The Simple Keynesian Keynesian Model of o f Income Determination
Introduction The model introduced here is the Simple Keynesian Model of Income Determination. The principle tool of analysis in this model is the µaggregate demand¶. The focus of this model is only the goods market and the influence of the money market on the goods market is abstracted away. There are ce cerrtain ass ssu ump mpttions on whi hich ch this model is built. It is assumed that prices do not change at all and that firms are willing to sell any amount of output at the given level of prices (the aggregate supply
Introduction The model introduced here is the Simple Keynesian Model of Income Determination. The principle tool of analysis in this model is the µaggregate demand¶. The focus of this model is only the goods market and the influence of the money market on the goods market is abstracted away. There are ce cerrtain ass ssu ump mpttions on whi hich ch this model is built. It is assumed that prices do not change at all and that firms are willing to sell any amount of output at the given level of prices (the aggregate supply
Determina Determination tion of Equilibrium Output It is important to know the meaning of aggregate demand. Simp Simply ly st stat ated ed,, ag aggr greg egat ate e de dema mand nd is th the e to tota tall amount of goods demanded in the economy. Aggregate demand (AD) is equal to the sum of consumption spending (C), investment spending (I), government purchases (G) and net exports (NX). AD = C + I + G + NX
Equilibrium Output Equilibrium level of output is that level of output at which the quantity of output produced is equal to the quantity demanded. However, it was seen earlier that any level of output, Y, was defined as being equal to C + I + G + NX. Given our definition of equilibrium output above and the definition of level of output Y, does it mean that all levels of output are equilibrium levels of output? The answer is µno¶. The concept of aggregate demand is in the µex-
In other words, aggregate demand tells us the total quantity of goods and services that people want to buy. However, national income accounts are all in the ex-post sense. Thus, consumption and investment in national income accounts means the amount of goods actually bought (need not be equal to the amount of goods wished to be bought). In particular, investment measured in national accounts includes involuntary or unintended inventory changes which occur when firms find themselves selling more or fewer goods than they had planned to sell.
We thus need to distinguish between the actual aggregate demand measured in an accounting context and the economic concept of planned (desired, intended) aggregate demand. In national income accounts, actual aggregate demand is always equal to the actual level of output (Y). This is in the ex-post sense. However, this is not the sense in which we are using the concept in our model. It is in the ex-ante sense and thus intended aggregate demand need not always be equal to the actual levels of output (Y). Therefore all levels of output are not equilibrium
Equilibrium level of output is that level of output at which the total desired spending on goods and services (desired aggregate demand) is equal to the actual level of output (Y). All other concepts introduced below are in the ex-ante sense (what is desired) and not in the ex-post sense (what is actually done).
Consumption Function Consumption expenditure is a very important part of aggregate demand, generally the largest component of aggregate demand. Of the many variables influencing consumption expenditure, income is the most important. The relationship between consumption and income is described by the consumption function. We assume that consumption demand increases linearly with increase in level of income: C = a + b Y; a>0, 0
C
C=a+bY
a 0
The Consumption Function
Y
The slope of the consumption function is equal to µb¶. It indicates the marginal propensity to consume (MPC). The marginal propensity to consume is the increase
In a two sector economy, income is either spent or saved, there are no other uses to which it can be put.
It follows that any theory that explains consumption is equivalently explaining the behavior of saving.
Let us derive the savings function (relationship between savings and income) from the consumption function.
As mentioned earlier, income can either be spent or saved.
Thus, Y=C+S; Which gives us S=Y-C Making use of the consumption function, we get
From the above savings function, it can be seen that when consumption increases linearly with income, so do savings. (1-b) gives the marginal propensity to save (MPS), which gives the increase in savings per unit increase in income. The sum of MPC and MPS has to be equal to one. For instance, if MPC = 0.8, then MPS = 0.2. Planned Investment (I), Government Purchases (G) and Net Exports (NX) We have now specified one component of aggregate demand, the consumption demand. For the time being, assume that the other components of aggregate demand I, G and NX are
Let the constant levels of investment, government purchases and net exports be indicated by I, G, and NX respectively. Now that we have all the components of aggregate demand defined, let us derive the equation of aggregate demand in terms of income. AD = C + I + G + NX = a + b Y + I + G + NX = ( a + I + G + NX ) + b Y =A+bY Where, A = a + I + G + NX and A is a constant. In the below figure, we have both the consumption function and the aggregate demand
AD
AD = A+ b Y
C=a+bY A I + G + NX a Y
Notice that AD line is parallel to the consumption line because the other components of aggregate demand are assumed to be constant. Part of aggregate demand A is independent of the level of income, or autonomous and the other part bY is dependent on income and output.
