Chapter 5 DEMAND ANALYSIS AND ESTIMATION
QUESTIONS & ANSWERS Q5.1
"The utility derived from consumption is is intangible and unobservable. unobservable. Therefore, the utility concept has has no practical value.” value.” Discuss this statement. statement.
Q5.1
ANSWER
The utility utility derived derived from from consumpt consumption ion is intangib intangible, le, and theref therefore ore unobser unobservabl vable. e. However, when goods and services provide utility to consumers, there is a direct and measurable influence on their purchase decisions. Through their revealed preferences, consumers convey their evaluation of the value, or worth, of individual products. While While the value value derive derived d throug through h consumpt consumption ion is intang intangible ible,, it leads leads to purchase purchase decisions that can be monitored and responded to by firms. Q5.2
Is an increa increase se in total total utility utility or satisfac satisfaction tion follow following ing an incre increase ase in incom incomee consisten consistent t with the law of diminishing marginal marginal utility?
Q5.2
ANSWER
Yes, the law of diminishing marginal utility states that the marginal utility derived from consumption will eventually diminish as consumption increases during a given time period. This means that the the addition to total utility per dollar dollar of income will tend tend to fall as total income rises. rises. Despite Despite the fact that total utility, utility, or well-being, tends to rise with income, it is typical that the marginal utility derived per dollar of income tends to fall as income rises -- as is predicted by the law of diminishing marginal utility. Q5.3
Prospecti Prospective ve car buyers are sometimes sometimes confronted confronted by sales representat representatives ives who argue that they can offer a vehicle that is “just as good as a BMW, but at one-half the price.” price.” Use the indifferen indifference ce concept concept to explain explain why the claims claims of the sales sales representative are not credible.
Q5.3
ANSWER
If two products provide the same amount of satisfaction or utility, the consumer is said to display indifference indifference between between the two. Indifference Indifference implies implies equivalence in the eyes of the consumer. consumer. A consumer can be indifferent indifferent between between goods and services services that are
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distinct distinct in a physical physical or material sense. sense. Similarly, Similarly, a consumer can display display distinctly distinctly different preferences for goods and services that are similar in a physical or material sense. What’s important in the case of consumer indifference is that two products yield the same amount of satisfaction or well-being to the consumer. This should make consumers skeptical of sales representatives who argue that a cheaper product is “just as good as” a more expensive competitor. First of all, cheaper substi substitut tutes es seldom seldom perform perform at the same high level as competi competing ng products products with a deservedly deservedly superior reputation. reputation. And second, it is important important to remember remember that when consumers buy a product, they purchase a whole range of attributes associated with that product product.. For example example,, the BMW 760i four-d four-door oor sedan sedan is a $125,00 $125,000 0 vehicle vehicle famous among car buffs for its awesome power, comfort, and styling . Buyers of a BMW 760i four-door sedan not only enjoy the creature comforts of a fine automobile, some also enjoy the “snob appeal” of owning a rare and exclusive automobile that tells all onlookers onlookers that they are successful. successful. While you and I might might think “snob appeal” appeal” is sill silly, y, some some consu consume mers rs have have a diffe differe rent nt opini opinion, on, and who who are are we to argue argue with with consumer preferences? Q5.4
Followin Following g a price price chang changee for Diet Diet Coke, Coke, expla explain in how retailers retailers use use sales sales informa information tion to to learn if Doritos snack chips represent a complement complement or substitute for Diet Coke.
Q5.4
ANSWER
Following a price change, companies use sales information to distinguish complements from substitutes by noting the size and direction of effects on demand for related products. products. Demand curves are downward downward sloping. sloping. As a result, result, when the price of a product is decreased, sales of that product rise. At the same time, sales of substitutes substitutes fall fall as custome customers rs switch switch to the now lower-pr lower-price iced d alterna alternativ tive. e. When When the price price of a product rises, rises, sales sales of that that product product fall but but sales sales of substitute substitute products products rise as customers customers switch to the substitute’s substitute’s relative bargain price. There is a positive correlation between price changes and units sold when two products products are substitutes. substitutes. Sales of substitutes substitutes change in the same direction of the price change for substitute products. Conversely, when the price of a product is decreased, sales of that product and complements complements both rise. When the price of a product rises, sales sales of that product fall as do sales of complementary complementary products. products. There is an inverse correlation correlation between between price changes and units sold when two products are complements. Q5.5
During During the past past 40 years years the average average price price of a new new singlesingle-fami family ly home home has risen risen by a factor factor of ten, making the cost of housing housing prohibitiv prohibitivee for many America Americans. ns. Over Over the same time time frame, however, however, the number number of units sold per year has more than doubled. doubled. Are these these data inconsiste inconsistent nt with the idea of a downwar downward-sl d-sloping oping demand demand curve curve for new housing?
Q5.5
ANSWER
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No, these data data are consistent consistent with with a downward-sloping downward-sloping demand demand curve for for new housing. housing. For most goods and services, the price charged is the most important determinant of sales. Quantity Quantity demanded falls with with a price increase, increase, and rises with a price decrease. decrease. In the case of housing, the quantity quantity demanded would have fallen fallen as prices rose except for the overwhelming overwhelming influence influence of rising rising incomes incomes over time. Housing is is a normal good. Housing demand rises sharply during economic expansions and and contracts during recessions. recessions. Over long periods periods of time, housing demand rises rises slowly and steadily steadily as economic economic growth raises disposable disposable income. income. It is vital that students students separate out price and income effects when considering the demand for housing and other products. Q5.6
What would an upward-sloping demand curve imply about the marginal utility derived from consumption consumption? ? Why aren't upward sloping demand curves curves observed observed in the real world?
Q5.6
ANSWER
The law of diminishing marginal utility states that the marginal utility derived will fall as the consumption consumption of a given product increases increases during a given time interval. interval. This gives rise to a downward sloping demand curve for all goods and services. For a given demand curve to be upward sloping, an increasing marginal utility of consumption would would have to be operati operative. ve. This This is counter counter to human human nature. nature. Despite Despite myths myths that that sometimes arise concerning the pricing of some luxury goods, like perfume, there is no real-world evidence of upward sloping demand curves. In this regard, it is worth emphasizing the fact that an upward sloping demand curve implies that higher higher prices lead to an increase in quantity demanded. Under such a wonderful circumstance, firms would have an incentive to charge higher and higher prices (“to infinity infinity and beyond!”). beyond!”). Nothing would limit the firm’s ability ability to gain revenues revenues by raising prices. In the real world, higher prices prices eventually result result in some buyers being being priced priced out of the market market and to to an eventual eventual downturn downturn in revenues revenues.. Q5.7
How is a price price-con -consump sumption tion curve curve related related to a demand demand curve curve? ?
