family, family, social social customs, customs, expectat expectation ionss and adverti advertisemen sement, t, etc. Similarly, Similarly, the case of a firm or producer producer the input input demand demand for commodity commodity depends on the factors like. i)
The tota totall outlay outlay or expend expenditur ituree of the the firm firm
ii) The price price of that that commod commodity ity iii) Prices Prices of other ot her substitute substitute and complementary complementary inputs. iv) The nature nature of technology technology etc. etc. For the sake of simplicity let us concentrate on consumer demand for a commodity leaving a side the producers demand at this stage since this will be a mere repetition on consumer demand in a slightly changed terminology. A consumer’s demand function for a commodity specifies the relations ship between quantity of the commodity that he is willing to buy and the demand factors. In other words, in a demand function, the quantity demanded is expressed as a function of the demand factors for the commodity. In mathematical form we can express the demand function for a commodity as: Q x = Dx (Px Ps Pc Y T)
...... . ( 1)
Where Q s is quantity of commodity X demanded, Px is the price of the commodity, P denotes the pric pricee of othe otherr commo commodity dity which which can be subst substitu itute ted d for for X,P X,P is the the price price of a commo commodity dity which which is a complement of commodity X,Y is income of the consumer and T represents other demand factors such as tastes, preference, social customs, etc D indicates the functional form of the relationship. There may be more more than than one one subs substi titu tute te and and / or comp comple leme ment ntar aryy good goodss for for comm commod odity ity X. in this this situ situat atio ion n the the specification of the demand function of commodity X can be expanded by including their prices. The The dema deman nd func functi tion on (1) (1) may may be linea linearr or non non-lin -linea earr in shap shape. e. If it is lin linear ear then then it can can be expresses as: qx = a o + axPx + asPs + ac Pc + By + cT ......(2) Where a is a constant q x = ao + axP x + asPs + ac Pc + By + cT are also constant parameters called “marginal “marginal coefficients. coefficients. These are nothing nothing but b ut values of partial derivative of the function. The i nterpretation nterpretation of these coefficients is straight forward. If P increase by one unit, the quantity demanded Q will then change by a units, other variables remaining unchanged. Similar interpretation can be given for q x = ao + axPx + asPs + ac Pc + By + cT . Some of these coefficients may e negative like a. a and some positive like a and b in some cases Why? We will find the reasons for this shortly.
25
If the function is non-linear in shape it implies changing marginal coefficients with the levels of the concerned demand factor. For example the coefficient or P, may increase or decrease on increasing P x. One standard standard non-linear non-linear shape of the consumer demand function is logarithmic logarithmic shows s hows as: Q x = A Pxxx Psss Py Y T Where ax as ac B and Y are constan constantt paramet parameters ers (these (these are elastic elasticity ity coeffic coefficient ientss which will be defined latter on) Some of these parameters may be negative and some positive depending on how the quantity quantity demanded responds to its determinants. determinants. We cannot cannot find find the the shape shape of the the deman demand d funct function ion a prio priority rity.. It is to be determ determin ined ed only only on estimating estimating or fitting fitting the demand function. The demand function shown either by (2) or (3) is very complex in the sense that if all determinants on right hand side change simultaneously, we will not be able to say on a – priority what will be the change in the the quan quantit tityy deman demanded ded unle unless ss we have have estim estimate atess of the the param paramete eters. rs. Some Some param paramete eters rs of these these functions will be negative and some positive, so the net results of a change in Q may be negative or positive. To know the precise nature of the effect of change in all the factors of demand on the quantity demanded of commodity by a consumer, we have to examine the factors individually keeping others as constants. “This is the assumption of” others things being equal” ceteras paribus. “Let us do this.” a) The Rela Relation tionshi ship p between between Q and and P It is a common observation that for most of the commodities the willingness to buy decreases as price of the commodity increase. Exceptions Exceptions are everywhere everywhere for certain very essential goods like medicines, medicines, however there may not be inverse relation ship between quantity demanded and price. It may be straight like showing fixed quantity of the commodity that the consumer is willing to buy at different prices. Let us conc concen entr trate ate on the the norma normall case case of inver inverse se relat relation ionshi ship p betwe between en price price and and quan quantit tityy deman demande ded d of a commodity. If we plot the relationship using price and x-axis and quantity on y-axis, the graph would be seen as follows. follows. 3.1 Demand Curve In this this curve curve quant quantity ity deman demand d (Q s) resp respon onds ds to pric pricee Px. It is call called ed “dem “deman and d curv curve” e” for for the the commodity. It is a convention in economics to take quantity on x-axis and price on y-axis while drawing a demand curve as shown in Fig. 3.2 This is for the sake of convenience of representing demand and other curves together understand the process of price determination. The demand curve for a commodity shows the relationship between the price of that commodity and the quantity that a consumer is willing to buy. It is drawn on the assumption that other factors of demand remain unchanged. It is normally a downward slopping curve as we told earlier. In the form of a law we can state the relationship as following. The Law of Demand Demand – Other things things being equal, equal, the quantity quantity demanded demanded of a commodity commodity varies varies inversely inversely with its price. price. Why a consumer buys more of commodity when its price deceases and less when the price increase? Two possible explanations may be give for this at this stage. Inverted demand curve 3.2 i) When When pric pricee dec declin lines the the consu onsum mers ers sav saves one one expe expen nditu diture re whic which h brin brings gs him commodity. We may call this as “income effect”.
more more
of
that that
26
ii) A consume consumerr can substitut substitutee that that commodit commodity, y, when its price declines declines and other other prices prices remaining remaining constant, constant, for some other other commodity, commodity, This T his is called “Substitution “Substitution effect”. There is a third explanation of declining marginal utility as quantity increase but we will discuss this in the chapter on the theory of consumer behavior. b) The relationship relationship between between quantity quantity demand of a commodity and prices prices of other commodities. commodities. A fall in price on one-commodity may lower the consumer’s demand for other commodity or may raise it or leave it unchanged. Those are only three possibilities. Let us take two commodities case, S and X. If prices of say S commodity (P) increases then demand for X commodity goes up. This is possible when these two commodities are substitute for each other, ie.., they are used to satisfy same need separately. Why this happens? The answer is simple. An increase in price of S other things being constant, reduces the quantity demanded for S and increases the quantity demanded for X. The reverse of this will also be true. Consider another set of commodities C and X. If price of commodity C increases, other things being constant, the quantity demanded of C declines and also the quantity demanded of X declines and if the price of C declines then the quantity demanded of C increases but the quantity demanded of X may increase or remain unchanged. This is possible when these two goods are complementary goods i.e. they are used jointly to satisfy same need of the consumer. The third situation concerns with the neutral or unrelated goods. In an increase or decrease in price of one commodity has no effects on quantity demanded of other commodities then they are neutral or unrel unrelat ated ed goods goods.. The The price pricess of othe otherr goods goods and and serv service icess will will not not appe appear ar in the the deman demand d functi function on as determinations determinations for such commodities. Fig 3.3 shows graphically the relationships for substitute and complementary goods as discussed above.
c) The Relationsh Relationship ip between between Quantity Quantity Demanded Demanded and Income Income There are three possibilities for this type of relationship. An increase (decrease) in income of the consumer increases (decreases) the demand for he commodity. The commodities for which we get this type of positive relationship are called “normal” goods. For certain commodities like foodstuff, a rise in income causes and increases in quantity demanded in the initial stage but after a certain level of the consumer’s income the quantity demanded becomes invariable with respect to the income i.e. it remains at constant constant level. For certain commodities, after a certain level of income of the consumer. The quantity demanded starts decreasing with increase in income. The commodities which deposit this type of relationship are called “inferior” goods. Through a diagram, we can show all the three situation of the income consumption relationship are called as following (See Fig. 3.4)
27
There is a simple generalization of the relationship between consumption of goods and income for a consumer. This is known as Engel’s Law. According to this la as income increases the proportion of income spent on food declines and the proportion spent on comforts and luxuries increase. This law is quite valid as we see form our own experience as consumers. d) Tastes and and Preferences Preferences,, Social Customs Customs and Demand Demand These are quite important factors of demand for different commodities. If the tastes and preference of consumes are in favour of a commodity then its demand will increase otherwise not. Social customs are also positive positive factors factors of demand demand for a large large number number of commodit commodities ies.. Some examples examples showing showing the relevance of all such factors for demands are as follows: i)
There There is no demand demand for wheat in South South India India as there is no preferen preference ce for bread bread in this part of the country.
ii) People prefer prefer different different brand brand of same commodity because because their their tastes differ differ iii) Some students students prefer prefer to write write by dot-pen and some by fountain-pen fountain-pen iv) Ladies buy “sindoor” “sindoor” in India since since it is social custom to use it on the forehead by Indian Indian ladies. v) Sweets Sweets are offered to “Gods” “Gods” in temple in India because because of social social and religious religious customs. Advertisement and other kinds of sales promotion activities are used by business units to induce consumers preference or tastes in favour of the commodities and hence an increase in their demand. From this point of view such activities are treated as additional demand factors. e) Expectations Expectations and other Factors In prices and income are expected to increase, the quantity demanded for certain commodities may go up them. In the situation of rising prices. Consumers generally buy more and stock the commodities for future consumption. If the prices are expected to fall, they may not buy more or postpone certain type of consumption for future. Apart from expectations there might be some other seasonal or temporary factors
28
affecting the demand for a commodity in some way or other Similarly, if income is expected to rise then a consumer may buy more of a commodity since he would be able to pay for this later on. 3.3 Market Market Demand Demand By estimating the demand function as discussed above we can find the demand for a commodity for a consumer. What will be the total demand for the commodity in the country as a whole is the next question that we should try to answer. Suppose there are no consumers or customers for a commodity in the market. The total demand or market demand for the commodity will be the sum of quantity demanded by each one of them at a given price for the commodity. In the terminology of economics we call it as horizontal horizontal summation of individual’s demand to get the market demand for the commodity. Figure
PRICE
PRICE
PRICE
P1
P1
P1
P2
P2
P2
O
X1
X2
N2
O
Y1
Y2
N2
O
Z1
Z2
N2
The demand curves for three consumers 1, 2 and 3 are given in the above diagram. At P price of the commodity consumer 1 buys Ox units of the commodity, consumer 2 but Oy 1 units and consumer 3 buys Oz1 units Total market demand for this three consumers economy would be Ox 1 + Oy1 + Oz1 units at P1 price and similarly Ox 2 + Oy2 + Oz2 + P2 price. Making such additions at different prices, we can finally find the market demand curve for the commodity as shown below.
PRICE
P1
P2 O
X1
X2
Qt
29
The market demand for a commodity depends on the factors like (1) Number of customers in the market, total population or a segment of that may be used for this depending on who use’s the commodity (2) level of income in the society and its distribution, say per capital income of the country (3) prices of the commodity (4) prices of the substitute and complementary goods for the commodity and (5) Expectations, lags, preferences and other miscellaneous factors. All of these factors may not be equally relevant for findin finding g the the mark market et deman demand d for for a commo commodi dity. ty. Thei Theirr contr contribu ibutio tions ns depen depend d on the the solely solely depen depends ds on population. Demand for writing paper depends on number of students or literate people in the society. One has to be careful in identifying the relevant market demand factors for the concerned commodity. 3.4 Shift of Demand Curve Curve and Movement Along the Demand Demand Curve If income income and other other determinan determinants ts of demand demand remain constan constantt and only price price of the commodity commodity changes then we move along the demand curve. These will be a change in quantity demanded simply because of a change in price of the commodity. In this case, the demand curve remains unchanged. The movement movement along the demand curve is designated as “change “change in quantity quantity demanded”. demanded”. But, if the price of the commodity remains constant and other factors changes then the demand curve shifts it position. This kind of movement of the demand curve is designated as “change in demand” Remember quantity demanded do change in this case also but it is because of a shift of the demand curve. Panel (a) of Fig. 3.7 shows movement along the demand curve while panel (b) shows the shifts of the demand curves as at a fixed price the consumer buys more or less if his income or any other relevant factor changes.
PRICE
PRICE
O
O
(A)
3.7 Change Change in Quantity Quantity Demand Demand (b) Change Change in Demand Demand
(B)
If income of the consumer increases (decreases) his demand curve for a commodity shifts to the right (left) indicating increase increase (decrease) in demand. Other factors remaining the same. In price of any other good increases (decreases) other things remaining the same, then the demand curve for a commodity shifts to the right (left) or left (right) depending whether the other commodity is a substitute good or a complementary good. To explain this let us consider the following situations. Let X be a commodity, say tea, and S be its substitute say coffee. Suppose price of Coffee(P) increases and price of tea (P1) remaining constant. A rise in pride of coffee means less quantity demanded of coffee and more quantity demanded of tea since people now shift to tea. This means at a given priced
30
of tea there is more demand for tea. This implies a rise or shift of the demand curve of tea to the right. The reverse sequences will take place when price of coffee decreases. Now let us take the case of complementary goods say tea leaves and sugar. A rise in the price of tea leaves means less quantity demanded to tea leaves. Since sugar is used in some fixed proportion with tea leaves in preparation of tea, it means less demanded for sugar though is price has not changes. (It is presumed here that tea without sugar is not used by people). The demand cure for sugar therefore shifts to the left showing a decrease in its demand. The demand curve of sugar shifts to the right if the price of tea leaves decline. Now we come to other determinants. If tastes or preferences of consumers change in favour of a commodity then is demand curve shifts to the right showing a rise in demand. Advertisement also shifts the curve to the right but expectations may shift it to the right or left depending on what is expected to change and in what direction. If price of the commodity is expected to rise the demand curve rises i.e., shifts to the right and vice versa. In conclusion, we may summaries the above discussion by saying that a rise in the demand for a commodity i.e., a shift of the demand curve to the right means more is purchased at each price of the commodity. This may be because of increase in income, increase in the price of substitute goods, decrease in the price of complementary goods, an increase in taste, preferences etc. in favour of the commodity and expected increase in taste, preferences etc. in favour of the commodity and expected increase in price of the commodity. The demand curve shifts to the left i.e., a fall in demand means less purchases at each price of the commodity because of decrease in come, fall in the price of substitute goods, rise in the price of complementary complementary goods g oods and changes changes in tastes, preferences preferences against the commodity. commodity.
31
A businessman may not be able to find the contribution of the factors affecting the demand for its product by using the demand function framework and by fitting it to date. It may be too complicated for him. He needs a simple operational approach for this. The elasticity concept is one which meets this requirement of a businessman. The elasticity is used to measure the responsiveness of the dependent variable, say quantity demanded of a commody, to the changes in any one of its explanatory variables like price or income. More precisely, the elasticity in the case of demand is defined as the percentage change in quantity demanded attributable to unit percentage change in a demand factor (ie. Its determinants). Symbolically, Symbolically, we define elasticity as: % change in Qty Demanded Elasticity Elasticity Coeff. Coeff. = -----------------------------------------------------------------------------------------% change in Qty Demanded Say X = ( / a) 100
a
x
----- ------------- = ------------ --------x/x 100
x
(4)
a
This formula is applicable for discrete change in Q and X ie. When we move from one point to another point. Its version for continuous changes in Q and X is give as: dQ Elast lastic icit ityy Coeff eff = -------------dX
X
(log
)
-------------- ---------------------Q
(5)
(log )
This formula gives us the elasticity of demand at a point on the demand curve. It is therefore called “point-elasticity”. Using the above two general specifications for finding the elasticity. We now go in discussion discussion of various various elasticities elasticities relevant relevant for demand analysis. analysis. (i) Price Elasticity Elasticity of Demand This This shows shows the the respo respons nsive ivene ness ss of quant quantity ity deman demande ded d of a commo commodit dityy when when price price of that that commodity commodity changes, changes, other factors being constant. That is. % change in Qty Demanded Price Elasticity Elasticity (ep) = -------------------------------------------------------------------------------% of change in Price In place of % change we can use the term proportionate change also Proportionate change in Qty Demanded
32
Price Elasticity Elasticity (eP) = --------------------------------------------------------------------------------------------------------------------Proportionate change in price Consider the changes in quantity demanded and price as we move from point A to point B in the following figure (a2 – a 1)a1
a
P1
Pric Pricee Elast Elastic icity ity (eP) (eP) = --------------------------------------- = ---------------------- -------------(P2 – P 1) / P 1
P
..... .....(6) (6)
a1
For a downward sloping demand curve eP will be negative since either numerator or denominator of the above mentioned formulae will be negative in Fig. 3.17 as we move from A to B point. Is negative. There is a convention in economics to show price-elasticity by a positive number. For this, we simply take the module or absolute value of the right hand side of the above expression or put a negative sigh before the elasticity expression, ie.
|
a/a1 |
Q/Q1
ep |-------|-----------| ---| = -(------(---------------) --) |
P/P1 |
....... ........... ....(7) (7)
AP/P1
Two things are necessary to find the price-elasticity of demand one of the slope of he demand curve and second, the ratio P/Q, At any point on the demand curve we can find the elasticity coefficient (eg) by using the expression |da
P|
ep =|----------|
dQ or ep =
P
-(------ --------)
.... (8)
33
|dP
Q|
dP
a
Whenever we more along an arc of the demand curve and use the discrete formula (Eq. 7) to find the price-elasticity, we find some discrepancy in the values of the elasticity when we more in different direction along the arc. In Fig. 3.17 we use point. A as base to compute the price-elasticity for this now suppose we change the direction of movement i.e., make B point as base and compute the elasticity for moving from B an A we will get another value. This discrepancy in computation of the price-elasticity arises because of either different slope of the demand curve at B and A points or different values for P/Q ratio at these points. To avoid the discrepancy in ep it is better to take the average base for the arc. AB That is, we use the following expression for this Q ep = -------P
(P1 + P2)2
Q
P 1 + P2
----------------------------- = ----------------- --------------------- (9) (9) (Q 1 + Q 2)/2
P
Q1 + Q 2
This is called “Are elasticity of Demand”. At any point on the demand curve however, we use the expression (8) which gives us precise value for the price elasticity as the point. Let us take the demand curve q= a-b a-b P. From From this this we get get dq/dp dq/dp = -b and Therefore, Therefore, price elasticity ep = -(b.p/d) Since q = a-bP so e-( bP/(a-bP) In a straight line demand curve as shown below we can measure price elasticity of demand at any point by taking the ratio of the distance between that point to x-axis to the distance between the point y-axis on the demand curve. That is, if we want to measure price-elasticity at point. A then we have to take the ratio of AC/AB for this.
PRICE
A
MID POINT
O
C
34
At the mid point of the demand curve BC we will get ep = 1 ep will be less than unity on the lower-half of the demand curve and more than one on its upper half in absolute term. Using the formula ep = -(dQ/dP – P/Q) we can test the above results. If the demand curve for a community is a curve of the shape given by the equation. Q=A P
.... (9)
This curve gives us constant price elasticity of demand which is equal to .... We can verify this. Transforming the function into the log form we get, log Q = log A –_l –_log og P by taking the differentials we get dQ/Q = -_dP/p or dQ
P
----- ---- = -_p#O dP
.....(10)
Q
This will be curve like a rectangular hyperbola which never meets either P or Q axes. Why to we take percentages or proportions instead of absolute values of P and Q while computing pric price-e e-ela lasti sticit cityy of demand demand?? Can Can we write write e = dQ/dP dQ/dP since since this this also gives gives the the respo respons nsee of Q when when P changes. The answer to these questions is no, because by taking ratios of absolute terms of Q and P we will face the problem of units of measurements of P and Q. for one kind of measurement units of either Q and P we will get on value of the price-elasticity an for the other units we get different values foe ep. Pric Pricee-ela elast stici icity ty of deman demand d like like any othe otherr elas elastic ticity ity conce concept pt is a numbe numberr free free from from the the dimens dimension ion so measurement of Q and P. for this purpose, we take percentage or proportionate changes in Q and P while computing the price elasticity of demand and, in fact, any other elasticity by taking the percentage or proportionate changes of the concerned variables. Consider Consider a demand function as: Q = A P 1 P2 P 3 Y
(11)
Transforming in logarithmic form and taking the partial derivatives, we will get the elasticities of demand with respect to different prices P 1 P2 P3 Y as: o(logQ) -1
= ----------------
o(logQ) -2
=
------------------
(11)
35
o(logP1) o(logQ) -1
= ---------------o(logP3)
o(logP2) o(logQ) -
2
=
------------------
(11)
o(logY)
This is a very convenient way to compute the elasticities provided the demand function is of the shape as given by This magnitude of price – elasticity in absolute term varies from zero to infinity. Let us consider different different ranges of variation variation in the price-elasticity price-elasticity for interpretation interpretation.. a) ep – O. This is defined as “perfectly in elastic demand”. Quantity demanded will be invariable with respect to changes in price. The demand cure will be vertical line in this case as shown by D. in fig. 3.19 some essential essential goods like medicines will have have perfectly perfectly inelastic demand
b) O
36
could be expected expected to result from a price change, change, but in practice tennis shoes are used for general general purposes which increases its overall sales significantly making the demand for its quite elastic. 3) The nature nature of use use of a commodit commodity, y, whether whether it is essential essential or a luxury, luxury, is anothe anotherr important important factor factor influencing elasticity of demand. Whatever e the changes in prices of such goods a certain quantity is purchased by the consumer. So quantity does not very much as compared to the price of such a commodity. In the case of luxuries or non-essential goods one can postpone consumption, buy more when price decreases or buy less when price increases. 4) Percentage Percentage of consumer consumer income that is spent on a good is another another factor which which influences influences demand elasticity. Consider for example, newspaper. The demand for is inelastic. A consumer spends a small proportion proportion of his expenditure expenditure on it so even if price of newspapers newspapers goes up considerably considerably say fro Rs. 1 to Rs. 1.20 per copy, there may not be any effect on this quantity demanded salt, writing paper, fountain pen ink etc., are other commodities for which the above result may hold true. What we can say it that demand for those goods on which a consumer spends very small proportion of his income will be generally inelastic as compared to the demand elasticity for the goods on which the proportion of income spent is high. 5) Anothe Anotherr factor factor that influenc influencee price-e price-elast lasticity icity is the time horizon horizon of consumpt consumption ion Demand in the short-run for some commodities may be inelastic but it may be elastic in the long-term. Cooking gas is an example for this. In the short-run because of absence of substitutes its demand is inelastic but in the long-run, other thing being the same, there might be good substitutes for this such as solar energy, elastic heaters which will make the demand for cooking gas elastic. 6) There are other other miscellaneous miscellaneous factors such as habitual habitual consumption, consumption, durability durability of goods etc. which affect the elasticity of demand, but they are not so important as compared to the factor discussed above. It is difficult to separate out the influence of the factors as discussed above on the price-elasticity. This is because more than one factors may operate at any given time for any particular commodity or service service.. They may affect affect the demand demand in the same direction direction or in the opposite opposite directi direction. on. For practic practical al purpose, it will be wise to take all factors together rather than going for the influence of individual factors. (i) Some Application Application of Price Price – Elasticity Elasticity of Demand Demand Price – elasticity of demand is a very useful concept. Apart from its uses in explanation of several economic theories, it has operational significance in decision – making. It is also an important factor which determines the shape and position of the demand curve. Some applications of price-elasticity of demand are as follows: a) If a prod produ ucer cer wan wants to sell sell more more by reduc reducin ing g pric pricee of his his prod produ ucts cts he will will be guide guided d by the price-elasticity. To show how he will be reacting in this situation consider the following figure:
A
P1
B
P2
P1 P2
C D
N 37
Two demand curve are shown separately in parts (a) and (b) of this figure. The demand curve shown in part (a) is steeper showing inelastic demand while the demand curve in part (b) is elastic. Let us take uniform P1 price that a producer charges in the two separate situations. He sells OQ 1 amount of output at this price. The revenue he gets from the sales in the situation as shown in part (a) is given by the area OQ 1AP1(OQ 1xOP1). In the second part, he gets similarly. OQ 1CP1 revenue. Now let there be a uniform reduction of price in both the situations. As a result of a decrease in price, quantity sold increases, so the new revenue levels in parts (a) and part (b) would be OQ 2BP2 and OQ 2BP2 respectively. In which case he gets greater increase in revenue? The gain of revenue in part (a) of the figure Q 1Q 2BN while loss is P2NAP1 because of less price charged for the unit which he was selling at higher price (P 1) earlier. The net gain to the producer will be the difference to gain and loss ie. Q 1Q 2BN P2NAP1. This seems to be very low or even negativ negative. e. in part (b) the net gain would would be the differen difference ce of the area Q 1Q 2DM – P 2MCP1. Just by seeing the diagram it is positive as Q 1Q 2DM> DM> P2MCP1. What is the conclusion? We can say that a price reduction will increase revenue more if the demand is elastic. This is very important result for pricing of products. A producer will gain by price reduction when its product has elastic demand. He should not reduce price in the situation of inelastic, demand because proportionate change in quantity demanded will be less than the proportionate change in price. Price is decreasing. So demand will not increase by the same proportion which means even a loss to the producer. The reverse situation is also valid, that is, if he wants to increase his revenue by increasing the price he will not gain much if the demand is elastic. Using simple calculus we can prove this as follows: L et R = P Q
..... (13)
Where R = Total Revenue, P = Product price Q = Quantity sold Differentiating R with respect to P we get dR
dQ
---------- = Q + P--P------dP
dP
Dividing and multiplying the second term on the right hand side by Q we have dR -----dP
P Q +
dQ ------
Q
---------- Q
dP
38
or dR ---------- = Q (1+ep)
.........(14)
dP where (P/Q) dQ -------------
= ep
dP Since ep is negative so we modify (14) as dR ----------------- = Q(1-|(e Q(1-|(ep)|)
.....(15)
dP dR/dP is the change in revenue by increasing price by one unit, We find that dR/dP> O. When ((1-|(e p)|) > O or/ep/<1 This is something as we have said above ie. There will be increase in revenue by increasing price when demand is inelastic ep/>1. Its reverse is that there will be increase in revenue by decreasing price when demand is elastic. This is the revenue test of price-elasticity. We find here how important it is for pricing decisions by a firm. b) Consider Consider another application application of price-elasticity price-elasticity,, We know k now items in food will generally generally show inelastic inelastic demand. Suppose there is a good corp. of say, wheat, then price of wheat in the market declines. Because of inelastic demand for wheat even though is price has fallen. With a decline in price and simultaneously without increase in quantity demanded of wheat, incomes of farmers decline in spite of good crop. This has policy implications. Government helps farmer in this situation by fixing higher prices that what market charges or by retracting farm output. In the familiar supply and demand interaction diagram. We can show how the government should help the farmers. The point here is that price-elasticity plays very crucial role in the respect. c) A third third example example showin showing g the uses of price-e price-elast lasticit icityy is that that of introductio introduction n of new technolo technology. gy. Suppo Suppose se new new techn technol ology ogy is cost cost savin saving. g. The The unit unit cost cost of produ product ction ion declin declines es when when such such a techn technolo ology gy is adopte adopted d for for produ producti ction on.. with with redu reducti ction on in cost, cost, produ product ct price price also also declin declines es.. It depends however on the types of market which we will discuss later on. If there is a decline in price, producer will gain when there is increase in sales. This depends on the price-elasticity of demand. A new cost saving technology will be feasible only if the demand for the products is elastic. If cost declines but price does not, it is a different situation. Producer gains hereby increasing price-cost margin. Again elasticity is coming into picture even in this situation. d) Price Price – elastic elasticity ity is very very much much useful useful in findin finding g the inciden incidence ce of a tax. tax. This This we will explain explain in detail detail later on in Chapter? Whether a commodity should be taxes or not, who bears the incidence of such
39
a tax are obviously very important aspects of public policies. The price elasticity of demand is a tool for formulation of such policies. ii) Income Elasticity Elasticity of Demand The The Incom Incomee elast elastici icity ty shows shows percen percenta tage ge chan change ge in quan quantit tityy deman demande ded d when when incom incomee of the consumer consumer changes by one percent other t hings hings being b eing constant. % change in Qty Demanded
(AQ/Q, 100)
ey = -------------------------------------------------------------------------------------------------- = ----------------------------------------------------- (16) o/o change in income
(AY/Y 100)
or Q
Y
ey = ----- ------- where Y = Income Y
(16)
Q
At a point, we define income – elasticity of demand as dQ ey =
Y
----- ------dY
(17)
Q
Where dQ/dY is the slope of the Income-consumption cure for the commodity. For most of the goods the income-elasticity of demand will be positive. All such goods are defined as “normal goods”. An increase in income increases the demand for such goods. If income-elasticity of demand is negative, it means the consumption of the commodity decreases as income increases. Such commodity will be defined as “inferior good”. Among normal goods thee will be certain goods for which income elasticity of demand is greater than one Such goods are called income-elastic as demand for them increa increases ses by greater greater proportion proportion when income change changes. s. Such Such goods goods might might be called called as luxurie luxuries”. s”. For certain other goods like food or other essential commodities we may have income elasticity positive but less than one. In this situation, we say that demand is income-inelastic. In between, there might be some commodities commodities which we call “semi-luxuries” “semi-luxuries” for which income elasticity is unity. A knowledge of income elasticity do demand is quite useful one can forecast demand on the basis of income changes. This kind of exercise is done both at enterprise level as well at national level. If income rises by 10% and if income elasticity for a commodity is 2, then the quantity demanded of the commodity would be expected to increase by 20%. Under planning exercises for a county, targets for income growth are fixed for say, 3 years or 5 years. How much would be the demand for different goods and services at the end of the period would be computer exactly in the way at this example shows. (ii) Cross – Elasticity Elasticity of Demand Demand
40
This is used to measure the responsiveness of quantity demanded of a commodity say X when there is a change in the price of some other commodity, say Y Two commodities may be either substitute goods or complementary goods when they are related together. The cross elastics well tell us about their relationship relationship as well ass the interdependence. interdependence. Qx Cross Elasticity exy = ----------------
P --------------
Py
Q
d Qx
Py
or exy = ---------dP x Wher Wheree
---------
(18)
Qx
Q = Aty Aty of comm commod odit ityy X P = Price of commodity Y
For substitute goods exy will be positive but for complementary goods it will be negative. if the two goods are unrelated then e xy = 0. A know knowled ledge ge of crosscross-el elast astic icity ity is very very much much essen essenti tial al when when two or more more goods goods,, or diffe differen rentt varieties of same goods are competing among themselves. Such a knowledge will pay crucial role in certain business decision such as pricing, investment, planning advertisement and so on. The inter-dependence between firms in the same or different industries can analyze apart other things, on the basis of cross elasticities elasticities of demand for their products. products. The The conc concep eptt of elas elastic ticity ity can can be applie applied d to other other facto factors rs such such as advert advertisi ising ng and othe otherr sales sales promotion activities. We can find, for example, “promotion elasticity of demand” as proportionate change in quantity demand divided proportionate change in advertisement expenditure for the commodity. The interpretation of the magnitudes of such elasticities can be done exactly in the same way as for the price or income elasticities.
41
The basic materi material al relatin relating g to demand demand,, supply supply and market market equilib equilibrium rium has been presented presented in Chapter – 3. The demand side of the market for a commodity concerns with consumer behaviour. Hitherto we have simply defined the term “demand”, identified is major determinants and examined its role in price determination determination i.e., in market market equilibrium for a commodity without going through the analysis of consumer’ consumer’ s behavioral patterns upto with it is based. In this chapter we discuss this aspect, i.e. we will present the modern theory of demand. We know that consumer is a very important factor in economic system. The goal of economic activities is ultimately to satisfy consumer needs directly and indirectly. Keeping this in mind, mind, we will will exami examine ne the prin princip ciple less or laws laws which which gives gives us the the too tools ls for for the the analy analysi siss of cons consume umerr behaviour behaviour in the market.
We start our analysis of consumer behaviour by posing a simple question : Why does a consumer purchase a particular commodity? The answer is simple: using the commodity the consumer satisfies his need or want. He buys food when he is hungry. In a technical terms a consumer purchases a commodity because it has utility for him. The term “utility” is defined as power of a commodity or service to satisfy human want i.e., to yield a consumer some satisfaction. Consumer’s Consumer’s preferences of goods and services services or any other thing, economics or non-economic non-economic,, are formalized by the concept of utility. It is a subjective phenomenon. The feeling of satisfaction or utility derived from consumption of a commodity or use of a service may vary from person to person because each person’s physiological and psychological make-up is different from every other. There will be several factors affecting an individual’s feeling of satisfaction and measurement of all such factors is an extremely difficult task. It not impossible. In view of such difficult economists concentrate their attention on certain basic quantifiable economic variable for explaining consumer’s feeling of satisfaction or utility. A number of non-quantifiable factors like aesthetics, love, friendship, security etc., do affect human behaviour but econom economists ists treat treat them constant constant in the consumpt consumption ion time horizon horizon.. In other other words, words, the utility utility analysis analysis carried on by economics runs in terms of quantities of goods and services, income, and prices, keeping all other things constants. A consumer at a time consumes one or more commodities. He gets satisfaction or derives utility by consuming the goods. The level of satisfaction or utility derived by him depends on quantities of the goods consumer. This is a basis hypothesis of the consumer theory. According to this, we say that utiity derived from consumption of a commodity depends exclusively in its quantity other things being constant. In symbo symbolic lic form form we write write the the relat relation ionsh ship ip betwe between en the the level level of util utility ity and and quan quantit tityy of a commo commodit dityy consumer as:
Where Us is a the level level of utility, utility, q is the quantity of o-th commodity and f denotes the shape of the relationship. There are n commodities.
42
When all n commodities are consumer simultaneously, the total utility derived by the consumer will be a sum of utilities derived form consumption of individual commodities. That is Substituting Substituting the right hand hand side of of equation (1) for U U......we U......we get This may be simplified as This is called called “utility function” function” A utility function specifies the relationship between total utility derived and quantities of different goods consumed at a time. We have used simple additive principle for getting total utility by summing up the utilities derived from from consum consumpt ption ion of differ differen entt commo commodit ditie ies. s. This This impli implies es that that the the util utility ity deriv derived ed form form one good good in independent of the rate of consumption of any other gods. This is an assumption which might no the true in practice. However, we take consumption of all goods simultaneously and derive utility from that, which the utility function shows us. The assumption of additives utility is not necessary for this, only it simplifies the complexity of utility analysis. It is presumed that utility can be measured just like any other economic magnitude. This is a cardinal approach for utility analysis. This approach has been challenged by several econ econom omist istss on the groun ground d that that utili utility ty being being a subje subject ct pheno phenomen menon on cann cannot ot be measu measured red in terms terms of numbers, weight or the like. They suggested a different approach by taking the stand that utility level though no measurable, can be compared with each other. This is ordinal approach for utility analysis. In this chapter, we will study both the approaches initially, we will concentrate on the cardinal approach to explain consumer behaviour. Every consumer will have a utility function showing his preferences. This function is assumed to be single-values and continuous. By single valued we mean the consumer gets only one level of satisfaction and not two or more when he consumes a given quantities of different goods. If we change the quantity of any one commodity keeping other constant or change the quantities of other goods also then of course he moves to different level level of utility. By continuous function function we mean that the first and second order order partial derivatives of utility with respect to quantities of goods and services can be derived form it. This is a necessary requirement of the function as on its basis we derived from it. The laws which govern consumer behav behaviou iours rs in pract practice ice it the consum consumpti ption on activi activity ty embod embodie ied d in the form form of a util utility ity functi function on is not continuous them it may be difficult to get any kind of generalized laws or principles regarding consumer behaviour. The level of satisfaction or utility derived from consumption depends on length of consumption period. From example consumption of 10 cigarettes per liour or per day or per week or per month will give different levels of satisfaction. Keeping this in mine, one has to define he consumption period very clearly for which the utility function has been defined. Let us take the first – order partial derivative from the utility function There are: òU/òq1 = F1(q1....qn) òU/òq2 = F2(q1....qn) òU/òqn = Fn(q1....qn) òU/òq1 = F1(q1,q2,qi ) i = 1, 1, ...n ...n A partial derivative of the utility function is interpreted as the change in total utility by consuming one more extra unit of a commodity keeping the levels of consumption of other commodities constant. In economic terminology, the partial derivatives are called “marginal utilities” of the commodities for the
43
cons consume umer. r. Marg Margina inall util utility ity of a commo commodi dity ty is defin defined ed as the the chan change ge (or (or addit addition ion)) in tota totall utili utility ty by consuming one more extra unit of the commodity, consumption of the other commodities remaining the same. If 10 units of a commodity y give 100 units of utility and if 11 units give 115 units of utility, then marginal utility of 11th unit of the commodity is 15 units.. How does marginal utility of a commodity change, if the quantity of consumption of the commodity increases? There is a basic law of economics known as the “law of diminishing marginal utility” which show this. According to this law. A quantity consumed of a commodity increases, the marginal utility of that commodity tends to decline. This say that declines as = q increases. It means the rate of change of marginal utility is negative. this expressed expressed using the second second other partial derivatives derivatives from the utility function function as One can cite several example from real life in support of the law of diminishing marginal utility. Take the example of a smoker. The first cigarette he consumes bring considerable amount of satisfaction to him. The satisfaction derivated from the second cigarette will be lower and this way succeeding units of cigarette give him less and less satisfaction. In fact, he may stop smoking cigarette alter two or three which implies zero marginal utility for any more cigarettes. It may be negative if he goes beyond the level of consumption which gives him zero marginal utility. The variation in total utility and marginal utility as quantity of consumption of a commodity increases can be shown graphically as following :-
The total utility as shown on the left hand side in the above diagram increases at a diminishing rate, reaches at maximum level for 6 units of he commodity. The slope of tangent at any point on total utility curve gives us marginal utility. Marginal utility is declining continuously. It is zero when TU is maximum. After this, it is negative as TU declines. A rational consumer would never go beyond the zero level of marginal marginal utility while consuming a commodity. commodity. The The law law of dimini diminish shin ing g margi margina nall util utility ity is valid valid only only when when (1) (1) there there is not not time-t time-tap ap betwee between n consumption of successive units of he commodity. In other words, consumption is continuous, (2) tastes or preferences of the consumer remain unchanged during the process of consumption : and (3) all units of the commodity are similar in size, quality and other attributes. There are some exception s to the law of diminishing marginal utility. Consumption of liquor defies the law. The more a person drinks, the more he like it giving a positive relationship between marginal utility and quantity of liquor consumed. This may be true initially but there will come a stage when the drunkard drunkard starts taking taking less and less liquor and eventually eventually stops it. Another exception exception to the law is that of hobbies like collection of stamps, coins, paintings etc. A person derives satisfaction from such collection and the more he collects the relevant item the more satisfaction he gets. This is not true. We find that under hobbies people collect different varieties of the item and not the similar one. For similar varieties we find find that that his his marg margin inal al utili utility ty decl decline iness very very fast. fast. Some Some econo economi mists sts argu arguee that that the the law law of dimini diminish shin ing g marginal utility does not hold true for money. Desire for more and more money is a universal phenomenon. Money is not a commodity, rather a medium of exchange and a standard for valuation. It is not consumed but used to buy goods for consumption. So it is unfair to apply the law of diminishing marginal utility to it. Even if we do so, we can safely say that marginal utility of money for a poor man would be more as compared to a rich man. So we can say that marginal utility of money declines with richness and hence the law is valid even in this case.