Equilibrium Income The next step is to use the aggregate demand function AD, to determine the equilibrium level of income and output. The equilibrium level of income is that level of income for which aggregate demand equals output (which in turn equals income). The 450 line which you see in the figure serves as a reference line that translates any horizontal distance into equal vertical distance. Thus, anywhere on the 45 0 line, the level of aggregate demand is equal to the level of output. The level of income at which the aggregate demand
We see from the figure that at an income level Y* the aggregate demand curve cuts the 450. At Y*, aggregate demand is equal to income and thus is the equilibrium income and output. At any income level below Y*, firms find that demand exceeds output and that their inventories are declining. This unintended decline in inventories is shown as I < 0 in the figure. In order to make up for the decline in inventories, firms increase production. Conversely, for output levels above Y*, firms find inventories piling up (I > 0) and therefore cut production. As the arrows show, this process leads to output level Y*, at which current production equals planned aggregate spending and unintended inventory changes are equal to zero.
Now, let us derive the formula for equilibrium output. At equilibrium, output is equal to aggregate demand.
AD I
>0
AD = A+ b Y
C=a+bY
A I <0
a 450 Y
Y = AD Y=A+bY Y(1-b) = A Y =A / (1-b) = (a + I + G + NX) / (1-b) From the above equation, we can see that larger A is, (for a given b) the higher is the equilibrium level of income. That is, the larger is the equilibrium level of income. Similarly, for a given A, the greater slope (b) of the AD AD cu curv rve e, th the e hig igh her is the eq equ uil ilib ibri riu um le lev vel of income.
MULTI MULTIP PLIER The concept of multiplier is a very useful one. The multiplier tells what the increase in the level of equilibrium income would be for a unit increase in autonomous spending.
In the above figure, AD 1 is th the e in initi itial al ag aggr greg egat ate e demand function with autonomous spending equal to A1. After an increase in autonomous spending by A the new autonomous spending is A 2 (= A1 + A) and the corresponding aggregate demand function is AD2. The equilibrium output corresponding to aggregate demand function AD, is Y* 1, and for AD2 it is Y*2. The multiplier is given by the ratio of increase in equil ilib ibri riu um in inco come me to in incr cre ease in autonomo mou us spending. Denotin Denoting g the value of the multiplier m ultiplier by . = ( Y*2 - Y*1) / (A2-A1)
Substituting Y*1 by A1 / (1-b) and Y*2 by A2 / (1-b) Then, = 1 / (1-b), 1-b is the marginal propensity to save.
Thus = 1 / MPS i.e. the value of the multiplier is the reciprocal of the marginal propensity to save. The larger the marginal propensity to consume, the lower is the marginal propensity to save, and thus larger is the value of the multiplier. Since MPS is less than one, the multiplier in our model is greater than one. However, it may be noted that when we extend our model, there may be circumstances in which the
The Government Sector The government can affect the equilibrium output in two ways. One, by changing its expenditure on goods and services, and two, by changing the income tax rate. So far, we have assumed that consumption expenditure is directly dependent on income. A better assumption would be to make consumption a function of disposable income. By making consumption directly dependent on disposable income rather than on income, we will be able to study the role of taxes in the determination of income. Let us first see how the government can influence the level of output by varying its expenditure on goods and services.
Assume as before that, the government expenditure is autonomous expenditure. If the autonomous government expenditure is raised, it would shift the aggregate demand function upwards and thereby result in an increase in the equilibrium income. This increase in equilibrium income would be equal to change in G (G) times the multiplier (). If the government reduces its expenditure, the opposite would happen. It should be noted that equilibrium output is not the same as full employment output and thus the two need not be equal. Equilibrium output depends on the slope and the
AD
AD2
AD1
A
G
a 450 Y Y*2 = YF
Y*1 Input, Output
If total autonomous expenditure (A) or the marginal propensity to consume (b) or both are less than what is required to achieve an equilibrium level that is equal to full employment output, we would have a situation of unemployment (of labor and other factors of production). What can the government do to raise the equilibrium output to the level of full employment output? Obviously, by raising autonomous government expenditure. But by how much? From above figure, it is seen that the gap in equilibrium output and full employment output is Y FY1*. This should be the increase in income as a result of
We have, G. = YF-Y1* G = (YF-Y1* ) / (YF - Y1*) = (full employment output - equilibrium output). The difference between the full employment output and the equilibrium output (or the actual output) is termed as the output gap. Thus, the desired increase in government expenditure to attain full employment is equal to the ratio of output gap (at the equilibrium level) and the multiplier.