Q5.7
ANSWER
If income and the prices of other goods and services are held constant, a reduction in the price of a given consumption item causes consumers to choose different market baskets. baskets. The various various market market baskets baskets that maximize maximize utility utility at different different prices prices for a given given item item trace trace out the consumer consumer’s ’s price-cons price-consump umptio tion n curve. curve. For example, example, the pricepriceconsumption curve shows how the optimal consumption of both goods and services are affected affected by changing prices prices for services. A similar price-consum price-consumption ption curve could be used to illustrate how the optimal consumption of both goods and services are affected by changing prices prices for for goods. On the other other hand, the demand demand curve curve for services services shows shows
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how the quantity demanded of services rises in a response to a fall in the price for service services. s. A simila similarr individ individual ual demand demand curve could be used used to illustrat illustratee how the quantity demanded of goods rises in a response to a fall in prices for goods. Q5.8
An estima estimated ted 80% 80% increa increase se in the retail retail price of cigaret cigarettes tes is necessary necessary to cause cause a 30% drop in the number number of cigarettes cigarettes sold. sold. Would Would such a price increase increase help or hurt tobacco tobacco industry industry profits? profits? What What would be the likely effect on industry industry profits if this price boost boost was simply simply caused caused by a $1.50 $1.50 per per pack pack increa increase se in cigare cigarette tte excise excise taxes? taxes?
Q5.8
ANSWER
The price elasticity of demand for cigarettes is highly inelastic if an 80% increase in retail prices prices would cause cause only a 30% drop in the number number of cigarettes cigarettes sold. An arc price elasticity elasticity for cigarettes cigarettes on the order of EP = -0.375 (= -30%/80%) implies that tobacco industry revenues would rise sharply following following a big price increase. Since the variable variable costs of producing producing and selling selling cigarettes cigarettes would fall with with a 30% drop in the number of cigarettes sold, a significant industry-wide increase in cigarette prices could cause industry profits to explode on the upside. It is less certain what would happen to tobacco industry profits if the price increase described above were the simple result of an increase in excise taxes on each pack of cigarettes cigarettes sold. For example, a new $1.50 tax on a pack of cigarettes cigarettes would increase increase typical retail retail prices from $1.88 $1.88 to $3.38 per pack, or by roughly 80%. If all new revenues went to the government in the form of taxes, then industry revenues and variable variable costs would both fall fall by 30% following following a 30% drop in unit sales. Unless the tobacco industry cut fixed expenses, industry profits would fall in the long run. On the other hand, with such inelastic demand and government-sanctioned price increases, the tobacco industry might be expected to lobby hard for further profit-enhancing price increases in the post tax-increase era. Q5.9
Individua Individuall consumer consumer deman demand d declines declines for inferio inferiorr goods goods as personal personal incom incomee increases increases because because consumer consumerss replace replace them with more desirable desirable alternative alternatives. s. Is an inverse inverse relation between demand and national income likely for such products?
Q5.9
ANSWER
No, not usually. usually. Theoretically, Theoretically, it is plausible plausible that the aggregate aggregate demand for some goods goods and serv service icess might might be count counter er-cy -cycl clica ical, l, actual actually ly risi rising ng during during a busine business ss recession recession and falling during an economic economic boom. After all, if individual individual consumers consumers shift from hamburger to steak as incomes rise, wouldn't it seem reasonable to expect hamburger hamburger demand to rise with with a fall in income? The answer answer seems to be yes and no. Yes, as incomes rise, demand from high-income individuals declines for “inferior” goods like hamburger, bus rides, and blue jeans as these consumers switch to more desirable substitutes such as porterhouse steak, automobiles, and designer clothing.
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However, as incomes rise, other low-income consumers move up the economic ladder. Perhaps for the first time, they are now able to afford hamburger, bus rides, and blue jeans. As a result, result, economy wide demand for so-called so-called inferior inferior goods may actually actually rise as income levels increase, albeit at a much slower pace than demand for other, more desirable products. Despite Despite a lack lack of empiri empirical cal evidence evidence,, the possib possibilit ility y of an inverse inverse relatio relation n between between aggregate product demand demand and income has intrigue intrigued d economists economists for a number of years. years. This This interest interest was original originally ly created created by an anomaly anomaly called called the “potato “potato paradox.” As legend has it, a Victorian Victorian economist economist named Robert Giffen Giffen discovered discovered that the potato crop failure of 1845 so depressed Irish incomes that the poor had to actually actually increase their consumption consumption of the now higher-priced potatoes. potatoes. Because they had to spend so much on potatoes, a necessary staple, the poor couldn't afford meat or other substitute substitutess and became even more dependent dependent than than before on potatoes. potatoes. Thus, potatoes potatoes became known as the classic classic case of the inferior inferior or, “Giffen,” “Giffen,” good. However, empirical evidence casts serious doubt on the credibility of such a chain of events. After studying studying the historical historical record, record, economists Gerald Gerald Dwyer and Cotton Cotton Lindsay found little support for the notion that the consumption consumption of potatoes potatoes in Ireland incre increase ased d duri during ng this this period. period. So widespr widesprea ead d were were the the effe effect ctss of the fung fungus us Phytopht Phytophthora hora infestans infestans that it destroyed roughly one-half of the 1845 potato crop in Ireland after inflicting serious damage in America, in England, and on the Continent. After September 1846 and until harvest time in August of the following year, few potatoes potatoes could be bought at any price. Without Without imports imports and with a decrease in domestic supply, how could potato consumption by the poor possibly have risen during the Irish potato potato famine? Moreover, Moreover, there is no evidence that low potato potato prices during good years had a depressing effect on potato consumption by the poor, as would be necessary necessary to classify potatoes potatoes as an inferior good. Therefore, Therefore, it is only reasonable to conclude that the increase in potato prices and the decrease in income caused by the Irish potato famine resulted resulted in a decline in the aggregate consumption of potatoes. As is typical for goods in general, a positive relation between potato demand and economy wide wide income seems seems to hold. hold. Despite Despite the legend legend of the potato potato paradox, paradox, concrete concrete evidence evidence of an inverse inverse relatio relation n betwee between n aggreg aggregate ate demand demand and income income remains remains elusive. (See: Gerald P. Dwyer, Jr. and Cotton M. Lindsay, “Robert Giffen and the Irish Potato,” America American n Econom Economic ic Review Review, March 1984, 188-192.) Q5.10
In the United States, high-wag high-wagee workers workers shun public public transit transit and drive cars to work. work. These same high-income individuals often support massive subsidies for public transit. Use Use the the conc concep eptt of reve revea aled led pref prefer eren ence ce to expl explai ain n the the publ public ic dem demand and for for transportation. Can you explain this consumer consumer behavior by high-income individuals? individuals?
Q5.10
ANSWER
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High-wage High-wage workers often often shun public transit and drive their cars to work. This stems from the fact that time in transit is a compelling consideration for such workers. Getting where they need to go, and getting there on time, matter much more than the out-of-pocket costs associated with driving to work. For example, Kobe Bryant’s time is valuable, valuable, and he drives to work. His time is much too valuable valuable to be spent waiting for the bus. At the same time, it is fascinating to note the almost universal political support for subsidize subsidized d mass mass transit transit among high-inco high-income me individ individuals uals.. While While high-incom high-incomee individuals have a documented revealed preference for driving to work, they prefer that others, others, including the less fortunate, fortunate, take public transit. transit. This makes makes economic sense from the standpoint that subsidized mass transit might reduce road and parking congestion, and thereby make driving to work easier for high-income individuals. These same high-income individuals often support massive subsidies for public transit. On the other hand, it is less obvious why high-income individuals might support woefully woefully underutilized underutilized mass transit. Perhaps they view support support for such mass transit as a type of income transfer to the poor and other beneficiaries of mass transit (government employees, equipment manufacturers, and so on). SELF-TEST SELF-TEST PROBLEMS PROBLEMS AND SOLUTIONS SOLUTIONS ST5.1
Individual Individual Demand Curve. Alex P. Keaton Keaton is an ardent ardent baseball baseball fan. The followin following g table shows the relation between the number of games he attends per month during the season season and and the total utility utility he derives derives from from baseb baseball all game game consum consumption ption:: Number Number of Baseball Games Games per Month
Total Utility Utility
0
0
1
50
2
90
3
120
4
140
5
150
A.