44
What about marginal utility of diamond? The situation is similar to that of liquor. Initially it may increase but eventually it will decline when there is no more scope for a man for demonstrating his wealth by having diamonds. Why does the law of diminishing marginal utility hold good in practice? The validity of the law is an empirical fact. It is widely believed despite the absence of a generally accepted measuring rod for utilities. What we find in reality if that a consumer may not be able to satisfy all his wants but his desires or wants for individual commodities are suitable. He consumes a commodity of the commodity at this point because he feels that the additional units of consumption would not increase his total satisfaction rather it would be reduced. This implies zero marginal utility of the commodity at the optimum consumption level and negative beyond that point. If this is not so, the consumer would never be situated with the consumption of the commodity. We do not find any support for this. What we observe in practice as consumer is that the feeling of satisfaction from incriminator consumption of a commodity gradually decreases with increase it consumption of the commodity. Greater the total satisfaction already achieved the lessor would be the effect of an extra or marginal unit of consumption. Thus, our own psychological reactions or feelings of satis satisfa facti ction on to extra extra cons consum umpti ption on of a commo commodit dityy provi provide de the the proo prooff for for the the vali validit dityy of the the law of diminishing marginal utility to practice. How this law helps us in finding the optimal level of consumption of a commodity by a consumer can be demonstrated through a numerical example. Consider the following one. The utility function for a commodity to a consumer is given as U – 100 Q – A. Where U is total utility and +Q is quantity of the commodity consumer. How much of Q the consumes? We maximize the total utility utility which gives us the condition condition for for zero zero margin marginal al utility utility and hence hence optimum optimum consump consumption tion of he commodity. Differentiating U with respect to Q we get. MU = dU/dQ = 100-2Q. for maximum utility MU=O ie., 100-2Q=0 which means Q-50 units. Beyond this level of consumption we find that MU is negative i.e., aU/dQ=-2 so the consumer will not cross the limit of consumption of the commodity beyond 50 units.
A consumer at a time needs several goods and services for consumption. His income is limited and it may not be possible for him to buy whatever he desires. He faces fixed prices of commodities in the market. In this situation how should he decide buying of the commodities? What commodity he should he decide buy and in what amounts that is to say how should he allocate his limited income on various goods and services so that the gets maximum satisfaction or utility? The problem here is that of maximizing total utility of consuming all goods and services subject to the income constraint. The solution of this problem for further discussion, let us make some assumptions to simplify the analysis. The The first first assum assumpt ption ion is that that util utility ity is measu measura rabl blee thou thought ght card cardina inall scale scale.. That That is what what we are assuming so far in the utility analysis. The second assumption is that goods and services are continuously divisible. The third assumption is that goods and services can be substituted for each other. The consumer can spend money on one commodity or the other. This kind of flexibility has to be assumed for attaining equilibrium conditions. The fourth assumption is that the consumer is rational. He has full knowledge about the market i.e. commodities, their attributes, prices etc. lastly, we assume that there is no negative consumption consumption of any commodity. Given the assumptions cited above, we can formalize a consumer’s problem as. max. U = f(q 1,q2,.......qn) Subject to yo = p1q1+P2q2+.......+Pnqn
45
Y is fixed fixed income income P P...P P...P are fixed fixed prices prices for q q...q q...q respec respecti tive vely. ly. The constr constrai ains ns specif specified ied cons consume umerr budge budgett line. line. The The right right hand hand side side of this this constr constrain aintt indic indicat ates es consu consume mer’s r’s expen expendi ditu ture re on different different goods and services. The total expenditure expenditure cannot cannot exceed total income. The consumer utilizes all his income, that is why we are equating total expenditure to total income. The utility function is assumed to have a maxima otherwise it may be difficult to find the consumer equilibrium position. For For solut solution ion of the the cons constr train ained ed utili utility ty maxim maximiza izati tion on probl problem em as speci specifi fied ed here here we apply apply the standard Lagrange Method: The steps involved here are: a) Find Find the first order order or neces necessary sary condition conditionss for a local local interior interior maximum, maximum, (b) verify verify the second second order conditions for this and (c) make sure that the conditions for global maximum are satisfied. Out interest here is in finding the global maximum for consumer’s utility. Using the utility function (4) and the budget constraint (6) let us define the lagrand function as V = f(Q 1,q2,q3,...qn) + /[Yn-P1q1-P2q2-Pnqn] Where Where is defined defined as the Lagran Lagrange ge Multip Multiplier lier.. Taking partial partial derivativ derivatives es of V with respect respect to q, = q q and. We get the first order condition for maximum uitility as òv/òq1 = f 1-/P1 = 0 òv/òq2 = f 2-/P2 = 0 òv/òqn = f n-/Pn = 0 òv/ò/=Yo-P1q1-P2q2...Pnqn = 0 Where Fi = aU/aqi = Marginal utility of fifty commodity I = 1 to n We have equated the first order partial derivatives of the Lagrange function to zero by assuming that the second order conditions for a local and the conditions for a global maximum are satisfied? From the first n equations of (7) we get the relations F1=/P1, F2=/P2 .....Fn=/Pn or F1
F2
F3
Fn
-------
---------- ----------- ----------- ---------- = /
P1
P2
P3
Pn
or more explicity explicity MU1
MU2
MU3
MUn
------- = ------- = ------- = ------- = MU of Money (= / ) P1
P2
P3
Pn
46
2. The second second order order condition conditionss for constrain constrained ed maximum maximum with one constrain constraintt are that the bordered bordered principal minors. F11 F12 - P1
F11 F12 F13-P1 F11 F12...FN-P1
F21 F22 – P 2
F21 F22 F23-P2 F21 F22...F2N-P2
-P1 – P2 O
F31 F32 F33-P1 Fn1 Fn2 Fnn - Pn - P1 – P2 – P3O -P1-P2....PnO
This is the equilibrium condition for maximum utility with income constraint. This relationship says that that for for obtain obtainin ing g maxim maximum um satis satisfa fact ction ion (ie. (ie. Utili Utility ty)) from from consu consumpt mption ion of goods goods and and servic services es,, the consumer spends his income on these goods and services in such a way that the last unit of money spent on each good or service brings him the same marginal utility. This is the law of equi-marginal utility or the law of commodity substitution. substitution. This is a very important condition for consumer equilibrium. On the basis of this the consumer allocates his income. He must ensure that marginal utility to the marginal utility of money For any pair of commodities commodities we can further write the equilibrium equilibrium condition as. MU1
P1
MUi
Pi
------ = ----- = ------- = -----MU2
P2
MU j
P j
The ratio of marginal marginal utilities utilities of two commodities must be equal to the ratio of their prices. The ratio of marginal marginal utilities utilities of tow goods defines the rate of substitu s ubstitution tion between these goods ie., Rate of substitution of X 1 for X2 dX2
MU1
P1
------------- = ------------- = ----------dX1
MU2
P2
Let us consider the two commodity case again. We have the equilibrium condition MU1
MU2
------ = ---------P1
P2
47
MU1 Supp Suppos osee
MU2
------------- >-->------------P1
Here the consumer is getting greater marginal utility per unit of money spent on commodity 1 than the marginal utility per unit of money spent on commodity 2. How he will react to this situation? He increases his expenditure on commodity 1 ie., buys more of it, but as his consumption of commodity 1 incr increa eases ses,, the the marg margin inal al utili utility ty deriv derived ed from from that that decre decreas ases. es. It mean meanss MU/P MU/P decre decreas ases es which which will will be eventually equal to MU/P ratio for the second commodity. This way he attains equilibrium. The ratio Mu/P must be equal to marginal utility of money. Consider just one commodity. We have the equilibrium condition for consumer in this case as: MU1/P1 = / (ie., (ie., MU of of money) money) or MU1 = / P 1 Equati Equation on (12) (12) expre express sses es a very very usefu usefull relat relation ionsh ship ip betwe between en marg margin inal al utili utility ty and and pric pricee of a commodit commodity. y. Using Using this this relatio relationsh nship ip we can establish establish the link, link, between between margin marginal al utility utility schedule schedule and demand schedule of a commodity. This was done intuitively by Mashall. When When a consume consumerr buys a commodi commodity ty he gains utility utility by having having it. At the same time he makes a sacrifice of utility of money by paying for the commodity. A rational consumer will buy a commodity if the gain of utility to him is more or atleast equal to the loss of utility of money. The gain of utility whey he buys the commodity is nothing but its marginal utility and the loss of utility of money. This is the same thing as shown by expression (12) which is the condition for the consumer equilibrium. On order to show this simple relationship between marginal utility and price of a commodity graphically, let us consider the information information given in Table 4.1 Table 4.1 Derivation of demand Curve from MU curve for a commodity. Qty. (No. of units) price
MU of Successive Successive units
Pric rice per unit
Loss of utility ity of money (MU of money) x
1.
MUn
Pn
/ Pn
2.
MU12
P12
/ P 12
3.
MU13
P13
/ P 13
4.
MU14
P14
/ P 14
5.
MU15
P15
/ P 15
48
6.
MU16
P16
/ P 16
7.
MU17
P17
/ P 17
MUn, MU12...MU17 represen representt margin marginal al utility utility of success successive ive units units of commodit commodityy 1 and P 11, P12, P17 represent variation in price of the commodity is marginal utility of money. Total utility of money given up for buying each unit of the commodity will be times the price. This is shown in the last column of the table. Let us assume that marginal utility of money is constant. From the law of diminishing marginal utility we can derive the implication as follows – MU11 > MU12 > MU13 .... .... > MU MU17 Since at the equilibrium MU = P so the right hand side will also show similar variation in the price of the commodity as is constant. Therefore, we say P11 > P12 > P13 > ....... P 17 By plotting (13) and (14) against quantity of the commodity we get, marginal utility and demand curves for the commodity. The two curves will show exactly similar variation. Both will be coinciding when /= 1 Demand curve will be above the marginal utility curve when and it will be below the marginal utility schedule when />1. This is the approach followed by Marshall to derive the demand curve form the marginal utility curve. Since marginal utility declines with increase in quantity consumed, so price of the commodity declines with increase in quantity bought. This gives us the explanation of way the demand curve slopes downward apart from the two other reason mentioned earlier in chapter 3.
If marginal utility is zero, then equilibrium condition MU = / P shows that price of the commodity will be zero since marginal utility of money is nor zero. This is the situation for all free goods. Such goods are freely available to consumers. They consume these goods at the level which gives them maximum total utility. At that level the marginal utility will be zero. There is not question of consuming less of them when they are freely available. available. The Paradox of value. In practice we find several commodities like water and air which are essential for life. Without such commodities we cannot survive. Their value to life a very high but they are almost free freely ly avai availa labl ble. e. On the the other other hand, and, ther theree are are some some comm commod odit itie iess like like diam diamon ond, d, whic which h are are quit quitee unnecessary for human life but their price is very high in the market. There is thus, a “paradox of value” which is to be resolve. We known, air and water are essential goods their “use – value” ie., “total utility” is very high but being almost free goods their “exchange-value” in market is very low of zero. This is because because their marginal marginal utility utility is zero. zero. The price of a commodity commodity it., its “excha “exchang ngee value” value” depends depends on marginally utility of that commodity and the use value depends on its utility. Thus there are two concepts of “value” which value depends must be clearly understood to remove the “paradox of value” seen in reality.
49
Consid Consider er the first order condition condition of constr constrain ained ed utility utility maximizat maximization ion as express expressed ed by the set of equations (7) we have n+1 equation in the set and the number of unknowns is also n+1, ie., n commodity levels q 1 > q2 and qn and / the value for the Lagrange multiplier. The system of equations is therefore soluable. The solution for the unknown would be to express their values in terms of known variables. There are q1 = -1(P1, P2, .... PnY0) q2 = -2(P1, P2, .... PnY0) qn = -n(P1, P2, .... PnY0) and / = / o(P1, P2, .....Pn, Yo) Where -1-2,..... -n and /o are functional relations These equations equations are demand functions for the different commodities. commodities. In each specification, specification, we are expressing the quantity demanded as a function of price of the concerned commodity, prices of other comm commod odit itie iess used sed by the the con consume sumerr and and his inco income me leve level. l. The The othe otherr thin things gs like like tast tastes es,, cust custom om,, expectations etc. mentioned as additional demand factors are treated to be constants. Intuitively, we have spec specif ifie ied d such such deman demand d func functio tion n for for a commo commodit dityy in chapt chapter er 3. Here Here we have have used used the the cons consume umerr equilibrium theory to derive them. They are related to the utility function from which they hate been deduced. Let us consider an example with two commodities. There utility function and budget constraint for a consumer are given as U = q1.q2 and yo = P 1q1+ P2q2 For maximizing (16) subject to (17) as constraint, we write the Lagrange function as V=q1q2 + / [Yo-P1q1-P2q2] By taking the partial derivatives of V with respect to q 1,q2 and / and equating each one of them to zero, we get, òV/òq 1=q2 - /P1 = O òV/òq 2=q1 - /P2 = O and òV/ òV/ò/ ò/ = yo-P1q1-P2q2=O and we get
50
Yo
Yo
q1 = --------- q2 = -----------------------2P1
2P2
As we have mentioned earlier, the shape of the demand curve for any commodity depends on the nature nature of the utility utility function. function. In this example example the utility utility funct function ion is such that it gives gives exactly exactly similar similar demand demand functio function n for the the two commodit commodities. ies. Demand Demand for for each one one depends depends direct directly ly on income income ( ) and inversely with price of the commodity. The marginal utility of money ie., can also be found from the system of firs order maximization conditions. In the above example it is Y / = ----------------------------2P1P2 If the utility functions are given as U – log(q.q) the solution or expressions for demand functions derived derived from from them them would would be be exact exactly ly simila similarr to (22) (22) when when U = q q. The The value value of ofcour ofcourse, se, will will chang change. e. All these utility functions belong to the same class ie. they are monotonic transformation of each other and therefore represent the same preference preference ordering ordering of the consumer reflecting reflecting the same behaviour. behaviour. We have defined / as marginal utility of money. Let us show how this interpretation of / is valid. Consider the first order conditions of constrained utility maximization expressed by the equations set (7). We find that at the equilibrium / is equal to marginal utility of any good divided by its price. That is F i = òU/òq1 = / P i or / = 1/Pi(òU/òPi) Since, Since, Pi is constant we can take it inside the bracket in the denominator òU / = ------------------ò(P1q1)i P1q1 shows the expenditure on its goods. At the equilibrium and additional unit of money spent on good i(i=q..n) therefore, provides the same increase in utility. (unit change in P is one unit of expenditure ie....of money) We can, therefore, say that is the change in maximized value for utility as income changes. / = òU/òY or / = 1/P i òU/òq1 Further, we can show it by using some mathematical expressions. U = F(q 1, Q 2) By taking total differential of this, we have
51
dU = F1dq¬ + F 2dq2 the income constant is Y = P 1q1+P2q2 By taking total differentiation of this, we have dY = P 1dq1 + P2sdq2, P1 & P2 are constant from maximization condition condition we have the equilibrium condition F1-/P1=O, F2-/P 2 = O Substituting Substituting values for F1 and F2 in (25) we get dU = / P 1dq1 + / P 2dq2 dividing (27) by 26) we have dU
P1dq1+P2dq2
----------- = / [ ---------------------------------------------------] --] = / dY
P1dq1+P2dq2
So, marginal utility of money equals / The demand functions derived above the homogeneous of degree zero in prices and income ie. if all prices and income change in the same proportion then the consumer equilibrium position, will not change change and quantities quantities demands will also be unchanged. unchanged. Let us reformulate the budget constraint of the consumer as KYo = KP1q1 + KP2q2 Using the utility function U = F(q 1q2) Langrange function for maximization U will be V = F(q 1,q2) + / [KYo=KP1q1=Kp2q2]
52
From this we have òV/òq 1 = F1 - / KP1 = O òV/òq 2 = F2 - / KP2 = O òV/ò/ V/ò/
= KYo-KP1q1 – KP 2q2 = O
This gives us the equilibrium situation as F1/F2
= P1/P2 = K/
This This is same same as before before except except a chan change ge in the the marg margin inal al util utility ity of mone moneyy which which is now now K/. The o o quantities demanded would be a function of KP 1 KP2) and KY instead of (P 1, P 2, U ) but they will not be different in these two situations. The second order conditions will also not change and so, we can safely say that demand functions are homogeneous of zero degree. There is a practical applications of this property. If income and prices are changing in same proportion then one need not to worry about inflation since real consumption of goods and services will not be affected by this. They property of zero degree of homogeneity of the demand function is a kind of restriction. If this is so, we can use it further to derive the relationships between price-elasticity and income elasticity of demand for a commodity. For this, let us take the help of the Euler’s there according to which a function Z = _(x,y) is homogeneros of degree r if the following condition is satisfied. òz n
òz
-------------- + Y -------------------- rz òn
òy
If we take a demand function for a commodity I as: qi = _(P1, P2,P3,.........y) and apply the above theorem to it, we get, òqi P1
òqi
òqi
òqi
----------------- + P2 --------------------- + ..... ........ ..... .. + Pi ------------------------ + .... .... + y -------------------- = O òP1
òP2
òPi
òy1
Since Since r=O (Demand function function being homogeneous homogeneous of degree zero) i=1,...n i=1,...n Dividing both the sides by q i, we have
53
P1
òqi
-------- ------------qi
òP1
P2 + qi
òqi
Pi
ò1i
V
òqi
------------- ----------- + ... ... ------------- ----------- + .... .... + ---------òP2
qi
òPi
qi
-------------
òy
Each element in this equation is an expression for the elasticity. So, we have the sum of “own” and cross elasticities of demand for a commodity I equal to minus of its income elasticity of demand. This is an import importan antt resul resultt which which we deri derive ve from from the the prope property rty of zero zero degre degreee of homo homogen geneit eityy of the demand demand functions for different commodities. The The util utility ity analy analysis sis discu discusse ssed d above above is essen essentia tiall llyy based based on card cardina inall appro approach ach ie, ie, the the basic basic assumption for this was that utility can be measured through cardinal scale of measurement as, in terms members of “utilize” . This assumption gives serious doubt about the validity of the entire analysis. Utility being a subjective phenomenon cannot be measured by numbers or weight or anything like that. If this is so, then the theory of consumer analysis based on cardinal approach is not verified. Marshall who was a strong supporter of the cardinal approach of utility analysis to some extend agreed with this criticism but the pointed out that utility is measurable indirectly if not directly. A person’s satisfaction on utility derived from consumption of a commodity can be measured indirectly by the amount of money he is willing to pay for that. For each unit of commodity how much price he is willing to pay gives us a measurement of utility of that unit of commodity. the units of price multiplied by the marginal utility of money is equivalent to the marginal utility of the commodity at the equilibrium (MU=/ P as we have been earlier). The marginal utility of money (/) is taken to be constant by Marshall. Even the approach of indirect measurement of utility using monetary units has been challenged by economists. The reason for this was mainly the unstable value of money. When it value is not stable how can it be used as a measuring rod for utility? What is needed of measuring utility at all? We use this concept to understand theoretically the behaviour of a rational consumer and derive the demand function in ex-ante sense from this. The demand function will have all measurable variables, quantity of the commodity on one side, prices and income on the other. Using data for all such variables, we can estimate the demand functions for commodities. This is the objective of the entire utility analysis. Measurement of utility is not necessary for this although it is desirable. There is another serious limitations of the cardinal utility analysis. We know a demand curve slopes downward because of “substitution effect” and “income effect”. These two effects cannot be isolated using he above frame work of utility analysis. There are some other drawn backs such as its failure to analysis demand for indivisible goods, inferior goods, etc. But these are minor issues. By and large, the whole theory based on the cardinal approach is highly abstract in nature, It does not explain all aspects of consumer behaviour but the major issues have been tackled well by this theory.
1. Conce Concept pt This is an alternative approach developed by economists like Edgeworth, Fisher, Slutsky, Hicks and Allen Allen to analysi analysiss consume consumerr behavio behavior. r. In this this approach, approach, the emphasis emphasis sis given on comparing comparing differen differentt utility utility levels levels instead instead of measur measuring ing them through through some cardina cardinall scale. scale. In other other words, words, this approac approach h is based on ordinal measurement of utility. Under ordinal measurement scale, the alternatives can only be ranked such as greater or smaller, higher or lower and the like. The approach of indifference curves
54
analyzing analyzing consumer behaviour behaviour is based on certain basic assumptions. assumptions. The assumptions are as follows: i)
Ther Theree is comp complet letee consis consisten tency cy in in order orderin ing g of pref prefer eren ence cess by the the consu consume mer. r. For For examp example le if two alternative bundles of consumption goods A and B are available, then the consumer must state state either either “ I prefer prefer A to B or “I prefer prefer B to A “ or “A and B are equally equally preferre preferred” d” The consumer is not in the state on indecision.
ii)
Along Along with with the the compl complete ete con consis sisten tency cy we we expect expect that that the the consum consumer er’s ’s prefe preferen rence cess are not not self-contradictory or conflicting with each other. This is the assumption of transitivity. This means if A is preferred over B and B is preferred over C then A is preferred over C.
iii) iii)
An indi indivi vidu dual al’s ’s prefe prefere renc nces es are are such such that that he prefer prefer more more or less. less. It mean meanss that that the individuals is not satiated atleast not in all goods. Keeping the consumption of other goods constant and increasing increasing consumption of atleast one good is definitely definitely a better situation. situation.
iv)
The goods goods consume consumed d by the the consu consumer mer are substitu substitutabl table. e. The The satisf satisfact action ion or or utilit utilityy can can be maintained at the same level by consuming more of some good.
v)
All commodit commodities ies in the consumpt consumption ion basket basket of the consume consumerr are divisib divisible. le.
vi) vi)
Indi Indivi vidu dual alss are are rati ration onal al in decis decisio ion n-mak -makin ing. g. This This is a requ requir irem emen entt for for the the cons consum umer er equilibrium analysis in general and not for only the indifference curve analysis. Further, we assume that eh preference scheduling of one consumer is independent of the preference schedules of other consumers. It means that there is absence of curve analysis is state in nature. nature. It I t presumes certainty certainty regarding the decisions situation faced by a consumer.
Given the conditions as specified by the above assumption, the indifferences curve technique as we have mentioned earlier, compares the different levels of satisfaction or utility rather than measuring them. This is the approach adopted for utility analysis. The indifference curve is a locus to different combinations of two or more goods which yield the same level of satisfaction or utility to the consumer. Ti is also called as “iso-utility “iso-utility curve”. curve”. Graphically, we can demonstrate an indifference curve as shown in Fig. 4.3
For the sake of simplicity we take two commodities Q and Q into consideration for drawing the indifference curve. In practice the number of commodities in the consumption basked will be more than two and different combinations of such goods yield some fixed level of satisfaction, but it is not possible to show it graphically. We, therefore, confine the indifference curve analysis to a case of two commodities. Point A,B,C,D and E show the different combinations of Q 1 and Q 2 commodities that yield a constant level of utility U1. By joining these points we get the difference curve as shown in the figure. The shape of he curve curve is convex convex towards towards the origin and it is downwar downward d sloping. sloping. We will be showing showing why it is so and what are the other possibilities for this. When we mover from point A to point B the consumption of commodity Q 2 decreases by two units and consumption of commodity q 1 is therefore -2/Q 1. Minus Minus sign sign indic indicat ates es decrease ion Q 2. This is approximately the slope of the indifference curve between A and B. when we more further from point B to point C the decrease in consumption of Q 2 is only by one unit and increase in consumption of +Q 2 for also by one unit. This implies that the consumer is giving up now only one unit of Q 2 for one additional unit of Q 1. The rate of substitution of Q 2 per unit of Q 1 is now -1. As we move still further to D or E we observe that the consumer gives up less and less quantity of Q 2 per additional of Q 1 ie., the rate of substitution of Q 2 by declines in magnitude. magnitude.
55
The rate of substitution of Q 2 by Q 1 is called “Rate of commodity substitution (RCS) in expanded from. It is computed at the margin (implying very small changes) so alternatively we call it “Marginal Rate of Commodity Substitution (MRCS). When we use the term RCS for this it is implicit that it is MRCS. The rate of commodity substitution or marginal rate of commodity substitution is that amount of a commodity, say Q 2 to be given up per unit of another commodity say Q 1 for consumption if the consumer remains remains on the same indifference indifference curve. In the consumption process we are substitution one commodity for the other but maintaining a constant level of utility derived from this. This is precisely what the RCS of MRCS tells us. In symbolic form the RCS or MRCS is denoted by. qe or –dq2 where q2 or dq2 expr expres esss the the chan change ge in q 1 dq1 quantity of commodity Q 2 and q1 or dq1 is the change in quantity of commodity Q 1. Why Why does does the the marg margin inal al rate rate of comm commod odity ity subs substi titu tuti tion on decl declin inee when when we move move alon along g the the indifference curve? Is it because we have drawn the indifference curve as a convex line towards the origin or these is a sound economic reason for that? Let us examine this issue. A consumer (s marginal marginal rate of commodity substitution substitution between the gods (Q 2 and Q 1) for a constant levels utility will in some way, depend on how many units of Q 2 and Q 1 he or she is currently consuming. Consider the point A in Fig 4.3 At this point the consumer consumes much more (6 units) quantity of Q 2 as compared to the quantity of Q 1 (two units). He is willing to give up two units of Q 2 for one unit of Q 1 and thus, moves to point B. at this point consumption of Q 2 decreases to 4 units and consumption of Q 1 increases to three units. He is interested in increasing consumption of Q 2. But this time, he is willing to give up only one unit of Q 2 for one additional unit of Q 1. As he moves down further, the willingness to give up units of Q 2 for each additional unit of Q 1 decreases further. Thus what we are observing here is that the willingness to give up the commodity Q 2 in favour of the other commodity (Q 1) directly relates to the quantity of Q 2 greater the quantity of a commodity already consumer the higher will be the willingness to give up a part of the commodity in favour of some other commodity and vice-versa. This explain why the magnitude of the marginal rate of commodity substitution of Q 2 for Q 1 declines as we decrease quantity of Q 2 and increase quantity of Q 1. The consumer prefers a balanced consumption of different goods. Too much consumption of one good induces him to substitute it for the other good in greater extent as compared to the extent of its substitution for the other when its consumption is low. The declining of the MRCS can be explained in a better way by using the marginal utility concept. From the law of diminishing marginal utility we know that there is an inverse relationship between quantity of consumption and marginal utility. When we decrease quantity of consumption of a commodity in favour of another, We marginal utility of the other commodity decreases. In the above diagram we have the sequence of decreasing quantity of Q 2 and increasing quantity of Q 1 as we move from A to E point on the indifference curve. Decrease in the quantity of Q 2 means increase in its marginal utility and increase in the quantity of Q 1 means decrease in its marginal utility. When marginal utility of Q 1 declines then lees and less quantity of Q 2 will be substituted for one unit of Q 1. To make it easier to understand we can bring the analogy of falling value of money. When the value of money falls then one rupee will fetch lesser amount of any commodity. This is the reason for diminishing rate of substitution and its is this diminishing rate of commodit commodityy substat substation ion which which makes makes the indifferen indifference ce curve curve convex convex toward towardss the origin origin.. Details Details of the indi indiffe fferen rence ce curve curve conve convex x towa towards rds the orig origin in.. Detai Details ls of this this prope property rty of the the indif indiffe feren rence cess cure cure are presented presented in the following section. Properties of Indifference Curve (a) An indi indiffe fferen rence ce curve curve is downw downwar ard d stopp stoppin ing g and and convex convex towar towards ds the the orig origin in.. To prove prove this this mathematically mathematically,, let us consider the utility function. function.
56
U = F(q 1,q2) By taking total derivaties of this function we have òU dU =
òU
------------------- dq1 + ---------- dq2 òq1
òq2
By the definition of the indifference curve, utility does not change when we move along the curves. So we can write dU=O. This gives us. òU O =
òU
-------------------- dq1 + ---------- dq2 òq1
òq2
dq2
òU/òq1
or -
------------ = dq1
F1
------------òU/òq 2
= --------F2
dq2/dq1 is the the slop slopee of the indi indiff ffer eren ence ce curv curve. e. Its Its negat egativ ivee i.e. i.e.,, - dq2/dq1 is the the marg margin inal al rate rate of commodity substitution. So equation (35) simply says that marginal rate of commodity substitution is equal equal to the the ratio ratio of marg margin inal al utili utiliti ties es of the the two two goods. goods. A ration rational al consum consumer er will will not not consum consumer er a commodity beyond beyond the level of when its marginal marginal utility is zero. So we have have òU/ò O&òU/òq2 O. The ratio (òU/òq1)/òU/òq 2) is therefore, therefore, positiv positive. e. This means the left hand side of equation equation (35) is also positive. positive. That is –dq 2/dq1 is positive . this is possible when there is one more negative sing attached to it. This condition is satisfied when the indifference curve is negative sloped, so negative of negative slope makes the MRCS positive. This proves that the indifference curve is downward sloping. Again, as quantity q 2 decreases, its marginal utility (F 2) appearing in the denominator of the ratio (òU/òq1)/òU/òq 2) increas increases, es, and and since since q 1 is being substituted for so the quantity of q 2 increases and so its marginal marginal utility (F1) in the numerator of the marginal utility ratio decreases. A decrease in F 1 simultaneously an increase in F 2 when q 1 is substituted for q 2 means a fall in the magnitude of the ratio which implies a fall in the marginal rate of commodity substitution. This gives us the reason for the indifference curve being convex towards the origin. origin. The property of convexity of the indifference curve will be proved if we show that the rate of change of slope of the indifference curve is positive i.e. d 2q2/dq21>O By taking taking the deriva derivativ tives es of (35) with respect to q 1 and simplifying the expressions we get the final condition for the rate of change of slope of the indifference curve as d2q2
1
-------------------- = - -------------------- [ F11F22-2F 1F2F12+F22F21] >0 >0 dq21
F 32
57
where òU/òq1 = F1>O, òq2 = F2>O ò2U/òq21 = F11
O In view of such restrictions, the bracketed terms in (36) is –ve so d 2Udq21 is positive. Thus implies that the indifference indifference curve in convex towards the origin. b) The curvature curvature of the indifferen indifference ce curve curve indicates indicates the degree degree of substitu substitution tion between between the goods represented by it. If the goods are perfect substitutes for each other then the indifference curves will be a straight line slopping downward and intersecting the commodity axes. Such line will show constant marginal rate of commodity substitution for the goods. The line intersects the commodity axes which means the utility level indicated by the line can be attained by consumption of one commodity alone keeping the other one at zero level. This is what perfect substitution implies. The minimum required proportion of the goods will be shown by a point through which the indifference curve will pass. On either side of this point the indifference curve will be straight line parallel to commodity axes. In other words, the indifference curve will be pass in the shapes of a right angle at the point showing the minimum proportion of the two goods. The marginal rate of substitution will be zero in this case. In Fib. 4.4 these two extreme types of indifferences curve are shown in panel(a) panel(a) and (b) respectively, respectively, Panel (c) shows the normal indifference indifference curve.
Between the two extreme cases of indifference curve we have normal curves sloping downward. Greater the curvature of the indifference curve lesser will be the degree of substitution for the goods. This reflects low MRCS. On the other hand if the curve is flater i.e., of less curvature, the degree of substitution between the goods will be quite high and MRCS will tend towards constancy. An indifference curve parallel to X-axis or Y-axis would not be possible. Suppose a consumer consumes a few units of d 2 and O units of q 1 to get some satisfaction U 1. Now without reducing the amount of q2 he increases q 1. This would give him higher level of satisfaction. So there would not be indifference between these two situations. It implies that a parallel line to q 1 axis or a parallel line to q 2 axis cannot be called as indifference lines. The indifference curve has to be downward sloping whether it is a straight line or a curve. c) Two indifference indifference curves curves cannot intersect intersect each other other for the given pattern of preferenc preference. e. The reason for this can be explained by referring to Fig. 4.5.
58
I1 and I 2 are two indifference curves showing different levels of utility. They are intersecting at E 1 point. By the definition of the indifference curve, a consumer would get same utility by consuming OA 1 + OB1 combination of q 1 and q 2 at E1 and OA2 + OB2 combination of the goods at E 2 point on I1. Similarly OA 1 + OB1 combination combination of q 1 and q2 would give same utility as OA 2 + OB2 combination at E on I 2 in other words. Utility of E1 bundle = utility of E 2 bundle of q 1,q2 Utility of E1 bundle = utility of E 2 bundle of q 1,q2 Since the consumer is indifferent between E 1 and E 2 bundle of q 1 and q 2 and E 1 and E 2 bundles of q 1 and q 2 he would would ther therefo efore re be indif indiffer feren entt betwe between en E 3 and and E2 bund bundle less of q1 and q2. But But this this is not so, so, the the combination of q 1 and q 2 at E2b is (OA2 + OB2) and the combination of these goods at E 3 is (OA2 + OB2) OA2 is common but OB 2 > OB2. It is, therefore, clear that OA 2 + OB2 is preferable over OA 2 + OB2 would give more utility than OA 2 + OB2 when E 3 preferred to E2, E1 cannot have the same utility as shown by E 2 and E1. What we find that it would be inconsistent to compare utility at E 1 and E2 to utility at E1 and E3. It is not possible. So we can say that intersection of two indifference curve is not possible at all given the definition of indifference indifference curve and the assumptions assumptions behind it. d) In the non-negative non-negative consumption consumption space i.e., i.e., positive quadrant quadrant of the graph (see (see Fig. 4.6) we find a set of indifferen indifference ce curves curves each one showing showing a different different level level of utility utility and sequenc sequenced ed on orderly way. An indifference curve that lies father fro the origin represents a greater level of utility than one one close closerr to the the origi origin. n. This This also also follo follows ws from from the the assumpt assumption ion or obse observa rvati tion on that that more more in preferred to less. In fig 4.6 as we move up, the level of utility shown by the indifference curve increases, that is I 3>I 2>I1>I0. All combinations of q 1 and q2, shown by I 3 are preferred over the combination combination of q 1 and q2 shown by I 2 similarly.
We say that the combination of q 1 and q2 shown by I 2 are preferred to the combinations shown by I 1 and so on. The difference curves will be parallel for a given utility function showing constant preferences. But that is not a necessary requirement. The necessary thing is that they will never intersect each other inspiet of being unparalled for some reasons. Difference individuals may have different sets of indifference curves because of differences in their preferences for the some types of goods.