APPENDIX CONSUMPTION AND SAVING FUNCTIONS We now move from the accounting or definitional aspects of consumptions and saving to the more interesting question of the determinants of consumer behavior or consumption function. The most important determinant of private consumption and saving is the level of private disposable income, which, in the absence of government, is equal to total income. In technical language both consumption and saving are positive functions of the level of income. That is, at higher levels of income the private
At lower levels of income, they will both consume less and save less. This is not to say that the amounts of consumption and saving depend solely on the level of disposable income. Many other factors help determine how any given level of disposable income will be divided between consumption and saving. Moreover, changes is these other factors can shift the consumption function up or down. This can lead to more or less consumption at each level of income. Some of the more important of these factors are
1.
The Stock of Wealth
Wealth has been regarded as the important determinant of consumption.
most
Other things being constant, a wealthy community might be expected to consume a larger part of its income than a group with the same income but less wealth. The larger the wealth possessed by a person, the lower would be the desire to add to future wealth, by reducing consumption spending. Consumption, therefore, will be higher with more wealth economies. µWindfall¶ capital gains (or loss) also have an
2.
Expectations
The consumption of a person is also influenced by expectations regarding future movements in income and prices. For example, when future levels of income are expected to be higher then present levels, the consumer community is likely to consume more out of its current disposable income. 3. Taxation Policy Taxation measures of the government may influence the average propensity to consume (APC) i.e. C/YD and bring about shifts in consumption function.
An increase in direct taxes will reduce disposable income at all levels of income and the reverse may occur when taxes are reduced. Similarly, a tax structure based on progressive taxation leads to increase in the level of consumption expenditure.
4.
Distribution of total household income by size of household income
For example, total saving out of a given level of total household income is likely to be higher if a greater part of the total income accrues to highincome classes, rather than to low-income groups.
5. Age composition of the population Both elderly and young families have higher propensities to consume than families in their middle year. A shift in age composition could shift consumption and saving function. Some consumption functions for India and other countries The following table represents the different time series estimates of MPC for India. The latest estimate available in case of India is given by M Thampy (1982). He has given estimates of various formulations of the consumption function for the period 1950-51 to
Estimates of MPC as per the Estimates of different Authors Authors
Estimates of MPC
Narasimham
0.9
Period 1919-1952
Iyengar and Murthy
0.71
1948-1955
Tintner and Narayanan
0.67
1948-1957
Chowdury
0.89
1930-1955
Moorthy and Thore
0.66
1948-1955
Iyenger and Singh
0.81
1948-1958
K Murthy
0.81
1948-1961
M Thampy
0.82
1951-1979
For the naive formulation he obtained following estimates: C = 19.60 + 0.824 Y D
the
Where, C = Private consumption spending, 1970-71 prices (billion Rs.) YD = Personal disposable income 1970-71 prices (billion Rs.) In terms of per capita consumption, C/N = 91.69 + 0.733 (Y D/N) Where, N is population, C, YD as above. Thus, marginal propensity to consume (MPC) out of personal disposable income is 0.82, while MPC with per capita real income is 0.73.
An estimation of the consumption function indicates that the MPC for India is 0.82. Next table gives the estimates of MPC for various countries. In general, the MPC is high for low income countries. Ethiopia and Israel have the highest MPC and Japan has the lowest MPC. India¶s estimates of MPC fall between the estimates given for these two countries.
Mar ginal Propensity to Consume in a Selected Number of Countries
S.No. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10
Country
Argentina Australia Bulgaria Brazil Canada Ceylon Chile Cyprus Ethiopia France
MPC S.No. 0.81 0.76 0.80 0.83 0.77 0.87 0.89 0.86 0.90 0.76
11. 12. 13. 14. 15. 16. 17. 18. 19. 20.
Country
Ghana India Iraq Israel Italy Japan Pakistan
MPC
0.87 0.82 0.75 0.90 0.78 0.66 0.89 South Korea 0.88 Taiwan 0.83 West 0.72 Germany
Others Factors Influencing Consumption Besides income, as shown by some studies, there are several factors that affect consumption function. Even in reduction to disposable income also, an aspect that needs to be studied is whether the relevant income is that of the current period or that of the previous period. According to Duesenberry, consumption did not fall proportionately to a fall in income, as the consumption behavior in the USA is used to a certain standard of living. They could not let down their consumption levels below a point.