Construct a table showing Keaton's marginal utility derived from baseball game consumption.
B.
At an average ticket price of $25, Keaton can justify justify attending attending only one game per month. month. Calculate Calculate Keaton’s cost per unit of margina marginall utility utility derived derived from baseball game consumption at this activity level.
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109
C.
If the cost/margina cost/marginall utility trade-off trade-off found found in part B represents represents the most most Keaton is willing to pay for baseball game consumption, calculate the prices at which he would attend two, three, four, and five games per month.
D.
Plot Keaton's Keaton's baseball baseball game game demand demand curve. curve.
SOLUTION SOLUTION
A. Number of Baseball Games Per Month
Total Utility
Marginal Utility
0
0
--
1
50
50
2
90
40
3
120
30
4
140
20
5
150
10
B.
At one baseball baseball game per month, MU = 50. Thus, at a $25 price per baseball baseball game, the cost per unit of marginal utility derived from baseball game consumption consumption is P/MU = $25/50 = $0.50 or 50¢ per util.
C.
At a maximum acceptable price of 50¢ per util, Keaton's maximum acceptable price for baseball game tickets varies according to the following schedule: Maximum Acceptable price at 50¢ per MU
Number of Games Per Month
Total Utility
Marginal Utility MU = ΔU/ΔG
0
0
--
--
1
50
50
$25.00
2
90
40
20.00
3
120
30
15.00
4
140
20
10.00
5
150
10
5.00
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Keaton's baseball ticket demand curve is:
D.
Keaton's B aseball Ticket D emand Curve $35
$30
Dem andcur ve $25
$20
$15
$10
$5
$0 0
1
2
3
4
5
Number o f games
Elasticity Elasticity Estimation. Estimation. Distinctive Designs, Inc., imports and distributes dress and sports watches. watches. At the end of the company's fiscal fiscal year, brand manager manager Charlie Pace has asked you to evaluate sales of the sports watch line using the following data:
ST5.2
Month
Number of Sports Sports Watches Sold
Sports Watch Watch Advertising Advertising Expenditures Expenditures
Sports Watch Watch Price, P
Dress Watch Watch Price, P D
July
4,500
$10,000 $10,000
26
50
August August
5,500
10,000 10,000
24
50
September
4,500
9,200
24
50
October
3,500
9,200
24
46
Novembe Novemberr
5,000
9,750
25
50
Decembe Decemberr
15,000 15,000
9,750
20
50
January January
5,000
8,350
25
50
February February
4,000
7,850
25
50
March March
5,500
9,500
25
55
Apr April
6,000
8,500
24
51
May
4,000
8,500
26
51
June
5,000
8,500
26
57
In particula particular, r, Pace Pace has asked asked you to estimate estimate relevant relevant demand demand elasticitie elasticities. s. Rememb Remember er that to estimate estimate the required required elasticities, elasticities, you should consider consider months months only when the other important factors considered in the preceding table have not changed.
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Also note that by restrictin restricting g your analysis analysis to consecu consecutive tive months, months, changes changes in any additio additional nal factor factorss not explic explicitl itlyy includ included ed in the analys analysis is are are less less likely likely to affect affect estimated elasticities. elasticities. Finally, the average arc elasticity of demand demand for each factor factor is simply simply the the average average of monthly monthly elasticitie elasticitiess calcula calculated ted during during the past past year. year. A.
Indicate Indicate whether whether there there was or was not a change in each each respective respective independ independent ent variable for each month pair during the past year.
Month-Pair Month-Pair
Sports Watch Watch Advertising Advertising Expenditures, Expenditures, A
Sports Watch Watch Price, P
Dress Watch Watch Price, P D
July-Aug July-August ust
_______ ___________ _____ _
________ ____________ ____
_______ ___________ _____ _
August-S August-Septe eptembe mberr
_______ ___________ _____ _
________ ____________ ____
_______ ___________ _____ _
September-October
____________
____________
____________
October-November
____________
____________
____________
Novembe November-De r-Decemb cember er
_______ ___________ _____ _
________ ____________ ____
_______ ___________ _____ _
December December-Jan -January uary
_______ ___________ _____ _
________ ____________ ____
_______ ___________ _____ _
January January-Febr February uary
_______ ___________ _____ _
________ ____________ ____
_______ ___________ _____ _
February February-Mar -March ch
_______ ___________ _____ _
________ ____________ ____
_______ ___________ _____ _
March-Ap March-April ril
_______ ___________ _____ _
________ ____________ ____
_______ ___________ _____ _
April-May April-May
_______ ___________ _____ _
________ ____________ ____
_______ ___________ _____ _
May-June May-June
_______ ___________ _____ _
________ ____________ ____
_______ ___________ _____ _
ST5.2
B.
Calculate and interpret the average advertising arc elasticity of demand for sports sports watche watches. s.
C.
Calculate and interpret the average arc price elasticity of demand for sports watches.
D.
Calcu Calculat latee and and interp interpret ret the avera average ge arc crosscross-pr price ice elasti elasticit cityy of demand demand between sports and dress watches.
SOLUTION SOLUTION
A.
Month-Pair
Sports Watch Advertising Expenditures, A
Sports Watch Price, P
Dress Watch Price, PD
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July-August
No change
Change
No change
August-September
Change
No change
No change
September-October
No change
No change
Change
October-November
Change
Change
Change
No change
Change
No change
December-January
Change
Change
No change
January-February
Change
No change
No change
February-March
Change
No change
Change
March-April
Change
Change
Change
April-May
No change
Change
No change
May-June
No change
No change
Change
November-Dec November-December ember
B.
In calcula calculating ting the arc adverti advertising sing elastic elasticity ity of demand, demand, only conside considerr consecu consecutive tive months when there was a change in advertising but no change in the prices of sports and dress watches: August-September
EA = =
∆Q ∆A
×
A2 + A1 Q2 + Q1
4,500 - 5,500 $9,200 - $10,000
×
$9,200 + $10,000 4,500 + 5,500
= 2.4
January-February
EA = =
∆Q ∆A
×
A 2 + A1 Q2 + Q1
4,000 - 5,000 $7,850 - $8,350
×
$7,850 + $8,350 4,000 + 5,000
= 3.6 On average, EA = (2.4 + 3.6)/2 = 3 and demand will rise 3%, with a 1% increase in advertising. Thus, demand appears appears quite sensitive sensitive to advertising.
Demand Demand Analy Analysis sis and and Estima Estimation tion
C.