59
e) The space space between between consecuti consecutive ve indiffe indifferen rence ce curves curves reflects reflects the strength strength of diminishin diminishing g margin marginal al utility. For a given level of q 2 how much q 1 is needed to sustain one unit increment in the total utility? It will be more and more when the law of diminishing marginal utility holds true. If this figure the quantity of q 2 is kept at a constant level q 1. A1, A2 quantity of q 1 is needed to push the total utility by one unit ie., from level 1 to 2 of indifference curve. Similarly A 2 and A 3 units of q1 are needed for increasing the satisfactions by one unit, say from level 2 and 3. This way we find more and more of q1 for the consecutive increase in the utility levels as reflected by the indifference curves of higher levels. A4A5 > A3A4 > A2A3 > A1A2 implies that the law of diminishing marginal utility is operating for consumption of additional units of commodity Q 1. We have have seen seen in the the earl earlie ierr sect section ionss how how a cons consume umerr attain attainss equil equilibr ibrium ium when when he spend spendss his his limited limited income income on variou variouss goods goods and services. services. He simply simply follows follows the principle principle of constra constrained ined utility utility maximization for this. Now we will see how his equilibrium position can be analysed using the indifference curve. curve. We presume presume that the entire set of indiffe indifferenc rencee curve curve ie., the indifferen indifference ce map is given for the consumer. The problem is to identify that particular indifference curve will be showing several plausible combin combination ationss of the goods that that the consume consumerr consume consumes. s. Which Which particu particular lar combin combination ation he will will finally finally pickup? The indifference curve as such taken alone cannot help us to find the equilibrium position. For this we need some additional information. This information is provided in the form of a budget constraint showing a fixed income and expenditure relationship. That is, the income of the consumer is fixed (Y o). The prices of the goods are also fixed. Let these be P 0 and P 2 for two commodities Q 1 and Q 2 respectively. In symbolic form, the budget constraint for two commodities consumption situation is Y0 = P1q1 + P2q2 In the cardinal utility maximisatoin we used expanded version of this budget line i.e., Y 0 = P1q1 + p2q2 + ....... + P nqn but in this section we confine to two commodities for which we draw the indifference curve. A budget constra constraint int is a locus locus of all combinatio combination n of two goods (or more) more) which can be purcha purchased sed with with fixed fixed incom incomee at fixed fixed pric prices. es. It is a bound boundary ary of cons consum umpti ption on for for both both the the commo commodi ditie ties. s. The consumer cannot cross this boundary line since his income would not allow this. The budget constraint is a downward sloping line, its slope would be equal to –P 1/P2 as we see below: Y0 = P1q1 + P2q2 So, Y0 q2 = ---------------- P2
P1 -------------------- q1 P2
By maximi maximizin zing g tota totall util utility ity UF(q UF(q1, q2) subje subject ct to the the budg budget et cons constr train aintt Y0 = P 1q1 + P 2q2 the equilibrium condition for the consumer would be as shown by equation (10) earlier.
MU1
P1
60
------------MU2
=
-------------P2
Also we have have seen earlier earlier that that the marginal marginal rate of commodity commodity substitu substitution tion equal equal the ratio of marginal utilities of the commodities Q 1 and Q 2 that is dQ 2 MRCS MRCS = - ---------------- = dq1
MU1
P1
------------------- = ----------------MU2
P2
combining this with the above equation ie. (eg. No. 10) we have MU 1 / MU2 is the slope of the indifference curve and P 1/P2 is the slope of the budget line. At the equilibrium situation the slopes of the two curves ie., of the indifference curve and of the budget line are equal. This implies that the budget constraint is tangent to the indifference curve. Thus the indifference curve (and hence the utility level represented by it) which is touched by the budget line would be preferred. The combination of the goods shown by the point of tang tangen ency cy would would give give the the opti optimu mum m leve levell of sati satisf sfac acti tion on to the the cons consu umer. mer. This This can can be show showss diagrammatically as follows.:
AB is the budget line Y 0 = P 1q1 + P2q2. This line shows the various combinations of the two goods Q 1 and Q 2 what the consumer can purchase by his fixed income Y 1. He may prefers any point on this line. If he buys only Q 2 then the quantity of Q 2 he can afford will be q 2 = Y0.P2 shown by the point A. similarly if he buys only Q commodity then the maximum quantity of Q 1 ie., q1 will be equal to Y0/P1 shown by the Point B. since since his preferenc preferences es are shown by the indifferen indifference ce curves curves and these these curves curves are not intersect intersecting ing the commo commodit dityy axes axes it implie impliess that that he prefe prefers rs both both the the commo commodi ditie tiess in some some combin combinati ation on and and the the two commodities are not perfect substitutes. So point A and B on the budget line cannot be considered for equilibrium position in this case. Any point above the budget line will also be unattainable since consumer’ s income is fixed, commodity prices are fixed so the attainable boundary given by the budget line is fixed. Any indifference curve which is above the budget line but untouched by it would not be considered for examining the equilibrium position of the consumer. The points on the budget line and below this in the commodity space are of course feasible or attainable. For simplicity we consider a few point such as F on I01 C and D on I 1 cure and finally E point. Let us consider point F on the indifference cure I 0. The combination of the two commodities Q 1 andQ 2 shown by point F would not yield maximum satisfaction satisfaction because the consumer consumer can move to higher higher indifference indifference curves by moving either horizontally horizontally or vertically as shown by the arrows (1) and (2) respectively or between them diagonally towards the budget line. These movements from point F indicate that the consumer gets either more to q 1 or q2 or both without decreasing the quantity of other commodity. He thus moves to a higher level of satisfaction by such movements. He has not move away from point F since it is far below are budget line and so the income is not utilized fully. For full utilisiation of income and for maximum satisfaction the consumer has to move long the budget line. So all points like F are inefficient combinations of Q 1 and +Q 2. Now let us consider point C on the budget line at which the indifference curve I 0 and the budget line (AB) intersect. The slope of the indifference curve is greater than the slope of the budget line at this point. That is : MU1 > P1
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or rearranging it we have the marginal utility per unit of money spent on commodity Q 2 is greater than the marginal utility per unit of money spent on Q 1. The consumer reacts to this situation by increasing his expenditure on Q 2 and hence increasing its consumption in order to increase his utility. This measn he moves on higher indifference curves by moving up along the budget line. By such movements the quantity q increases and its marginal utility decreases and q decreases its marginal utility increases. The inequality (MU1/P1)
We have already seen that the quantity demanded of a commodity primarily depends on its price, prices of other commodities and services and income of the consumer. Now let us examine the effects of income income and price changes on the consumer equilibrium situation situation within the t he indifference indifference curve frame work. Through the budget line we have specified he expenditure pattern of the consumer using fixed income, fixed prices of the commodities (P 1 and P2) and the quantities q 1 and q2. Let us change income and prices one by one said see what happens to consumer behaviour by this. i)
Chang Changee in Incom Income, e, Prices Prices Bein Being g Constan Constantt
When for instance, income of the consumer increases the budget line shifts upward. The shift of the budget line would be parallel as we keep prices of the goods constant and so slope of the budget line does not change. Because of parallel shifts of the budget line, the equilibrium position will be on higher indifference indifference curves implying increasing increasing utility utility derived. derived. This is shown in Fig. 4.9
That line formed by joining the equilibrium points on the indifference curves which we get by shift shiftin ing g the the budge budgett line line up becau because se of incre increasi asing ng incom income, e, other other thin things gs being being consta constant nt,, is calle called d income-consumption curve”. This shows how a consumer will consume the goods when his income rises. The income consumption curves need not to be a straight line. It may be a straight line or a curve depend depending ing on the consumer consumer’s ’s preferen preference ce for the goods goods as reflect reflected ed by eh indiffe indifferenc rencee curves curves.. If the changes in quantities of the goods are uniform in proportions in moving up on the indifference curves then income consumption curve will be linear otherwise not. A non-linear income consumption curve will show show eith either er incr increa easin sing g or dimin diminish ishin ing g propo proporti rtion onss of the the chan change gess in quan quantit titie iess of the the goods goods.. If the income-consumption curve this towards a commodity axis then that commodity is treated as “superior” as compared to the other as income-consumption curve is positively sloped then both the commodities will be “no “normal rmal goo goods” ds”. If it is nega negati tivvely slop sloped ed then then one one of the the commo ommodi diti ties es is “infe inferi rio or”. r”. The The income-consumption curve may be positively sloping upward for a certain ranges of income shifts and then negative sloping indicating that the commodity from whose axis it is deviated away is inferior. The
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other commodity is a normal one. From the knowledge of the income-consumption curve ICC we can draw the Engel curves. An engel curve curve is a relatio relationsh nship ip between between quantity quantity of a commodi commodity ty say Q purcha purchased sed and income income of the consumer, consumer, prices being constant. The name “Engel curve” is derived after the name of Prussian economist Ernst Engel (1821 – 1946) who first studied the income – consumption relation – ship for goods. In the case of luxury goods, goods, the demand demand increas increases es proportio proportiona nately tely more more rapidly rapidly than than income, income, while while for “necess “necessitie ities” s” the deman demand d grow growss propo proporti rtion onate ately ly less less rapid rapidly ly than than income income.. For For infer inferio iorr gods gods the the Engl Englee curv curvee will will not negatively sloped. Consider the Fig. 10. In part (a) of the figure we find the income-consumption curve ICC sloping negatively and tilting towards q axes. The commodity Q is therefore “superior” and the commodity Q is inferior because its quantity declines as income increases.
In part (b) of the figure three Engel curves have been shown, one each for a luxury good, for a necessary and for an inferior goods. The trends of the changes in these curves when income increases are self-explanatory. (ii) Changes Changes in Commodity Commodity Price Price We keep income of the consumer at constant level and change the prices of the goods in order to find the effect of such changes on the equilibrium position. Changing both the prices simultaneously is a complex situation for analysis. Let us keep this pending for some time and just take the price of one commodity constant constant and that of the other varying. varying. Here we keep P unchanged unchanged and P decreasing. decreasing. Because of a decrease in P the slope of the budget lien will also be decreasing which means it will shift to the right. Consider the following figure.
A B is the initial budget line. When price of Q decreases the consumer will be able to buy more of Q with his fixed income when spent entirely on it. This means shifting of the line to A B position. This new budget budget line will, will, be a tangent tangent to a higher higher indiffer indifferenc encee curve curve at E. The total total satisfa satisfactio ction n goes up and the quantity consumed of q also goes up. Quantity of Q may decrease or increase or remain constant. Further decr decrea ease se in the the pric pricee of Q shif shifts ts the the budg budget et lin line to AB posi positi tion on whic which h agai again n brin brings gs highe igherr leve levell f satisfaction to the consumer as this new budget line touches a higher indifference curve U at E point. This way the equilibrium position shifts to higher and higher indifference curves when price of Q continuously decr decreas eases es.. The line line joini joining ng the the equil equilibr ibrium ium point pointss on diffe differen rentt indif indiffe feren rence cess curve curve is calle called d “Pric “Pricee Consumption Curve (PCC). It indicates how quantities how quantities of both the commodities vary when price of Q changes, price of the other commodity and income remaining unchanged. It is not an ordinary demand curve. It shows variation in quantities of both the goods with the changes in the price of one of them. We can of course, find the ordinary demand curve from this. we know the changes in price of Q which are exogenously given and also we know how much quantity q the consumer buys with different price levels for Q. as can be seen in Fig. 4.11 we can draw the demand curve for the commodity without
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any difficulty. The price-consumption curve need not to be a straight line. It may be a straight line. It may be a stra straigh ightt line line or a curv curvee sloppi slopping ng upwa upward rd or downw downwar ard d depen dependi ding ng on the the two impor importan tantt effec effects ts associated with price changes which we will discuss in the following section. Substitution and Income Effects from a Fall in Price As we have have seen seen in the the prec precedi eding ng sect section ion,, the the effec effectt of a price price chan change ge on the the quan quantit tityy of a commodity is more complex to analyze than is the effect of income change. In this case, the budget line shifts and its slope also changes with changing price of the commodity. consequently, the equilibrium shifts on a new indifference curve. The quantity demanded of the commodity changes with price changes because because of “Substitution effect” effect” and “Income effects”. effects”. These two “effects” “effects” have been listed as reasons for downward slope do the demand curve. (Vide Chapter 3). By using the equilibrium analysis within the indifference curve framework these two effects can be isolated from each other. We will see now how this can be done. Some clarification is needed about the precise nature of the substitution and income effects. If utility is held constant, consumer will move along an indifference curve substituting the commodity that has become relatively cheaper for the one that has become relatively more expensive because of the price change. The type of movement shows the substitution effect. Further, when there is a decrease in price, the consumer saves expenditure which means his real purchasing power increase. Because of a change in purchasing power, the consumer moves on to a different indifference curve showing a different level of utility. This is income effect. The role of “income effect” is to push up or down the level of satisfaction depending on decrease in the price of a commodity and thus moving to different indifference curves. The The proc procedu edure re of “isol “isolat ating ing”” the the subst substitu ituti tion on and and incom incomee effect effectss in quite quite simpl simple. e. We will will use use graphical graphical demonstration for this first and then use the algebraic algebraic expressi e xpressions. ons. Consider the following figure. AB is the budget line for the two commodities Q and Q. The budget line touches the indifference curve for U and E point showing the equilibrium position for the consumer with X and Y quantities of Q and Q commodities. Now let use consider the effect of a decrease in price P for O other things remaining constant. The budget line now shifts to AB position since the consumer will be able to buy more of Q with fixed income if he wants to spend it entirely on Q. the new budget line (AB) touches a higher indifference curve for U level of utility at point E. The consumer now buys X quantity of Q and Y quantity of Q for consumption. Because of a decrease in price of Q the consumer is buying more of Q and less less of Q. The total change change in quantity quantity of Q is shown by X X distance distance on q axis. The total total effect effect on quantity quantity demanded demanded of Q ie. X X is the sum of substitution effect effect and income effect effect
To isolate these tow effects, we keep the prices of the two commodities Q and Q same as shown by the new budget line AB and somehow push back the consumer to his old level of satisfaction ie., to the indifference curve marked by U. This type of exercise helps us to find these two effects separately. Because of a decrease in price P there is increase in real income of the consumer which causes an increases in his satisfaction from U to U level. Suppose we tax the consumer ie., withdraw the increased amount of real income from him. This pushes him to the original level of satisfaction U. how much tax is to be imposed on the consumer? We do not know it but we can have an idea of this by shifting down the budget line AB parallelly till it touches the indifference curve for U level of utility. The shifted budget line A B which is parallel to AB touches the U indifferences curve in the diagram at E level. This point(E) shows the equilibrium equilibrium position for the consumer consumer with substitute effect effect only ie., because of a decrease in price P1 the consumer substitutes some quantity of Q for relatively costly commodity. Q This is substitution effect
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which which is shown shown by the the distanc distancee X X. The differ differenc encee between between total total effe effect ct X X and substit substitutio ution n effect effect X X that is X X is the income income effect. effect. So what we are gettin getting g here here is an identity identity showin showing g the sum of the two effects. Total effect = Substitution effect + Income effect. X1 X 2 = X 1 X 3 + X 3 X 2 (-)
(-)
(- )
Both the effect effect and unidir unidirect ectiona ional. l. Substitu Substitution tion effect effect is always always negativ negativee in the sense that that an increase in price of a commodity means a decrease in the quantity of that commodity which is substituted for anther commodity ofr maintaining constant utility level and a decrease in price means an increase in such a quantity of the commodity. the income effect may be working in the same direction or opposite to the direction of change of the substitution effect. In the above case it is in the same direction because a change in real income increases the quantity demanded of the commodity Q – total effect is thus a sum of both the effects. This is the case of a normal good. A normal good is that one whose quantity demanded increase with increase in income. For “inferior” goods the income effect will operate in opposite direction to the substitution substitution effect effect but the net effect effect will still be negativ negativee it., in the direction direction of he substitut substitution ion effect. effect. Let us show s how this through through a diagram In this diagram (Fig. 4.13) the total effect effect is market by X X. The substitu substitution tion effect effect is X X. The The income income effec effectt is therefo therefore re X X. What What we find find in this this is that that the total total effec effectt is less than the substitution effect but still it is negative working in the direction of substation effect. That is, quantity bought is increasing with decrease in price of the commodity. the income effect is operating in the opposite direction of he substitution effect. The quantity demanded of the commodity decreases with increa increase se I real real income income but becaus becausee of greater greater magnitu magnitude de of the substituti substitution on effect the tot total al effect effect is negative. X1 X 2 = X 1 X 3 + X 2 X 3 (-)
(-)
(+)
and X1X3 | > |X2X3|
|X1X2| < | X1X3|
This This result result holds holds for an inferio inferiorr commodit commodity. y. There There is still still anothe anotherr possibil possibility. ity. There may be a decline in quantity purchased and consumed with decline in price of the commodity. This is a situation when there is positive relationship between charges in price of the commodity and quantity demanded at least for a certain range of variation in the price of the commodity. to understand this situation consider the following diagrams (fig. 4.14) E1 is the original equilibrium position and E 2 is the one when price P 1 decreases. decreases. The quantity OX 2 of Q 1 corresponding to E 2 is less than the quantity of Q which the consumer was buying earlier. Thus, there is a decrease in
Quantity of Q when price of Q is decreasing. The commodity Q which is depicting this type of result is called as “Giffen Good”. This peculiar type of behaviour is called “Giffen Paradox” after the name of
65
English economist Giffen who first observed it. A “Giffen good” is an inferior good for which the income effec effectt is very very stron strong g comp complet letely ely out-st out-stri ripin ping g the the substi substitu tutio tion n effect effect in magn magnitu itude de.. This This would would be in opposite direction as in eh case for an inferior good. A consumer spends a large proportion of the income on such such a commo commodity dity and if pric pricee of the the commo commodit dityy decl declin ines es he save savess cons conside idera rabl blee amoun amountt of his his expenditure from which he can buy a better substituted for the commodity. Hence the consumer reduces its consumption and moves to the other commodity. Form the diagram (Fig. 4.14) are find that. X1 X 2 = X 1 X 3 + X 3 X 2 (-)
(-)
(+)
The The direct direction ion of total total effect effect (X X) is similar similar to that that of incom incomee effect effect (X X) and opposi opposite te to the substitution substitution effect effect (X X) and and |X1X3 | < |X 3X2| It is difficult to find a “Giffen good” in practice. Nevertheless, it is very useful at least concentually to understand understand “income” and “substitution” “substitution” effects in i n indifference indifference curve framework. We have gone through a graphical analysis for separation of the substitution and income-effect. Let us use the algebraic expressions for this purpose now. By maxim maximizin izing g total total utility utility U = F(q q) subjec subjectt to the the income income const constrain raintt Y = P q + p q we got got the first order conditions for maximization as shown by the equations set (7) in section 4.2 Our objective is to find find the magnit magnitud udee of the effect of price price and income changes changes on the consume consumerr equili equilibriu brium m when all variables vary simultaneously. For this we take the total differentiation of Equations (7). This gives us F11 dq1 + F12dq2
- Pd/ = /dp1
F12 dq1 + F22dq2
- P2d/ = /dp2
-P1sq1 - P2dq2 = -dy+q -dy+q1dP1 + q2dp2 We have three equations equations for finding the values values for three unknown dq dq dq and. The right –hand side is known to us. Assuming that only P price changes by dP other things being constant ie., dP = O dy = O. We can solve (39) using the Cramer’s route to get the following final expression. òq1
òq1
--------- = (--------------) òP1
òP1 U=constt
òq1 -q1 (---------) òY Pr Price = Constt.
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This is Slusky Equation, named after the Russian Economist E E Slutsky defines the effect when P chan change ges, s, other other thin things gs remain remainin ing g const constant ant is the the “subst “substitu itutio tion n effect effect”. ”. The The quant quantity ity demand demanded ed of Q changes but utility remains at the consent level. This much quantity of Q is being substituted for other commodity without moving from the indifference curve. The substitution effect will be negative since with a rise in the price of the commodity less of it would be substituted for other commodity and vice-versa. The last term q1(òq1/òY) price=constt. is the income effect. It may be positive or negative depending whether the commodity is a normal good or an inferior good. We know, for a normal good or an inferior good. We know, for a normal good òq 1/òY is positive so (q 1/òq1/òY) is positive. There is a negative sing before it in the Slytsky equation that means it works in the negative direction with the substitution substitution effect. Both have negative signs so we add them to find the total effect. For an inferior commodity òq 1/òY is nega negativ tive. e. So, So, (q1 òq1/òY)p=constt. in negative and in the Slutsky equation, because of double negative sign. It is positive. This means it is working in the opposite direction of the substitution effect. The net result ie., total effect depends on the sign of the effect which has greater magnitude for inferior goods total effect will be negative because of greater absolute size of the substitution effect than that of income effect. For a Giffen good the total effect will be positive because of greater absolute size of the income effect as compared to the substitution effect. All these three possibilities have been shown above through graphs in Fig. 4.12 to 4.14. Some further deductions can be made from the Slutsky equation. Multiplying both the side of (40) by P/q and multiplying and income-effect term on the right by y/y alos, we get the Slutsky equation in terms of elasticities as: E11 = e11 = -1n1 Where En price elasticity of the ordinary demand curve, e is the price elasticity of compensated demand curve, is the proportion of total expenditure spent on commodity Q and is income elasticity of demand for Q (The compensated demand curve shows the change in quantity Q demanded when price of the commodity changes but the utility level remains unchanged. We will derive it shortly in this chapter itself. itself. This This equation equation says that ordinary ordinary demand demand curve curve will have have a greate greaterr demand demand elastic elasticity ity than the elasticity of demand is positive (n 1>O) and E is less than when n 1 <0 is in the case of inferior goods. For a Giffen good E will be positive. The slutsky equation (40) and its elasticity version (41) can be extended to account for change in the the deman demand d for one one commo commodit dityy resu resultin lting g from from chan change gess in the the pric pricee of the the other other commo commodit dity. y. The expression for this is òqi --------- = òPjû
òqi
òqi
-----------òP j U = constt.
-q (----------) òy
Price = constt
and E ij = eij - -jni for i,j = 1,2 The interpretation of these equation is straight forward. If i=j then we get the original Slutsky equations (40) and (41) which we have already interpreted. When i=j then òq 1/òP j or òq1/òP j) u=constt. will show the cross effects indicating the change in quantity demanded of i th commodity when price of jth commo commodit dityy chan change ges. s. The The sign signss of cross cross effec effects ts are are not not know known n in gener general. al. They They depen depend d wheth whether er the commodities commodities concerned are s ubstitutes ubstitutes if this cross-substitution cross-substitution effect is independent independent of the income effect. In other words, if Q and Q are substitute gods and if the consumer remains on th same indifference curve, an increase in price of Q will induce the consumer to substitute Q i Q j then (òqi/òP j) U=constt. is greater than
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zero and if +Q i and Q j are complement then (òq i/òP j)u-constt will be negative. negative. There are other uses of the generalized Slutsky equation. With the help of this equation and its elasticity version, it can be shown that (i) the substitution effect on the ith commodity resulting from a change in the juthy price is the same as the substitution effect on the jth commodity resulting from a change change in the ith price (ii) the sum of compens compensated ated demand demand elasticit elasticities ies for commodity commodity Q as a result of changes in price P and P would be zero, and (iii) the income elasticity of demand for a commodity equals the negative of the sum of ordinary price elasticities of demand for the commodity with respect to its won and othe otherr price prices. s. For For proof proof of all all thes thesee resu results lts and and for for their their gener generati ation on to n vario various us some some advan advance ce text-books text-books on Microeconomic. Microeconomic. Theory may be consulted. How How Sluts Slutsky ky equati equation on for for a commo commodit dityy is deriv derived ed can be expla explain ined ed by usin using g a speci specific fic utili utility ty function, Let us utility function be U=q q and the income constraint for this, is given as y=P q + P q Putting them together in the form of the lagrange function we have V = q1q2 + / [Y-P 1q1 – P 2q2] Setting the partial derivatives equal to zero, we have òV -------- =
q2 - / P1 = O
Òq1 òV -------- =
q2 - / P2 = O
Òq2 òV -------- =
y- P1q1 - P2q2 = O
Ò/ By taking the total differentials for each of these first order partial derivatives we have dq2 - P1d/ = / dP1 dq1 - P2d/ = / dP2 -P1dq1 –P2dq2 = -dy+q1dp1 + q2dp2 The right hand side of these equation is known. Concentrating on the lefthand side, the value of the determinants of the coefficients for dq.dq by denoted by D is. O
I
-P 1
I
O
-P 2
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D=
= eP 1P2 -P1
=P2
O
Let the cofactor of the element in the ith row and jth column be denoted as D so we have. D11
= P22, D21 = P1P2, D31 = -P2
Solving for dq by the Cramer’s rule we get dq1=
/D11dq1 + / D 21dp2 + D31 (-dy+q 1dP1+d2dP2) ---------------------------------------------------------------------------------------------------------------------------------------D
or dq1=
-P22/dp1 P1P2 / dP d P2-P2 [-dy+q1dP1+q2dp2] ---------------------------------------------------------------------------------------------------------------------------------------2P1P2
Since we assume that only P, changes so dP2 = O, dy = O so dq1 = -P22/dP1 – P 2q1dP1 -----------------------------2P1P2 or dq1
P2
----------- =
q1
----------- - -------------
dP1
2P1
2P1
substituting substituting the value value of / = y/2P1P2 obtaining from the first order maximization condition we have dq1
-P2 Y
-------------- =
------------------------- - -----------------
dP1 dq1
q1
2P12P1P2 2P1 Y
q1
------------------- = - ---------------- - ----------------
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dP1
4P21
2P1
Let y Rs. 100, P 1 = Rs. 2, P2 = Rs.5 & q 1 = 25 at the equilibrium, So, dq1
100
25
------------------- = - ---------------- - ---------------- = -12.5 -12.5 units units dP1
4x4
2x2
The total effect of change in price P 1 is a reduction of demand for q by 12.5 units. Out of this, the substitution effect is -6.25 (=P 2/ /2P1) and the income effect is also -6.25 (=0q/2P 1). The commodity q1 is a normal good since both the effect are unidirectional.
While While examin examining ing the properties properties of the indifferen indifference ce curve curve we can across across two extreme types of indifference indifference curves, one downward sloping straight line i n the positive commodity space ie., quadrant, quadrant, and second second,, fixed fixed propert properties ies ie., right angle angle type. type. The former former one reflects reflects perfect perfect substitu substitution tion among he commodities concerned and the later one showing only one fixed proportion for the use of commodities together ie., perfect complements of each other. What would be the equilibrium position for the consumer with such types of other. What would be the equilibrium position for the consumer with such types of indifference indifference curves and how to isolate the “substitution” “substitution” and “income” “income” effect effect associated with price changed in such situations? This is quite an interesting question. Let us examine this: If the indifference curve is a downward sloping straight line, it reflects constant slope and hence constan constantt margin marginal al rate rate of substitu substitution tion between between the goods. goods. Such Such line as we said earlier earlier intersect intersectss the commodity axes. This implies that the level of utility of or which the straight – line indifference curve stands can be achieved by consumption of either of the two commodities. This is what we mean by perfect substitution. It is not necessary that both the commodities should be consumed. The budget line for the consumer will also be a downward-sloping straight line. One straight the cannot be a tangent to the other straight line except when they coincide with each other. In this situation how to find the equilibrium position for the consumer? The equilibrium will be attained at the corner point share the budget line and ht eindifference line meet each other on the axes of the commodities. That corner point through which the indifferent indifferent lines showing the maximum attainable attainable utility level posses will be the equilibrium equilibrium point Consider the following diagram (fig. 4.15
AB is the budget line Y = P 1q1 + P 2q2 and U1, U2, U3 & U4 represen representt the indiffe indifferenc rencee curves curves U4>U3>U2>U1. The equilibrium position for the consumer is shown by B point from where the highest attainable indifference curve U 4 passes. If the budget line shifts upward parallel to the origin then the equilibrium will shift outwards on q 1 axis. To clarify the equilibrium position at either of the two corner points, let us use algebraic equations and find the solution. Let the utility function be given us.
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U = q1 + q2 and budget line y = P 1q1 + P2q2 The marginal utilities of q 1 and q2 are 1 and 2 respectively. An increase in q 1 by one unit gives a units of utility to the consumer. The consumer spends P 1 units of money to get one unit of q 1 means from P 1 expenditure expenditure he gets 1 utility. utility. Similarly from P2 expenditure on one unit of q 2 the consumer gets a units of utility. Simple calculation shows that from y units of money the consumer consumer gets 1/P1 units of utility when entire money is spent on Q 1 commodity, commodity, and 2/P2 when y is spend on Q. If 1y/P1 (or 1/P1) in greater then 2y/P2 or 2/P2) equilibrium lies on q axis where budget line meets if (e.g. Point B in fig. 4.4) and if 2Y/P2 (or 1/P1) is greater that it will be at A point on q axis. The way we find the corner solution for the equilibrium equilibrium position when goods are perfect p erfect substitutes. substitutes. Then the budget line and indifference curve coincide and every combination of q and q will be optimal 1
y/P1 = 2y/P2 P1 = ----------------------------------P2
What will be the substitution and income effects in this case when price of a commodity changes other things remaining? If and price decreases further, the budget line shifts to the right on q axis, this means equilibrium will be further away on a q axis implying increase in utility for the consumer. If we withdraw the increased real income associated with the decrease in P by taxing the consumer, he will be pushed back to the old level of utility and the equilibrium will be at B point. this means there is only income effect when price P decrease which pushes the consumer on higher indifference curve. There is no substitution effect because it is a corner case. The other commodity has already been fully substituted earlier. Suppose P increases then the budget line shifts inwards i.e., to the left on q axis. The equilibrium position will depend on the magnitude of increase is still greater than then the equilibrium will be on q axis meaning less quantity of q and hence the reduced level of utility shown by a lower indifference curve. However, then the consumer shifts of q commodity q will be completely replaced by q. the new equilibrium and q axis will however, show lower level of utility attained than the level of utility given by the original budget line AB. It is obvious from the figure. The new utility level will be shown by indifference curve passing through point A which is less even than U. The earlier attainable level was U. Let us now examine the case of complementary goods. The indifference curve for complementary goods will be right angle shape showing on fixed combination of the goods. The budget line touches such an indifference curvet the corner showing the fixed proportion of the commodities. In figure 4.16 AB is the budget line. This line is touching he corner of U indifference curve at E it is this. the equilibrium point. if there is a decline in price of Q then the budget line shifts to AB position touching the higher indifference curve U at E corner. The quantities q and q of Q and Q will change in such a way, while moving for E to E that the original proportion of consumption of the goods together is maintained. This means the locus of equilibrium points will be a straight line emerging from the origin. Since the two goods are complementary, there will be only “income effect” associated with the price changes for a given level of income. This can be checked by pushing back the consumer to the original level of utility (E) by shifting down the budget the AB to AB touches the U indifference curve exactly at E point showing no substitution effect.
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Indif Indiffer feren ence ce curve curve is a tool tool to anal analyse yse econo economic mic behav behaviou iourr of a cons consum umer. er. We have have seen seen how how consumer attains equilibrium position on an indifference curve and changes in prices of the goods and income affect his equilibrium position. Beside this, the technique of indifference curve is applicable to solve a number of other problems related to consumer behaviour. A few of them are being discussed here. a) Measur Measuremen ementt A consumer buys a commodity only when the gain of utility from that is greater or atleast equal to the loss of utility of money spent on the commodity. using he equilibrium concept we can show this condition condition by b y the expression. expression. gain of utility loss of utility of money ie. where = marginal utility of money. when the consumer actually buys the commodity he says uniform price for all the units of it, but we know the marginal utility of different units will be different, first unit of the commodity having higher and then declining gradually as quantity increases. It means the total gain of utility will be more than the total loss of utility by giving up the money when the commodity is purchased by the consumer. This gain of excess utility is the consumer surplus. How to measure it precisely is a problem. Marshall who first coined the concept of consumer surplus used simple demand curve to measure it. He defind consumer surplus as the difference between total amount of money the consumer would be willing to pay for a given quantity of some good and the total amount he actually pays. Here, both gain of utility and loss of utility are being assessed on the b basis of money. The willingness to pay depends on the utility gained by having the commodity. To explain how consumer surplus occurs, let us consider the following figure. In this figure we have have show shown n a down downwa ward rd slopin sloping g deman demand d curve curve for the the commo commodity dity.. Let the the mark market et pric pricee fort fort the commodity be Rs. 4 which is determined by the interaction of supply and demand for the commodity. At this price the consumer consumer buys 4 units of the commodity. According According to the demand curve, the consumer consumer is willing to Pay Rs. 7 as price of the first unit of the commodity. He actually pay Rs. 4 for that. This means that there there is a gain to the consumer consumer of Rs. 3 from the first unit unit of the commodity commodity.. The second second unit unit of the commodity is giving him Rs. 6 – Rs. 4 – Rs. 2 as surplus. The third unit give Rs. 5 – Rs. 4 = Rs. 1 as surplus ant last unit pays nothing (Rs. 4-Rs. 4 = 0). Total surplus from all four units is Rs. 6.
Actually, the surplus is nothing but the area of the triangle over the total expenditure rectangle. This is equal to Rs. 8 when we take continuous change in the demand rather than discrete changes. Analytically the difference between the areas OLCA and OLCD is the consumer surplus. Using the demand equation P=f(Q) and Q and P as given set of quantity and price for the commodity, the consumer surplus can be expressed in money terms as. If the given set of quantity and price changes to q and P then the change in consumer surplus (BC) would be.
72
Q2 BC =
Sjgl Sjglh hljk ljkj hkgy kgygjh gjhljuh ljuhjji ;i8u ;i8u jnm jnm j hu huh huh ji hj ij
This is Marshallian approach of measuring consumer surplus. Hicks in his book “Value and Capital” (1939) and later on in the “revision of Demand Theory” (1956) has provided an alternative approach for this using the indifference curve technique.” A full discussion on the Hicksian approach is not intended here, rather rather we will go briefly through through its conceptualiz conceptualization ation within the indifference indifference curve framework. framework. For F or this, let us consider the following figure. IC represents various combinations of income and a commodity say which yield the same level of utility to the consumer. OA is the amount of income that the consumer had. The indifference curve IC originates from point. A showing the stage when he retains all of his income and zero units of X for a given level of utility. He moves along the curve IC down. This curve is not touching the quantity axis for X showing consumer’s preference for money rather than for more of X. Suppose the price for X is known to him and so AB line shows the income-price frontier for the consumer.
The income-price line touches the indifference curve IC at point R. The consumer and OS quantity of X and OY amount of income corresponding to this point. He gives up AY income to buy OS units of X. Now suppose the consumer does and know the price of X, but plans the same quantity of X ie. OS units to get IC units of utility. He is willing to sacrifice AY amount of income for this. But having known the price of he commodity he caually spends only AY income on OS units of X. Moreover, he moves up to higher utility curve curve IC by this. this. Thus, Thus, we can infer infer from this this that AY-AY ie. Y Y is the consume consumerr surplus surplus because because this is the difference between the amount of income the consumer was willing to spend and what he actually spends. This surplus is shifting the consumer on higher level of satisfaction from IC to IC. This is infact, MArshallian MArshallian concept of consumer consumer surplus which we are measuring measuring using the indifference indifference curves. The consumer moves to IC curve from Ic because of lower price of X and hence gets consumer surplus. If we withdraw some income from him through a tax and push him to the old level of utility Ic by shifting down the line Ab parallel, he would attain equilibrium at L point on Ic by this. His consumption of X decrease in this situation. However, we allow him to buy the same units of X as before i.e, OS units. The consumer would nto be able to cross the new income-prince line, so hypothetically we say that he will be in equilibrium at R point on the line. The amount of income deducted from the consumer’s income i.e., RR or AA which which leave leavess him in a posi positi tion on stil stilll to cons consum umer er the the same same quan quanti tity ty of X ie.. ie..,, OS is call called ed “Compensating Variation of Income” which is also a type of consumer surplus according to Hikes. If the consumer is not buying any units of X how much income subsidy should be given to him to move from IC to IC. This is equal to Ac. This is called “Equivalent variation” of income which is yet another concept of consumer surplus. There are several other types of “surplus” which are associated either with a fall or a rise in price of a commodity in whose details we are not interested at this stage. They may be read from the other sources. (b) Income tax Vs-Commodity Tax. The indifference curve technique can also be used be demonstrate that taxes on purchasing power such as income tax are “more efficient” than taxes imposed on commodities i.e., indirect taxes. The term “more efficient” means that even if the two types of taxes reduce yield the same amount of revenue to the government, income or direct taxes reduce consumer’s utility of lesser magnitude as compared to the commodity taxes. To show this result, let us take the budget line Y = P q + Pq. In fig 4.19. this is shown by the line AB which touches an difference curve IC at E showing the equilibrium position. Corresponding to this, the optional combination of q and q is and = q. This point lines of the budget line, so we have Y =
73
P. Now let us consider a commodity tax of I per unit of commodity Q. The price P will now be changed to P + 1 and the budget line would be. This line is shown by AB and the new equilibrium at E on IC in the Fig. 4.19. The choice of Q and Q commodit commodities ies would now be qq. The satisfac satisfaction tion or utility utility derived derived now now decline decliness to IC level. level. Total Total tax revenue would be occurring to government. Suppose the government collects amount of tax in the form of income or lumpsum tax i.e. As a result o this the new budget line would be. This means the original budget line AB shifts down parallelly because of a reduction in disposable income and unchanged commodity prices. This is shown by AB. This line passes through the equilibrium point E and also. T which causes the intersection of AB and AB since the line AB is passing through point point E it i t will be a tangent tangent to an indif i ndifferenc ferencee curve between IC and IC say to CI. This implies higher utility than IC level, So it is proved that direct taxes would be more efficient as compared to indirect taxes from the point of view of consumer welfare. There are several other applications of the indifference curve technique such as in the field of exchange exchange between individuals individuals or countries, rationing, rationing, subsidy programmes, product quality improvement, improvement, supply or labour, index numbers, etc. Due to paucity of space we are excluding then from the scope of this chapter.