This is a situation where household find it easier to adjust to rising incomes than falling incomes. This is what we call the ³rachet effect´. As we have discussed, state of assets also has an impact on consumption behavior. The larger the current stock of assets, the less is the motive for saving out of a given disposable income. Therefore, the propensity to consume which varies from one income group to another is higher for lower income groups. In a latest study of consumption behavior, M Friedman has made a distinction between income actually received i.e. measured income and income on which consumers base their spending i.e. permanent income. A similar distinction is drawn between measured and permanent consumption.
Friedman suggests that individual consumes a constant proportion of the present value of income while maintaining his holding of wealth intact. He maintains permanent consumption is proportional to permanent income, the proportionality being dependant upon various economic and demographic factors. There is another theory of consumer behavior based on the pattern of earnings of an individual in his lifetime. This theory is associated with Ando Modigliani and Brumberge. It attempts to explain the empirical evidence or the specification of the consumption function by reference to the pattern of lifetime earnings of the average
Steady State Level of Consumption in the Long Run Consider Consumption function of the form Ct = a + b Yt d + g Ct-1 Where, Ct = Consumption expenditure for the current year a = Autonomous consumption b = Short run MPC Yt d = Disposable personal income for the current year g = Coefficient indicating the relation between current period consumption and previous period consumption Ct-1 = Previous period consumption expenditure
This consumption function considers the µhabit persistence¶ of consumers, is captured by the g. In the long run you can reach a steady state level of consumption where your consumption expenditure year after year will be constant. That is, Ct = Ct-1 Therefore, the consumption function in the long run under steady state level of consumption is; Ct = a + b Yt d + g Ct (Since Ct = Ct-1) Ct ± g Ct = a + b Y td Ct (1 ± g) = a + b Yt d Ct = [a / (1-g)] + [b / (1-g)] Yt d This is the long run consumption function under steady state level of consumption. Now, autonomous consumption is [a / (1-g)] and long run
Investment Function In this section, we discuss the factors that determine investment function. Investment is the most volatile of the major components of aggregate demand and output because of the operation of the multiplier mechanism. Why is investment so volatile? What are the determinants investment in an economy?
of
the
level
of
What type of policy decisions will affect decisions to invest? These are the basic questions to which we seek
Investment spending, as discussed earlier, is the addition to the stock of real assets. An investment demand function indicates the values of output demanded for investment purposes at each possible rate of interest, the later denoted by r. Most of the components of Investment demand are demands by business for output with which to maintain or increase stocks of capital goods, these demands are presumably motivated by a desire of profits perhaps a desire to maximize their profits. For this purpose they compare the expected
Demand, notably expenditures by households for new residential constructions, may not be profit motivated. However, even these Investment demands presumably arrive at decisions by balancing expected benefits and costs, and other conditions being constant they will presumably buy less when the cost to them is higher. Interest costs account for an important part of the carrying changes of owning a house for households. An investment demand function is a typical demand curve showing the relation of quantity
In this case the price of loanable funds or the interest rate on investable funds is measured along the horizontal axis. The values of output demanded for investment are measured along the vertical axis. The II curve depicts the size of investment demand at the various possible levels of r. From the point of view spenders for investment, r is the cost. If they get the money to finance investment by borrowing from others, r is the annual interest rate they must pay to lenders. If they finance their investment spending by using
Then it is the interest rate they sacrifice by using the money rather than by lending is to someone else. It is therefore plausible to assume that, other things remaining the same, a rise of interest rates will decrease the actual investment demand for output and a fall of interest rates will stimulate it. Thus, the primary variables that enter into investment function for a given capital stock are income and the rate of interest. Therefore, we write in general terms, I = f ( y, r) f y > 0; f i < 0
As in the case of consumption function, if we ignore the interest rate, investment function can be written as I = f (y) = + Y
( and > 0)
The parameter is autonomous component of investment, independent of income and measures the marginal response of the investment to change in income. The investment demand function can also be stated as I = ± (I/r) r Where, = a positive constant. It is the intercept on the vertical axis and establishes the location of the I function.
I/r = the marginal responsiveness of investment to the interest rate. I/r is to be interpreted as a positive.