113
In calculating the arc price elasticity of demand, only consider consecutive months when there was a change in the price of sports watches, but no change in advertising nor the price of dress watches: July-August
EP = =
∆Q
P 2 + P1 Q2 + Q1
×
∆P
5,500 - 4,500 $24 - $26
×
$24 + $26 5,500 + 4,500
= - 2.5 November-De November-December cember EP = =
∆Q
×
∆P
P 2 + P1 Q2 + Q1
15,000 - 5,000 $20 - $25
×
$20 + $25 15,000 + 5,000
= - 4.5 April-May EP = =
∆Q ∆P
4,000 - 6,000 $26 - $24
x x
P2 + P1 Q2 + Q1 $26 + $24 4,000 + 6,000
= -5 On average, EP = [(-2.5) [(-2.5) + (-4.5) (-4.5) + (-5)]/3 (-5)]/3 = -4. A 1% increase increase (decrea (decrease) se) in price will lead lead to a 4% decrease decrease (increase) (increase) in the quantity demanded. demanded. The demand for sports watches is, therefore, elastic with respect to price. D.
In calculating the arc cross-price elasticity of demand, we only consider consecutive months when there was a change in the price of dress watches, but no change in advertising nor the price of sports watches: September-October May-June E PX = =
∆Q ∆ PX
×
PX 2 + PX 1 Q2 + Q1
3,500 - 4,500
=3
$46 - $50
×
$46 + $50 3,500 + 4,500
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E PX = =
∆Q ∆ PX
×
PX 2 + PX 1 Q2 + Q1
5,000 - 4,000 $57 - $51
×
$57 + $51 5,000 + 4,000
=2 On average, EPX = (3 + 2)/2 = 2.5. Since EPX > 0, sports and dress watches are substitutes. PROBLEMS & SOLUTIONS SOLUTIONS P5.1
Utility Theory. Theory. Determine whether each of the following statements is true or false. Explain Explain why. why. A.
According According to the theory theory of consu consumer mer behav behavior, ior, more more is is always always better better..
B.
Consumers must understand how much one product is preferred over another in order to rank-order consumption alternatives.
C.
A market market basket basket is a descrip descriptive tive stateme statement nt that relates relates satisf satisfactio action n or well-being to the consumption of goods and services.
D.
The nonsatiation principle abstracts from time and place considerations.
E.
Marginal Marginal utility utility measures measures the consume consumer's r's overall overall level level of satisfactio satisfaction n derived derived from consump consumption tion activ activities ities
P5.1
SOLUTION SOLUTION
A.
True. Consumer behavior theory rests rests upon the “more is better” assumption regarding the utility tied tied to consumption. All goods and services services are desirable desirable in the sense of being able to satisfy consumer consumer wants. As a result, consumers will will always prefer more to less of any good or service.
B.
False. The consumer’s understanding of ordinal utility makes possible a rank ordering of pref prefer erre red d goods goods and servi service ces. s. Noti Notice ce that that kno knowl wledg edgee conce concerni rning ng comp comple lete te consumer preferences does not necessarily include understanding about how much one product is is preferred preferred over another. another.
C.
Fals False. e. A util utilit ity y funct function ion is a desc descri ripti ptive ve stat stateme ement nt that that rela relate tess sati satisf sfact actio ion n or well-being to the consumption of goods and services.
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D.
True. At any specific specific place and time, time, consumers consumers do become become sated. sated. Therefore, Therefore, the nonsatiation principle involves a certain amount of abstraction from time and place considerations. considerations. It is best considered considered within the context of money income where more money brings additional satisfaction or well-being.
E.
False. False. Whereas Whereas total utility utility measur measures es the consumer's consumer's overall overall level level of satisf satisfact action ion derived from consumption activities, marginal utility measures the added satisfaction derived from a one-unit increase in consumption of a particular good or service, holding consumption of other goods and services constant.
P5.2
Law of Diminishing Diminishing Marginal Marginal Utility. Indica Indicate te wheth whether er each each of the follow following ing statement statementss is true true or or false. false. Explain Explain why. why. A.
The law of diminishing marginal utility states that as an individual increases consumption of a given product within a set period of time, the utility gained from consump consumption tion event eventually ually declines. declines.
B.
When prices are held constant, a diminishing marginal utility for consumption decreases the cost of each marginal unit of satisfaction.
C.
Marginal Marginal utility utility measures measures the added added satisfactio satisfaction n derived derived from a one-unit increase increase in consump consumption, tion, holding consumpti consumption on of other other goods goods and services services constant.
D.
When goods are relatively scarce, the law of diminishing marginal utility means that the added value of another unit of goods will be small in relation to the added value of another unit of services.
E.
The law of dimini diminishi shing ng margi margina nall utility utility gives gives rise rise to a downw downward-slop ard-sloping ing demand curve for all goods and services.
P5.2
SOLUTION SOLUTION
A.
False. In general, general, the law of diminishing diminishing marginal marginal utility utility states that as an individual increases consumption of a given product within a set period of time, the marginal utility gained from consumption eventually declines.
B.
False. When prices are held constant, constant, a diminishing diminishing marginal marginal utility for consumption consumption increases the cost of each marginal unit of satisfaction.
C.
True. True. Wherea Whereass total total utilit utility y measur measures es the consume consumer's r's overall overall level of satisf satisfact action ion derived from consumption activities, marginal utility measures the added satisfaction
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derived from a one-unit increase in consumption of a particular good or service, holding consumption of other goods and services constant. D.
False. When goods are relatively scarce, the law of diminishing marginal utility means that the added value of another unit of goods will be large in relation to the added value of another unit of services.
E.
True. True. This law gives gives rise to a downward-s downward-slopi loping ng demand demand curve curve for all goo goods ds and services.
P5.3
Indifference Indifference Curves. Suggest briefly whether each of the following statements about indifference curves that show preferences between goods and services is true or false and defend your answer. A.
Cons Consum umer erss pref prefer er high higher er indi indiff ffer eren ence ce curv curves es tha that repr repres esen entt grea greate ter r combinations of goods and services to lower indifference curves that represent smaller smaller comb combinati inations ons of of goods goods and and service services. s.
B.
Indifferen Indifference ce curves curves slope downwar downward d because because if the quantity quantity of one consume consumer r product product is reduced, reduced, the quantity quantity of the other must must also decrease decrease to maintain maintain the same same degree degree of utility. utility.
C.
The slope of an indifference curve shows the rate at which consumers are willing to tradeoff goods and services.
D.
The fact that indifference curves do not intersect stems from t he “more is better” principle. principle.
E.
Indifferen Indifference ce curves curves bend inward inward (are convex convex to the origin) origin) becaus becausee if goods are relatively abundant, the added value of another unit of goods will be small in relation to the added value of another unit of services.
P5.3
SOLUTION SOLUTION
A.
True. Consumers Consumers prefer more to less, less, so they prefer higher higher indifference indifference curves that represent represent greater combinations of goods and services to lower indifference indifference curves that represent smaller combinations of goods and services.
B.
False. Indifference curves slope slope downward. This stems from the fact that the slope of an indiffer indifference ence curve curve shows shows the tradeof tradeofff involve involved d betwee between n goods goods and service services. s. Because consumers consumers like both goods and services, services, if the quantity of one is reduced, the quantity of the other must increase to maintain the same degree of utility.
Demand Demand Analy Analysis sis and and Estima Estimation tion
117
C.
True. True. The slope slope of an indiffere indifference nce curve shows shows the rate rate at which consume consumers rs are willing to tradeoff goods and services. For example, when goods are relatively scarce, the law of diminishing marginal utility means that the added value of another unit of goods goods will be larg largee in rela relati tion on to the the added added value value of anothe anotherr unit unit of serv service ices. s. Conversely, when goods are relatively abundant, the added value of another unit of goods will be small in relation to the added value of another unit of services.