The indifference curve analysis carried on so far runs in terms to two commodities Q an Q. in practice a consumer at a time may buy several commodities and if we consider all of them together it is impossible to draw indifference curves of multiple dimensions. What is the use of having a two commodity indifference curve analysis then? The analysis is logically consistent and provides us useful insights to understand consumer behaviour in ordinal utility framework, but because of its abstract nature if cannot be applied applied in practi practice ce to derive derive simultan simultaneous eously ly the demand functi functions ons for all commodit commodities ies and several several relate related d results results such as income income and substitu substitution tion effects effects associat associated ed with price change changes, s, except except in the limiting case of one or two commodities. We know that price and income changes are not equiproportional, the optimal consumption bundle is generally changed then. The simple approach for this is to consider first the effect of an income change, holding all prices constant, and then the effect of a change in one prive, holding all price constant, and then the effect of a change in one prive, holding all other prices nd income constant. The analysis for two commodities case has been done using this approach. Now suppose we want to consider more than two commodities to find the effect of an income change and that of a chan change ge in one one price price,, other other pric prices es remain remaining ing cons constan tant, t, we can can still still do it usin using g the the two dimen dimensio siona nall indifference curve diagram. For this what we have to do is to take the commodity whose price is changing on one axis and the aggregate expenditure on all other commodities on the other axis for drawing the indiffe indifferen rence ce curves curves and then carry carry on the analysis analysis as we have done earlier. earlier. The total expenditu expenditure re on all other commodities is interpreted as a “Composite commodity”. the results of such analysis we give us optimal consumption of the commodity concerned and optimal expenditure on all other commodities. Hick Hicks, s, in his his “Valu “Values es and and Capit Capital” al” has has proves proves this this and and genera generaliz lized ed the the outcom outcomee in the the form form of the “Composite “Composite commodity commodity theorem”. theorem”. According According to this theorem, If the prices of all but the its commodity are fixed, utility can be expressed as a differentiable function of the consumption of the its commodity, x and expenditure on all other commodities, m i.e. Moreover, the indifference curves in x and m space representing U are continuous and strictly convex to the origin, Finally maximizing this utility function subject to Y = m+P m+P x
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yields the optimal consumption of the its commodity and optimal expenditure on all commodities.
The theory of revealed preference was originally developed by Samuelson He tried to provide an alternative approach to study consumer behavour free from the cardinal and ordinal concepts of utility samuelson has shown that significant generalizations concerning consumer choice can be derived from the observing the choices that a consumer makes. The consumer’s choice reveal his preferences. For a give given n set set of pric prices es of he pref prefer erss a comb combin inat ation ion of quan quanti titi ties es of diff differ eren entt gods gods or what what we call call “consumption bundle” it means al other consumption bundles that could have been purchased with the fixed income of the consumer are inferior to him. The basic relationship of the revealed preference theory is thus the comparison of the commodity bundle that the prefers to all other commodity bundles that are rejected by him for given prices and income. In order order to develop develop the theory, theory, Samuel Samuelson son took help help of some some basic, basic, axis regard regarding ing consumer consumer behaviour. These are (i) the tastes of the consumer are unchanged during the period of analysis (ii) the consumer choices are transitive “. That the to say they are consistent. It means if a commodity bundle A is chosen form a set of alternatives that includes B bundle, then any set of alternatives from which B is chos chosen en must must not cont contai ain n. A (iii (iii)) It is poss possib ible le to indu induce ce a pers person on to purc purch hase ase a good good if pric pricee is appropriately changed i.e. if the price is lowered sufficiently. On the basis of these assumptions or axis, as argued by Samuelson, most of the standard results of the theory of consumer behaviour such as the existenc existencee of demand demand functio functions ns,, their their homogene homogeneity ity of degree degree zero, zero, and the fundame fundamenta ntall theorems theorems of consumption theory in its weaker form can be derived. The fundamental theorem of consumption theory states that if the demand for a good always increases (decreases) when income increases (decreases), then the quantity of the good demanded will always decrease (increase) when price of a good rises (falls). In order words this theorem means that positive income elasticity implies negative price elasticity for a good. Let us consider two commodity diagram to explain the theory of revealed preference. As usual, we consider a given budget constraint for the consumer in the form Y = Pq + Pq. The income and price of the two commodities are given. In fig. 4.20 this is shown by the line AB. Following the basis axiom of the revealed preference theory let us take R as the combination of Q and Q commodities chosen by the consumer. The consumer has revealed or shown his preference for this combination whatever be the reason for this ie. either this is cheaper or he likes, or all other combinations of Q and Q shows by the line AB or below this, inside the triangle OAB are inferior to R. The consumer, following the axiom of consistency will not prefer any other combination of Q and Q so long his income and prices of Q and Q are constant. The can prefer the combinations on the right hand side of AB but his budget line is a constraint for this. if his income increases of price of Q or Q declines the he must prefer some combination of Q and Q from this side of the line AB as compared to R. Let us consider the situating when price of commodity Q decreases, price of Q and income remaining unchanged. The budget line AB shifts to AB position. The consumer responds to this new situation by shifting his preference to the combination S on the new budget line AB. He does this because his real income, due to a fall in P increase so he buys more of Q. The consumer is buying more of Q because of positive income effect or there is a substitution substitution effect. We cannot say anything about the substation substation effect since there is no indifference indifference curve. In orde orderr to find find the the subst substitu ituti tion on or effec effectt since since ther theree is no indif indiffer feren ence ce curve curves. s. In order order to find find the substitution of quasi-substitution effect in movement form R to S let us “eliminate” the income and effect associated with purchase of Q in the new situation and then evaluate budget in such a way that he buys the same done by reducing consumer budget in such a way that he buys the same amount of Q and Q as before. For this, the new budget line AB is shifted down parallelly till it passes through point R. The effective budget line without income effect is nor AB is flatter than AB since the price of Q has fallen. What will the consumer do now? He may continue to be at point R since it lies on the line AB. But since price of Q has declined the consumer would now prefer to move form this point. he will not move to the left or R
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and RA section since all such combination fall within the triangle OAB which the consumer had already rejecte rejected d earlie earlier. r. Simila Similarly, rly, moving along RA was ruled out earlier earlier becaus becausee of reveal revealed ed preferen preference ce to combi combina natio tion n R over over the the othe others rs.. One One possi possibi bility lity to shift shiftin ing g from from R is now now on the the line line RB which which gives gives superior combinations of A and A as compared to R. The other possibilities including moving along AB. All such such poss possib ibil ilit itie iess inc includi ludin ng movi movin ng alon long RB segm segmen entt of AB lin line imp implies lies that that the the quasi-substitutions effects of a fall in price of Q cannot reduce the quantity of Q contained in R but may leave it unchanged. Assuming that the consumer acts in a rational way and utilizes his full income, We may take T as the new combination which in now revealed preferred to R. so we infer from this that the movement from R to T is because of substitution effect, i.e., a decrease in price of Q increase the quantity purchased or Q. if we give back the income “with drawn” from the consumer, he would move to point sampling positive income effect for the commodity i.e., an increase in quantity of Q demanded with a rise in income of the consumer. Suppose price of Q decrease further. We would then have AB as the new budget line and U as the revealed preferred combination of Q and Q. as in the earlier step, we withdraw the increased income associated with further decline in price P to trace the associated quasi-substitution effect. This is done by shifting AB line down paralled till it passes through point T. the new effective budget line would now be A B. for the same reasons as given above, the consumer would now prefer any combination on segment TB and A B. Let this be W. This again implies that the substitution effect is working in negative direction implying more of Q with a fail in P. the locus of the preferred points RTW is a convex boundary towards the origin. This is not the indifference curves since W is preferred over T and T is preferred over R. Any pointy on an indifference curve is equally preferred such as R between R and T and T and W. The locus of all such point pointss will will be a part part of the the indif indiffe feren rence ce curve curve.. Now Now supp suppose ose we have have suff suffici icien entt data data on revea revealed led preferen preferences ces then we can drawn drawn an indiffe indifferen rence ce curve from that. We keep income income (Y) and other price (P) constant and vary the price (P) in both the side to get a convex boundary showing an indifference curve. The revealed preference theory provides empirical approach to fit an indifference curve and from this link we can argue that indifference indifference curve analys a nalysis is and revealed revealed preference analysis are complementary each the. Houthakkar, in fact, has demonstrated the fundamental equivalence between the utility theory and the revealed preference theory.
Duality is an important feature of several of modern economic theories. Consumer theory which we have have discu discusse ssed d so far far in one of them. them. Dual Duality ity,, in gener general al is defin defined ed as the the of two logical logical system systemss characterized by certain interrelationships. The essence of a dual system is a correspondence or similarly between concepts in one system and concepts in the other which help us to derive similar results from both both the the system systems. s. The The dual dual appro approac ach h in study studyin ing g econo economic mic pheno phenomen menaa is very very helpf helpful ul in appli applied ed econometrics research as well as in development of economic theories. We will show its importance in this section by taking concrete exemptless from the consumer theory. Major contribution in the duality of consumer theory came from Hetelling. Following his contribution and of other we will go through indirect utility utility functi function on showin showing g dependen dependence ce of utility utility on prices prices and income income and the consumer consumer expend expenditu iture re function function showing the minimum minimum cost of attaining a given utility level for a given set of prices.
The Utility function introduction in section 4.1 is direct in the sense that total utility derived by a consumer depends directly on the level of quantities of different goods and services he consumes at a time, i.e., U=F(q q..q). Through constrained maximization of such utility function we get ordinary demand equations for the goods which are expressed in terms of prices and income. That is, reproducing the set of demand function derived earlier (see equation set (15) Sec. 4.3) we have
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qi = i(P 1,P2,.......Pny0); i=1, .....n Substituting the value or Qq i(i=1,....n() in the utility function we get maximum attainable utility in terms of prices and income levels as: U* = F[(iP1,P 2,.....,P ny0), O 2(P1,P 2,...Pn,y0).....0n (P1,P2,.....Pn,y0) This, on simplification can be expressed as: U* = F* (P 1,P2, ....,Pnyo) This is, the maximum attainable utility is functions of prices and income this is called “Indirect Utility Function” U is the highest utility that may be obtained with given prices and income to the consumer. We have seen earlier that the demand functions obtained from the direct utility function are homogeneous of degree zero in income and prices (see sec. 4.3). Since the direct utility function is expressed in terms of prices and and income, if these variable variable change in the same proportion, proportion, the optimal utility utility level U will not be changed. changed. The price-income price-income difference surface surface will be fixed i.e., F* (P1, P2,......y0) This surface can be represented by three dimensional graph (P 1,P2 and y) y being on vertical axis. The shape is like a cone having its vertex at the center. The maximum value is shown by the point of origin. The duality duality between between U=Fq1,q2) and U*=F*(P 1, P 2 and Y) that both of them represent the same preference preference ordering. ordering. Maximization Maximization of U=F(q1,q2...qn) with respect to q i(7=1...n) with given income and price leads to the same demand functions as minimization of U*=F*(P 1,P2,....PnY0) with respect to prices and income for given quantities. The direct utility function can be expressed in normalized form also. For this, we have to change the constraint slightly. Let y-=P 1q1+P2q2+....+Pnqn be the budget constraint. Dividing both the sides of this by y0 and letting vi=Pi/Yo i=1, n we write the utility maximization problem as Max U = F(w 1,w2.....wn) subject to I=V 1w1+V2w2+....Vnwn. By solving the first order maximization condition from this, we find the demand relations for in terms of normalized prices. V1 = (i=1,n (i=1,n)) as , wi = qi (V1V2....Vn) = 1,n 1,n 50 50 By substituting (51) in the utility function we get the indirectly utility function. U* = F[ U | V 1V2....Vn) = 1,n 1,n (51) (51) That is, the maximum value of utility is a function of normalized prices, V i,V2....Vn F0 denotes the functional shape of the relationship. The properties of this function are the same as described above. The “indi “indirec rectt indi indiffe fferen rence ce curve curves” s” gener generate ated d by the the util utility ity functi function on (51) (51) will will be very very much much simila similarr to the indifference curves generated by the direct utility function with the difference that on the axes we will have now V the origin will show lower level of the utility and the one which is the nearest to the origin will show the highest level of utility. The optima will of course coincide with the origin. b) Derivation Derivation of Demand Function Function : Roy’s Identity Identity To derive the demand functions for difference commodities we minimize the indirect utility subject to the budget constraint. That is Min: U* = F*(P 1,P 2...Pn,y)
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Subject to y = P1q1+P2q2+Pnqn Transforming the problem of minimization in the form of the Lanrange function, we have Z = F*(P1,P 2,Pn,y)+K(Y-P 1q1-P2q2,........,P nqn) The first order conditions for minimization of this function are: F*(.) -------------------- -kq1 = 0 òP1 òF*(.) --------------------------- -kq2 = 0 òP2 òF*(.) --------------------------- -kq2 = 0 òPn òF*(.) òF*(.) ---------------------- +k = 0, -------------------- = y-P1q1-P2q2...Pnqn = 0 òy òk From the first n equation we have òF*(.) -------------- = òP1 -----q1
òF*(.) ---------------òP2 òPn -------q2
òF*(.) =.. =..... ...... --------------
= K = 0 òF* òF*(.)
- --- --- ---- --- --- --- --- ---- ---
----------
,
òy
qn
or òU* òU* òU* -òU* ----- q1= ------------ q2 = ------ qn = k = ----------òP1 òP2 òPn òy -òU*/òP1 q1 = ------------------------------òU*/òy -òU*/òP2 q2 = ------------------------------òU*/òy qn=
-òU*/òPn òU*/òP1 --------------------------- or q 1 = --------------------- , òU*/òy òU*/òy
i= 1,.. 1,.... .... ...n .n
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This This is defi defin ned as “Roy “Roy’s ’s Iden Identi tify fy”” whic which h expr expres esss the the dema deman nd fun functio ction n for for the the comm commod odit ityy in the the consumption consumption bundle of the consumer. “Let us take a simple example for for this. the indirect utility utility function function is given as: U* = a1(y/P 1)b1 + a2(y/P2)b2 From this, this, òU*/òP òU*/òP1 = -a1b1, yb1,P 1-b1-1 òU*/òP2 = -a2b2, yb2,P2-b2-1 òU*/òy = a1b1yb1-1 P-1-b1+a2b2yb2-1P2-b2 By using the Roy’s Identification we get òU*/òP1 q1=
-------------------------òU*/òy
{0a1b1yb1P1-b1-1] = ---------------------------------------------------------a1b1yb1-1P1-b1+a2b2yb2-1P2-b2
q1 =
òU*/òP2 [0a2b2yb2P2-b2-1] ------------------------------- = -------------------------------------------------------------------------b1-1 b2-1 -b2 òU* /òy a1b1y P1-b1+a2b2y P2
q1 =
aibiybiP1-b1-1 ----------------------- ------bj-1 -bj P j ja j b jy
j
i=
,
2;
j =
1, 2
There are the demand equations for and derived from the given utility function. In general, by solving the first order minimization conditions (53) we will get the standard demand functions for q1 =
01[P1,P2,.........P n,y] ,y],
i = 1,.... ............,n
There are similar as the demand functions derived from the direct utility function (Ref. Eq. Set No. 15) c) The Expenditur Expendituree Function and Compensated Compensated Demand Demand – Relations Relations A compensated demand function expresses the relationship between quantity demanded of a commodity and prices to maintain constant utility. Due to a change in price of a commodity the quantity demanded of that commodity will be affected and there may be effects on quantities demanded of other commodities as in the case of substitute and complementary goods. The change in the quantities of the commondities in turn turn will will affect affect the the utili utility ty deriv derived ed from from consum consumpti ption on.. In orde orderr to main mainta tain in the the same same utili utility ty level level,, the consumer is provided either a subsidy or taxes depending on rise or fall n the price. In this situation, the compe compens nsate ated d deman demand d curve curve play playss very very cruci crucial al role. role. This This type type of deman demand d funct function ion can can be deri derived ved by minimizing consumer total expenditure subject to the constraint that total utility is fixed. That is Min y = p 1q1 + p2q2 + .... + Pnqn Subj Subjeect to U
= F(q F(q1,q2,......,qn)
Using the Lagrange Multiplier method we write the function
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L = P 1q1+P2q2+......+Pnqn+ [U -F( -F(q1,q2...qn)] Sett Settin ing g the the parti partial al deriv derivat ative ivess of the the functi function on with with resp respect ect to q 0,q2,....q n equ equal to zero zeros, s, we get get the the conditions conditions for minimum (provided the second order conditions conditions are satisfied) satisfied) as òL/òq 1 = P1- F1 = O òL/òq 2 = P2- F2 = O òL/òqn = Pn- Fn = O òL/ò
= U = F(q1,q2,.......qn)= 0
Thes Thesee equati equation onss on solut solution ion for for q 1,q2,....qn will will give give us the the compe compens nsate ated d deman demand d functi functions ons for for the commodities commodities as: q I = i[P1,P 2,....PnU ], i=1,.. i=1,.... ...n .n = [P1,P2,....P n,U ] Let us take a specific utility function U = q 1q2 as we have taken earlier Minimizing y = P 1q1 + P2q2 Subject to U 0 = q1q2 P1-bq2 = 0 P2-bq1 = 0 U0-q1q2 = 0 From these we have q1 = [P2/P1 U0]1/2, q2 = [P1/P2 U0]1/2 It can be verified easily that the compensated demand function (57) like ordinary demand function, is homogenous of degree zero and at the optimum level of utility we get the familiar identify. Pi ----Pn
òU/òq1 =
------------------òU/òqn
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Substituting Substituting the compensated demand functions for q 1q2,....qn in the budget equation y = P1q1 + P2q2 + ....+Pnqn y = P1h1(P1,P2,.....,Pn,U0)+ P2h2(P1,P 2,.....,P n,U0) + ....+ P nhn(P1,P2,.....,Pn,U0) Since we are substituting optimal values commodities, we can write y-y indicating minimal level of expenditure to attain an constant level of utility U the expression (59) can be now simplified as: y0 = H (P0,U0) = P1h1[P0,U0]; P0 is a nectar of prices ie [P 1, P2,....P n] This function is called “Consumer’s Expenditure Function”. It can be shown that this function is continuous in U and P concave, homogeneous of degree zero and non-decreasing in prices, m and increasing in U. The expenditure function has an important property which is given by the Hotelling’s theorem. According to this theorem, if the expenditure function is differentiable, the optimal consumptions bundle is given by
òH(P,U) q0i – h1 (P,U) (P,U)
= ----------------------------,, i = 1, .... ....... ....n .n òPi
P is the vector of Prices [P 1, P, P n] That is, optimal consumption of the ith commodity is obtained by the partial differentiation of the expenditure expenditure function with respect o the ith price. price. To prove the theorem, let q 0 be chosen at prices P and utility U i.e. q 0i = Hi(P0U0). Comparing the expenditure expenditure function and budget equation we can write. By taking total differentiation of both the sides we get: H1(P0U0)dP1+Hu(P0U0)dU = q 01dPq + P01dq1
(62)
Where H1(P0U0)dP1+Hu(P0U0)dU = q 01dPq + P01dq1
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and H1 (P0U0) = òH (P 0U0) /dP 1 H1 (P0U0) = òH (P 0U0) /dn Again, at the optimum we had the relationship P0n =
U/òqi = òF (q (q0) /òqi
(63)
Substituting (63) in (62) and setting dU = o we get, H1 (P0U0) dP 1
= q01dPq +
Sin Since U = F (q1...q3...qn) òU/ò òU/òq qn
F1(q0)dq 1 = òF (q01/òq1 = F1(q0)
If there is a change in jth price, all other prices being contant ie., dP = oi# then we get H j (P0,U0) = q j
(64)
The second term on the right hand side vanishes when utility is constant.
Let us consider utility function of the type This is liner expenditure expenditure system. This expression expression is telling us that quantity quantity demanded of a commodity Q 1 is a funct function ion o tot total al expen expendi ditu ture re y and and pric prices es of all all commo commodit ditie iess in the the consum consumpti ption on baske baskett of the consumer q is a constant interpreted as basic or committed consumption of ith commodity Y is defined as super-numera super-numerary ry income or uncommitted income. income. And B are simply the marginal marginal propensities to consumer. consumer. In terms of expenditure we interpret (66) as the expenditure (P q) on a commodity at the optimum which is a sum of committed (or essential) expenditure on that commodity and a protion of the super-numerary income B. The The linea linearr expen expendit ditur uree system system is based based on the the util utility ity functi function on havi having ng al prope propert rties ies of the conv convent ention ional al util utility ity funct function ion.. The The system system has has addit additive ive prope property rty i.e., i.e., the the cum of diffe differen rentt types types of expenditure equals local expenditure. The system is homogenous of degree zero in income and prices. Stone has used this system to estimate and demand for various goods and services in the United Kingdom.
Kelvin Lancaster has developed a new approach to analyse consumer demand for different goods. The essence of his theory is to provide a fully integrated theory of consumer choice and demand, in which the characteristics of good are taken explicit into account. Such a theory provides a basic structure which product product varia variation tionss and new product productss fit easily while while analyzin analyzing g the demand demand.. The traditi traditiona onall theory theory of demand demand is too abstract abstract accordi according ng to Lancaste Lancasterr as it is based based upon preferen preferences ces along ignorin ignoring g highly highly pertinen pertinentt and obviou obviouss informat information ion about about the propert properties ies of goods goods which which play crucial crucial role role in consume consumerr decision-making. The physical properties, for example, size, shape, colour, smell, chemical composition, abili ability ty to perfo perform rm a varie variety ty of funct function ionss and and so on are quite quite import importan ant. t. If we look look at the analys analysis is of deman demand d from from the the point point of view view of mark marketi eting ng.. Some Some of thes thesee prope properti rties es which which Lanca Lancaste sterr terme termed d as “character “characteristics” istics” are relevant for making choices choices and they must be incorporated incorporated explicitly explicitly in the demand analysis for goods and services.
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Lancaster’s theory is quite interesting and complex. We will not go into its details here buys simply cover the basic reference reference model to understand understand its conceptual conceptual functions. functions. The crucial element element of Lancaster Lancaster theory is the the conce concept pt of the the “con “consum sumpti ption on techn technolo ology” gy” which which speci specifi fied ed a relat relation ionsh ship ip betwee between n goods goods and char charac acte teris risti tics. cs. The The char charact acter erist istic ic are are assume assumed d to be objec objectiv tively ely measu measura rable ble.. The The “unit” “unit” in which which a particular characteristic is measured is not important except that it must be same for all goods possessing that characteristi characteristics. cs. Defining as the quantity of ith characteristic characteristicss possessed by a unit amount amount of ith good, and x as quant quantit ities ies of its char charact acter eris istic ticss and and jth jth good, good, a linea linearr relat relation ionshi ship p has has been been postu postulat lated ed by Lancaster as: z1 = bijX j
i,e bij
= ZiX j (65)
If there are more than one good then the above relationship changes to Z1 = bijX1 + bizX2 + .....binXn This additively assumption for the model showing that the total amount of ith characteristics posses by the goods collection of x 1x2....xn) is the sum of the amount of the characteristics by the good separately. Suppose there are characteristics and n goods then we have In matrix from we write this as: Z = Bx Wher Wheree Z = Zi a vector of characteristics it is called as consumption technology matrix X = { X j } a vector of goods Where Z = { Z j } a vector of characteristi characteristics cs B = { b ij } a matrix of coefficients relating of good and characteristics It is called as “consumption technology matrix” X = { X j } a vector of goods This is a kind of input-output model. Inputs are gods and putouts are characteristics. Sizes of B matrix is r x n. r may be greater than n or equal to n or less than n. Nothing can be said about this at this stage. A simple example of this type of relationship can be given as that of different foods such as milk. Eggs, Eggs, oranges, oranges, bread bread havin having g charact characteri eristic sticss like like calorie calories, s, protein protein vitamins vitamins in specifie specified d units. units. B matrix matrix represents represents these t hese characteristics characteristics possessed by the different foods. For the sake of simplicity it was assumed that all elements are non-negative and all goods are non-negative. a some what stronger assumption made by Lancaster about the consumption – technology matrix is that it is semi-positive having atleast one positive element in each row and each column. This ensures that the tabulation of the technology does not include any good which has none of the relevant charac character teristi istics cs or any charact characteri eristic sticss which which is not possesse possessess by atleast atleast one of the goods. Further Further the consumption technology is assumed to be universally valid in the sense that all consumer “see” it in the
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same same say. say. This This simp simple less that that ther theree is no diff differ eren ence ce betw betwee een n con consume sumers rs as to what what coll collec ecti tion on of characteristi characteristics cs is associated associated with any specific collection of goods. As ment mentio ion ned earl earlie ierr the the cons consum umpt ption ion – tech techno nolo logy gy expr expres esss the the rela relati tion onsh ship ip betw between een charac character teristi istics cs and good. good. The relation relation-shi -ship p between between charact characteris eristics tics and people people is express expressed ed by their their preference. It is assumed that the interest of consumer is in characteristics, and not in good purifies. Any preference preference for a collection of goods is because of preference preference of the characteristic. characteristic. Lanchasters Lanchasters adopted the traditional preference theory of consumer with such a modification. The assumptions of traditional cons consump umptio tion n theor theoryy were were adopte adopted d by him him with with modif modific icati ation on e.g. e.g. char charact acteri erist stics ics in place place of goods, goods, preferences preferences for characteristi characteristics cs rather than goods g oods etc., Complete Complete quasi-ordering quasi-ordering of preferences, preferences, transitivity of preferences, completeness, convexity non-satiation etc., are the standard requirements of consumer theory which are applicable to Lancaster’s Lancaster’s theory also The behavioral assumption for the demand analysis made by Lancaster can be stated as follows:“The consumer acts in accordance with his preferences, that is, gives the opportunity to choose from some set Z of characteristics collections, the consumer will choose that collection which maximize U(Z) over Z.” The consumer’s budget line can be postulated as usual P1X1+P2X2+ ........ + PnXn or PX Y where where P is a vect vector or of prices prices,, is a vector vector of goods, goods, Y is inco income. me. The consum consumer’ er’ss choic choicee prob problem lem under the regular budget constraint will be as: Max U(Z) Subject to Z=BX PX Y Simplifying this we can write Max U(Z) = U(BX) = V(X) since Z=BX Subje Subject ct to PX y X O We cannot say that this is similar to the simple utility maximization case. There will be major differences if the member of characteristics is less than the number of goods. In this case, the partial derivatives of v with respect to the gods (x) and the partial derivatives of U with respect to the characteristics Z are related by Since Since there there are only only r deriv derivati atives ves òU/ò òU/ò2, 2, it follo follows ws than than n-r n-r of the the deriv derivat ative ivess òU/òx òU/òx can be expressed in terms of the remaining r. thus, all first order conditions of the traditional utility maximization model ie.,
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òv/òx j = /P j cannot be satisfied. The simple new-classical optimizing technique cannot the applied here. The problem can only be tackled by complex techniques of non linear programming. The concept of consumption – technology, its universal validity etc., are no doubt simple in conception but when it is the question of application, it may create complexity as we have been just above. Lancaster, however analysed the different situations arising by the inequalities between r and n and gave equilibrium posit position ion.. He exten extended ded this this mode modell furth further er and and gave gave examp examples les from from real real life life indic indicati ating ng oper operati ation onal al usefulness of this demand theory in terms of characteristics of goods rather than the goods per sec. it hs potential potential uses in industrial industrial and managerial managerial economics.
The analysis of consumer behaviour through which we have gone so far is based on certainty of events. The The con consume sumerr has has full full info inform rmat ation ion or data data for for deci decisi sion on-m -mak akin ing. g. Real Real worl world, d, howev owever er,, is full full of uncertainties. The consumer may not posses complete information concerning the problem he is trying to solve. He may buy a TV but whether it works satisfactory or not is not known to him. There may be uncertainty about the earnings of the consumer itself. How should a consumer take decisions about his choices in such situations? There is not unique procedure for this. different people may have their own individual ways of tacking uncertainties, but the one that is widely used to economics or statistics is the approach approach of probabi probability lity and expect expected ed value value maximiz maximizatio ation. n. The probabi probability lity of an event event happen happening ing is, roughly roughly speaking, the relative relative frequency with which which it will occur. Consider two players A and B playing playing a game. Both are equally strong. What will be the chance or probability of either winning? It may be say 50-50 i.e., 50 percent chance for each one to win the game. Here we say that the probability of winning the game is 0.50 for A and also 0.50 for B. Suppose a is stronger than b then a may have a 80% or 0.80 proba probabil bility ity of winni winning ng the the game game and and B a proba probabi bility lity of 20% or 0.20. 0.20. When When outc outcom omee of nay nay event event is unce uncert rtain ain it may be guess guessed ed on basis basis of proba probabi bilit lity. y. This This helps helps us in findi finding ng expect expected ed valu valuee of the outcome. Let us take two possible outcomings of an event say Z 1, and Z 2. The probability of Z1 is P1 and the probability of Z2 is P2. The expected value of the outcome in the situation of uncertainty would therefore be E(2)=P1Z1+P2Z2... If there are some more than two plausible outcomes, we can extend this formula to E=Z=P1z1+P2z2+P3z3+...Pnzn Remember P1+P2+P3+......P n = 1. So, under certainly a rational decision maker will maximize the expected value of outcomes. This principle we do apply in the analysis of consumer behav behavior ior also. also. The The first first majo majorr work work in this this direc directio tion n came came from from D Bern Bernou oull llii more more than than 200 200 year year ago. ago. Bernoul Bernoulli li argues argues that individu individuals als,, in decidin deciding g on their their bahavio bahaviour ur in uncerta uncertain in situatio situations ns,, conside considerr the expected utility of their various options rather tan the expected money value of these options. It is the average utility value of a game that matters and not its monetary value. Bernoulli thought of diminishing marginal utility of income as income increases. Because of diminishing marginal utility of money or what Bernoulli called as physic value it is quite reasonable for an individual to refuse to pay a large amounts for the right to play a game since the game is not worth very much in utility term. The expected utility hypothesis has been applied by Von Neumann and Morgenstern to constructed a utility index which can be used to predict choices in uncertain situations if the consumer conforms to the following basic assumptions. a) Compl Complete ete orde orderin ring g : This This is trans transti tigit gityy assum assumpti ption on.. Acco Accordi rding ng to the the if the the cons consum umer er prefe prefers rs alternative B and alternative B to alternative C, then the prefers alternative A to alternative c. b) Continu Continuity ity assumption assumption:: If A is preferr preferred ed to B and B to C, then this assumption assumption asserts asserts that there there exists some probability P, O P 1 such that the consumer is indifferent between outcome B with certainty and expected value of outcomes of A and C with probability P and 1-P respectively. c) Indep Indepen enden dence ce Assum Assumpt ption ion : If one one lotte lottery ry tick ticket et or inves investme tment nt offe offers rs outco outcomes mes A and and C with with probabilities P an 1-P respectively and another the outcomes B and C with same probabilities P an
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1-P, the consumer is indifferent between the lottery ticket or investment plans. d) Unequal Unequal Probability Probability Assumption : The essence essence of this assumption is that, other things things being equal, we will always prefer the investment investment opportunity opportunity with greater probability of favourable outcome. e) Compound Compound Probability Probability Assumption: Assumption: If the individual individual is offered a lottery ticket ticket whose prizes prizes are, in turns, other lottery lottery ticket, he will view the compound lottery lottery ticket in the same manner as if he has gone through all the probability calculations of ultimate odds of winning and losing. Each one of these assumptions has considerable considerable implica i mplication tion for constructed constructed of the utility indices. In construction of the utility index, Neumann and Morgenstern implicit assumed cardinal measurement for utility. There There is not set origin for this type of measurement measurement of utility in N-M (i.e. Neumann Neumann & Morgenstern) Morgenstern) framework rather it starts for some arbitrarily chosed point. Consider three events A,B,C for which the order of the individuals preferences is to be stated. Let us take that outcomes of A and C are uncertain. Then the consumer while making the choice will use the expected utility derived from these two events jointly that is, if P is the probability of occurring A and (1-P) is the probability of C then expected utility from then is PU+(1-p)U cUA and Uc are utilities derived from the event A and C respectively. Suppose an event B has U utility which is certain. If we compare between the expected utility of A and C and the utility of B, we may may have the the poss possib ibil ilit itie iess of UB PUA+(1-P)Uc. Even Even B ie., ie., alte altern rnat ativ ivee B is pre preferr ferred ed if 1 UB>P(UA)+(1-P)Uc and it is rejected if U B
This This is a fair fairly ly long long chapt chapter er deal dealing ing with with vario various us aspec aspects ts of consu consume merr theo theory ry starti starting ng from from the conventional the theory of utility to the contemporary approaches. Some of the advance topics like duality approach of utility analysis. Lancaster theory of demand analysis, Von Neumann & Morgenstern approach of deling with uncertainty were discussed in brief. It is expected that an interested student will cover them in full from the relevant original that an readings. Emphasis has been given in this chapter on understanding consumer behaviour in different decision situations. No attempt has been made to go into details of measurement or estimation of the functions. This is the task of applied economies or econometrics.
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Forecasting is like trying to drive a car blind-folded and following directions given by person who is looking looking out of the back-window.” back-window.” PHILIP KOTLER The area of production planning and control is one in which the firm concerns itself with means for the the attain attainmen mentt of two object objective ivess the the produ product ction ion of requ require ired d quant quantiti ities es of a given given produ product ct and and the product production ion of these these quantit quantities ies at appropri appropriate ate time. time. This This means means that that the produce producerr must anticipat anticipatee the future demand for this product and on this basis, provide the production capacity which will be required. This calls for forecasting the future demand of a given product, translating this forecast into the demand it generates generates for various various production facilities and arranging for the procurement procurement of these facilities. facilities. The discussion of demand forecasting is divided into seven sections. The first describes the meaning, nature and the vital role played by demand forecasts in the operations of business. The second deals with the type of forecasting which arise out of the planning needs of business firms. The third explores the various approaches to demand forecasting. The fourth explains the major determinants of demand. The fifty fifty deal dealss with with the the major major metho methods ds adopte adopted d in estima estimatin ting g futu future re deman demand. d. The The sixty sixty expla explain inss the forecasting methods for new products. The last discussed how forecasting methods can be evaluated in terms of their accuracy and costs.
Estimates of expected future conditions are called forecasts and estimates of expected future demand conditions conditions are called called demand forecasts. Prec Precise ise fore foreca casts sts of futu future re devel developm opmen ents ts are clea clearly rly imposs impossib ible le.. Expe Expect ctat ation ionss depen depend d on the assumption made. The reliability of the forecasts, hence depends on the reliability of the assumption. The assumption assumptionss and methods methods employe employed d in forecas forecastin ting g depend depend upon the natur naturee of the planning planning required. There are two major types of planning which require the use of forecasts. They are (i) Short term planning and (2) long-term planning. In industrially well developed countries, these grow out of planning which the need to predict short-term and long-term changes in demand conditions facing industries. This has been so because demand conditions were always more uncertain than supply in industrially advance countries. In recen recentt times times fore foreca casti sting ng has has come come to play play an import importan antt role role in busin busines esss decis decision ion –mak –making ing.. A compa company ny is in busin busines esss to serve serve its custo custome mer’ r’ss need needss in some some way way or the the other other.. Its Its survi surviva vall and properity depends on its ability and willingness to adopt its operations to customer’s needs, to create or simulate the need. And serve it adequately and efficiently when the need arises. Demand forecasts serves as the link between the evaluation of external factors in the economy which influence the business and the management of the company’s internal affairs. The very term “planning” is intimately connected connected with forecasting forecasting because it is concerned concerned with the future. More often than not, one finds forecasting forecasting decisions which have an important important influence on production production planning operations being made by store-keepers or stockroom clerks with little or no procedural or policy guidance. Determination of the types of forecasts required and establishment of procedures
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governing governing generation of these forecasts forecasts are fundamental steps in the organization organization of well-conceived well-conceived production production control system. For production planning purpose it is particularly important to distinguish between forecasts of sales may be important for estimating revenue, cash requirements, and expenses, a production planning system is designed primarily to react to customer demand. Demand may differ from sales for a variety of reasons. For example, example, there may be substantial lag between between customer orders and billings, billings, or sales may understate demand to the extent that the manufacturing and distribution system is unable to cope up with the volume of customer demand. The particular characteristics of demand forecasts demand are pertinent of production and inventory control and the timing, detail and reliability of forecasts, and the assignment within the organizations of the responsibility for making forecasts and controlling or improving improving the quality of forecasts. forecasts.