D.
True. Indifference Indifference curves curves do not intersect. intersect. Holding goods constant, constant, an an indifference indifference curve involving a greater greater amount of services must give greater satisfaction. Similarly, holding services constant, an indifference curve involving a greater amount of goods must give greater greater satisfaction. satisfaction. This stems from from the fact that goods and services services both provide consume consumerr benefits, benefits, and reflects reflects the the “more is is better” better” principle. principle.
E.
True. Indifference curves bend inward (are convex to the the origin). For example, when goods are relatively scarce, the law of diminishing marginal utility means that the added value of another unit of goods will be large in relation to the added value of another unit of services. services. Conversely, Conversely, when goods are relatively relatively abundant, abundant, the added value of another unit of goods will be small in relation to the added value of another unit of services.
P5.4
Budget Constraints Constraints . Holdin Holding g all else else equal, equal, indica indicate te how each of the followin following g changes would affect a budget constraint that limits consumption of goods (Y) and services services (X). Explain Explain your your answ answer. er. A.
Deflation Deflation that unifo uniformly rmly drops drops the price price of of all goods goods and servic services. es.
B.
Inflation Inflation that consis consistently tently increases increases the price price of all all goods goods and and services services..
C.
Techn Technica icall change change that reduce reducess the price of goods, goods, but leaves leaves the price price of services services uncha unchanged nged..
D.
Economi Economicc growth growth that that boosts boosts the level level of dispos disposable able incom income. e.
E.
Government-mandated Government-mandated health care coverage for workers that boosts the price of goods goods by 3% 3% and and increase increasess the price of service servicess by 5%. 5%.
P5.4
SOLUTION SOLUTION
A.
Deflation that drops the price of all goods and services results in a parallel rightward (outward) (outward) shift in the budget constraint. Holding income income constant, lower prices make it possible for consumers to buy more goods and services with the same total amount of spending. spending. This beneficial beneficial impact impact on consumption consumption is similar to that following following an increase in income.
118
B.
Chapter 5
Inflation that increases the price of all goods and services results in a parallel leftward (inward) shift in the budget constraint. Holding income constant, higher prices reduce the amount of goods and services that consumers can buy with a fixed amount of spending. This harmful impact on consumption is similar to to that following a decrease in income.
C.
Technical change that reduces the price of goods, but leaves the price of services unchanged results in an outward rotation rotation of the budget constraint along the goods (Y) axis. axis. After After such a change, change, the budget budget line interse intersects cts the Y axis at a higher point, indicating indicating that a greater amount of goods can be purchased purchased with a fixed budget. The amount of services that can be purchased for a fixed amount is unaffected by such a change, and the X intercept (services axis) of the budget constraint is unaffected by such a change.
D.
Economic growth that boosts the level of disposable income results in a parallel rightward rightward (outward) (outward) shift in the budget constraint. Holding prices prices constant, growing income makes it possible for consumers to buy more goods and services with the same total amount of spending. spending. This beneficial beneficial impact on consumption consumption is similar to that following deflation that drops the price of all goods and services.
E.
Government-mandated health care coverage for workers that boosts the price of goods by 3% and increases increases the price of services services by 5% will have a negative impact on consumption of both goods and services, but the negative impact will be worse in the case of services. services. Following Following such a change, the relative relative price of services services will rise relative to the price of goods. The new budget line will move inward 3% along the X axis reflecting the fact that a fixed budget will only be able to buy 97% of the previously previously affordable affordable goods. The new budget line will move inward inward 5% along the Y axis reflecting the fact that a fixed budget will only be able to buy 95% of the previously previously affordable affordable services. services. The net effect is similar similar to a decrease decrease in income followed by a unilateral increase in the price of services.
P5.5
characterized by the following Elasticity. Elasticity. The demand for personal computers can be characterized point point elasticitie elasticities: s: price elastic elasticity ity = - 5, cross-pri cross-price ce elasticity elasticity with with software software = - 4, and income elasticity = 2.5. 2.5. Indicate whether whether each of the following statements is true or false, false, and explain explain your your answe answer. r. A.
A price price reduction reduction for person personal al compute computers rs will will increase increase both both the the number number of units units demanded and the total revenue of sellers.
B.
The cross-price elasticity indicates that a 5% reduction in the price of personal computers will cause a 20% increase in software demand.
C.
Demand Demand for personal personal computers computers is price price elastic elastic and computer computerss are cyclical cyclical normal goods.
D.
Falling Falling software software prices prices will increase increase revenues revenues received received by sellers sellers of both computers and software.
E.
A 2% price price reduction reduction would would be necessary necessary to overcom overcomee the effects effects of a 1% decline in income.
P5.5
SOLUTION SOLUTION
A.
True. True. A price reductio reduction n always always increase increasess units units sold, sold, given a downwar downward d sloping sloping demand curve. curve. The negative negative sign on the price elasticity elasticity indicates indicates that this is indeed indeed the case here. The fact that price elasticit elasticity y equals -5 indicates that demand demand is elastic with respect to price, and that a price reduction will increase total revenues.
B.
False. The cross-price cross-price elasticity elasticity indicates indicates that a 5% decrease in the price of software programs programs will will have the effect of of increasing increasing personal personal computer computer demand demand by 20%.
C.
True. Demand Demand is price price elastic elastic (see part part A). Since the income elastici elasticity ty is positive, positive, personal computers computers are a normal good. Moreover, Moreover, since the income elasticity elasticity is greater than one, personal computer demand is also cyclical.
D.
False. Negative Negative cross-price elasticity elasticity indicates that personal computers computers and software are compliments. compliments. Therefore, Therefore, falling software software prices prices will increase increase the demand for comput computers ers and result resulting ing revenues revenues for sellers sellers.. However However,, there there is no inform informatio ation n concerning the price elasticity of demand for software, and therefore, one does not know the effect of falling software prices on software revenues.
E.
False. A 2% reduction reduction in price will cause a 10% increase increase in the quantity quantity of personal computers computers demanded. demanded. A 1% decline in in income will cause cause a 2.5% fall in demand. demand. These changes will not be mutually offsetting.
P5.6
effort to reduce reduce excess excess end-of-th end-of-the-mo e-model-y del-year ear inventory inventory,, Optimal Pricing. In an effort Harrison Harrison Ford offered offered a 1% discount discount off the average average price price of 4WD Escape Escape Gas Electric Electric Hybrid Hybrid SUVs SUVs sold during during the month month of August. August. Custome Customerr response response was wildly enthusiastic, with unit sales rising by 10% over the previous month's level.
P5.6
A.
Calculate the point price elasticity of demand for Harrison Ford 4WD Escape Limited Limited SUVs SUVs sold sold during during the month month of of August. August.
B.
Calculate the profit-maximizing price per unit if Harrison Ford has an average wholesale (invoice) cost of $23,500 and incurs marginal selling costs of $350 per unit. unit.
SOLUTION SOLUTION
VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV. εP = ΔQ/Q ÷ ΔP/P = 10%/-1% = -10 -10 (Hig (Highly hly elast elastic ic)) WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW W. The prof profit it--maxi maxim mizin izing g pr price ice ca can be be fou found nd using sing the opti optima mall pr price ice for formu mula la:: P* =
MC/(1 + 1/εP)
= ($23, ($23,50 500 0 + $350) $350)/[ /[1 1 + 1/(-10 1/(-10)] )] = $26,500
P5.7
P5.7
Beach Cafe recently reduced reduced appetizer prices prices from Cross-Price Cross-Price Elasticity Elasticity . The South Beach $12 to $10 for afternoon “early bird” customers and enjoyed a resulting increase in sales sales from 90 to 150 orders orders per day. day. Beverage Beverage sales sales also increase increased d from 300 to 600 units per day. A.
Calculate the arc price elasticity of demand for appetizers.
B.
Calculate the arc cross-price elasticity of demand between beverage sales and appetizer prices.
A.
Holding Holding all else else equal, equal, would would you you expect expect an an addition additional al appetize appetizerr price decrease decrease to $8 to cause both appetizer appetizer and beverage revenues revenues to rise? Explain
SOLUTION SOLUTION
A.
EP =
∆Q ∆P
×
(150 - 90) ($10 + $1 2) P 2 + P1 = × = - 2.75 Q 2 + Q1 ($10 - $12) (150 + 90)
B.
E PX =
B.
P5.8
∆Q ∆ PX
×
600 - 300) ($10 + $12) P X 2 + P X 1 (600 × = = - 3.67 ($10 - $12) (600 600 + 300) Q 2 + Q1
Yes, the |EP| = 2.75 > 1 calculated in part A implies an elastic demand for appetizers and that an additional price reduction will increase appetizer revenues. EPX = -3.67 < 0 indicates that beverages and appetizers are complements. Therefore, a further decrease in appetizer prices will cause a continued growth in beverage unit sales and revenues. Alternatively, If P = a + bQ, then $12 = a + b(90) and $10 = a + b(150). Solving for the demand curve gives P = $15 - $0.033Q. At P = $12, total revenue is $1,080 (= $12 × 90). If P = $10, total revenue is $1,500 (= $10 × 150). At P = $8, total revenue is $1,680 (= $8 × 210). In any case, to determine the profit effects of appetizer price changes it is necessary to consider revenue and cost implications of both appetizer and beverage beverage sales.
Income Elasticity Elasticity . Ironside Ironside Industri Industries, es, Inc., is a leading leading manufactu manufacturer rer of tufted tufted carpeting under under the Ironside brand. Demand for Ironside's Ironside's products is closely tied to the overall pace of building and remodeling activity and, therefore, is highly sensitive to change changess in natio national nal income income.. The The carpe carpett manuf manufact acturi uring ng indust industry ry is highly highly competitive, so Ironside's demand is also very price-sensitive. During During the past past year, Ironsi Ironside de sold 30 30 million million square square yards yards (units) (units) of carpeting carpeting at an average wholesa wholesale le price of $15.50 per unit. This year, year, household household income is
expect expected ed to ssurge ssurge from $55,50 $55,500 0 to $58,50 $58,500 0 per year year in a boomi booming ng econom economic ic recovery. A.
Without any price change, Ironside's marketing director expects current-year sales to soar to 50 million million units units because because of rising rising income. income. Calculate Calculate the implied income arc elasticity of demand.
B.
Given the projected rise in income, the marketing director believes that a volume of 30 million units could be maintained despite an increase in price of $1 per unit. On this basis, calculate the implied arc price elasticity of demand.
Holding all all else equal, equal, would would a further further increase increase in in price result result in in higher higher or lower lower C. Holding total revenue? P5.8
SOLUTION SOLUTION
A.
EI = =
∆Q ∆I
×
I 2 + I1 Q 2 + Q1
50 - 30 $58,500 - $55,500
×
$58,500 + $55,500 50 + 30
= 9.5 B.
Without Without a price increase, sales this year would would total 50 million units. units. Therefore, Therefore, it is appropriate appropriate to estimate estimate the arc price elasticity from a before-price-i before-price-increase ncrease base of 50 million units:
EP =
=
∆Q ∆
P
×
P 2 + P1 Q +Q 2 1
30 - 50
$16.50 - $15.50 = - 8 (Elastic)
$16.50 + $15.50 ×
30 + 50
C.
Lower. Lower. Since carpet carpet demand is in the elastic elastic range, EP = -8, an increase (decrease) (decrease) in price will will result result in lower lower (higher) (higher) total total revenues. revenues.
P5.9
retailerr of a wide variety variety of sporting sporting Cross-Price Cross-Price Elasticity. B. B. Lean is a catalog retaile goods goods and recreatio recreational nal products. products. Although Although the market market response response to the company company's 's spring spring catalog catalog was generally generally good, good, sales sales of B. B. Lean's Lean's $140 deluxe garment bag declined declined from 10,000 10,000 to 4,800 units. units. During During this period, period, a competito competitorr offered a whopping $52 off their regular $137 price on deluxe garment bags.
P5.9 A.
A.
Calcu Calculat latee the arc crosscross-pri price ce elasti elasticit cityy of demand demand for B. B. Lean' Lean'ss delux deluxee garment garment bag. bag.
B.
B. B. Lean's Lean's deluxe deluxe garmen garmentt bag sales sales recov recovered ered from 4,800 units units to 6,000 6,000 units units following following a price reduction reduction to $130 per unit. Calculate Calculate B. B. Lean's arc price elasticity of demand for this product.
C.
Assuming Assuming the same arc price elasticity elasticity of demand demand calculate calculated d in Part Part B, determine the further price reduction necessary for B. B. Lean to fully recover lost sales (i.e., regain a volume of 10,000 units).
SOLUTION SOLUTION
EPX =
=
QY 2-QY1 P X 2 -P X1
×
P X 2 + P X1 QY 2+QY1
4,800 - 10,000 $85 - $137
×
$85 + $137 4,800 + 10,000
= 1.5 1.5 (Subs (Substi titu tute tes) s) B.
EP =
=
Q 2 - Q1 P 2 - P1
×
P 2 + P1 Q 2 + Q1
6,000 - 4,800 $130 - $140
×
$130 + $140 6,000 + 4,800
= -3 (El (Elas asti tic) c)
C.
EP =
Q 2 - Q1 P 2 - P1
×
P 2 +P1 Q 2 + Q1
-3 =
10,000 - 6,000 P2 + $130 x 10,000 + 6,000 P2 - $130
-3 =
P 2 + $130 4( P 2 - $130)
-12P2 + $1,560 = P2 + $130 13P2 = $1,430
P2 = $110 This implies a further price reduction of $20 because: ΔP = $130 - $110 = $20 P5.10
P5.10
Enchantment ent Cosmetics, Cosmetics, Inc., offers a line of cosmetic cosmetic and Advertising Advertising Elasticity. Elasticity. Enchantm perfume perfume products products marketed marketed through through leading leading departme department nt stores. stores. Product Product Manager Manager Erica Erica Kane recently recently raised raised the suggested suggested retail retail price price on a popular popular line of mascara mascara products products from $9 to $12 following following increases increases in the costs of labor labor and materials materials.. Unfortuna Unfortunately, tely, sales dropped dropped sharply sharply from 16,200 to 9,000 units per month. In an effort to regain lost sales, Enchantment ran a coupon promotion featuring $5 off the new regular regular price. Coupon printing printing and distribution distribution costs totaled $500 $500 per month month and represented a substantial increase over the typical advertising budget of $3,250 per month. month. Despite Despite these these added added costs, costs, the promo promotion tion was was judged judged to to be a success, success, as as it proved proved to be highly highly popular popular with consumer consumers. s. In the period period prior to expiratio expiration, n, coupons were used on 40% of all purchases and monthly sales rose to 15,000 units.