From the point of the view of the time span and from the planning requirements of business firms, demand forecasting can be classified under two headings (i) short-term demand forecasting, and (2) long-term demand forecasting.
Short-term forecasting is limited to short periods, usually not exceeding an year. It relates to policies rega regard rdin ing g sale sales, s, purch purchas asin ing, g, prici pricing ng and finan finance ces. s. Hence Hence the the refer referen ence ce is only only to the the exist existin ing g production production capacity of the firm. In most companies, a knowledge of conditions in the immediate future is essential for formulating a suitable sales policy-production schedules have to be geared to expected rather than actual sales. Often, bu assuming that prevailing conditions will continue, a firm may find itself faced with a problem of over production or short supply. An understanding of near future prospects would make it possible to avoid some of the violent fluctuations which occur in production scheduling and sales planning. Knowledge of immediate future conditions is important in pricing. If prices of materials are expected to go up or shortage are expected, businessman may take advantage of the rise by earlier buying. Proper price forecasting forecasting may, thus help the firm in reducing reducing the cost of operation. operation. Demand forecasting is also useful to the businessman in determining his price policy. An increase of prices is avoided when future market conditions are not expected to be good and the lowering of prices is avoided when costs or sales levels are likely to rise considerably. Many companies use forecasting for setting sales targets and for establishing controls and incentives. Sales targets will not accomplish their objectives if not geared meaningfully to the sales levels likely to be achieved. If set too high, the targets will be discouraging to those who have to meet them. If the targets are very low, they will will be met very easily and incentives incentives will prove meaningless. meaningless. Above Above all, all, deman demand d fore foreca casti sting ng of the the types types mentio mentione ned d above above will will be consid consider erabl ablee assis assistan tance ce in short-te short-term rm financ financial ial foreca forecastin sting g also. also. Cash Cash requiremen requirements ts will will depend depend upon upon the levels of sales sales and production sales. Some prior information is usually neede to procure additional funds on reasonable terms. Neglect of demand forecasting will complicate financial planning through its repercussion on produ product ction ion schedu schedulin ling g and and invent inventory ory accum accumul ulati ation on.. In the the prepa prepara ratio tion n of budg budgets ets,, ther therefo efore, re, short-term forecasts have come to play and important part.
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In short short-te -term rm forec forecast astin ing g a compan companyy is conc concer erne ned d only only about about the the use use of its exist existin ing g produ product ction ion capa capacit city. y. But But when when quest question ionss of long-t long-term erm plan planni ning ng are are invo involv lved ed the the busin busines essma sman n must must know know something about the long-term demand for this product. Thus the planning of a new production, unit or the expansion of an existing existing unit must start with an analysis analysis of the long-term demand demand potential of the products in question. A multi-product firm must ascertain not only the total demand situation, but also the demand for different items. This will involve the study of consumer preferences and trends, the economy, and technological developments and trends. Once the demand potential is assessed, it will be easier for the company to engage in long-term financial planning. Again manpower planning for existing as well as new firms must be based on long-term forecasts of the company’s growth. When forecasts covering long periods are made, the probability of error is high. Competent forecasts predict he conditions that are likely to prevail in the near future with comparative confidence, and with a relatively high degree of accuracy; the results are much less reliable when they attempt to forecast conditions over longer periods. This is because, as the period becomes longer certain factors that forecasters take into account in making their estimates becomes more volatile. It is very difficult to predict over extended periods such items as the probable costs of production, the trend of prices and the changing nature of competition. Moreover the longer the term covered by the prediction, the more likely it is that unanticipated events such as international conflicts including wars, periods of major depression depression and prosperity and inventions inventions and technologica technologicall advances advances will upset the calculation. calculation. It is function of the top management in each firm to make it own decision regarding the span of time to be covered by demand forecast. It is safer to forecast for longer periods, when the volume of demand has held fairly constant from year to year. If demand has been erratic for reasons that are largely unexplainable unexplainable,, the forecasting forecasting period should be shorter. shorter. The The follo followin wing g four four distin distinct ct steps steps must must be kept kept in view view in dealin dealing g with with any any deman demand d forec forecast astin ing g problems. i) Identify Identify and clearly clearly state the objectives objectives of the foreca forecastin sting g problem. problem. In certain certain cases the required required forecasts may e short term nature. The approach needed here may be quite different from what long-term forecasts will call for. In certain other cases forecasts of market shares may be required which calls for an approach different from that needed for a general industry forecast. ii) Ascerta Ascertain in the determina determinants nts of demand demand for the particul particular ar product or product product group. group. The factors factors influencing demand differ widely depending on the products or industry or industries involved. Economis Economists ts have have a tendency tendency to categor categories ies goods goods and service servicess into three three broad broad catego categorie riess for facilitating demand analysis. These three categories are:a. Consumers Consumers non-durable non-durable goods b. Consumers Consumers durable durable goods c. Capita Capitall goods goods We follow here the same kind of categoristation for purpose of demand analysis. The determinants of demand pertaining to these categories are different, they are discussed in detail in the next section. iii) Select Select appropriate methods of forecasting. forecasting. The method selected will depend upon the purpose or objective of the demand forecasts, the nature of the product’s involved, the types of data available etc. iv) Pres Present ent the the find findin ings gs in a reada readabl blee form. form. This This is import importan antt becau because se the the mana managem gemen entt will will be interested only in the actual forecast, its meaning and implications for policy.
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Once a product forecast for the whole industry is available it is easy for the company to estimate its share of the market. Analysis of past data can indicate the trends in market share among the competitions. In preparing preparing company forecasts the management management may relay r elay on two varying assumptions. assumptions. i)
The ratio ratio of company company sales to to total industry industry sales sales will continue continue as in the past. past.
ii) The ratio ratio of company company sales to to total industry industry sales sales will change change Deman Demand d forec forecast astss for for the the compan companyy mat be made made based based on eithe eitherr of these these assum assumpt ption ions. s. And And often often companies companies prepare alternative alternative forecasts based on them. Forecasting must be a continuing activity. Every forecast is based on a given set of data and assumptions and is relevant only as long as the underlying assumptions hold good. As improved information becomes available, forecasts must be relieved and revised so that the management is provided with a better basis for decision making.
There are atleast three basic factors indulencing the demand for non-durable consumer goods. They are (a) Purchasing Purchasing power income (b) price and (c) demography. demography. (a) Purch Purchas asin ing g power power:: One One of the the majo majorr determ determin inan ants ts of deman demand d is the the purch purchas asin ing g power power of the consumer and this is determined by the income or rather disposable personal income. (Personal income minus direct taxes and other deductions, if any) of the consumer. In India, data on disposable income is not directly available. The Central Statistical Organization has not yet started the public publicatio ation n of data data or disposa disposable ble income, income, indirect indirect estimates estimates can, howeve however, r, be obtained obtained from the published data. Use of disposable income for estimating demand has been criticized by some writers on the place that it does does not constitut constitutee free free purchasin purchasing g power. power. Hence Hence they prefer prefer to use the concept concept discretion discretionary ary income in place of disposable income. Discretionary come can be estimated by deducting three items from disposable income, viz imputed income and income in kind, major fixed outlay payments such as mortgage debt payment, insurance premium payments and rent and essential expenditures such as food and clothing and transport expenses based upon consumption in a normal year. But here is may be pointed out that the disposable income concept is considered to be equally satisfactory by many experts. b) Pric Price: e: The The import importan ance ce of price price of a parti particu cula larr produ product ct and and its subst substitu itutes tes in deter determin minin ing g the demand has always been emphasized by economists. A measure of the price-demand relationship for for a produ product ct is given given by the the conc concept ept elas elastic ticity ity of deman demand. d. Conc Concept eptss such such as price price elast elastic icity ity,, income elasticity, cross elasticity etc of demand are used in economic analysis. c) Demo Demogr graph aphy: y: Expe Experi rien ence cess show showss that that the the dema deman nd for for a prod produc uctt is dete determ rmin ined ed by cert certai ain n population characteristics also. For example, a study of the demand for lipstions must take into the account the number of women by age. Again, in a study of the demand for tyres, the populations consists of the number of cars, buses trucks and other motor vehicles in use. This shows that demography does not necessarily relate exclusively to human population. In fact, this uses is in differentiating differentiating,, between total market demand demand on the one had and “market segments” segments” on the other. The segments on the other. The segments represent divisions of the total market into homogenous groups. The idea is to construct one or more segments the demand for the product Demography or population groups can be defined in terms of educational background, sex, age, income, social
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status, geographic location etc. The segment if qualified, can be used as an independent variable affecting the demand for the product in question. Purchasing power (Y) Price (P) and Demography (D) can be combined in an additive relationship in order to get a formula which can be used for predicting the demand (d) for a consumer good. The formula may take the form: d= Y + P + D Three different purchase characteristics can be distinguished in the case of durable consumer goods, they are i)
Time – use use chara characte cterist ristic; ic;
ii) Use-facilities Use-facilities characteristic characteristics; s; and iii) Demographic Demographic characteris characteristics. tics. i)
This use characte characteristics ristics consumer consumer durable durable have get extended extended use and and as such they are never never used up in a single act as are match-stricks or ice-cream. This feature enable the consumers to go on using them by repairing if necessary, or to scrap them and get new ones. Experience shows that emergencies such as war or sacristy force people to postpone replacement of durable goods and thereby to lower the effective scraping rate. The decisions to replace goods is influence also by considerations considerations such as social prestige and status, income and product obsolescence obsolescence..
ii) Use-Fac Use-Facilit ilities ies charact characteri eristic stics: s: General Generally ly durable durable goods require require special special facili facilities ties for their their use. use. For example, to use or truck, one needs to have roads and petrol or diesel stations. Again, to use a refrigerator or a radio, one needs electricity. The existence and growth of such facilities is an important variable in determining the volume of sales or quantity demanded of the products in question. question. Hence due consideration consideration must be given in choosing choosing the variables variables influencing influencing the demand for durable consumer goods. iii) Demograph Demographic ic charac characteri teristic stics. s. The decision decision to purcha purchase se consume consumerr durable durabless is influen influence ce also by facto factors rs such such as size size of famil families ies age distr distribu ibutio tion n of adults adults and and child children ren,, popul populat ation ion group groupss in differe different nt income income state, state, price price and other other conside considerat rations ions.. Demogra Demography phy here here include includess a study study of populations other than human also. A study of the demand for commercial airlines has used the numbe numberr of comme commerci rcial al airpo airports rts as both both a use use facil facilit ities ies char charac acte teris risti tics cs and and as a demog demogra raph phic ic different purchase characteristics may be considered independently, or in combination depending on the product and the economic judgement of the analyst. The total demand for durable goods, in fact, is the sum of two demand viz i) a new owner demand and ii) a replacement demand and ii) a replacement demand. The new owner demand will increase the stock of the goods. Replacement demand tends to grow with the growth in the total stock with consumers and at times it may even exceed the new demand. For certain well established products, life expectancy tables are made available available in i n advanced countries countries in i n order to estimate the average or near average average replacement rates. The basic demand equation for durables may be stated as follows: d=N+R Where Where (d) represents total demand, (N) new-owner new-owner demand and (R) replacement replacement demand. demand. Each of these independent variables may be forecast separately. It must be borne in mind that in the case of most durable goods there is an upper limit beyond which demand cannot grow. This upper limit refers to the “saturation point”. for example, even if income goes up, there is a limit to the number of radios that
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people will buy. it is to this level towards which the actual volume of consumer stocks tends to gravitate. The difference between the “saturation point” or the “maximum ownership level” and the actual stock shows the growth potential of the demand for durable goods. Capital goods are produced means of further production. They are used to facilitate the production of other goods. Examples are machinery of all kinds, factory buildings etc., The demand for capital goods is a case if “derived demand”. Hence, the demand for capital goods depends upon the profitability of the industries using the capital goods. The ratio of profitability of the production to capacity in user industries, the level of wage rates, the policy of the Government, business prospects etc., Where the wage rates go exceptionally high. The management will have an added tendency to go for labour saving equipments. Two types of data are required for forecasting the demand for capital goods intermediate of industrial goods. They are:i)
The growth prospects prospects of the user user industries industries and
ii) The criteri criteriaa or norm of consump consumption tion of the capital capital goods goods per unit of each end use. The critical critical assumptions assumptions underlying underlying the end-use end-use approach are: a) The demand demand estimates for for the end end use products products are available. available. b) The norms of consumptio consumption n (the (the techno technology logy of the industry) industry) will remain remain unchan unchanged ged during the period under consideration. c) Norms Norms based based on present present consumptio consumption n pattern patternss in industry industry may, may, impart, reflect reflect existing existing shortag shortages es are import import restrict restrictions ions in the economy. economy. In building building bridges bridges,, for example, example, mild steel might be in use at present instead of constructional steel (which is more suitable for the purpose . This might be due to the non-availability of high cost of constructional steel. But as the pattern of availability changes, the consumption pattern in the industry may also vary, changing the norms of consumption in the process. Several methods are employed for forecasting demand. However, this usual starting point is to have an ideal of the general business forecasts relating to the economy for the period under consideration. Such macr macro-e o-eco conom nomic ic or GNP GNP forec forecast astss enab enable le an indu indust stry ry or firm firm to cons constru truct ct its own own micro micro-e -econ conom omic ic demand demand forecas forecasts. ts. Macro Macro economic economic forecast forecasting ing is a highly highly develope developed d techni technique que in western western countr countries, ies, especially in the United States of America, but in India it is only in its infancy. In India the perspective plannin planning g Division Division of the Plannin Planning g Commissio Commission n periodic periodicall allyy prepare preparess aggreg aggregativ ativee forecas forecasts ts of nationa nationall income and its components which can be made use of by industries and firms for their own individual purposes. Here Here we propose propose to discuss discuss the most commonly commonly used methods methods by industri industries es of firms firms for forecastin forecasting g demand for established established products.
a. Opinion Opinion Surveys Surveys The first method we shall consider is called opinion surveys or survey of buyer intentions. Forecasting is essen essenti tial ally ly the the art of anti anticip cipat atin ing g what what buye buyers rs are are likel likelyy to do unde underr a given given set of condi conditio tions ns.. This This immediately suggests that a most useful source of information would be the buyers themselves. Ideally, a list of all potential buyers themselves. Ideally, a list of al potential buyers could be drawn up, each buyers would be approached, preferably on a face-to-face basis, and asked how much he plans to buy of listed
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products in the stipulated future time period under the given conditions. He would also be asked to state what proportion of his total needs he intends to buy from the particular firm or atleast what factors would influence his choice among suppliers. With this information, supposing it is both obtainable and valid, the firm would seem to have an ideal basis for forecasting its demand. This This method method is most useful useful when bulk bulk of the sales sales in made to industrial industrial producer producers. s. Here the burden of force casting is shifted to the consumer (Customer). But unfortunately, this method has a number of limitations in practice. It would not be wise to depend wholly on the buyers estimates since the buyers are likely to exaggerate their requirements if shortages are expected. Again, this method is not very useful in the case of household consumers for several Reasons, vix irregularity in consumers buying intentions,. Their in ability to forecast what choice they will make when faced with multiple alternatives or choices, prohibitive costs etc. a basic limitation of this method, according to Dufty, is that it is passive and does not expose and measure measure the t he variable under managements managements control. control. The favourite forecasting technique employed by industrial manufacturers appears to be the “sales fore composite method”. Under this system the company asks its salesmen to submit estimates of future sales in their their respect respective ive territor territories ies.. The sales sales force force composite composite method method is popular popular with industrial industrial concerns concerns because they have a limited number of customers needs. Forecasts prepared by salesman may be biased, however, however, due to the following reasons. reasons. Firstly, a salesman may be consistently pessimistic or optimistic or he may go to one extreme or another beca becau use or a rece recent nt sale saless setb setbac ack k or succ succes ess. s. Seco Secon ndly, dly, he is ofte often n unaw unawar aree of larg larger er econ econom omic ic developments and of company marketing plans that will shape future sales in his territory. Thirdly, he may understate demand so that the company will set a low sales quota. Finally he may not have the time or concern concern to prepare prepare careful careful estimates estimates.. Because Because of these these defects, defects, salesman salesman’s ’s estimate estimatess are aggreg aggregate ated, d, reviewe reviewed d and adjusted adjusted at highe higherr managem management ent levels. levels. In making making the necessa necessary ry adjustme adjustments nts the higher higher management takes into consideration such factors as expected salutary changes in product design, a plan for increased advertising, a proposed increase or decrease in selling prices, new production methods which will improve the product’s quality, changes in competition and changes in such economic forces as purchasing power, income distribution, credits, population and employment. This method is often termed as “jury of executive opinion method”. An evalu evaluat ation ion The The opin opinion ion surv survey ey meth method od is relat relative ively ly simple simple and stra straigh ightt forew forewarn arned ed.. One One of its advantages is that it make use of the people in the organization who are directly involved in the activities which will influence the level of sales, who are in a position to become acquainted with the forces and factors which will affect sales, and who probably have the opportunity to acquire the experience and judgments which will enable them to evaluate the effects of these factors and factors. Another advantage of this method is that, unlike some of the other techniques discussed in this chapter, it requires no special technical skill. Finally, this method leads itself to use in the forecasting of sales of new products. However, this method is subjected to a number of criticism the most important among them then is that it is almost almost comp complet letely ely subje subject ctive ive.. This This is of no conse conseque quenc ncee if the the firm firm is fortun fortunate ate enoug enough h to have have personnel in its sales and managerial ranks who have the inherent ability to make this type of subjective analysis analysis.. But unfortun unfortunately ately many many organiz organizatio ations ns are not endowed endowed with personn personnel el of such quality quality and caliber. The appropriateness of the sales force opinion method increases to the extent that (1) the salesman are likely to be the most knowledgeable source of information, (2) the salesman are co-operative (3) the salesman are unbiased or their biases can be corrected and (4) there are some side benefits from the salesman’s participation in the procedure. b) Expert Opinion
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Taking the opinion of well-informed persons other than buyers or company salesmen, such as distributor or outside experts is an other method of forecasting. In the United States of America the automobile companies slicit estimates of sales directly from their dealers. But according to Philip Kotler these estimates are subject to the same strengths and weakness as salesman estimates, like salesman, distributors may not give the necessary attention to careful estimating, like salesmen, distributors may not give the necessary attention to careful estimating, their perspective concering future business conditions may be too narrow, and they may supply biased estimates to gain some immediate advantage. Firms in advanced countries also tap outside experts for assessments of future demand. In effect, this happiness when a firm uses or buys general economic forecasts of special industry forecasts prepared outside of the firm. In the United States of America, for examples, various public and private agencies issues or sell periodic forecasts or short or long term business conditions. While the experts are supplying what amounts to opinion, the “opinion” may be the joint outcome of specially conducted surveys among buyers and suppliers as well as statistical mathematical analysis of past data. A related but a slightly variant of the expert opinion method is used by Lockhead Aircraft Corporation. As a manufac manufactur turer er of aircraft aircraft frames frames and missiles, missiles, the company company deals deals with a relativ relatively ely small number number of custome customers, rs, each each of which which account accountss for a relativ relatively ely large large percent percentage age of sales. sales. Therefo Therefore re Lockhe Lockhead’s ad’s forecasting problems is to predict what each particular customer will order during the forecast period. The marketi marketing ng research research group group works works up a prelimin preliminary ary foreca forecast st on the basis basis of survey surveyss and statistica statisticall or mathematical technique. Independently, a group of Lockheed executives assume the roles of different major customers and in a hardheaded way they evaluate Lockheeds’ offering in relation to his competitors offerings. A decision on what and where to by is made for each customer. The purchases from Lockhead are totaled and reconciled reconciled with statistical statistical forecast to become Lockheeds’ Lockheeds’ sales forecase. forecase.
The use of expert opinion has a number of advantages and disadvantages. Its main advantages are (1) forecasts can be made relatively quickly and cheaply (2) Different points of view are brought out and balanced in the process and (3) There may be no alternative if basic data are locking or difficult to collect, as in the the case case of new new prod produ ucts. cts. The The impo import rtan antt disa disadv dvan anta tage gess are are (1) (1) opin opinion ionss are are gen general erally ly less less satisfactory than hard facts, 2) responsibility is dispersed, and good and had estimates are given equal weight, and (3) the method usually is more reliable for aggregate forecasting than for developing reliable breakdown breakdown by territory, territory, customer customer group or product.
Delphi Technique is an extension of systematic analysis into the areas of opinion and value judgements. It countries the limitations of traditional quantitative methods. In areas where information is dispersed and scanty, scanty, judgements judgements and expert opinions are valuable, valuable, historical data can lend itself to many interpretations. interpretations. Delphi offers a scientific and systematic procedure for evaluation. In a way, it is sophisticated statistical method to arrive at a consensus. One of the drawbacks of any quantitative procedure is its inability to incorpo incorporate rate behavio behaviour ural al elements elements like persona personality lity,, institut institution ion and retrospe retrospection ction.. Delphi Delphi has has a built built in capacity capacity to take account of these variables. variables. Delphi technique was initially developed by Olaf Helmer and T.J. Gordon of Rand corporation, U.S.A. since then it has found its application in technological and environmental forecasting, selection of industrial targets in war, estimation of strength of bombardment and in futurology. In the business management area its relevan relevance ce is in manpow manpower er plannin planning, g, Bayesi Bayesian an probabi probability lity estimatio estimation, n, busines businesss foreca forecastin sting g and demand estimation. Other applications are in civil defence policy, computer applications, applications, education, education, urban
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planning planning and other policy, determinants, determinants, evaluations evaluations of research prospects, foreign a ffairs ffairs and information proc proces essin sing. g. In fact, fact, Delph Delphii is the the most most appli applied ed of the the techn technolo ologi gica call forec forecast astin ing g metho methods ds and and it has has acquired acquired a good standing standing among forecasters forecasters a long range planners.
The major features features of Delphi techniques techniques are the following: 1) A panel is select selected ed to give suggestio suggestion n to solve solve the problems problems in hand Both internal internal and outside outside experts can be the members of this panel. 2) Panel members members are kept physically physically apart from each other other and express their their views in an anonymous manner. 3) There There is a programme programme coordin coordinator ator who acts as in intermedia intermediary ry among the panelists. panelists. His role is essentially of a coordinating nature. He prepares questionnaire and sends it to the panelists. He also also prep prepar ares es summ summar aryy at the the end end of each each roun round d of anon anonym ymou ouss disc discu ussion ssionss and and prov provid ides es composite composite feedback feedback to the panel members. 4) The The views views of the the membe members rs of the the panel panel are are obtain obtained ed in a numb number er of round rounds. s. In the the first first round, round, panel panel member memberss are asked asked to express express their their views views on the forecastin forecasting g problem. problem. These These views views are analysed by the programme coordinator. The panel members are given a second questionnaire together with the summary report of the first round of discussion. On the basis of the summary report, the panel members are supposed to give more anonymous suggestions. They are asked whether they could revise their opinions in the light of the summary report of the first round. The esti estima mate tess rece receiv ived ed in the the seco second nd roun round d are are also also summ summar ariz ized ed,, and, and, if requ requir ired ed,, a furt furthe herr questionnaire together with the second summary report is sent to the panel members. The process is repeated several times till the panel members stop changing changing their opinion.
Time series analysis or trend projections rely on past data. In this approach, a company analysis its past sales to determine the nature of existing trend. This trend is then extrapolated into the future, and the resultant indicated sales are used as the basis for forecast. The mechanics if this technique can be best illustrated by means of an example. Suppose Suppose that a manufa manufactu cturer rer of radios radios decides decides to forecast forecast the next year year sales sales of his product product by this method. He begins by collecting data on his sales for the past five year When he does this be obtains the following results. Year
Sales
1989
45
1990
58
1991
45
1992
55
1993
60
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If the sales are plotted against the years in which they take place, a graph representing th time series is obtained. The graph for our data is shown in the figured. An examination of this graph reveals that the sales are definitely following an upward trend. The next step is to develop an equation which which can give the nature nature and magnitude of this trend. trend. This is done by fitting a so called trend line to the points depicting the firm’s sales. A number of ways for doing this exist, but a fairly common one is to construct the line of best fit by the method of least squares. Doing so means that the trend is assumed to be linear. Whereas it may actually be curvilinear. If the later is true, more complex methods of constructing the trend line must be used. However, we shalllimit ourselves in this presentation to linear trends for purposes of simplicity. In simpl simplee linea linearr regr regress ession ion,, the the relat relation ionsh ship ip betwe between en he depen dependen dentt varia variable ble (y) (y) and and some some independent independent variable variable (x) can be represented represented by a straight straight line. The equation of this line line is where “a” is the intercept and “b” shows the impact of the independent variable. The key step in deriving linear regression equat equation ionss is findin finding g value valuess for the the coef coeffic ficien ients ts (a, b) that that give give the the best best fit fit to the the data. data. One One way to determine these coefficients is to plot the data on a graph and make free hand estimate of the line that represents represents the t he relationship relationship between the two variables. variables. Since in our case sales are to be forecast, they are considered to be the dependent variable, Y also, since sales will be assumed to vary with time, the time period (years) will be the independent variable, X. The The Y inter interce cept pt and and the the slope slope of the the line line are are found found by makin making g the the appro appropri priat atee substi substitu tutio tions ns in the following “normal” equations. Calculating the magnitudes of the required from our original data, we get the following: 1
2
3
4
5
Year
(sales 000 units)
X
X
XY
1989
45
1
1
45
1990
52
2
4
104
1991
48
3
9
144
1992
55
4
16
220
1993
60
5
25
300
When we substitute the value of – EX,-EX,-EXY,-EY and n in equations I and II, we get 260 = 5a + 15b
......
III
813 = 15a + 55b
......
IV
Solving equations III & IV, we get b = 3.3 substituting value of b in equation III above we get, 260 = 5a + 15 (3.3) 260 = 5a + 49.5 260 – 49.5 = 5a 210.5 ------------------ = a = 42.1 5
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Therefore the equation of the line of best fit in equal to Y = 42.1 + 3.3 X Using this equation we can find the trend values for the previous years and estimate the sales for 1977. The trend values and estimates are given below: Y 1989 = 42.1 + 3.3 (1) = 45.4 Y 1990 = 42.1 + 3.3 (2) = 48.7 Y 1991 = 42.1 + 3.3 (3) = 52.0 Y 1992 = 42.1 + 3.3 (4) = 55.3 Y 1993 = 42.1 + 3.3 (5) = 58.6 Y 1994 = 42.1 + 3.3 (6) = 61.9 The trend line represented by this equation is shown in the following figure. An examination of this line reveals that most of the points representing actual sales do not fall on it. For this reason, one would be hesitant to forecast sales by projecting the line and reading off the value of sales for some future year. Instead, consideration would be given to the fact that, in the past, actual sales varied from the sales as calculated from the equation of the line. Since these variations existed in the past, there is reason to believe that they will exist in the future, and therefore, it would be only natural to modify the value of future sales obtained from the trend line to reflect the expected variation. Ti is said that the real test of this this method method relates relates to predicti prediction on of turnin turning g points. points. Time series are charac character terized ized by fluctu fluctuatio ations ns and turning points. Fluctuations and turning points occur because of four factors. They are (1) a secular trend (T) (2) seasonal seasonal variations (S) (3) Cuclical Cuclical fluctuation in economic economic conditions (C) and (4) Irregular, Irregular, random or residual forces (I) so the real problem in forecasting is to separate and measure each of these four factors. Unfortunately no reliable quantitative methods for handling cyclinical and residual variations exist. Classical time-series analysis involves procedures for decomposing the original sales series (Y) into the components T.S.C and 1 (trend, season, cycle and irregular or random events) respectively. According to one model, these components interact additively that is Y=T+S+C+I according to another model, they intract multiplicatively that is Y=TSCI. The multiplicative model makes the more realistic assumption that the seasonal and cyclical effects are proportional to the trend level of sales. T is stated in absolute values, and S,C and I are stated as percentages. The decomposition of time series data is a useful analytical tool for understanding the nature of business fluctuations. But it is of limited value in actual business forecasting. This is because of the fact that the prediction of cycles in difficult as there is no regularity in the cyclical behaviour.
Another method used to follow trends in demand data is the moving average. The forecaster simply computes computes the average volume achieved achieved in several recent periods periods and uses it asa prediction prediction of demand in the next period. This approach assumes that the future will be an average of past acthievements. Although moving average can provide good forecasts when demand is stable, they are apt to lag behind when there is a strong trend in the data. A decisive issues in moving averages is determining the ideal number of periods, to include the average. With a large number of periods, forecasts tend to react slowly whereas low values lead to predictions that respond core quickly to changes in a series. For a better understanding of the assumptions underlying underlying he techniques techniques od moving moving avera a verages ges and some of its advantages advantages and limitations limitations it is necessary to look briefly at the mathematical representation of this method. In simple terms the techniques techniques of forecasting forecasting with moving moving averages averages can e represented as follows:follows:-
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Where S_ = the forecast for time t, X_ = the actual value at time t, N_ = the number of values included in the average In can be seen from the above equation that the method of moving averages, equal weight as given to each of the last N values observed before that time. In can also be seen from the equation that to compute the moving average we must have the values of the last N observations. a somewhat shorter from of the above equation (1.1) for calculating calculating the moving average average can be developed. developed. Now it can be seen from equation (1.1) That S+I is simply
Written in this form it is obvious that each new forecast forecast based on moving average average is an adjustment of the preceding moving average forecast. All the forecast needs to do is to apply moving averages to obtain historical data and them use either (1.1) or (1.2) to compute the forecast for the coming period. But it is necessary that he must also specify the number of periods to be used in the moving averages.
A feature of the moving averages that detracts from their ability to follow trends is that all time periods are weighted equally. This means that information from the oldest and newest periods is treated the same way in making up the forecast. But a strong argument can be made that since the most recent observations contain contain the most informa information tion about about what what will will happen happen in the future future they should should be given relative relatively ly more more weight than the older observations. what we should like is a weighting scheme that would apply the most weight weight to the most recent observed observed values values and decreas decreasing ing weights weights to the older older values. values. Exponen Exponential tial smoothin smoothing g satisfie satisfiess this this requirem requirements ents and eliminat eliminates es the need need for storing the histor historica icall values values of he variables. In principle exponential smoothing operates in manner skin to moving averages by “smoothing” historical observa observation tionss to eliminat eliminates es randomn randomness. ess. The techn technical ical of exponen exponentia tiall smoothin smoothing g can be develop developed ed by using equation (1.2) for computing the moving average. Suppose we had the most recent observed value and the forecast made for that same period. In such a situation equation (1.2) might he modified so that in place of the observed value in period (t-n) we could employ an approximate value. A reasonable estimate would be the forecast value from the proceeding period. Thus equation (1.2) could be modified to give equation (1.3)
This equation can be written as What we not have is a forecast the weights the most recent observation with the weitht of value I/N and the most recent forecast with the value of (1-1)/N. if we substitute x in place of I/N we have
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This equation is the general form used in computing a forecast by the method exponential smoothing The The main main decis decision ion with with expon exponent entia iall forec forecast astin ing g is select selecting ing an appro appropr priat iatee valu valuee by the the smooth smoothin ing g constant smoothing factors can range in value from zero to one with low values providing stability and high value allowing a more rapid response to demand change.
Perhaps the most common forecasting situation encountered in business is that of a time series in which a number of observation are taken over several periods of time and a forecast of some future time period is desired. As we have already seen all forecasting methods designed to handle such situations assume that there is a basic underlying pattern represented by the historical data and that in addition to that pattern some randomness has been exhibited. Thus the focus of the forecasting method is to isolate that basic patte pattern rn as far far as possi possible ble and to sue it as the the basic basic for futu future re forec forecast asts. s. Althou Although gh a meth method od such such a exponential smoothing may be suitable for short term forecasting of time series in which there is not much fluctuation and the pattern is made up of combination of trend, a seasonal factor, and a cyclical factor as well as the random fluctuation. In such situation a much more complex forecasting method is needed. The Box-Jenkins method of forecasting is one that is particularly well suited to handling complex time series and other forecasting situations in which the basic pattern is readily apperent. The real power and attractiveness of this forecasting approach is that is can handle complex pattern with relatively little effort on the part of the forecaster. However, because it is dealing with much more complicated situation, it is much much more more diffic difficul ultt to unde underst rstan and d the the fundam fundament ental alss of this this techn techniqu iquee and the the limit limitati ation onss of its applic applicati ation ons. s. In addit addition ion,, the the cost cost associ associate ated d with with the the Box-J Box-Jen enkin kinss appro approach ach in a given given situ situati ation on in generally much greater than any of the other quantitative methods, but with this greater cost, much greater accuracy be can achieved.
We have have noted noted that simple trend trend project projections ions are incapab incapable le of foreca forecastin sting g turning turning points. points. Baromet Barometric ric techniques are based on the ideas that certain events of the present can be used to predict the direction of change in future. This is accomplished with the help of relevant economic and statistical indicators which are selected time series related to the variable to be predicted. Here the key issue is finding indicators that have forecasting value for particular products. Some of the most commonly used indicators are listed below: 1. Construction Construction contracts contracts awarded awarded 2. Person Personal al income income 3. New order orderss for dura durable ble goods goods 4. Employme Employment nt 5. Agricul Agricultur tural al income income 6. Non-agricultu Non-agricultural ral placements placements 7. Gross Gross Nation National al income income
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8. Industrial Industrial Materials Materials prices 9. Wholesale Wholesale commodity prices 10. Industrial Industrial production production 11. Change Change in manufactur manufacturing ing and trade inventories inventories 12. Bank Bank deposits deposits etc. etc.
Econometric model building holds considerable promise as a method of forecasting demand. The best starting point towards an understanding of the basis of econometric forecasting is regression analysis. But the difficulty with regression analysis is that it is used to forecast a single dependent variable based on the value and the relations between one or more independent variables. each of these independent variables is assumed to be exogenous or outside the influence of the dependent variable. This may be true in many situations. But unfortunately, in most broad economic situations an assumption that each of the variable, is independent is unreaslistic. For example, let us assume that demand is a function of GMP, price and advertising. In tegression terms we would assume that all three independent variables are exogenous to the system and hence are not influenced by the level of demand itself or by one another. This is farily correct assumption so far as GNP is concerned. If, however, we consider price and advertising, the same assumption may not hold good, for instance, of the per unit cost is of some quadratic form, a different level level of cost. cost. Again, Again, Adverti Advertisin sing g expend expenditu itures res will will often often influen influence ce the price of the product, product, since since the production and selling cost influence the per-unit price. The price, in turn, is influenced by the magnitude of demand, which can also influenced by the magnitude of demand, which can also influence the level of advertising or promotional expenditure. All of these point to the independence of all four of the valuables in our equation. When this independence is strong, regression analysis cannot be used. If we want to be accurate, we must express this demand relationship by developing a system of four simultaneous equation that that to be accu accura rate te,, we must must expr expres esss this this dema demand nd rela relati tion onsh ship ip by deve develo lopi pin ng a syst system em of fou four independence idredtly. Thus is econometric form we can have Demand
= f (GNP, price advertising)
Cost
= f (production and inventory levels)
Sellin lling g expen xpense sess
= f (adver dverttisin ising, g, oth other sell sellin ing g expe expen nses) ses)
Price
= f (Cost and selling expenses)
That is, instead of one relationship, we now have four. As in regression analysis, we must (a) determine the functi function onal al form form of each each of the the equat equation ionss (b) (b) estima estimate te in a simul simultan taneou eouss manne mannerr the the valu valuee of their their parameters and (c) test for the statistical significance of the results and validity of the assumption. It should be realized that the advantages of econometric forecasting is that is provides the values of several of the independ independent ent variab variables les from within the model model itself, itself, thus thus freein freeing g he foreca forecaster ster from having having to estimate them exogenously. The estimation of the equation parameters involves problems for more complex than those encountered in regression regression analysis. This makes the application application of econometric forecasting forecasting difficult difficult and expensive. expensive.
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A number of mathematical techniques have been developed to help solve, econometric models. Some with manages manages may be familia familiarr are the method method of least least square squares, s, the full informat information ion maximum maximum likelihood likelihood method of estimation, two-stage least square methods and three stage least square methods. The details of these techniques are well beyond the scope of our discussion. An econometric model includes a number of simultaneous equation that can be of different types and functional forms. The translation of econometric theory to the right type of form of equation and their develop development ment into a set of funct functiona ionall relation relationshi ship p is termed termed as specifi specificat cation ion.. The accurate accurate and most appropriate specification of an econometric model is a key step in use of this technique of forecasting. A major part of specification is the identification of the exogenous and endogenous variables. one must arbitra arbitrarily rily decide on the degree degree of influence influence of the different different factors factors and choose those that that are least determined within the system as exogenous factors. This is kind to the distinction made in regression analysis between the independent variables and the dependent variables. in an econometric model we will want to separate those factors that are most strongly influenced by one another into the endogenous group and those than can be assumed to be determined outside the system of simultaneous equations into the exogenous exogenous group. Once the choice of endogeneous and exogenous variables has been made, on equation must be specified for each of the endogenous variables. When the number of the equations specified is equal to the number of exogenous variables, the model is said to be just specified. When the number of equations, the model is under specified and one or more of the variables has to be set arbitrarily to some initial value. these variables then become exogenous variables is greater than the number of equations, the model that is most often used for estimating the parameters of a set of simultaneously equations. Econometric models are used most widely to forecast macro series of inter related economic data such as income, income, consumption consumption and capital capital spending and much less for business forecasts. forecasts. The great advantage of an econometric model is indirect. It can be used to predict the direction and extent of change of the overall economic activity or any its components. This information can then become the input required to estimate the independent variables of a single equation forecasting model. Since this information can be obtained from outside sources, organizations do not have to develop their own models but but can can rely rely on outsi outside ders rs to provi provide de them them with with fore forecas casts ts when when they they are are requ requir ired. ed. Thus Thus indi individ vidua uall companies can forego all the high costs associated with developing maintaining, and running a large scale econometric econometric model and obtain he information it offers through third parties. An additional experience is gained in the use of econometric models for forecasting, their application will undauntedly become more widespread at both government and industry levels. These econometric model of the future should be substantially more accurate than they have been in the past and should provide the managers with additional information he can use in applying other forecasting techniques that are less costly and more suitable for his purpose. In addition to these mostly commonly used methods, there are certain other methods of forecasting which are used by certain companies in advanced countries. For the benefit of our readers we propose to discuss these methods very briefly in the following paragraphs. paragraphs.
Under this method an attempt is made to vary separately certain important determinants of demand such as price, advertising etc., which can be manipulated and conduct the experiments assuming that the other factors factors will remain-constant. remain-constant. Thus, the effect of price, advertisements, advertisements, packaging packaging etc., on demand can be assessed by either varying them over different markets or by varying them over different time periods in the same market. For instance, different prices would be associated with different sales and on that basis the price-quantity price-quantity relationship relationship is estimated in the form of regression equation equation and used for forecasting forecasting
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purposes. It must be noted that the market division here must be noted homogeneous with reference to income, tasks etc. In the U.S. the parker pen company used this method to find out the effect of a price raised on the demand for Quick Ink. But this method is yet to establish itself as a variable one. This is due to a number of reasons. They are (1) Such Such expe experim riment entss are are expen expensiv sivee and and time time consu consumin ming. g. (2) They They are are risky risky becau because se they they may may lead lead to unfavorable reactions on dealers, consumers and competitors 3) there is great difficulty in planning the study so far as it is not always easy to determine what all factors should taken to be constant and what factors should be considered as variables so as to segregate and measures their influence on demand. 4) it is difficult to satisfy the condition of homogeneity of markets. Industry sales potentials can also be derived from input – output tables for states and nations that show how businesses buy and sell goods from one another. Potentials can be extracted from input – output data by dividing sales to particular industries by the total sales made to all sectors of the economy. The derivation of relative market potentials from input-output tables allows a firm to compare its own sales to particular market segments with the levels achieved by all firms in the industry. Although these comparisons look backward in time, they can reveal important market sectors that have been ignored by current marketing programmes. Input-Output tables provide a useful way to construct relative sales potentials for areas based on current levels of sales achieved by different industries. Input-output tables can also help in estimating the impact of some change within the market (an input-output table for a simplified economy is attached). Purch Purchase ased d by Sales by Ordinary
Prima Primary ry Manufacturing Servicer Industry Industry Industry 50
Final Buyers Consumer Investment Government
Total output
250
10
60
0
30
400
Manufacturing 100
500
40
500
200
160
1500
Service
200
100
10 100
0
30
500
Primary Inputs 18 18 0
550
350
Gross domestic product = 1800
Total inputs
1500
500
20 400
2400
Demand potentials for individuals products can be determined by applying a series of ratios or usage rates to an aggregate measure of demand. A firm might start with a total population figure for an area and then multiply by average annual per capital expenditures to give an estimate of maximum possib possible le sales sales for a gener general al produ product ctss clas classs (Rad (Radios ios). ). This This numb number er coul could d then then the redu reduced ced by multiplying by a percentage that reflected sales of a particular type of radio (two Transistors) and still further by a percentage customers that bought a particular type (two bands). The resulting estimate of total sales for two band radios could could then be divided among the firms in the industry.
Comput Computer erss are frequ frequen ently tly used used to demand demand fore forecas castin ting g becau because se they they are are fast fast and and they they can make make predictions from masses of figures using complex procedures. This allows the firm to make more frequent forecasts for much wider range of products. The computer can also be programmed to make adjustments
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in raw date, compare predictions generated generated by alternative methods and keep track of forecasting forecasting errors. It may be pointed out here that no single method in foolproof. All are characterized by certain pita fails into which the unwary analyst is prone to fail. Therefore, the forecaster should beware of putting all his eggs in one basket. It is better not to rely entirely upon a single method. The wiser course and the one best for most forecasting situations, is to solve the problem from a number of different angles. If all individually constructed forecasts seem to point in the same direction, more confidence can be placed in the forecast that is finally transmitted to top management.
Demand forecasts for new products call for more ingenuity and skill. Forecasting methods need to be tailored tailored to the particular particular product. Joel Dean has suggested six possible possible approaches for forecasting forecasting demand for new products. They are :
Under this approach, the demand for the new product is projected as an outgrowth and evaluation of an existing old product. For instance, the demand forecast for colour television sets starts with the assumption that colour television picks up from where black and while left off. But this approach is useful only when the new product is so close to being merely an improvement of an existing product that its demand can be pretty a projection of the potential development of the underlying product. Under this technique, the new product is analysed as a substitute for some existing product or service. service. This approach has great promise when applicable. applicable.
Here the rate of growth and ultimate level level of demand for the new product is estimated, estimated, on the basis of the patterns patterns of growth growth of establis established hed produc products. ts. For instance instance,, analyz analyzee the growth curves curves of all established motor cars and try to establish an empirical law of market development applicable to a new brand of car. This method, even if it can be developed, has narrow applicability, and is useful primarily at the latter stages of demand projection.
Under Under this approach, approach, demand for new new products products is estimated estimated by makin making g direct direct enquirie enquiriess form the ultimate purchasers, either by the use of samples or on a full scale. The method is widely used to explore the demand for new products. But this method encounters problems of sampling, probing real intentions, and conveying the complexity of multiple alternative choice, even for established products. For new products these problems become more complicated. The forecaster has to clarify what a new produce is and what it will do. New product is offered in a sample market either by direct mail or through a chain store and thus attempts attempts to estimat estimatee the total demand demand for all chann channels els and fully fully develop developed ed market. market. The main problem here lies in determining what allowance is to make for the immaturity of the sample
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market and its peculiar peculiar characteristic characteristics. s.
Under this technique consumer reactions to a new product are surveyed indirectly with the help of speci special alize ized d deal dealers ers who are are suppo suppose sedly dly infor informe med d about about consum consumer erss needs needs and and altern alternati ative ve opportunities. This method is temptingly easy and distressingly hard to quantify. Generally, it is usable only only as cheap horsebac horseback k sally. The various methods adopted for forecasting demand for new products are not mutually exclusive. A combinations of several of them is often desirable when the can supplement and check each other.
Generally a producer will not purchase new durable producers good unless he can reasonally expect that the return attributable to the new good over its life span will be sufficient to cover all the costs (including a reasonable profit) attributable to the purchase must be expected to be a profitable one. According to Joel Dean the most important factors determining the profitability of such purchasers are:a) The current current demand and the future future demand expected expected by the producer5 producer5 for his output of goods and and services. b) His present present stock (number (number of units, units, age and efficien efficiency cy of the units units and expected expected life span of the stock) durable goods. c) The expecte expected d life life span and efficien efficiency cy of the new durable durable good i.e. the expected expected life “capacity “capacity”” of the new durable good. d) The “cost of using” using” the good i.e. the labour labour materi material, al, manageri managerial al costs etc., involv involved ed in the use of the good. e) The expected expected sale sale price per per unit of the the output of the the good. f) The current current and anticipate anticipated d cost of (including (including the cost of of using) substitutes, substitutes, such such as labour, labour, for the new durable goods. The ideal forecasting method, according to Joel dean, is one that yields returns over cost in accuracy, seems reasonable (consistent with existing knowledge) can be formalized for reasonably long periods, can meet new circumstances adeptly, and can give up-to data results.
In recen recentt times times fore forecas castin ting g has has come come to play play an import importan antt role role in busin busines esss decis decision ion-ma -makin king. g. Determin Determinatio ation n of the types types of foreca forecasts sts required required and establi establishme shment nt of procedu procedures res governin governing g generat generation ion of these these forecas forecasts ts are fundame fundamenta ntall steps in the organi organisato satoin in of a well-con well-concern cerned ed prod produc ucti tion on cont contro roll syst system em.. From From the the poin pointt of view view of time time span span and and from from the the plan plann ning ing requirements, firms will be interested in estimating both short term demand, the firm may use one or may combination of the following forecasting methods. Opinion surveys expert opinion, chain ratio method, trend projections, barometric techniques, econometric models, input-output model, computer-assisted computer-assisted forecasting forecasting etc., these method very in their appropriatene appropriateness ss with the purpose of
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the forecast, the type of product and the availability and reliability of data. Probably every firm can be improv improvee the the accur accurac acyy of its forec forecast astss by colle collect ctin ing g more more data data and/o and/orr adopt adopting ing a better better methodology. Demand forecasting for new products calls for more ingenuity and skill. Forecasting methods need to be tailored tailored to the t he particular product. The ideal forecasting method, according to Joel Deam is one that yields returns over cost in accuracy, seems reasonable (consistent (consistent with existing e xisting knowledge) knowledge) can be formalized for reasonably reasonably long. Periods, Periods, can meet new circumstances circumstances adeptly, and can give up-to-date results.
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Managerial decision making is facilitated by information that shows the cost of each rate of output. But short-run and long run cost functions are considered in this section. Consider a production process that combines variable. Amounts of labour with a fixed capital stock, say, then ten machines. In this process, the rate of production is changed by varying the rate of labour input. Assume that the firm can vary the labour input freely at a cost of Rs. 100/- per unit of labour per period. Ther Therefo efore re,, the the expen expendit ditur uree for labou labourr is the the vari variab able le cost. cost. If the the ten mach machin ines es are are rented rented unde underr a long-term lease at Rs. 100/-, per machine per production period, the fixed cost would be Rs. 100/- per period. The table be low summarize the relevant production and cost data for this production process. The total cost data from the table are shown graphically in the following figure. Note that fixed cost is indicated by a horizontal line. That is, it is constant with respect to output. Total variable cost (TVC) begins at the origin, increases at a decreasing rate upto an output rate between (3) and (4) and then increases at an increasing rate. Total cost (TC) ahs the same shape as total variable cost but is shifted upward by Rs. 1,0000/- . The amount of fixed cost. Average or per unit cost functions often are more useful for decision making than are total cost functions. This is because managers must compare cost per unit of output to the market price of that output. Recall that that mark market et pric prices es is meas measur ured ed per per unit unit of outpu output. t. By divi dividi din ng a tota totall cost cost func functi tion on by outp output ut,, a corresponding corresponding per unit cost function is determined determined that t hat is, Average total cost
: AC = TC/Q
Aver Averag agee varia ariabl blee cost cost
.. ...(1)
: AVC = TCV TCV/Q .... ....(2 (2))
Input Rate Capital
Rate of output
Labour
Total fixed cost
Total variable cost
Total cost
10
0
0
1,000
0
1,000
10
2.00
1
1,000
200
1,200
10
3.67
2
1,000
367
1,367
10
5.10
3
1,000
510
1,510
10
6.77
4
1,000
677
1,677
10
8.77
5
1,000
877
1,877
10
1 1 .2 7
6
1,000
1727
2,727
10
1 4 .6 0
7
1,000
1460
2,460
10
2 4 .6 0
8
1,000
2460
3,460
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FIGURE COST FUNCTION AVERAGE FIXED COST : AFC = TEC/Q...(3) The Marginal cost per unit of output (MC) is the change in total cost associated with a 1-unit charge in output that is Marginal cost : MC = STC/SQ ....(4)
Output
Average fixed cost (AFC)
Average variable cost (AVC)
Average total cost (ATC)
Marginal cost (MC)
0
-
-
-
-
1
1,000
200
1,200
200
2
500
185
684
167
3
333
170
503
143
4
250
169
419
167
5
200
175
375
200
6
167
188
355
250
7
143
209
351
333
8
125
307
432
1,200
As it is true of all associated total and marginal functions, marginal cost is the slope of the total cost functio functions ns,, using using calculus calculus,, margin marginal al cost is determin determined ed as the as the first first derivative derivative of the total total cost function. That is, if the total cost function is, TC = T(Q) Marginal would be MC = d(TC)/dQ Based on the total cast function in table – 1, data for each per unit cost function are reported in table 2 and shown graphically in figure 1b. there average cost, average variable cost, and marginal cost functions are important in managerial decision making. In contract the average fixed cost function ahs little value for decision making. Further the difference average total cost and average variable cost is average fixed cost.
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Thus the Ac and AVC curves contained the information on fixed cost per unit in the unlikely event that such information is needed. needed. The per unit cost functions fore many production systems have the U shape shown in the figure 1.b. If two low rates are production, there is too little of the variable input variable to the fixed output. At the variable, input is increased, output is increased, output raised rapidly, and therefore the cost per unit falls, Initially total cost increases but at a decreasing rate. This implies that marginal cost (the slope of the total cost) is falling. Because of the low of diminishing marginal returns, additional units of the variable output result in smaller additions to output and thus marginal cost rises. When marginal cost exceeds cost, the average cost functions begin to rise. At it is true of all marginal and average functions as long as marginal cost is below the average cost curve, the average average functio functions ns will decline. decline. When margina marginall is above above average average,, the average average curve curve will will rise. rise. This implies that marginal cost intersects both the total cost and variables cost functions at the minimum point of the average curves (points a & b in figure 1.b) FINDING MINIMUM AVERAGE VARIAB V ARIABLE LE COST:COST:Given the total cost function TC = 1,000 1,000 + 10Q 10Q - 0.9Q 0.9Q 2 + 0.04Q 3 find the rate of output that results in minimum average variable cost. Solution: Marginal cost is the first derivatives of the total cost function d(TC) d(TC) = MC = 10 – 1.8Q 1.8Q + 0.12 0.12 Q² --------d Q now, find the total variable cost function (TVC) by substracting the fixed cost component (Rs. 1000) from the total cost function that is, TVC = 10Q = 0.9Q² + 0.04Q 3 Then find average variable cost (AVC) by dividing TVC by output (Q). That is AVC = TVC = 10Q – 0.9Q 2 + 0.04Q 3 ------------- ---------------------------------------------------------Q Q AVC = 10-0.9Q + 0.04Q² 10-0.9Q 10-0.9Q + 0.04Q² 0.04Q² = 10 = 108Q + 0.12Q² 0.12Q² Rearrangind terms yields the quadratic equation. -0.08Q² + 0.9Q = 0 Or Q(-0.08Q Q(-0.08Q + 0.9) = 0 Which has the roots Q1 = 0 and Q2 = 11.25
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Disregarding the root associated with a zero output rate, it is seen that the minimum AVC is achieved at an output rate of 11.25 units. Alternatively, the minimum point of AVC could be found by getting the first derivative of AVC equal to zero and solving for Q that is, D(AVC)= D(AVC)= 0.9 + 0.8Q 0.8Q = 0 -----------dQ 0.08 Q = 0.9 Q
= 11.25
Average cost functions and production theory:There is a correspondence between the production functions developed and the per unit cost of functions. Recall that average product is defined as output divided by the variable input. If labour is the variable output, output, the average product function is AP1 = Q/L Or 1
L
---------AP1
-----------
Q
Because, labour is the only variable input, average variable cost is the expenditure, on labour (WL) divided by output. Or AVC = WL/Q But between L/Q = 1/AP L It follows that AVC = W 1/APL
.... (5)
Thus Thus ther theree is an inver inverse se relat relation ion betwe between en avera average ge produ product ct and and aver averag agee cost. cost. If avera average ge produ product ct is increasing, increasing, average variable cost will be decreasing decreasing and vice-versa. vice-versa. The marginal product of labour is defined as the change in output divided by the change in labour, that is MPL = Q/L or 1/MPL = L/Q And marginal cost is the additional expenditure on labour (W L) divided thus. MC = TC/Q TC/Q = W.L/Q W.L/Q But becau because se L/Q = 1/MP 1 it follows follows that that MC = 1/MPL
.......... (6)
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This is, marginal cost is the price of the input times, the reciprocal of marginal product. As before, if marginal product is increasing. Marginal cost will be decreasing and vice-versa. The law of diminishing marginal returns implies that as input increases due to the addition of name of a variable input to a fixed input a point will be reached where marginal product will decrease. As that point
Figure 2 Relation between product functions and per unit functions functions The total marginal cost of function will begin to increase. These relationships between the product and per unit cost function are depicited in figure – 2 is efficiency in the production process are captured initially by using more variable input in combination with the fixed input, input, margin marginal al cost falls. falls. When these efficien efficiencies cies are exhaust exhausted, ed, margin marginal al cost increa increases. ses. Thus Thus the concept of U shaped average and the marginal cost curves is slopes the principles of marginal production. Key concepts: Per unit or average cost functions tend to be more useful than total cost functions in making, sound decisions. The average cost functions are found by divided the relevant total cost of function by output, that is, Average cost
:
AC = TC/Q
Aver Averag agee varia ariabl blee cost cost :
AVC = TVC/ TVC/Q Q
Average fixed cost
:
AFC = TFC/Q
Marginal cost per unit is the change in the total cost function associated with a 1 unit change in output, that is, MC = TC/Q There is an important relation between the product and the per unit function. When average or marginal cost per unit will be decreasing and vice-versa. The law of diminishing marginal returns implies that as more of a variable input is combined with a fixe fixed d amoun amountt of anoth another er input input,, a point point will will be reach reached ed where where marg margin inal al produ product ct will will decre decreas ases es and therefore therefore marginal marginal cost will increase. increase. Long run cost functions:Firms operate in the short run but plan in the long run. At any point in time, the firms has one more fixed factors of production. Therefore, production decisions must be made based on short run cost curves. However, most firms can plant to change the scale of their direction by varying all inputs in the long run and by doing so, more to a preferred short run cost functions. Returns to scale are increasing, decreasing or constant depending on whether a proportional change in both inputs results in output increasing more than in proportion less than in proportion or in proportion to the increase in input. These possibilities are shown in the left had panels of figure 3.
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(a) Increasing Increasing Returns Returns to scale
(b) Decreasing returns to scale
There is a direct correspondence between returns to scale in production and the long run cost function for the firm. It returns to scale re increasing, inputs are increasing less than in proportion to increases in output. Because input prices are constant, it follows that total cost of also must be increasing less than in proportion to output. This relationship is shown in figure 3(a). if decreasing returns to seak apply, the total cost function increases at increasing rate. Constraint returns to seak implies that total cost will change in proportion to changes in output. The later two relationship are sho0wn in the parts (b) and (c) figures 3. The production process of many forms is characterized first by increasing returns and then by decreasing returns. In this case, the long – run total cost function first would increases to a decreasing rate of and then increase at an increasing rate as shown in the figure 4. Such a total cost of function would be associated with a U shaped long run average cost function. Suppose that a firm can expand the scale of operation only in discrete units. For example, the generators for large electric power plants are made in only a few sizes. Often, these power plans are built in multiples of 759 megawatts (MV). That is, output capacity of alternative plants would be 750 MV 2250 MV and soon. The short-run average cost functions in figure 5 (Labeled (sac., through SAC) are associated with each of four discrete scales of operations. The long run average cost function for this firms is defined by the minimum average cost of each level of output. For example, output rate Q1 could be produce by plant size 1 at an average cost of C1 or by plant size 2 at a cost of c2, clearly, the cost is lower for plant size 1, and thus point a is our point on the long run average cost curve. By repeating this process for various rates of output, the long run average cost is determined. For output rates of zero to Q2, plant 1 is the most efficient and that part of SAC 1 is part of the long run cost function. For output rate Q2 to Q3 for output is the most efficient, and for output rates Q3 to Q4, plant 3 is the most efficient, and for output rates Q3 to Q4, plant 3 is the most efficient, and for output rates Q3 to A4, plant 3 is the most efficient. The scallop shaped curve shown in bold face in figure 5, is the long run average cost curve for this firms. This bold faced curve is called an envelops curve. In general, a firm will have a great many alternatives, plant fixed to choose front, and there is short run average cost curve curve corresponding corresponding to each. A few of the short run average cost curves for these plants are shown in figure 6. Only one point or a very small of each short run cost curve will lie on the long run average cost functions. functions. Thus long run average cost can be shown as the smooth U shaped curve labeled LAC. Corresponding to this long run average cost functions is a long run marginal cost cure LMC which intersects LAC is at its, minimum point and which is also the minimum point of short run average cost curve 10. The short run marginal cost curve (SMC 10) corresponding to SAC 10. But SMC 10 = SAC 10. Thus at point a and only at a poin pointt a the the foll follow owin ing g uniq unique ue redu reduce ce occu occurs rs.. SAC SAC = SMC SMC = LAC LAC = LMC .... ...... ..(7 (7)) The long run cost curve serves as a long planning mechanical for the firm. For example, suppose that the firm is operating an short run average cost curve SAC, in figure 6, and the firm is currently producing an output rate of Q*, by using, SAC7 it is seen that the firms cost per unit is C2. Clearly, if projections
112
future demand indicate that the firms could expects to continue, selling Q* units per period. At the market price profit would be increased significantly by increasing the scale of plant to the size associated with short run average curve SAC 10, with this plant cost per unit for an output rate of Q* would be C1 and the firms profit per would increase by C1-C2. Thus total profit would increase by (C1-C2). Q*. This firms long run average cost function will be: Decreasing Decreasing where returns to seak in production production are increasing increasing Constant Constant where returns to scale are constant Increasing Increasing where returns to scale are decreasing decreasing The long run average cost function is the envelope curve consisting of point arcs on a number of short run average cost curves. curves.
The Cobb – Douglas production function owes it origin to Douglas observations of certain characteristics in a vast amount of data be analyzed. In particulars he had observed that: That is
(W/Y) = a
...(1)
(Wh)/Y = a or w = a(Y/L)
...(2)
where where W – Wage Wage hill hill Y – Value of national output a – a constant w – money wage rate L – total labour employed In other words, Douglas Douglas observed that the wage bill was a constant proportions proportions of the value of the national output. Note that this observation implies that the real wage per head is a constant proportion of the output per head, Now according o the marginal productivity theory, in competitive, equilibrium the money wage rate ‘w’ is equal to the value of the Marginal product of labour that is, w = (SY/ (SY/SL SL)) using (2), we have (SY/SL) = a (Y/L)
...(3)
This means that the marginal product of labour is a constant proportion of the average output product of labour. labour. Lobb. Suggested such a result would follow from a production function. function. Q = AK BL
....(4)
Where Q = Total physical product
113
L = Total labor input K = Total physical capital input = Elasticity of output with the respect of labour B = Elasticity of output with respect of capital A = A constant is the efficiency parameter. Differentiating – (4) with respect of labour we obtain, (SQ/SL) = (Q/L) But in competitive competitive equilibrium, equilibrium, (SQ/SL) = w* Where w* is the wage rate in real terms, Therefore, W*L)/L or W* = (Q/L)
...(5)
Allowing for a given commodity price, the experience in (2) & (5) are similar. Thus, lobb’s formulation confirms, to Dougla’s observation of the wage bill being constant proportions of the National income. We now turn to the characteristics of the function first, its slope, since on a single isoquent the level of output is constant Q = Q. Taking the total derivaties of the production function and putting d-Q=O, we obtain after rearranging rearranging the term. (DK/DL)O = (K/L)
...(6)
The ratio dK/dL defined the marginal rate of technical substitution between the inputs k and l. in view of the implicit assumption that both inputs are necessary to produce any positive output K and L, and are both positive positive.. Moreove Moreover, r, L and B are assumed to be positive positive,, that is O/..... O/......& .& / _____1 _____1;; similar similarly ly for B, hence the slope of a Cobb-Douglas constant product curve is negative We can also show that an isoquant isoquant obtained obtained from such a function function is convex convex to the origin origin.. Connex Connexity ity implies that the marginal product of an input decreases as the quantity of the input increases. Now; (SQ/SL)= AKBL-1
.... (7)
Note that the O/____& / ______ 1, (-1) is negative. Hence, as L increases, SQ/SL, the marginal product of labour increases, K increases similarly, it can be shown that the marginal product of capital decreases as K incr increa eases ses and and incr increa ease se as L incr increas eases es henc hencee the the isoqu isoquant ant is conne connex x to the the origi origin. n. The The elast elastic icity ity of substitution, substitution, is obtained as follows. We know that the marginal marginal rate of technical substitution substitution of labour for capital. (DK/DL) Let Let R
= - ( K / L)
...(8)
= 1-(K/ 1-(K/L) L)
114
And K = K/L Therefore, R = -(L/B) k Now,
= (dk/kj)/dR/R) = (dk/DR) (R/K) = -(B/L) (-1K) (BL) ----------------------------------------------- =1 (K/L)
The elasticity of substitution in a Lood Douglas function is equal to unity note that this value of does not depend on the specificaoitn of L + B = 1. Any general form of the Cobb-Douglas function will have an elasticity elasticity of substitution equal to one. We now examine examine the nature nature of the returns returns to seak. If we specify specify L + B = 1, the Cobb – Douglas Douglas function function become becomess linera linera homog homogenou enouss in capit capital al and and labour labour input. input. In particu particular lar,, after after substitu substitutin tin –(4) –(4) (1-L) for , the exponent of the capital input, we obtain, Q = Ak -1 L
...(10)
Note that the sum of the exponents of capital and labour is unity. If we now substitute mk for k and ML for L, observe that output is increased m – fold. Hence with the constraint of L + B = 1, the Cobb Douglas function has the written in per capital terms. METHODS OF ESTIMATION – There are several ways of estimating a Cobb-Douglas production function. The first, is to estimate the function in its logarithmic form. Assume that he function to be estimated in for the I and h firm. The function may be written as Log Qi = a + B logn Ki + L Log Li + Ui
....(11)
Where a = Log A and Ui is the Stochastic disturbance term. If we have a data on output, capital and labour inputs, then the parameters a, B can be estimated. In the above form of the equation, no assumption is made of the nature of the returns to scale. If, however, we assume constant return to scale, so that L + B = 1, It can be written as Log (Qi / Li) = a’ (1- ) Log Log (Ki / Li) + Ui
...(1 .(12)
In this tem, output per head is a function of capital per head. With data on these, the parameters, as a and can be estimated. Note that is the elasticity of output with respect to labour and (1- ) is the elasticity of output with respect of capital. capital. A secon second d metho method d of estima estimati ting ng the the produ producti ction on funct function ion is to assum assumee perf perfec ectt compet competit ition ion and and the waxination, of profit. Then the real returns to capital and to labour are given by their respect marginal products. It ‘w’ is the money wage ‘r’ is the price of the services of capital, and ‘p’ the price of the product,
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we have, W/p = SQi / SLi and r/p = SQiSKi
...(13)
These conditions may, as before be written as, = WLi / Yi + B = rKi / Yi
...(14)
Where Yi is the value of the output of the firm 1. The parameters and may be obtained from data on relative chares of wages and profits in the total value of the output of the firm. A variant of the above method, of estimation, may be obtained by adding to the above, this assumption of the constant returns of scale, we know that the share of labour is = (WLi/Y) and the share of capital B=1. If, therefore, we have data on the share of labour estimated of can be obtained. Alternatively the equation for the share of labours may be written as, Log Log ( Qi/Li Qi/Li)) = log log (w/p) (w/p) - Log x ..... ......(1 .(15) 5) That is a log linear relation between output per head and real wage with data on these can be estimated. EMPIRICAL FINDINGS:The Cobb-Douglas production function is the most widely used function at the applied level. It has been used in both, time series, as well as cross section studies of industrial sectors of most economics. It has also been sued in its specific level, in which the exponents of capital and labour add to unity, capital and labour ad to unity and in its more general form, where the exponent of capital is not ... to the exponent of labour. There has been a fair amount of unifernity in the empirical findings. Broadly, these are as follows. First, the fit has in general, been good. This means that, if in an given situation, due to the quantities of capital and labour inputs are known, the output can be predicted with fair accuracy. Secondly when as in the earlier studies, it has been assumed that the sm of and is equal to one, the exponent of labour has in general general been been estimated estimated at 0.78, 0.78, so that , the exponent exponent of capital capital is 0.25. 0.25. Even in studies studies in which which the constant returns to scale assumption has nto been invoked, the sum of the estimated exponents of laour and capital has continued to a approximately unity, thus suggesting either constant returns to scale or only only marg margin inal al deviat deviation ion from from them them.. There There has has also also been been consi conside derab rable le measu measure re of conf conform ormity ity in the numerical values of the exponents of capitals and a labour obtained for a particular sector over several years, and also for difference sectors. The numerical values of he exponents of labour & capital have corresponded fairly closely with the respective shares of labour and capital in the national income of various countries. This appears to indicate that the factors of production, capital and labour, receive the share they expect to under under competitive competitive conditions.
The The fun functio ction n is gen general erally ly esti estima mate ted d at he aggr aggreg egat atee leve level, l, for for exam exampl ple, e, for for the the non non-for -form m or the the manufacturin manufacturing g sector of the economy. They assumption that labour labour and capital capital inputs are homogeneous has limitations. The Batergeneous output is measured by the value – added method, that is the difference between the gross name of output and the new material cost and the resultant series in defeated by prices of output, in order to obtain an index of physical production. Capital is generally measured in value terms, as the sm of net investment investmentss overtime overtime.. This This method method implicit implicit assumes assumes that depreciatio depreciation n is correc correctin ting g estimated. However, it fails to take note of changes in the quality of capital assets. Moreover, it igneous the difficulties in estimating the correct degree of utilization of capital stock. Further input is measured in
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physical units. In terms of the number of persons, employed or if TA/DA are available, in man hours or maymay-day days. s. Wher Wheree labou labourr is measu measured red as a stock stock,, two prec precaut aution ions, s, appea appears rs to be nece necessa ssary. ry. First, First, adjustment for changes in the degree of utilization of labour which in view of the better data available, may be easier for labour than for capital and second correction for changes in the working week. An additional precaution is to allow for changes in the quality of labour over time. Secondly, Secondly, there t here is the t he problem concerning concerning aggregation, in i n particular, the question whether an aggregate aggregate Cobb-Dou Cobb-Dougla glass product production ion functio function n preserv preserves es the charac characteri teristic sticss of the neocla neoclassic ssical al micro micro product production, ion, function. The condition so far such valid aggregation appear to be rather stringent. For example it has been shown that for consistent aggregation, the production function should be’ additively separately’ this means that output is them equal to a labour component plus a capital components. The fixed proportion production function satisfies this conditions.
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The determinations of prices and output levels is very much affected by the competitive structure of the market. Here, “competitive structure” is a phrase which refers to the nature and extent of the monopolistic elements, if any, that are present in any particular market situation. There exists a large body of literature which discusses discusses various various types of competitive competitive conditions running the range from perfect competition to pre monopoly, and which seeks to analyze their effects on prices and output. It is convenient to start oru discussion by listing some of the important market situations which have been investigated.
MARKET STRUCTURES
Perfect
Monopolistic Competition
Imperfect
Oligopoly
Duopoly
Monopoly
An industry is said to be operatin operating g under under perfect perfect competition competition when the followin following g condit conditions ions are satisfied.
There must be a large number of firms in the industry. Each firm controls only a very insignificant share of total output so that any action (addition to or removal from the market) on its own part will have little or no effect on the price and output of the whole industry. The same holds god in the case of consumers.
Each firm in the industry must be making a product which is accepted by buyers as being identical, or homogeneous, with that made by all the other producers in the industry. This ensures that no producer can put his price up above the general level.
Any individual or company with the funds and inclination must be able no enter the industry without artificial hindrances being erected against him, and any owner of affirm in the industry, who wants to leave the field in free to do so. iv) Independent Independent Decision Making: Making: Firms take independent independent decisions. decisions. There should not be any collusion or agreement between firms in decision making. making.
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v) Perf Perfect ect Knowl Knowled edge ge about about the the Mark Market: et: Ther Theree is perfe perfect ct knowl knowled edge ge on the the part part of all all produ produce cers rs consumers, consumers, and resource owners regarding regarding the conditions conditions prevailing prevailing in the market. vi) Perfect Perfect mobility of Factors: There is perfect mobility of factors of production among among different firms in the industry and among different industries in response of pecuniary signals and transport costs are ignored. ignored. Now let us examine some immediate consequences of the definition of perfect competition. Under perfect competition the demand curve of the firm is always a horizontal straight line. The follows from the first two features of he definition of perfect competition, viz large number of producers and homogeneous product. product. For example, no single wheat farmer farmer can do anything about the day’s price in Madhya Madhya Pradesh Pradesh or Uttar Uttar Pradesh Pradesh.. If he raises raises his his wheat wheat price price abov abovee the the goin going g pric pricee he can sell sell any any amoun amountt he can be expected to produce. For him, then, there is no price decision to be made-the price figure is simply handed to him. In the short run the firm may make either profit or less. But in the long run the free entry and exit feature of perfect composition sees that these profits or losses will disappear altogether. If the Industry earns prof profits its,, new new firms firms will will be prompt prompted ed to enter enter it and and compet competee with with the the alre already ady estab establi lishe shed d firms firms.. The resulting increase in demand for inputs may enhance their prices and hence raise costs – on the other hand, the increased product supply may result in a reduction in its market price. The result of third double pronged action will be that profit will be squeezed down towards zero or atleast until no additional firms find it worth moving in. Similarly, if there is initially a net loss to firms in the industry, the exist of concern’s especially those who are not earning any profit, will raise profits and ultimately it will eliminate loss. The above reasoning holds good only if there are no autonomous changes in demands or casts during the period the adjustment. For example, a crop failure or the invention of more efficient equipment may suddenly restore high profits to wheat farming and so offset the influence of new entrants. Since, to some extent, such changes are always taking place, the adjustment toward zero profits will always be imperfect. However, the forces working in that direction will never the less be there. In the the follo followin wing g para paragra graph phss we propo propose se to examin examinee in some some what what grea greater ter detail detail the natu nature re of this this competitive equilibrium towards which the market tends to adjust. Such a situation is shown in figure 12.1 (1) and 12 (b). In these diagrams the horizontal line DD is the firm’s demand curve. The curve is a horizontal straight line because, as already pointed out, no change in the firm output is a sufficiently significant significant contributions contributions to total market supply to affect the price. As there is no price discrimination, the firms demand curve will also be its average revenue curve. The rationable is that if all units of a commodity are sold at the same price, the revenue brought in by an average unit must be its price. Hence DD is also the average revenue curve. It is known fact that where an average curve is neither rising nor falling it will coincide with the corresponding marginal curve. Here, since the average revenue curve is horizontal throughout its length, it must everywhere coincide with the marginal revenue curve.