A.
Calc Calcul ulat atee the the arc arc pric pricee elas elasti tici city ty impl implie ied d by the the init initia iall resp respon onse se to the the Enchantm Enchantment ent price price increase. increase.
B.
Calculate the effective price reduction resulting from the coupon promotion.
C.
In light of the price price reduction reduction associate associated d with the coupon coupon promotio promotion n and assuming no change in the price elasticity of demand, calculate Enchantment's arc advertising elasticity.
D.
Why might the true arc advertising elasticity differ from that calculated in part C?
SOLUTION SOLUTION
EP =
A.
=
∆
Q
∆
P
×
P 2 + P1 Q 2 +Q1
9,000 - 16,200 $12 - $9
×
$12 + $9 9,000 + 16,200
= -2 B.
The effective price reduction is $2 since 40% of sales are accompanied by a coupon: ΔP
= -$ -$5(0.4)
or
P2 = $12 $12 - $5(0. (0.4)
= -$2
= $10
ΔP = $10 - $12 = -$2 C.
To calculate the arc advertising elasticity, the effect of the $2 price cut implicit in the coupon promotion must first first be reflected. With just a price cut, the quantity demanded would rise to 13,000, because: EP
=
-2
=
-2
=
Q* - Q 1 P 2 - P1
×
P 2 +P1 Q* + Q 1
Q* - 9,000 $10 - $12
×
Q* + 9,000
- 11(Q* - 9,000) (Q* + 9,000)
-2(Q 2(Q* + 9,0 9,000)
= -11(Q* - 9,00 ,000)
-2Q* - 18,000
= -11Q* + 99,000
9Q*
$10 + $12
= 117,000
Q* = 13,000 Then, the arc advertising elasticity can be calculated as:
EA =
=
Q 2 - Q* A 2 + A 1 ×
A 2 - A 1 Q 2 + Q*
15,000 - 13,000 $3,750 - $3,250
×
$3,750 + $3,250 15,000 + 13,000
= 1 D.
It is important to recognize that a coupon promotion can involve more than just the independent effects of a price cut plus an increase in advertising as is implied in Part C. Synergistic Synergistic or interactive effects effects may increase advertising effectivenes effectivenesss when the promotion promotion is accompanie accompanied d by a price price cut. Similarly, Similarly, price price reductions reductions can have a much much larger impact impact when advertised. advertised. In addition, addition, a coupon is a price cut for only the most
price sensitive sensitive (coupon-using) (coupon-using) customers, customers, and may spur sales by much more than a dollar equivalent across-the-board price cut. Synergy between advertising and the implicit price reduction that accompanies a coupon promotion can cause the estimate in Part C to overstate the true advertising elasticity. elasticity. Similarly, Similarly, this advertising advertising elasticity will be overstated overstated to the extent that targeted price cuts have a bigger influence on the quantity demanded than similar across-the-board price reductions, as seems likely.
CASE STUDY FOR CHAPTER 5 Demand Estimation Estimation for for Mrs. Smyth’s Smyth’s Pies
Demand Demand estimation estimation for brand-nam brand-namee consumer consumer products products is made made difficult difficult by the fact that managers must must rely on proprietary data. There simply is not any publicly publicly available data which which can be used to estimate demand elasticities for brand-name orange juice, frozen entrees, pies, and the like--and like--and with good reason. reason. Competit Competitors ors would be delighted delighted to know profit profit margins margins across a broad array of competing products so that advertising, pricing policy, and product development development strategy could all be targeted for maximum maximum benefit. Product demand demand information is valuable and jealously guarded. To see the process that might be undertaken to develop a better understanding of product demand conditions, consider the hypothetical example of Mrs. Smyth's Inc., a Chicago-based food company. company. In early 2008, 2008, Mrs. Smyth's initiated initiated an empirica empiricall estimatio estimation n of demand demand for its gourmet gourmet frozen frozen fruit pies. pies. The firm is formula formulating ting pricing pricing and promoti promotional onal plans plans for the coming coming year, year, and managem management ent is interested interested in learning learning how pricing pricing and promotion promotional al decisions decisions might might affect sales. Mrs. Smyth's has been marketing marketing frozen fruit pies for several years, and its market market research department has collected quarterly data over two years for six important marketing areas, areas, including including sales quantity quantity,, the retail price charged charged for the pies, pies, local local advertis advertising ing and promotio promotional nal expenditu expenditures, res, and the price charged charged by a major major competin competing g brand brand of frozen frozen pies. pies. Statistical data published by the U.S. Census Bureau (http://www.census.gov) on population and disposable income in each of the six Metropolitan Statistical Areas were also available for analysis. It was therefore possible to include a wide range of hypothesized demand demand determinants in an empirical estimation estimation of fruit pie demand. demand. These data appear appear in Table 5.9. The following regression equation was fit to these data: Qit = b0 + b1 P P it Ait + b3 PX PX it Popit + b6 T Tit it + b2 A it + b4Y it it + b5 Pop i t + uit Q is the quantity of pies sold during the tth quarter; P is the retail price in dollars of Mrs. Smyth's frozen frozen pies; A represents represents the dollars spent spent for advertisin advertising; g; PX is the price, price, measured measured in dollars, dollars, charged for competing competing premium-quality premium-quality frozen fruit pies; Y is the median dollars of disposable income per household; Pop is the population of the market area; T is the trend factor (2006-1 = 1, . . . , 2007-4 = 8); and u it is a residual (or disturbance) disturbance) term. The subscript subscript i indicates the regional market from which the observation was taken, whereas the subscript t represents the quarter quarter during which which the observati observation on occurred. occurred. Least Least squares squares estimation estimation of the regression regression equation on the basis of the 48 data observations (eight quarters of data for each of six areas) resulted in the estimated regression coefficients and other statistics given in Table 5.10.
A.
Describe Describe the economic economic meaning meaning and statistica statisticall significa significance nce of each individua individual l independent independent variable included in the Mrs. Smyth's frozen fruit pie demand equation.
B.
Interpret Interpret the coefficie coefficient nt of determin determination ation (R 2 ) for the Mrs. Smyth's Smyth's frozen frozen fruit pie demand equation.
C.
Use the regression model and 2007-4 data to estimate 2008-1 unit sales in the Washington-Arlington-Alexan Washington-Arlington-Alexandria dria market.
D.
To illustrate use of the standard error of the estimate statistic, derive the 95 percent and and 99 perce percent nt confid confiden ence ce interv intervals als for 2008-1 2008-1 unit unit sales sales in the Washin Washingto gtonn Arlington Arlington-Ale -Alexand xandria ria marke market. t.
CASE STUDY SOLUTION A.