Figure12.1(a) represents the situation of a competitive profix maximising firm in short run equilibrium. Its profit-maximisin profit-maximising g output id OM where its marginal cost curve MC interse i ntersects cts the marginal revenue(demand) revenue(demand) curve curve DD. At this point it is earning earning a profit profit RP on each unit unit it produce produce (=unit (=unit revenu revenuee minus minus unit cost ) Thus its total profit (=unit profits multiplied by the number of units produced0 id represented by area ERPD. ERPD. Note Note that that outpu outputt ON wher wheree also also its marg margin inal al cost cost curve curve .MC inter intersec sects ts the the marg margin inal al reven revenue ue (demand) curve DD is not the profit –maximising output. A careful examination of the figur12.1(a) will
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make this point very clear. At output ON marginal cost has only just become equal to marginal cost is less than marginal revenue and has previously been greater. Beyond output ON marginal cost is less than marginal marginal revenue and the shows that it is profitable profitable to produce more. The favourable situation situation continues upto OM where marginal cost and marginal revenue are equal .So if output in fixed at ON, the firm would b rearing rearing only minimum and not maximum profit. So here we may state that at the profit –maximizing –maximizing point the marginal marginal cost curve must out the marginal marginal revenue curve from below. below. A firm can never earn maximum maximum profits unless this happens. Figure12.1(b)represent a long run equilibrium situation . here the average cost curve must be a tangent to the demand cureve.DD the reason is that if the units costs were everywhere higher than price, every output would be unprofitable, and firms would leave the industry, thus shift the curve as well. Similarly, if the average cost curve were to interest the demand curve. There would be some output at which profits could be earned and an influx of new firm would soon shift the cost and revenue curves sufficiently to wipe out these profits. Only when there is tangency will the “no-profit “,”no-less” position of long-ru long-run n equilibr equilibrium ium be the best the firm can do, and and no firm will will tempted tempted to enter enter or leave leave the field if this is the typical situation of all firms in the area. Since the demand curve is horizontal, the profit of tangency. Q of the average cost curve with the demand curve must occur at an output at which the unit costs are at a minimum. For that reason the marginal cost curve will also intersect the average cost curve at that point .In short, at the point of equilibrium we have the impressive set of eqalifies, marginal cost equals marginal revenue equals average cost equals equals a average average revenue revenue equals equals price. price. (MC (MC = MR = AC = AR AR = P) P) It is to be noted that two essentia essentiall conditions conditions are to be fulfill fulfilled ed if there there is to equilibr equilibrium ium in a perfect perfectly ly competitive industry. First ,each and every individual firm must be in equilibrium. This will happen when each and and every individual firm must be in equilibrium. equilibrium. This will happen when each each firm in the industry is earning maximum profits by equating marginal revenue with marginal cost. Second , the industry as a whole must be in equilibrium. This will occur when there is not tendency for firms either to enter or leave the industry, which will only happen all the produce in the industry are earning enough money to induce them to stay in the industry, and when no producer outside the industry thinks that he could earn enough money, where he to enter it, to make the move worthwhile. The equilibrium position of an industry under perfect competition can be depicted with the help of an industry industry supply curve and i ndustry demand curve. The The supp supply ly curv curvee can can give give an inte interp rpre reta tati tion on in term termss of cost costs. s. In fact fact,, in the the lon long run run it ten tends to approx approxima imate te a curve curve of avera average ge costs costs for the the indu industry stry.. This, This, as we know, know, is a cons consequ equen ence ce of the free-entry-an free-entry-and d exist assumption assumption and its zero profit profit result if the industry industry were to supply supply its commodity at a price which exceeds its average cost, some firms would be making a profit. But we know tat the entry of new firm will wipe out that profit. We must analyze the stability of this industry equilibrium in order to see whether this equilibrium point can be expected to be of direct relevance to any real market situation .i.e. whether there is any mechanism which pulls competitive priced and output into line with their equilibrium levels. It is neither deasible nor appropriate here to go into a full dynamic analysis of this stability question. But we propose to examine the mechanism which can work in the direction of stability. Fig.12.2(a) shows the usual supply and demand diagram for the competitive industry. Figure no.193
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The equilibrium occurs at the point of intersection of industry supply curve SS and industry demand curve DD at E and PE and Me constitute the equilibrium price-quantity combination of the industry. Imagine now that, for one reason or another, the market price falls below the equilibrium price, say to Pr. In this case the quantity demanded will exceed the quantity supplied by quantity DR-SR and we may expect price to be pushed back toward the equilibrium price. Similarly, a price PW, which is above the equilibrium at least give an appearance of stability which dynamic analysis can rationalize. But it need not and often does not follow that the supply demands equilibrium position will always be stable. On the other hand, it is easy to find a case where the system worked in the wrong direction fig.12.2(b) fig.12.2(b) depicts such s uch a system. Here ,when the price falls to PQ, below the equilibrium price supply will exceed demand (by quantity SR.DR) Hence price will by driven down even further. In the same way, we can see instability on the upward side. Of course such cases are rare in practice ,nevertheless the illustration atleast that we must be cautious in assuming that our models are always well behaved. Figure no.194
There id one other type of change in demand and supply conditions which id important enough to merit special study. We know that the longer the period of them which we take into consideration, the greater the difference in the supply conditions. For instance, if demand suddenly increase, price is likely to rise sharply in the short run because firms will be expanding output along fairly steep run marginal cost curves. But in the long-run, firms will be reorganized so as to produce the new and higher output more efficiently. For firms will now be producing along their rather flatter long-run marginal cost curves. Moreover, new firms will have been able tot enter the industry. The initial change in equilibrium prices is caused by the changed conditions of demand, but the succeeding changes in price over time depend on the response of conditions of supply to the new demand situation. And the magnitude of such changes in supply will usually differ according to the length of time being considered. Figures 12.3(1), (b) and (c) depict the impact of changes in supply and demand positions upon price under three different situations.
Figure 12.3(a) represents the market period. The fundamental features of this period is that supply is absolutely limited. Under such a situation demand exerts a dominating influence on the price. A rise in demand will push the market price from OP to OPO and a fall in demand will push down price from OP to OP. Figure 12.3(b) depicts the position in the short period. Under this situation. Supplies can be altered by increase or decreases in current output. But the time is not enough to bring about changes in fixed equipments and there by adjust production. so when demand increases from DD to DD price is pushed up from OP to OP. but as the supply is also adjusted to some extent, the rise in price is not so sharp as in Figure 12.3(a). Figu Figure re 12.3( 12.3(c) c) repre represen sents ts the the long long perio period d situ situati ation. on. In the the long long perio period d ther theree is time time for for firm’ firm’ss fixe fixed d equipment to be altered to that output is capable of adapting itself more fully to changes in demand conditions that it was in the short period. In figures 12.3(c) SS is the original supply curve and DD the original demand curve. They intersect at point E and the resultant market price is given by OP. Now demand increases from DD to DD.
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Consequently the price is pushed up to OP. but now supply is enhanced and this is indicated by the new supply curve SS. The new supply curve S S intersects the new demand curve DD at point G. the resultant price is OP which is a bit higher than the original equilibrium price OP but much lower than OP the price resulting from the original shift in demand. Under prefect competition, the market of each seller is perfectly merged with those of his rivals. But under monopolistic competition the market of each seller is in some measure isolated, so that the whole market is not a single large market of many sellers, but a network or related markets, one for each seller. This is because of the special feature of monopolistic competition viz. product differentiation. Differentiation of product means that no two firms put out the same item. Products are differentiated either by trade marks or wrappers or through some other device. Under perfect competition, the individual seller’s market being completely merged with the general one, be can sell as much as he pleases at the going price. Under monopolistic competition, however, his market being separate separate to a degree from those of his rivals, rivals, his sales are limited and defined defined by three new factors 1) his price, 2) the nature of his product, and 3) his advertising outlays. The divergence of the demand curve for his product from the horizontal straight line imposes upon the seller seller a price price problem problem which is absent absent under perfect perfect competiti competition. on. The problem problem is very similar similar to that associated with the monopolist. Depending upon the elasticity of the curve and upon its position relative to the cost curve for the product, profits may be increased, either by raising the price and selling less, or by lowering it and selling more. That figure will be sought which will ensure maximum profit. The The adju adjust stme ment nt of his his prod produ uct simi simila larl rlyy is a new prob proble lem m impo impose sed d upon the the sell seller er by the the fact fact of differentiation. The volume of his sales depends in part upon the manner is which his product differ from that of his competitors and in part upon the skill with which the good is distinguished form others and make to appeal to a particular group of buyers. Again, the seller may influence the volume of his sales by incurring advertisement expenditures. Such expenditures increase both in demands for his product, and his costs, and their prices will be adjusted as are prices and “products” so as to render the profits of the enterpr enterprise ise a maximum maximum.. The advertis advertisemen ementt expendi expenditur turee is peculia peculiarr to monopo monopolist listic ic competit competition ion in the sense that it has no purpose to serve under perfect competition where any producer can sell as much as he wants without it. Gains from advertisement advertisement un monopolistic are possible on two accounts. accounts. i)
Imperfect knowledg knowledgee on the part part of buyers buyers as to the the means whereby whereby wants wants may be most effective effectively ly sansfied, and
ii) The possibility possibility of altering altering wants wants by advertising advertising or selling appeal. appeal. Under monopolistic competition the demand curve for the product of the firm may be expected to have negative slope, even though the firm is as small as one operating under conditions of perfect competition. This is because customers will have different degrees of loyalty to the firms from whom they make their purchases. A small reduction in one firms (price may only attract is competitors most mercurial customers. But as larger and larger price reduction are instituted, it may acquire more and more customers from its rivals by drawing on customers who are less anxious switch. The equilibrium of the firm involves the usual conditions marginal cost is equal to marginal revenue. In the short-run the firms may or may not earn a profit. Under monopolistic competition oven can even expect something like freedom of entry. Since firms are small, relatively very small amount of capital is required to set up business and turn out a product not quite the same as but still very like those already in the market. The consequence is that, as under perfect competition, both profits and losses will tend to be eliminated in the the long long run. run. The The two two situa situatio tions ns expla explain ined ed above above i.e. i.e. equili equilibr brium ium with with profi profitt and and no profit profit are
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represented represented in figure 12.4(a) and 12.4(b). In figure 12.4(a) the firm is in equilibrium when it produces OM units. At this level of output the firm is equating marginal cost and marginal revenue and each unit is sold at a price OP and there by earns a profit to the area of the shaded rectangle PTQR. Figure 12.4(b) depicts a situation where the firm is not earning any profit. The equilibrium output here is attained by the tangency between the average cost curve and the negatively sloping demand curve DD. It can be seen from this figure that at any other output, unit cost will be larger than price and so such as output will involve loss to the firm.
The The aver averag agee cost cost curv curvee is gener general ally ly taken taken to have ave the the “U” “U” shap shapee indi indica cate ted d in the the diag diagra ram m on the the assum assumpti ption on that that both both very very small small and and very very large large outpu outputt are are diffi difficu cult lt and and expen expensiv sivee to produ produce ce.. Even Even economics of large scale apply only up to appoint, beyond which administrative costs and diminishing returns, because of the presence of source (bottleneck) inputs, are generally expected to raise the unit costs of production. production. If this a valid, the point of tangency R between the U-shaped average cost curve and the negatively sloping demand curve must be found somewhere to the left of the minimum average cost point Q. This is in direct contract with the equilibrium of the competitive firms whose long run position is Q (of Figure 12.1(b) above). Therefore, the output of the firm under monopolistic competition must be smaller, and its unit cost and price higher higher than it would be under under perfect competition.
The The analy analysis sis of group group equil equilibr ibrium ium with with price price compet competiti ition on is acco accompl mplish ished ed in two two phas phases. es. The The first, first, depicted in Figure 12.5(a) certain to the situation in which the “proper” or “optional” number of firms is already in the product group. In figure 12.5(a) DD and dd (solid) give two demand curves dd shows the increased sales any entrepreneur can expect to enjoy by lowering price provided all other entrepreneurs maintain their original prices. DD on the other hand, shows the actual sales to be gained as a general downward movement of price take plac place. e. LAC is the the long-r long-run un aver average age cost cost curve curve for for the the typic typical al firm firm in quest question ion.. We assum assumee an initia initiall (short-run) equilibrium attained at point. a with output OM and price OP. Short run profit is represented by the area of the shaded rectangle P ABC Each entrepreneur, regarding dd as his demand curve, realizes he can increase profit by reducing price and expanding output (according to the elastic dd) Therefore each redu reduces ces price price.. But But inste instead ad of expan expandin ding g along along dd each each in fact fact move movess alon along g DD. DD. In chamb chamber er line’s line’s terminology, terminology, dd slides downward along DD.
Despite the frustration of their initial plans, producers hold firm in their belief that dd represents their demand curve. So they continue to reduce price in an attempt to augment profit and dd continues to slide downward along DD. The downward movement will continue until it comes to point Q. where it is shown as the broken curve. Of course dd might fall below the broken curve’s position in that case all entrepreneurs would incur loss and so price would be raised shifting dd upward. The position of long run equilibrium is Q where dd is tangent to LAC. Each firm while having a monopoly of its own product, is pushed to zero
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profit position by the competition of rivals producing producing readily r eadily substitutable substitutable products. In summary we can state that long run group equilibrium under price competition is attained when the antic anticipa ipate te deman demand d curve curve (dd) (dd) is tangen tangentt to the the long-r long-run un unit unit cost cost curv curve. e. If dd lies lies above above LAC each producer believes he can increase profit by reducing price if dd is below LAC price must be increased to eliminate the loss incurred. Now let us see what happens if the anticipated demand curve dd does not have precisely the right slope so as to be tangent to LAC at the point where DD cut LAC. For getting an answer to this question we have to se how long run equilibrium adjustments take place when there is entry of new firms. This situation is explained with the help of Fig. 12.5(b).
Consider that in Fig. 12.5(b) DD represents the initial demand curve and LAC the long run unit cost curve. The firm in question and any other in the product group reaps a very substantial pure profit. Since entry into the product group is open, new firms selling slightly differentiated products are attached. The greater variety of available products causes the demand for each seller’s product to shrink. In the process DD shifts to the left and probably becomes somewhat more elastic. Side-by-side if entrepreneur’s experiment with price policy, dd slides down the instantaneously existence DD and also probably becomes somewhat more elastic. The change from the initial DD curve to the ultimate long-run equilibrium at point E cold come about in several ways. One method is illustrated in fig 12.5(b) which it is assumed new firms enter the product group group unti untill the propo proportio rtiona nall deman demand d curve curve shif shifts ts from from DD to DD. DD. It might might seem seem that that equil equilib ibriu rium m is attained at F. With output OM and price OP per unit, in as much as pre profit is zero at that point. however, each each entre entrepr prene eneur ur thin thinks ks dd is his his deman demand d curve curve.. A reduc reductio tion n is price price would would in his belief belief caus causee an expansion expansion along dd profit would accordingly accordingly be expanded. expanded. But each entrepreneous entrepreneous has the same incent i ncentive. ive. So as price is reduced by all, dd slides down DD for each. Suppose now that price has fallen to OP with output OM Each firm incurs a pure loss represented by the area of the rectangle CBAP. It might seem that each firm could eliminate its pure loss by reducing price to OP and moving moving to point E. Yet with the number number of firms firms giving rise to DD and reduction reduction in price price to OP would shift the subjective demand curve further down DD to the position dd Temporary equilibrium would be attained at G with sales of OM rather than OM per firm. The situation is necessary transitory, however, as each firm incurs a pure loss at G ultimately some firms must leave the product group and there is an incentive to do so. As firms leave the group the proportional demand curve shifts to the right, together with the anticipated demand curve and both probably become somewhat less elastic. The exist of firm must must cont contin inue ue unti untill the the propo proporti rtion onal al curv curvee becom becomes es DD and and the the antic anticipa ipated ted curve curve dd. Long Long – run equilibrium equilibrium is attained attained at a t E with identical identical long-run conditions explained explained above. above. Oligopoly exists where a few sellers sell either similar products or slight differentiated products. When the product productss are slightly slightly differen differentiat tiated, ed, oligopo oligopoly. ly. The oligopo oligopoly ly situatio situation n (inclu (includin ding g the limiting limiting case case of duopoly) has one feature on which most of the economist’s attention had been centered. This is the interdependence in the decision making of the various firms, an interdependence of which is recognized by all of them. In an industry which consists largely of a small number of sizeable companies, each seller must be actually conscious of the actions of his rivals and of their reactions to changes in his policies. This is because a major policy change on the part of one firm is likely to have obvious and immediate effects on the other other firms firms which which comprise comprise the industry. industry. In other other words words there there exists exists suffic sufficien ientt cross-e cross-elast lasticity icity of
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demand so that each seller must take in his pricing decisions, the rival’s reactions into account. As a result, the oligopolist has developed an armoury of aggressive and defensive marketing weapons. For example, it is only under oligopoly that advertising comes fully into its own. Oligopolistic Oligopolistic interdependence interdependence has another consequence. That is under under oligopolistic oligopolistic inte i nterdependen rdependence ce a very wide variety of behaviour patterns becomes possible. Rivals may decide to together and operate on the pursuit of their objective, at least so far as the law permits or, at the other extreme, they may try to fight each other and perish. Even if they enter into agreement it may follow a wide variety of patterns. Because of this, the literature of oligopoly theory if full of different models, many of which described, at most, one particular arrangement a price leadership agreement or some particular method of using fright charges charges as a means for sharin s haring g (dividing) market territories. Here we are more concerned with the explanation of rigidity of oligopoly prices or what is known as the kinked demand curve.
Now we propose to examine why, once a price-quantity combination ahs been decided upon, it will not readily change. The answer can be given with the help of kinked demand curve illustrated in figure 12.6 Consider the impace on quantity demanded of a reduction in the price of a commodity. this is illustrated by the demand curve for the product. Suppose, first that the reduction in the price which is charged by one firm is matched by other competing firms. In that case the firm may expect to increase its sales slightly, but since it is not possible to get any customers away from its rivals in these circumstances, no large addition to its sales is to be expected. Its demand curve (DD in Figure 12.6) will be relatively inelastic. Imagine, on the other demand, the turn in question is the only one to reduce its price. If so, a much larger increase in its demand is to be anticipated. Thus, where no other firm follows its price moves, the firm in question is likely to have a relatively elastic demand curve such as dd. In figure 12.6 let point G represent the firm’s current price combination. It has often been suggested that the large large oligopo oligopolist listic ic firm is likely likely to anticip anticipate ate the follow following ing competit competitive ive reactio reaction n pattern pattern to a price price change. 1) Price reductions reductions:: If the firm in question reduced its price, price, its competitors will feel the the drain on their customer quickly and so they will be forced to match this price reduction. On other words, for downward price movements from G the relevant portion of the firm’s demand curve will be GD of the demand curve DD (see fig. 12/6) 2) Price Price hike: If the firm increas increases es its price, price, it may expect expect that its competit competitors ors will welcome welcome the new customers which they gain from the price-raising firm as a result, and they will have no inclination to match the price hike. Hence, for price hikes the relevant part of the demand curve will be elastic segment dG.
In short, given this view of competitive reaction patterns the firm’s demand curve will be the composite curve dGd. Characterized by the kink (a bent) at the point G which represents the current price – output combination. Now it is easy to visualize that a firm with such a competitive response pattern will be extremely reluctant to vary its price. For a fall in its price will not bring about any substantial increase in its sales. While a price hike hike will will resu results lts in a subst substan anti tial al cut cut in busin busines ess, s, and and neith neither er of thes thesee is a very very attra attracti ctive ve
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proposition. It may be noted here that the kink in the demand curve causes a finite discontinuity (break) in the marginal revenue curve, which is given by the dashed line dRQV dR is the segment corresponding the dG portion of the demand curve QV corresponds to the less elastic Gd segment. At point G there is a finite discontinuity represented by the segment RQ. The chief feature is the absolutely vertical section RQ. If the marginal cost curve happens to pass through anywh anywhere ere throu through gh gap gap RQ in the the marg margin inal al revenu revenuee curve curve,, the the profit profit maximi maximizi zing ng firm firm will will have have no motivation to leave the current price OP Event if there is a sharp rise in costs, as long as the marginal cost curve does not rise above R it will lead to no price change. Geor George ge J Stigl Stigler er ahs ahs quest question ioned ed this this propo proposit sition ion on empir empirica icall groun grounds. ds. It seems seems eviden evidentt that that in an inglationary situation oligopoly firms do often follow one another’s price rises. However, as pointed out by Baumol Baumol the (oligopoly) (oligopoly) analysis analysis does show how the oligopo oligopolist listic ic firm’s firm’s view view of competit competitive ive reaction reaction patterns can affect the chargeability of whatever price it happens to be charging. Duopoly is a limiting case of oligopoly. Under duopoly there are only two sellers. A certain move, say a price reduction, any be advantageous to one seller in view of his rival’s present policy i.e., assuming it not to change. But if rival is sure to make a counter move, there is no reason to assume that he will not, and for the first seller to recognize the fact that his rivals policy is not a datum, but is determined in party by his his own, own, cann cannot ot be cons constru trued ed as a nega negatio tion n of inde indepen penden dence ce.. It is simply simply to cons conside iderr the the indi indirec rectt consequences of his own-acts-the effect on himself of his own policy, mediated by that of his competitor. Of course, he may or may not take them into account, but he is equally independent in either case. If a seller determines upon his policy under the assumption that his rivals are unaffected by what he does. We may, say that he takes into account only the direct influence which he has upon the price. Since the problem od duopoly has usually been conceived of in this fashion. We shall analyze first the results under such an assumption. Following this, it will be argued that the only solution fully consistent with the central hypothesis that each seller seeks his maximum profit is one in which he does take into account the effect of his policy upon his arrivals ( and hence upon himself again). In this latter case, we may say that he considers his total he considers his total influence upon the price, indirect as well as direct. One more distinction is made before we analyze the problem, i.e. his rival’s policy may remain fixed with respect either to the amount he offers or to the price at which he offers it. The solution will be different in the two cases. First we give the solution offered by curnot? Here mutual dependence is ignored. Each seller assumed his rival’s rival’s supply constant. Curnot assumed that each seller determines the supply which is most profitable for himself in the light of his rival’s present offering which do not change. He gives the example of two mineral springs, exploited by two owners without expenses of production, and contribution to the same market. For simplicity it is assumed that the demand curve for the mineral water is a straight line. DQ This is illustrated in figure 12.7.
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In figure 12.7 OA = AQ the daily output of each spring. The price is zero when the total possible output (OQ) is put upon the market. Suppose there is initially only one seller in the market. To maximize his profit he sells OA nits of mineral revenue with the zero cost. Price is OP(=AC) per unit and profit is OACP. Now suppo suppose se that that the the other other sell seller er ente enters rs the the mark market. et. Here Here come come curn curnot’ ot’ss cruci crucial al assum assumpt ption ion.. To get get an analytical solution of a duopoly one must make a behavioral assumption concerning each entrepreneur’s expecta expectation tion of his rival’s rival’s policies. policies. Curnot Curnot’s ’s assumpt assumption ion is that (as already already stated stated at the outset) outset) each entrepreneur expects his rival never to change his output. So the best encroachment that his rival can make is to offer AB rendering area ABRT, being the largest which can be drawn in the triangle AQOC). The first producer now finds his profits reduced to OATP. Thereupon he tries to increase them by reducing his output to ½(OQ-AB). The process will continue, the first producer being forced gradually by the moves of the second to reduce his output, the second producer being able slowly to increase his share of the market until each one is contributing equally to the total market. In these adjustments, each producer will always find his maximum profit by making his supply equal to ½ (OQ minus the supply of the other). The total output will be OQ ( 1 – Y gedgdf gefgd gefgd gdf gdfgdgd gdfgdgd gdfg dg dgdf dgdf g 2/3 QCgdfgj The output of the first producer will be OQ ghjdgkd gdgdfgd gdfg df gdfg df gdf The output of the second producer will be Gdgdf gdg stss s gs gsd gdg The successive terms of each series indicate the successive adjustments, as they have been descried. The ultimate equilibrium will be the same, however, no mater from which point the movements start. It will also be the same if, instead of the wide movements described here, the two producers increase their outputs gradually and at the same time, from ½ OA ech, or if they move in any other conceivable way, so lon long as the the init initia iall con conditi dition onss of the the prob proble lem, m, are are kept kept,, that that each each trib tribes es to maxi maximi mize ze his prof profit it independently of the other, and neglecting his influence upon the other. It is clear from Figure 12.7 that if either producer is offering OF (=1/3 OQ) the best his rival can do is to offer ½ (OQ-OF) which is FE and equal to OF, securing profits of FEWS. Since the other is in the same position, stable equilibrium is attained at this point. Simil Similar arly, ly, it can can be shown shown that if there there were were three three produc producer erss the the tot total al supply supply would would be ¾ OQ. Each Each supplying supplying 1/3 of this amount, and so on for larger number. number. If there were 100 producers producers the supply would be 100/101 OQ. And if the number were extremely large, it would be virtually OQ. When supply tends to OQ price tends to zero. The addition of cost curves will not in any way affect the essential conclusion, which is that as the number of producers increases form one to infinity the price is continually lowered from what is would be under monopoly conditions to what it would be under pure or perfect completion. The price is perfectly determinants irrespective of the number of sellers, would be closer to the purely competitive price diminishing cost than under constant cost, and closer under constant cost than under increasing cost. Edgeworth’s analysis is based on Joseph Bertrand’s criticism about Curnot’s analysis. Curnot assumed, as we have already noted, that each seller assumes his rival supply constant. Bert Bertran rand, d, on the the other other hand hand,, believ believed ed that that a solut solution ion shoul should d be work worked ed out out on the the assump assumptio tion n that that entrepreneurs believe their rivals maintain a constant price. this suggestion was developed by Edgeworth into duopoly solution. solution. Mutual Dependence Dependence Ignored: Each seller assumes His Rival’s Price Constant. Edgeworth’s Edgeworth’s solution is illustrated illustrated in Fig.12.8
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As in Curnot’s situation, let us suppose two firms situated side by side. Selling a homogeneous product produced at zero marginal cost. The entire market is pictured as being divided equally between entire preneurs X and Y DD is the demand facing entre preneur X and DQ is the demand Facing Y Each producer has a maximum achievable rate of output and, therefore rate of sale. These maxima are represented by CO units for X and OC units for Y. finally thrordinat OD is the price axis. Figure no209 By construction OB=BD and Ob=BQ If X enters the market first, he will produce and market OB units, units, selling selling each for OP price. price. He thus thus will reap the maximum maximum monopoly monopoly profit profit OBEP. OBEP. Now Y enters enters the market under the assumption that X will not change his price. So he set his price alightly below that of X (=OP) and sells his maximum producible output OC. In other words, Y price being lower than that of Xs and their products being identical,Y sells as much as he can produce, capturing a substantial portion of Xs market. Now it is Xs turn to evaluate the situation Assuming (as he does) Y will never change his price. X can lower lower his price slightly slightly below Ys and sell his maximum producible output output OC. In the process he captures most of Ys market. Then Y still assuming X will not change his price, reduces price below that of X and so off. Thus, according to Edgeworth, will ne successively lowered by Y and X until the level of OP is reached. OP is the total disposal price both X and y can sell their maximum outputs. But once the price OP is attained, one of the entrepreneurs (say X) will notice an interesting fact. At price OP, Y sells his entire output. Thus if Y retains that price, X can raise the monopoly profit OBEP. Consequently, X raise the price to OP. then Y observes that if he raises his price from OP to an amount slightly below OP, he can dispose of his entire output and enjoy a greater profit. So he raises his point accordingly. Them X recognizes that if he lowers his price slightly below that of Y he can sell his entire output and so on. Consequently price continuously move between OP and OP. the duopoly situation, according to Edgewo Edgeworth, rth, is unstab unstable le and indetermina indeterminate. te. The Edgewo Edgeworth rth case, case, just at the Curnot Curnot case, case, requires requires no comment because it is based upon a naïve assumption that is itself continually shown to be wrong by market results. Chamberlin’s analysis is based on the assumption of mutual dependence. Chamberlin’s analysis is very similar to that of Curnot except for the result. Chamberlin’s analysis is illustrated in Figure 12.9 In figure 12.9 CC represents the linear demand for mineral water X first enters the market and sells Om un its at price OP thereby reaping a monopoly profit OMEP. Now Y enters the market. Seeing that x produces Om units Price falls to OP ad total profit for both produce is given by OMFP. FIGURE NO 211 The difference difference between Curnot and Chamberlin Chamberlin is take according to Chamberlin Chamberlin X will survey s urvey the market situation situation after Y’s entry, recognize heir mutual mutual interdependence interdependence and recognize recognize also that sharing monopoly profit OMEP is the best either he or Y can do. Consequently X reduces his output to OM=1/2 OM. Y also recognizes the best solution and as such he maintains is OM price is OP and X abd Y share equally the monopoly monopoly profit OMEP The most important thing that is to be noted in Chamberlin’s solution is that his entrepreneurs behave in a sensible manner. This is a great improvement: but in addition he obtains a stable solution that is not too far from reality in homogeneous oligopoly situations. Figures 12.10(a) 12.10(b) illustrate the price output policy under duopoly. Reaction curve R r in figure 12.10(a) contains the relevant information about the price reaction of one firm Y to the
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decision if another firm X. For example, point p on this curve indicates that if firm X sets price OP= for its product, and if firm Y reactw in accordance with the information given by its reaction curve, the price of Y’ s product will become OP. If Y does stick to this reaction pattern, X’s optimal price decision can be represented quite easily. The broken curve in Figure12.10(a) represent the indifferent curve of X’s objective function i.e they are his iso profit curves if X is a profit maximize. Than the highest indifference curve which x can attain ?(the highest indifference our a compatible with Y’s Y’s reaction reaction pattern) pattern) is II which is tangent tangent to Y’s reaction reaction curve curve at point point Q. To get this point X must set his price OX and accordingly. This must be his optima price. Do far so good. But unfortunately for the analysis, two can play at optimization. Figure 12.10(b) contains in addition to Y’s reaction curve R R which indicates the manner in which expects X to react to his price. Y in turn may mow pick an optimum point, say R on X’s reaction curve. R R and thus he will set price at OP. But if both X and Y choose these ”optimal” price they will end up neither on point Q nor on R. Rather the resulting point combination will be represented by T a point which lies on neither reaction curve. The result will be that both producers will be surprised at their earnings- they may either be pleasantly surprised (on higher indifference curves than they expected) or they may be disappointed. More important, they will realize that the reaction curves have become falsehoods, for neither producer is now reacting in accordance with the dictates of hos reaction curve. Once they realize this , they will also know that their optimality calculations have gone astray. What was optimal for X so long as y struck to his reaction curve need no longer be optimal once Y struck to his reaction curve need no longer be optimal once both firms must began their calculations afresh and according to Baumol we cannot say where they are likely to go from here. In the beginning of the chapter we analyzed one limiting case perfect competition–where completion is keen and the demand curve is horizontal. Here we propose to analyze the other limiting case where competition, far from being keen is completely absent. This case is called monopoly. In case of ”pure” or ”perfect monopoly” a producer is so powerful that he is always able to take the whole of all consumers incomes whatever the level of his output. In the case of “pure” monopoly the the elast elastic icity ity of the avera average ge revenu revenuee curv curvee for for the the monopo monopolis list’ t’ss firm firm is unita unitary. ry. (This (This is shown shown in fig.12.11) To put in other words, the total outlay on the firm’s product is the name at all price and therefore the marginal revenue is always zero i. e the marginal revenue curve coincides with the X axis. Unde Underr this this situ situat ation ion all all con consume sumers rs spen spend d all all thei theirr inco income mess on the the firm firm’s ’s prod produ uct irrespective of high or low price it charges. but this does no mean that the “pure” monopolist can fix both the price and the output at the same time. When he fixes the price quantity demanded will be decided by what the consumers will take at that price. On the other hand, when he fixes his output, the price will be decided by what his customers will play for that much of output. The “pure” monopolist can fix either the price or the output, but not both at the same time, anyhow, within these limitations his power is complete.
Howev However er,, pure pure mono monopol polyy like like perfe perfect ct compet competit ition ion,, is just just a theor theoreti etica call limit. limit. A produ produce cerr who controls controls the whole supply of a single commodity without without close substitutes substitutes is called called a “monopolist” “monopolist” and it is to his analysis that we must give attention. To interpret strictly a monopolist is the sale producer of his
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produce and there is no distinction between the firm and the industry ie. the firm of the monopolist is not only a firm but it is also an industry. It is the only one firm which produces that particular product. The firm’s average revenue curve slopes downwards just as the deman curve for the product of an industry sloped downwards. The main differences between perfect competition and monopoly are the following:following:1) In case of perfect competition competition the price is the result of the interaction interaction of the forces forces of demand and supply, whereas, in monopoly the price is deliberately fixed by the monopolies. 2) In perf perfec ectt comp compet etit ition ion a sing single le pric pricee prev prevai ails ls for for each each comm commod odit ity. y. on the the oth other hand, and, the the monopolist ahs got the possibility of discriminating between different customers and might charge from them different prices for the same commodity. 3) Under perfect perfect competition competition any attempt from the part part of a producer to charge charge higher price price will only face with failure, because the customer has got the choice of deserting this particular producer and going to a different producer (seller). But under monopoly there is only a single producer and the customer is forced to buy the commodity from him at whatever price he (the monopolist) charges for it. Now we shall analyze the following sources of monopoly. 1. There are occasions occasions when a producer producer possesses certain scarce scarce raw materials materials or secret methods of production. production. and their possession gives him monopoly monopoly power. p ower. 2. Sometimes Sometimes the Government grants grants licence to some particular particular individual individual to produce some particular commodity. this is a special privilege conferred on him by the state. This kind of privilege creates monopoly conditions. 3. Another Another sources of monopoly monopoly is the ignorance, ignorance, laziness and and bias of the buyer himself. Sometimes Sometimes a producer convincers him customers that his commodity is superior to the commodities produced by other other produ producer cerss and and this this gives gives him mono monopol polyy power power.. For For maint maintain ainin ing g this this illus illusion ion he (the (the producer) producer) makes use of different different types of advertisement advertisement and publicity. publicity. As we already saw, unlike in perfect competition in monopoly price is deliberately fixed by the monopolist. He will fix that price at which the excess of gross receipts (revenue) over total costs will be the greatest. He can achieve this by regulating output in such a say, that the marginal revenue is than he saved of cost, and if he produced one unit more, he would incur more of cost than the gained of revenue. Both will result in the reduction of profit. profit. Now we shall analyses the price determination determination under monopoly. First of all we shall analyze the situation where there is absolutely no cost of production e.g. the case of a mineral spring. This situation is illustrated in fig. 12.12. The monopolist maximizes his profit when the equates his marginal revenue with his marginal cost. And this happiness when he produces OM quantity of output and sell at the price of GP per unit. Note that the elasticity of demand at the point R on the average revenue curve is equal to one and therefore at this point the total receipts will be the maximum. At this point marginal revenue and marginal cost will be zero.
Y
P
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AR Another situation is the one with positive marginal cost. Fig. (12.13). this is a more useful situation. To simplify the analysis we shall assumes that those costs are constant. Beyond the point R in the average revenue cure the elasticity of demand is less than one and so the monopolist is not interested beyond point R. between the points R and R the curve’s elasticity is equal to one. And since the monopolist’s marginal costs are positive, it will be better for the monopolist to reduce his output atleast as far as A. A is shown in the figure, to the left of point R it is likely that all monopolists will have ranges on their average revenue curves with elasticities of demand for their products greater than one. Thus the monopolist will produce upto OM quantity where marginal revenue equals marginal cost. At this point the elasticity of the average revenue curve will be greater than one.
Next is the situation where the marginal cost is rising and the monopolist is working under diminishing returns. Such a situation is illustrated in Fig. 12.4 In fig. 12.14 the monopolist is in equilibrium when the equates his marginal cost with marginal revenue. This happens when he producers OM units of output.a t this output he earns a profit which is shown by the rectangle PRLW. Another situation to be analyzed is that of constant marginal costs or constant returns. This situation is illustrated in Fig. 12.15. Here the monopolist is in equilibrium when the producer OM units of output. At this level of output his marginal cost and marginal revenue are equal. The monopoly price is OP and the area PRLW repres r epresents ents monopoly profit.
The last situation is the one where the monopolists produces under conditions of failing marginal cost or increasing returns. This is shown in Fig. 12.16 Here also equilibrium position is possible, provided marginal cost curve falls less rapidly than marginal revenue curve. In fig. 12.16 the monopolist is in equilibrium when he produces OM units of output. At this output his marginal cost and marginal revenue are equal. The monopoly price is OP and the monopoly profit PRLW. If the marginal cost curve falls throughout more rapidly than the marginal revenue curve equili equilibr brium ium will will be impos impossib sible le and this this is the only only situa situati tion on unde underr mono monopol polyy when when equil equilibr ibrium ium is impossible. In the other hand for a firm under perfect competition equilibrium position can only occur when the marginal cost curve of he firm is rising at the near the equilibrium output.
“Discriminating monopoly” or “Price discrimination” occurs when a monopolist charges different prices for different units of a commodity, even though there units are in fact homogeneous so far as their physical nature is concerned. Depending on the nature of the circumstances the possible extent of discrimination will vary. There is a theoretical possibility that every individual unit of a commodity is charged a different price, which situation is called perfectly discriminating monopoly. But, in practice, discrimination between
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buyers is more common than between units of a homogeneous good. In the case of perfect competition price discrimination between customers is nor alt all possible, because the customer who is charged more by one particular seller has got the opportunity of going to a different seller and buying form him. But even under monopoly it is not always possible to discriminate between different customers. The fundamental condition for price discrimination to take place is that there should not be any possibility of resale of the commodity from one consumer to another. In case of the following three main types of situations price discrimination can occur even if there is no fundamental difference between the goods sold to the different buyers. 1. Discrimination Discrimination owing owing to Consumer’s Consumer’s Peculiarities Peculiarities “discrimination “discrimination in this type of case can occur for three reasons: a. It can happe happen n where where consu consume merr A in unaw unawar aree that that consum consumer er B gets gets the the same same good more cheaply. Or, to put it more generally, it can happen when consumers in one part of the market do not know that prices are lower in another. b. It can exist where the consumer consumer has an irration irrational al feeling feeling that that though though be is paying paying a higher higher price he is paying it for a better good. For instance, it is probably irrational to think that one gets a better view of the firm from the front row of the Rs. 3.00 seats than from the back row of the Rs. 1.50 seats. Even in case of the same good different prices can be charged from the same consumers depending on the purpose for which it is used e.g. different rates charges for electricity for different purposes such as domestic, agricultural and industrial uses. In the foregoing paragraphs we have analyzed the conditions where price discriminiation is possible. Now we propose to examine the situations when price discrimination is profitable. For analyzing this we can apply the equilibrium theory of the firm to a case where there are two markets. If the monopolist is to be in equilib equilibrium rium the follow following ing conditions conditions should be fulfil fulfilled. led. First of all, margin marginal al revenue revenue in both the markets must be equal. Moreover, marginal revenue should be equal to the marginal cost of a producing the whole output. In fig. 12.17 the seller is a monopolist in market H the home market, where the elasticity of demand for his product is not very great. Therefore his average revenue curve AR and marginal revenue curve MR slope downwards. In the World W there is perfect completion and the demand is perfectly elastic. For the World Market the average revenue curve (AR) and the marginal revenue curve (MR) coincide and that is a horizontal straight line. The curve MC represent the marginal cost. To determine the equilibrium output the meeting point of marginal cost curve and the combined marginal revenue curve must be found. The total output should be allocated for the two different markets is such a way that the marginal revenues are equal in each market. The composite curve ZARQ represents the combines marginal revenue curve. The marginal cost curve and the combined marginal revenue curve intersect at R. Thus OM is the equilibrium output. As is already mentioned equilibrium output is at that point where the marginal revenue of both the markets are equal and at the same time equate with the marginal cost. Therefore OE quantity should be sold in the home market at a price of OP. at this point the marginal revenue is AE. The rest of the quantity should be sold in the home market at a price OP. here the marginal revenue is MR which is equal to Op. MR and AE are equal. Thus the price OP in the monopolistic home market is higher than the price (OP) in the world market. The equilibrium profit, which is contributed to by both the markets is equal to the area ZARF. Figure 12.18 shows the monopolist’s price-output price-output when both the markets are monopolistic. monopolistic.
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Figure 12.18(a) and 12.18(b) show the marginal and average revenue curves of a particular firm for two different markets. The elasticities of demand at each price are different in these markets. Figure 12.12(c) illustrates the profit-maximising output. This is determined at that point where the marginal cost curve for the monopolist’s whole output (MC) and the curve showing the combined marginal revenue received from the two markets (CMR) intersect. It is by adding the curves MR and MR together sideways that we get the curve curve CMR. Thus the equilibr equilibrium ium output output in OM and the marginal marginal revenue revenue is OK-MN. OK-MN. The total total output output is OM and the marginal revenue is OM should be allocated for the two different markets in such way that the marginal revenue in both the markets is OK. Thus in the first market (Fig. 12.18(a)) the price is OP and the quantity sold OM. In the second market (Fig 12.18(b)) the equilibrium output is OM the price OP and the marginal revenue OK. The area ZNL in Fig. 12.18(c) represent the monopoly profit.
Formulating price policies and setting the price is often a critical factor in the successful operation of business organizations. Even through the basic pricing ingredients are the same for all firms (costs, competition, demand and profit), the optimum mix of these factors varies according to the nature of products, markets and the overall objectives of the firm. Thus, the job for the management is to develop and implement an appropriate pricing strategy that meets the needs of the company. Here we propose to discuss at first the most widely used pricing methods adopted by firms. These include cost-plus cost-plus or mark-up mark-up pricing, break-even break-even pricing, pricing, rate of return pricing, pricing, variable variable cost pricing peak-load peak-load pricing, going-rate pricing, product tailoring, cyclical pricing, and other related pricing techniques. The chapter chapter concludes with a discussion on new product pricing and environmental environmental pricing factors.
Generally businessmen prefer a pricing procedure which is easy to implement and require only very few assumptions on demand. The simplest method which satisfied the above conditions is known as cost-plus pricing or mark-up pricing. Cost-Plus or Mark-up pricing: Two studies of pricing behaviour have been made in the United Kingdom, one by a group at Oxford University. Who interviewed business magnates and another by Clive Saxton who depended on a mial questionnaire? These studies revealed that a majority of businessmen set prices on the basis of cost plus a “fair” profit percentage. By cost they usually mean full allocated cost at current output and wage levels. By “fair profit” is meant a fixed percentage mark-up which differs greatly among industries and firms. Some of this variation may be due to differences in cost base and some to difference in turn over rate and risk. Does the use of rigid customary mark-up over cost make logical sense in the pricing of products? The answer is usually, no any pricing technique that ignores current demand elasticity in formulating prices is not likely to lead, except by chance to the achievement of maximum profits, either in short-run or in the long-run. As elasticity of demand changes, as it is likely to do seasonally, cyclically or over the product life cycle, the optimum mark-up should also change. If mark-up remains a rigid percentage of the cost then under ordinary conditions it would not lead to maximum profits.
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Under special condition it may be possible that a rigid mark-up at the right level may lead to optimum profits. The two conditions are that average (unit) costs must be fairly constrantover the range of likely output and price elasticity must be fairly constant constant for different different points on eh demand curve and over time. In spite of the shortcomings mentioned above, cost-plus pricing continues to be popular with a sizeable population of the business community. The reasons for this popularity are mentioned below: i)
There is less less uncertainty uncertainty about about costs than than about demand demand so by relying relying on cost, cost, pricing pricing a simplified and the seller does not have to make frequent adjustments as demand conditions change.
ii) Where all firms firms in the industry use cost-plus pricing pricing approach, approach, their prices are likely likely to the similar. This helps to minimize price competition which would not be the case if firms paid attention to demand fluctuations when the priced. iii) There There is the feeling feeling that cost-plus cost-plus pricing pricing is socially socially fairer fairer to both the buyer and the buyer buyer when his demand becomes acute. Yet the seller earns a fair return on his investment. iv) Cost – plus pricing pricing is the safest though not the most profitable profitable method of pricing pricing In short, the popularity of a cost-oriented approach to pricing rests on considerations of administrative simplicity, simplicity, competitive harmony and social fairness. fairness. Break-even pricing indicates how may units must be sold at selected prices to regain the funds invested invested in a product. A break-even chare chare prepared prepared for ABC Ltd., is given below. The figure figure assumes that product production ion and selling selling of ABC’s ABC’s product product involve involve annua annuall fixed fixed expense expense of Rs. 85000 85000 and the variab variable le production costs for direct labour materials, and factory overhead are Rs. 2 per unit. When the fixed and variable costs are added, total cost intersect the revenue price curves at points A,B and C. These points show the volume neede to recover full costs at factory prices of Rs. 3 Rs. 3.60 and Rs. 4.60. Profits are generated when sales exceed break-even points and losses occur when sales fails to reach the break-even levels.
Although a break-even chart provides a useful visual representation, it lacks some of the details that can be included in a tabular analysis. The following table gives break-even volumes for xis potential ABC’s prices by dividing total fixed costs by the margin generated at each price. The table also indicates the final prices the consumer would pay when the wholesale and retain margins are added to ABC’s selling prices. It may be pointed out that the price of Rs. 2.60 requires sales of about 141.700 units to break-even while a price of Rs. 5 required only 28,300 units to be sold. The most serious defect associated with break-even pricing is its inadequate treatment of demand. The relationship between the final retain price and the number of ABC’s products that will be purchased by consumers is crucial to the selection of the optimum price is obvious. Break-even diagrams, however, usually indicate total revenue as straight lines implying that larger volume can be sold without lowering prices (see the break-even charts). This is rather unrealistic and the company management must consider which combination of price and break-even volume will lead to maximum profits. Some of the factors influencing this decision are rival’s offerings, previous pricing experience, and the special features (if any) of ABC’s products. Finally, the decision depends on the ability of the company management to estimate the number of units that will be sold at each possible price. Rate – of Return Pricing
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Pricing to achieve a planned rate of return on investment is popular among a number of business firms. It is also closely associated with the pricing policies of the public utility concerns. Calculating Calculating Break-even Break-even Volume for ABC Ltd. Using Margin Margin Per Unit. Rs. Sales Forces salary and expenses
25,000
Advertising and Propaganda
40,000
Expenses relating to Amortization of R&C
5,000
Overhead expense allocation
10,000
Other expenses
5,000 85,000
Retail Price (Rs.) (inclu (includin ding g whol wholesa esale le & retail margins
5.42
6 .2 5
7 .5 0
8.33
9.58
1 0 .4 2
Possibl Possiblee manufac manufactur turing ing (seeing price (Rs.)
2.60
3 .0 0
3 .6 0
4.00
4.60
5 .0 0
Variable Cost (Rs.)
2.00
2 .0 0
2 .0 0
2.00
2.00
2 .0 0
Margin (Rs.)
0.60
1 .0 0
1 .6 0
2.00
2.60
3 .0 0
141.7
8 5 .0 0
53.0
42.5
32.7
28.3
Brea Breakk-ev even en volu volume me in 1000s of units (Rs. 85000 mfg’s margin)
* The fixed costs could be increased to include a profit so that the break-even volumes would show the sales needed to return planned planned profit. The pricing procedures used in rate of return pricing can be illustrated by referring to ABC’s Ltd. mentioned earlier. Here the management’s first task is to estimate its total costs at various levels of output. The The tot total al cost cost curve curve is shown shown risin rising g (see (see fig. fig. 13.1) 13.1) at a cons constan tantt rate rate unti untill capa capacit cityy is appro approach ached. ed. Management’s next task is to estimate the percentage of capacity at which is likely to operate in the coming period. Suppose that ABC’s capacity is 1,00,000 units and the total cost of producing this volume is Rs. 250000 Assume Further that the firm expects to operate at 70 percent capacity. This means that it expects to sell 70,000 units. The total cost of producing 70000 units, according to figure (No. 13.1) is Rs. 2.25000 or about Rs. 3.21 per unit. Management’s next task is to specify a target rate of return so that the planned planned return on investments will be achieved. achieved. If ABC aspires for a 20 percent after-tax rate of return on its Rs. 250,000 (0.20X Rs. 250,000 = Rs. 50,000) and the tax rate is 50 percent, then the price must be set to product Rs. 1,00,000 in total profits. Since ABC plans to sell 70,000 units a factory selling price of approximately Rs. 4.64 per unit well generate the desired profit and return on investment.
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Rate – of – return pricing, however, has a major defect. Sales estimates are used to derive a price ignoring the fact that price is an important factor that influences sales. A price of Rs. 4.64 may be too high or too low to sell 70,000 units. What is missing from the analysis is a demand functions, indicating how many units ABC Ltd., could expect to sell at different prices. With an estimate of the demand curve and with the requirement to each 20 percent on costs. ABC Ltd., could solve for those prices and volumes that would be compatible with the each other. In this way, ABC Ltd. would avoid setting at a price that failed to generate the estimated level of output.
Variable-cost pricing is often based on the idea that the recovery of full costs is not always realistic or necessary for the profitable running of business firms. Instead of using full costs or standard costs as the lowest possible price, this system suggests that variable cost of incremental cost represents the minimum price that can the charged. For instance, assumed that company ABC Ltd products have been marketed successfully through normal whole sale-retail channels and a total of 70000 units have been sold in the past year at a price of Rs. 4.64 per units. This price covers full cots of Rs. 3121 and allows company “ABC Ltd, a 20 percent after-tax return on its investment of Rs. 2,50,00. Company ABC Ltd., is now approached by a new customer who wants to make a special purchase of 20,000 units of its product at a price of Rs. 2.50 per unit. To evaluate this proposal company ABC Ltd., must know how much it will cost to produce this 20,000 units. If the variable cost per unit comes to Rs. 2 per unit ABC Ltd., cold make a contribution of Rs. 10,000 out of this order. Under what circumstances company ABC Ltd. can accept this order is a big question. Some would suggest that the order can never be accepted as the price offered does not cover full costs. others would point out that if company ABC Ltd. were to cut prices for this particular customer other customers would demand an equal cut in prices. This could result in losses because there would be no way for Company ABC Ltd., to recover full expenses. While there is an element of truth in this line of argument, the crucial point is that the full costs of manufacturing each unit is not constant but, in reality, is quite sensitive to changes in volume. This is shown in Fig. 13.2 where unit cost decline as the fixed expenses are distributed over a larger volume. If we assume that ABC Ltd’s variable costs are produced for Rs. 62.5 per unit and 70,000 for Rs. 3.21 per unit. If volume could be expanded further to 170,000 unit cost would be reduced to Rs. 2.50 offered by the new customer. This indicates that a very low price can cover full costs if volume of production expands sufficiently. In the present situation, adding 20,000 units to the current production of 70,000 units lower estimated fixes costs per unit to Rs. 0.94(85000/90,000). When fixed cross are added to variable costs of Rs. 2.00 (which is constant) total costs (Rs. 2.94) exceed the Rs. 2.50 offered by the new customer. Since the order will bring less than full costs, it is important to consider whether the two markets being served are really insulated. Will sales to the new customer in any way reduce existing sales. If the two markets are really separated, then the new order will look more attractive. Acceptance of the new order will also depend upon the availability of unused capacity. Variable cost pricing is often encountered in situation where fixed costs make up a large proportion of tota totall unit unit costs costs.. the rail rail roads roads and airl airlin ines es are are two industr industries ies with high fixed fixed cost costss that that have have made made effective use of the volume-gene acting aspects of variable costs pricing. The underline idea is that it is better haul bulk-commodities and special classes of travelers at low rates and make some contributions than not to have the business at all. Railways typically face a declining unit-cost curve except when volume approach approaches es capacit capacityy and tracks and yards yards become become congest congested. ed. This This means means that more volume volume usually usually increases increases profits by reducing reducing the average cost of hauling hauling merchandise. merchandise. The airlines airlines have used variable cost pricing when they set fares for excursions or special groups of customers. Variable cost pricing when they set fares for excursions or special groups of customers. Variable cost pricing is not a panacea for all
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produ product ctss or for all all firms firms,, but but it can can lead lead to high higher er revenu revenues es and and profit profitss for for sophi sophisti stica cated ted firm firm who understand understand the potential potential and limitations. A special form of variable cost-pricing can be used when there are definite limits to the amount of goods and services a firm can provide and customer demand tends to vary over time. For instance, the telephone indust industry ry builds capacity capacity to satisfy satisfy 80 to 90 percen percentt of its caller callerss during during peak periods periods that occur occur during during week week days. days. This This resul results ts in a lot of unus unused ed phon phonee circu circuits its at night night and and weeken weekends. ds. PeakPeak-loa load d prici pricing ng suggests that phone rates should raised above average costs during high-demand periods and reduced towa toward rdss vari variab able le costs costs durin during g low low deman demand d period periods. s. This This tends tends to shift shift price price sensit sensitiv ivee calle callers rs to low demand periods and allows the phone industry to operate with below full capacity, Again, the very low off-peak rates may help to increase revenues by attracting some callers that normally do not use the phone for communication purposes. This form of pricing is also adhered by Telegraph Telegraph departments electricity undertaking undertakingss etc., The The most most import importan antt advan advanta tage ge of peakpeak-lo load ad pric pricin ing g is that that it depre depress sses es peak peak deman demands ds and and there thereby by redu reduce cess the the tota totall resou resourc rces es neede eeded d to sati satisf sfyy cust custom omer er dema deman nd. Again gain,, it stimu stimula late tess offoff-pe peak ak consumption consumption and allows more efficient efficient utilization utilization of existing facilities. facilities. The most popular from of competition-oriented pricing exists when a firm tries to keep its price at the average level charged by the industry. This form of pricing is knows as going-rate or imitative pricing. This system of pricing is popular for a number of reasons., some of them are mentioned below: i)
Where Where costs are difficu difficulty lty to measure measure,, it is felt that the going going rate represen represents ts the collectiv collectivee wisdom of the industry concerning the price that would yield an attractive return.
ii) It is also felt felt that conforming conforming to a going going price would would be least disruptive disruptive or industry industry harmony. harmony. iii) The difficulty difficulty to knowin k nowing g how buyers and competitors would react to price differentials differentials compel the producers to adhere to the going rate-pricing. Going-r Going-rate ate pricing pricing primari primarily ly charac character terize izess pricing pricing practic practicee in homogen homogeneou eouss product product market markets, s, although the market structure itself may vary from pure competition to pure oligopoly. Under pure or perfect competition a firm has actually no choice about the setting of its price. There is about to be a market-determined price for the product which is not established by any single firm or group of firms but through the collective interaction of a multitude of knowledgeable buyers and sellers. The firm daring to charge more than the going rate will attract no customers. The firm need not charges less than the going rate as it can dispose of its entire output at the going rate. Thus, under highly competitive conditions in a homogeneous product market the firm really has not pricing decision to make. The major challenge facing such a firm is good cost control. In pure oligopoly also the firm tends to charge the same price as competition, although for different reasons.
Product tailoring refers to a policy of determining the selling price in advance and then working back to the design of the product. It is an inverted cost-price relationship in which the price of the product appears to determine its cost, instead of the other way round discussed for far. Product tailoring is directly applicable only when product design in fluid and when the target price is sharply defined by the economic situation in respect of substitutes and demand. This approach has the virtue of starting with market-price relatives it looks at the problem from the view point of the buyer in terms of what he wants and what he will pay. This technique may profitably be employed in an aircraft industry.
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Refu Refusal sal pricin pricing g is rela related ted to produ product ctss that that are are design designed ed to the the speci specific ficat ation ion of a single single buyer buyer.. Such Such products are priced on the basis of estimated incremental cost plus a gross margin equivalent to the opportunity cost. The producer’s pricing is called refusal pricing because he is deciding whether or not to make the product at all in other words, he has the option to refuse the order if he wants. but it may be noticed that even here cost sets only a floor for prices otherwise, the seller might miss potential immediate profits and ignore the effects of price upon future business.
The pricing decisions of a firm have to take to account flunctionations in inventory, in capital outlays, in national income and in employment. It is of common knowledge that the prices of agricultural products and certain raw materials and manufactured goods have been predominantly flexible over the cycle. But the prices of certain other raw materials and the products of price leaders are relatively inflexible over the cycle. This is because of the fact that the price leaders are reluctant to change their prices frequently and they often try to limit price costs in periods of declining demand. They also refrain from major price increases in periods of rising demand. The main reasons for this type of price inflexibility can be grouped under four heads on the basis of cyclical changes in conditions of (1) demand (2) competition (3) Costs and (4) Profits. On the demand side, producers often believe that the demand for their products is highly in elastic and henc hencee price price chan change ge will will not not lead lead to any appr apprec ecia iabl blee chan change ge in deman demand. d. From From the the point point of view view of competition, it may be stated that much industrial pricing is done under oligopoly conditions and that been the price leaders has to maintain a degree of price stability in order to ward off retaliation from others. This effect freezes prices and delays changes, usually until other prices have started moving. On the cost, side variable costs per unit tends to remain relatively constant over long periods and widely differing outputs on account of the rigidity of prices of raw materials and labour. Fixed cost per unit, as reported reported in convent conventiona ionall accoun accounts, ts, varies varies inversel inverselyy with volume volume and with cyclic cyclically ally sensitiv sensitivee materi materials als prides. Current full costs-pricing imports some of the cost rigidity to prices. On the side of profits, many firms, especially the price leaders who have considerable latitude in price-making, have generally as their goal a “reasonable” profit rather than profit maximization. Hence they many not lower or raise prices appreciably appreciably during business cycles. The main practical problems of cyclical pricing arise as to the degree, the timing and the pattern of cyclical pric pricee chan change ges. s. The The actu actual al chan change gess affect affected ed in net net price pricess may may take take many many forms forms of which which the the most most important are: 1) changes in list prices 2) changes in product-mix and product-line differentials and 3) changes changes in the structure of discount and merchandising merchandising allowance. allowance. In formulating policy on crucial crucial pricing, a potenti potential al price price leader leader or firm havin having g substan substantia tiall indepen independen dence ce in price price determin determination ation can conside considerr several possible policies some of which are mentioned below: 1. Price Price rigidity rigidity 2. Price fluctu fluctuations ations that that conform conform to cost changes changes a. Current Current full full cost cost b. Standa Standard rd full full cost cost c. Incremen Incremental tal cost 3. Price fluctu fluctuation ation that conform conform to prices of of substitutes substitutes
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4. Price fluctu fluctuations ations that that conform conform to price of of substitutes substitutes 5. Price fluctu fluctuations ations that that stabilize stabilize market share share 6. Price fluctuatio fluctuations ns that conform conform to change in industry industry demand determinants determinants.. These policies might be characterized more accurately as objectives, since some of them cannot be fully attained.
Absolute or approximate stability of the firm’s price level over the course of the business cycle is a policy follo followed wed by some some produ produce cers rs of indus industr tria iall mater materia ials ls and and equipm equipmen ent. t. It is larg largely ely base based d upon upon two assumptions 1) what the wide cyclical fluctuations in demand are caused by basic economic changes (e.g. in income, profits, expectations etc) and 2) that changes in the firms prices within the range of feasibility will be ineffective ineffective in altering altering these conditions conditions or in tempering tempering these cyclical cyclical fluctuations in demand. demand.
Confining cyclical changes in price to changes in production costs in another popular price policy. This policy has several variants depending upon which of the cost concepts viz full cost, incremental cost, or some forms of standard cost, that are employed.
The use of substitute products as a cyclical pricing guide is an appropriate price policy in many situation. By keeping the spread between the firm’s product and substitute products stable, or by manipulating it to obtain specified volume objective, this cyclical pricing policy can protect pricing policy can protect or improve the company’s market position. Such a policy may also help to stabilize the industry’s share of the vast substitute market. Under conditions of homogeneous homogeneous oligopoly, where there is strong price leadership, leadership, the cyclical price policy followed by many price followers of this types.
Keeping the price in line with the declining purchasing power of money is a depression pricing standard that has strong appeal. But it may be pointed out that this kind of blanker index of purchasing power is an inferior pricing guide. Price Fluctuations that Stabilize Market Share: Price is one important background background determin d eterminant ant of that market share especially especially when products products and services are dissimilar. Again, price policy has considerable effect upon the larger share of the substitute market. Market share can be a useful pricing guide for cyclical pricing. But the administration of such a policy are suppose moderately accurate and current information about what is happening to market positions. It also demands demands alertness and flexibility flexibility in pricing. pricing. It is a known fact that the demand schedules, both of the Industry and of the firm, shift continuously consequent upon changes in general business conditions and changes in special outside conditions that affect the product. If these shifts in demand are marked, they should be taken into account in formulating prices. In reality, they are often more important than the elasticity of demand.
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Changing prices in relation to some appropriate index of shifts in demand for the product is a form of recession pricing policy. Sometimes it is possible to find a direct relationship between some index like disposable income and past fluctuations of the price of the product. This functional relationship can then provide a rough criterion of the appropriate price at any given or forecasted level of demand. The use of any such historical relationship as an absolute recession pricing criterion has severe limitations that destroy its usefulness in most industries. This pricing method implicitly assumes that (1) flexible rather than rigid prices are appropriate (2) changes in the price in the past have adjusted for changes in demand correctly (3) Past pricing objectives are today’s objectives and (4) cost behaviour and competitive reactions will be the same as in similar periods in the past. So far we have been discussing the different pricing techniques that are popularly followed by business firms under different situations. Here we propose to start a discussion on new product pricing. In this discuss discussion ion we focus focus attention attention on the specif specific ic plans plans and strategies strategies needed needed durin during g each each phase phase of the product life cycle to improve the competitive position of the firm.. All successful products follow a four-phase life cycle that includes introduction, growth, maturity and decline. decline. These T hese “typical” stages are “illustrated “illustrated for a hypothetical hypothetical product” in the following following figure.
At the introductory stage products are not known to the consumers. So here the emphasis should be on promotional activities so as to acquaint customers with the product and gain acceptance. The sales of the product rise slowly and if it “catches on”, follows a period of rapid growth in sale volume. This stage is characterized by increase in the number of competitors, major product improvements, line productions methods, penetration of other market segments etc., So during this phase emphasis must be given in opening opening new distribution channels channels and retail outlets. When the product product reaches maturity, sales grow slowly or remain remainss stables stables.. Specia Speciall promotio promotions ns are needed needed to cope cope with such a situatio situation. n. Finally the product product reaches a stage of prolonged or rapid sales decline. At this stage the products need to be redesigned or the cost of production should be reduced so that they can continue to make some contribution to the company. When products become unprofitable, the firm must decide whether the products should be carried at a loss or phased out to make room for more profitable lines. Product cycles very in length from few weeks for fashion goods to a number of years for appliances and food items. The length of time a product stays in any one stage of the life-cycle depends on customer adoption rates and the amount of news product competition. Three strategies that can be employed to stretch product markets are promotion of more frequent and varied usage among current users, finding new uses for the basic material, and creating new users for the product product by expanding the market. Formulating prices for new products is one of the most difficult problems, faced by company management these decisions are often complicated by lack of adequate information on both demand and costs. as the product has not been sold before, price elasticity cannot be estimated from an analysis of past data. Even the simple expedient of following the competitor’s price is not a practical alternative for new products. In spite of all these problems the firm must set a price that will help to sell the product and at the same time contribute something to the profits of the firms. A common approach to new product pricing is to make an intuitive appraisal of the product and to supply either a skimming or penetration price strategy.
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The The basic basic idea idea is to set set a relat relative ively ly high high pric pricee that that skim skim the cream cream of deman demand d coupl coupled ed with with heavy heavy promotional expenditures in the early stages of market development. The price is lowered atleast stages. The objective of skimming price is to gain a premium from those buyers who always stand ready to pays much higher price than others because the product, for one reasons or another, has high present value for them. The skimming lowered atleast stages. The objective of skimming price is to gain a premium form those buyers who always stand ready to pays much higher price than others because the product, for one reason or another, has high present value for them. The skimming price policy assumes that demand for the product is likely to be more inelastic with respect the price in the early stages than it is when the product is full-grown. The situation is illustrated by the downward downward sloping curve DD in i n the following following figure.
The high initial price (P) us designed to skim of the segment of the market that is insensitive to price, and subsequent price cuts (P P) broaden the market by tapping more elastic segments of the market. The logic of skimming price strategy is further supported, by the assumption that many new products have no technical substitutes and price is not as significant as it is for traditional products. The skimming pricing strategy has the advantages that it generates greater profits per unit than would be possi possibl blee with with lower lower price prices. s. By setti setting ng a high high init initia iall price price and and then then gradu gradual ally ly lower lowering ing the price price,, the company is able to reap the maximum that each market segment is willing to pay for the product. Another advantage of a skimming price strategy is that helps to restrict sales at a time when the firm may be unable to keep up with customers orders. A policy of slowly lowering prices to expand sales makes it easier for the firm to increase production capacity to meet the growing demand. The strongest strongest argument for adhering adhering to the skimming price strategy strategy is that it generally generally is the t he safest and most conservative approach available. By starting with a high price the company can find out how many customers are willing to pay for the product while retaining the ability to lower the price of competitive conditions warrant such an action. If the company should accidentally set a price that is too high, it can always be reduced, whereas a price that is too low may be difficult to raise. The most important disadvantage of the skimming price strategy is that the high margins associated with such a strategy strategy attract competitors competitors into the field. This suggests that the skimming skimming price strategy can be best used when the products has patent protection or when there is barrier to entry such as technical know-how or high capital requirements. A Penetration price is a relatively low price designed to stimulate the growth of the market and to capture a large share of it. The penetration price strategy is based on the following assumptions. (1) Demand for the product is highly elastic such as shown by the curve DD in the following figure (Fig. 13.5) (2) There is no elite market that can be exploited with high. Initial prices. prices. Under these conditions, conditions, a high price (P) may actually actually result in zero sales.
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D1
e c i r P
D
Fig. Fig. 13.5 Quantity Quantity demande demanderr (3) The unit costs of production and distribution fall fall with increased increased output. (4) A low price would discourages actual and potential competition. But it may be pointed out that penetr penetrat ation ion pricin pricing g is a high high risk risk strat strategy egy that that can lead lead to losses losses if sale saless do not not live live up to expectations. Another problem is the low margins which suggest that it will take longer time to recoup development expenses than it would with a skimming price policy. The problem here is to determine a pricing policy for later stages of the cycles, i.e. after imitators have involved the market of the once unique product. To formulate such a policy the producer must know when a product is approaching maturity. Hence, we propose to list some of the symptoms of product maturity.
1) Weaken Weakening ing in brand brand preferen preference ce is the first symptom symptom of product product maturity maturity.. This This is evidenced evidenced by a higher cross-elasticity of demand among leading products. Now the leading brand will not stand as much price premium as it started with, without losing position. 2) Redu Reducin cing g physic physical al vari variati ations ons among among produ products cts in anot anothe herr sympto symptom m of produ product ct matu maturi rity. ty. This This happens happens when w hen the best designs are developed developed and standardized. standardized. 3) The The thir third d sympto symptom m of produ product ct matu maturit rityy is mark market et satu saturat ration ion.. This This is gener general ally ly indic indicate ated d by an increase in the ratio of replacement sates to new sales. 4) The stabilization stabilization of of production production methods is the last last symptom of product product maturity. maturity. As soon as the products show the maturity the management must think in terms of granting appropriate appropriate price reductions taking into account the cross-elasticity of demand.
So far far we have have been been focus focusin ing g our our attent attention ion on the the immedi immediat atee deman demand d and facto factors rs that that influ influen ence ce pricing activities in mono products firms. There are however, a number of other consideration that
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frequently influence pricing policies. These include the effects of multiple product lines, restriction imposed imposed by governmen government. t. All these these factors factors tend tend to influen influence ce profit profit and revenu revenuee maximiz maximizing ing prices prices derived from an analysis of demand and cost data.
Since almost every firm has several items in its product line, product line pricing becomes an important phase of price policy. The problem of product-line pricing is to find the proper relationship among the prices prices of number numberss of a product product group. group. Product Product-lin -linee pricing pricing may refer refer to product product group. Product-li Product-line ne pricing may refer to products physically the same but sold under different conditions. This gives the seller an opport opportun unity ity to char charge ge diff differe erent nt price prices. s. Thus Thus sue sue diffe differen renti tial alss (e.g (e.g.. hot hot coffe coffeee versu versusic siced ed coffe coffee) e) seasona seasonall differen differentia tials ls (e.g. (e.g. night night fights fights or night night telephon telephonee calls), calls), and style style cycles cycles differen differentia tials ls are all phases of product-line pricing. The rationale for this heterodox approach to pricing is that the essential economic features of the product line is the cross-elasticity of demand that exist among parts of the seller’s output.
The under underlyin lying g princip principle le in product-l product-line ine pricin pricing g is that that demand demand elastici elasticities ties and competit competitive ive situatio situations ns rather than cost should form bases for determining the patterns of relative prices of the firm’s products. And the role of cost should be confined to set lower limits for price and to help select the price. Output combin combination ation that is most most profitab profitable. le. But in reality reality this princip principle le is not widely widely employed employed in product product-lin -linee pricing. pricing. Instead firms fix prices in such a way that they are proportiona proportionall to full cost (i.e. that produce produce the same percenta percentage ge net profit margin margin for all products) products) or (increm (increment ental al cost) cost) (i.e. (i.e. that produce produce the same percentage percentage contribution contribution – margin over incremental incremental costs for all products) or with profit margins that are proportional to conversion cost. Prices are also set in such a way that type produce contribution margins that depend upon elasticity of demand of different market segments or that are systematically related to the stage of market market and competitive competitive development of individuals members of the product line.
Ther Theree are are two two dema deman nd rela relati tion onsh ship ip that that are are impo import rtan antt in prod produc uctt-li line ne pric pricin ing. g. The The firs firstt is the the interdependence of the demand for various members of the product line. This interdependence may result from from their their nature nature as substitu substitute te or compleme complement ntary ary products. products. The second second demand demand charact characteri eristic stic is the importance importance of the products as instruments instruments for f or market segmentations segmentations and price discrimination. discrimination. Prod Produc uctt-lin linee pric pricin ing g has has also also to take take accou account nt of compet competit itive ive diffe differen rence cess in respe respect ct o fhte fhte diffe differen rentt products in the line. The number of competitors, the extent of the firm’s market share and he degree of substitu substitutab tabilit ilityy of the competit competitors ors product product are symptoms symptoms with which which the existing existing competit competition ion can be measured measured and the price adjusted accordingly. accordingly. The The relev relevant ant conce concept pt of cost cost applic applicab able le in produ product ct line line pric pricin ing g is incr increme ement ntal al cost. cost. Norma Normally lly,, the incr increme ement ntal al cost costss of each each membe members rs of the the produ product ct line line can be compa compare red d with with its pric price. e. The The marg margin in between incremental costs and price will differ greatly from products to product depending on the depend conditions. Incremental cost set a floor below which the price should not go normally. Sometimes strategic considerations warrant the continuance of a product in a line even when its contribution to the profit margin is below average, such a product may be “loss-limiter” (i.e. it completes a product line by offering a fall range of colours, sizes, design etc.) or “price meter” (i.e. its role is to carry out the firms’ policy of meeting every competitive price with some member of the product line).
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The two parts of price price are (1) the basic list price and (2) the net price price actuall actuallyy charge charged. d. The differen difference ce between the two are due to the trade status of the buyer, the amount of his purchase, the location of the buyer, the promptness of payment, the time of purchase and the personal situation. The total returns realized by the manufacturer depends on the price charged on each section of the buyers and also on the size of their purchase. An important aspect of price differentials is price discrimination. By price discrimination is meant a policy of charg chargin in diff differe erent nt price pricess for the the same same produ product ct,, in other other word words, s, price price discr discrimi imina natio tion, n, exist existss when when differences in prices charged by a seller do not exactly match difference is cost. The relevant cost concept applicable in this context is the marginal cost, though it has limitations when the plants do not function as full capacity and also when joint products involving common costs go into the product mix. From the welfare point of view, price discrimination often acts as an instrument for the equalization of real burden. And even governments increasingly resort to various measures of price discrimination in the form of farm price support. The practical problem of price discrimination is to break the market into segments that diffe differr in price price elast elastici icity ty of deman demand. d. Marke Markett segme segment ntati ation on can can be just justifi ified ed only only on the the basis basis of he incremental concepts cost and revenue i.e. only on the basis of the incremental concepts cost and revenue. The extreme from of price price discrimin discriminatio ation n is practic practiced ed by medical medical practi practition tioners ers in whose whose case case market market segmentations may extent to the level of individual clients. The manufacturer will have various goals in adopting differential prices for his products. Some of such goods goods are are 1) Implemen Implementat tation ion of a mark marketi eting ng strate strategy. gy. Diffe Differen renti tial al pric prices es may may be part part of an over over-al -alll marketing strategy in order to reach particular sectors of the market. 2) Market differential prices help in achiev achievin ing g profit profitab able le marke markett segme segment ntati ation on when when lega legall and and compet competiti itive ve consi consider derat ation ionss permi permitt price price discrim discriminat ination ion 3) Market Market expansion expansion differen differentia tiall pricing pricing that is designe designed d to encour encourage age new new uses uses or to attract new customers is a common goal of product-line pricing, but it also extends to discount structure. 4) Competitive adaptation differential prices are a major device for selective adjustment to competitive situ situati ation on.. When When ther theree are are stan standar dardiz dized ed produ products cts in the indu industry stry,, differ differen enti tial al price pricess help help to achie achieve ve competit competitive ive partite partite with customer customerss of differen differentt backgroun backgrounds. ds. 5) Ruction Ruction of productio productions ns cost seasona seasonall discounts and the like reduce the over all production costs by encouraging off season purchases.
These are price deductions that systematically make the net price very according to the buyer’s po.
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Answer any six questions. Answer shall not exceed one page for each question. 1. 2. 3. 4.
5. 6. 7. 8. 9.
Explain the scope scope of Managerial Managerial Economic Economics. s. Indicate the role of unce uncertainty rtainty indecision indecision-making -making.. Compare Compare incremental incremental reasoning reasoning with managerial managerial analysis. analysis. How do you you define define the term ‘demand’ ‘demand’ and and demand function function for a commodity? commodity? What are the general determinants of demand for a commodity that appear in the demand function for that? How do you determine determine consumer consumer choice choice under uncerta uncertainty inty Enumerate Enumerate the steps in demand forecasting. forecasting. Define Define a) Break Break even pricing pricing b) Peak Peak loud loud pricing pricing Define Define price leadership. leadership. Explain opportunity opportunity cost concep conceptt
Answer to each question shall not exceed three pages. 10. 10. “Man “Manag ager eria iall econom economic icss is the the inte integr grati ation on of econo economi micc theo theory ry with with busin busines esss prac practi tice ce fort fort the purpose of facilitating facilitating decision making making and forward forward planning planning by management”. management”. Explain. 11. Enumerate Enumerate the steps in demand forecasting. forecasting. 12. Explain Explain how an individua individuall firm attain equilibr equilibrium ium in the short and long periods periods and under under perfect perfect competition. 13. How is price determined determined under conditions conditions of duopoly. 14. Define Define price-ela price-elastic sticity ity of demand. demand. How How it is computed computed and what are its determin determinant antss and uses in economic analysis. 15. Explain Explain the term marginal marginal rate of commodi commodity ty substitu substitution tion (MRCS) (MRCS) What What is the significan significance ce of this term in the theory of consumer behaviour? 16. 16. What What are are the the poin points ts base based d on which which indi indiff ffer eren ence ce curv curvee anal analys ysis is is rega regard rded ed supe superi rior or to Conventional Utility Analysis.
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