The individual coefficients for the Mrs. Smyth's pie demand regression equation can be interpreted interpreted as follows. The intercept intercept term, 529,774, has no economic economic meaning in this instanc instance; e; it lies lies far outside outside the range of observe observed d data data and obviously obviously cannot cannot be interpreted interpreted as the demand for Mrs. Smyth's frozen fruit pies when all the independent variables variables take on zero values. The coefficient coefficient for each independent variable indicates indicates the marginal relation between that variable and sales of pies, holding constant the effect of all the other other variables in the demand demand function. For example, example, the -122,607 coefficient for P , the price charged for Mrs. Smyth's pies, indicates that when the effects of all other demand variables are held constant, each $1 increase in price causes causes quarterl quarterly y sales sales to decline decline by roughly roughly 122,607 pies. pies. Simila Similarly rly,, the 5.838 coefficient for A, the advertising and promotion variable, indicates that for each $1 increase in advertising during the quarter, roughly 5.838 additional pies are sold. Demand for Mrs. Smyth's pies rises by roughly 29,867 pies with every $1 increase in competitor prices, and a $1 increase in the median disposable income per household leads leads to roughly roughly a 2.043-u 2.043-unit nit increase increase in quarterl quarterly y pie demand. demand. Similar Similarly, ly, a one person increase in the population population of a given market area leads to a small 0.030-unit increas increasee in quarterl quarterly y pie demand. demand. Finally Finally,, the coefficie coefficient nt for the trend trend variable variable indicates that pie demand is growing in a typical market by roughly 2,815 units per quarter. Mrs. Smyth's is enjoying secular growth in pie demand. Individu Individual al coeffici coefficient entss provide provide useful useful estima estimates tes of the expected expected margina marginall influ influenc encee on dema demand nd follo followi wing ng a one-un one-unit it chang changee in each each respe respect ctive ive varia variabl ble. e. However, However, they are only estimates. estimates. For example, example, it would be very unusual unusual for a $1 increase in price to cause exactly a -122,607-unit change in the quantity demanded. The actual effect effect could be more or less. For decision-maki decision-making ng purposes, purposes, it would be helpful to know if the marginal influences suggested by the regression model are stable or instead tend to vary widely over the sample analyzed. In general, if it were known with certainty that Y = a + bX , then a one-unit change in X would always lead to a b-unit change in Y . If b > 0, X and Y are directly related; if b < 0, X and Y are inversely related. If no relation relation at all holds between X and Y , then b = 0. Although the true parameter b is unobservable, its value is projected by the coefficient estimate. To
be statisticall statistically y reliable, reliable, the coefficient coefficient estimate estimate must be large relative to its standard standard deviation over the sample. In Mrs. Smyth's frozen fruit pie demand equation, the coefficient estimates for P ), PX ) and population ( Pop Pop) are all more price ( P ), advertising ( A), competitor price ( PX than twice as large as their respective standard errors. Therefore, it is possible to reject the hypothesis that each of these independent variables is unrelated to pie demand with 95 percent confiden confidence. ce. These These coeffic coefficient ient estimate estimatess sugges suggestt an especi especiall ally y strong strong rela relati tion on betw betwee een n pie pie dema demand nd and the P, A, and Pop variabl variables. es. Each Each of of these these coefficient estimates is over three times as large as its underlying standard error and therefore is statistically significant at the 99 percent confidence level. Once the effects of these these indep indepen enden dentt varia variable bless have have been been const constra raine ined, d, there there is no addit additio ional nal independent influence noted for income (Y ) or the time trend variable (T ). ). B.
The coefficient of determination R2 = 0.871 or 87.1 percent indicates that the regression model has explained explained 87.1 per cent of the total total variation in pie demand. demand. This is a very satisfactory level of explanation for the the model as a whole. The corrected coefficient of 2 determination R = 0.85 0.852 2 or 85.2 85.2 per per cent cent is a rela relati tive vely ly mo mode dest st down downwa ward rd 2 adjustment from R ; it suggests that the high level of explanatory power achieved by the regression regression model cannot be attributed attributed to an overly small sample sample size. Finally, Finally, the F statistic statistic is used to indicate whether a significant significant share of variation variation in the dependent variable has been explained by the regres regression sion model. The hypothesis actually tested tested is that the dependent dependent Y variable variable is statisticall statistically y unrelated to all the independent independent X variabl variables es included included in the model. model. If this hypothesi hypothesiss cannot cannot be rejecte rejected, d, variati variation on explained by the regression is small. The critical value for F is denoted as F f 1 , f 2 , where f 1, the degrees degrees of freedom for the numerator, numerator, equals k - 1, and f 2, the degrees of freedom for the denominator, equals n - k . For example example,, the the F statistic for this example involves f 1 = k - 1 = 7 - 1 = 6, and f 2 = n - k = 48 - 7 = 41 degrees of freedom. Also note that the calculated F6,41 = 45.16 > 3.29, the critical F 6,40 6,40 value for the α = 0.01 or 99% confidence confidence level shown shown in Appendix B. This means there there is less than a 1% chance of observing such a high F statistic when there is no link between the dependent Y variable and the entire group of X variables. Given the the ability ability to reject reject X variables. the hypothesis of no relation at the 99% confidence level, it will always be possible to reject this hypothesis at the lower, 95% and 90%, confidence levels.
C.
To project the next quarter's sales of frozen fruit pies in the Washington, DC-ArlingtonAlex Alexand andri riaa mark market et,, the the comp company any mu must st simp simply ly ente enterr expec expecte ted d valu values es for for each each independ independent ent variable variable in the estimate estimated d demand demand equation. equation. Mrs. Mrs. Smyth' Smyth'ss expects expects an average price for its its pies of $7.95, advertising advertising expenditures expenditures of $30,487. The prices of competing pies are expected to be $5.69; median disposable income per household is $53,235; population in the market area is 5,445,382 persons; and the quarter for which demand is being forecast forecast is the ninth quarter quarter in the model. Inserting Inserting the appropriate appropriate unit values into the demand equation results in an estimated demand of: Q = 529 529,77 ,774 4 – 122,60 122,607( 7(7.9 7.95) 5) + 5.83 5.838( 8(30 30,48 ,487) 7) + 29,8 29,867( 67(5.6 5.69) 9) + 2.0 2.043( 43(53 53,23 ,235) 5)
+ 0.030(5,445,382) + 2,815(9) =
200,430 pies.
Mrs. Smyth's could forecast the total demand for its pies by forecasting sales in each of the six market areas, then summing these area forecasts to obtain an estimate of total pie demand. Using the results results from the demand estimation estimation model and data from each individual market, it would also be possible to construct a confidence interval for total total pie demand demand based on the standard standard error error of the estimate. estimate. Note (Note: Be sure to remember that 2008-1 is time period T = 9!) D.
Although 200,430 is the best estimate of pie demand for the Washington, DC-ArlingtonAlexandria market during the 2008-1 period, it is highly unlikely that precisely this number of pies will be sold. Either more or less may be sold, depending on the effects of other factors not explicitly accounted for in our pie demand estimation model. The standard error of the estimate is a very useful statistic because it allows us to construct a range range or confi confide dence nce interv interval al with within in whic which h actu actual al sale saless are are likel likely y to fall. fall. For example, sales can be projected to fall within a range of ± 2 standard errors of the 200,430 expected expected sales level level with a confidence confidence level of 95 per cent. cent. There is only a 5 per cent chance that actual sales in the Washington, Washington, DC-Arlington-Al DC-Arlington-Alexandria exandria market market during the coming coming period will fall outside outside this range. Similarly, Similarly, there is a 99 per cent chance that actual sales will fall in the range of 200,430 ± 3(67,584), 3(67,584), and only a 1 per cent chance that actual sales will fall outside this range.