I2 I0 I1
I1 = f(Y1) I0 = f(Y0)
O
The investment function allowing for the effect of income. Let the initial income level be Y 0 , is the initial rate of interest be r 0 and the investment function be f(Y 0). If investment is strictly a function of the rate of interest, a rise in the rate of interest will reduce investment to I 1. However, if income rises to Y 1, the entire investment demand function shifts to the right and becomes f (Y1). Consequently, at interest rate r 1 the level of investment becomes I 2. Therefore, both the rate of interest and investment
Consequently, income change explains the observed fact that investment and the rate of interest move in the same direction over the business cycle, falling during periods of recession. If investment were not a function of the level of income, we would confine to a single investment demand curve and investment would then have to decline whenever the rate of interest increases. We are trying to make it oversimplified by assuming a single interest rate in the market. In fact, there are many rates. Moreover, other terms of lending and borrowing may change: the length of time for which lenders
The risks that they will take at any given interest rate, the amount of security demand for loans. Nevertheless, it will be convenient to let r represent the height of the structure of interest rates and the annual cost of borrowed funds. In drawing any investment demand curve, we have assumed that all other conditions affecting demand are given and unchanged. But it is important to know what determines the pos ition of the demand curve. To answer such questions we need to know the motivations of those who spend for investment, and the nature of the benefits they balance against risks in arriving at decisions as to whether and how much
Mar ginal Efficiency of Investment Spending (MEI) The bulk of investment spending is made by business firms¶ intent on making net profits. Hence, in determining whether or not to make a capital expenditure, they are interested in net revenues over costs. This applies to purchases for replacement as well as to net additions to capital. Decisions as to the amount of new investment therefore depend on a comparison of interest costs and the expected annual rate of return on new investment. The latter has been given many names, including marginal revenue product of capital and marginal
We shall use the latter term and define it as the annual amount ( stated as a percentage of the cost of the capital goods) that the acquisitions of the new capital goods is expected to add to the enterprise¶s net revenues after deduction of all additional costs of operation except interest costs on the money used. We shall view the marginal efficiency of investment as a schedule or function showing the various amounts of new investments that are expected to yield at least various rates of return. The demand for investment is derived from the marginal±efficiency-of±investment schedule.
Entrepreneurs intent on maximizing their profits tend to buy those types and amounts of capital that they expect to yield a rate of return in excess of the interest cost of the money used to purchase them. Presumably, they will not buy capital whose expected rate of return is below the interest rate. Note that we have emphasized that the expected annual rate of return is a prime consideration in the selection of a new investment. Entrepreneurs select their investments on the basis of their expectations as to future yields. Their decisions are based on the best forecasts they can make.
They cannot be certain that the returns will meet their expectations because many types of capital yield returns only over a long period and much can change in the interim. Even then, they must act and take decisions. Of the many factors that affect the schedule of the marginal efficiency of investment, some of the more important are enumerated below. 1. Size and Composition of Stock of Capital Goods If the existing stock of capital goods is largely obsolete and too small to produce most economically the output currently demanded, large amounts of new investment may be expected to
But if the existing stock of capital goods is efficient and very large relative to the current demand for output, only small amounts of new investment will be profitable. If there is already excess capacity, business firms may refrain from replacing some of their equipment when it wears out.
2.
Rate of Innovation
If the rate of innovation is high, it may be profitable to undertake much new investment in order to produce the new types of products or to use new and more economical processes of production.
3. Expected Future Behavior of Demands for Output
If demands for output are expected to rise rapidly, much new investment may be expected to yield high profits.
If demands for output are expected to remain at existing levels and the present stock of capital goods is adequate, the demand for new capital goods may be largely a replacement demand. And if demands for output are expected to decline, potential spenders for investment may not replace their capital equipment when it wears out.
4. Expectations and Business Confidence Expectations and business confidence as to future wages, other costs, taxes, and government policies also determine investment efficiency. Estimates of the probability of new investment may be greatly affected by expectations regarding the future course of these factors. If business sector thought that future economic conditions will be depressed they will be reluctant to invest. On the contrary, when business sector see the likelihood of a sharp economic recovery in the near future, they begin to plan for plant expansion. Thus investment demand to a greater extent depends
Many studies have been conducted to find out the influence of interest rate on investment decisions. In addition, surveys have been conducted to find out the reactions of business firms to changes in interest rates. According to these studies, even in developed economies, investments decisions are not strongly influenced by changes in interest rates. Interest rates play a minor role in investments in plant and equipment and particularly in those industries where technological innovations and changes are quick. A type of capital goods may become obsolete in a short time and hence, firms expect capital goods to
Therefore, the expected payback period is small and such conditions interest rate need not play a crucial role. However, even in such cases also a steep rise in interest rates affect investment decisions. Investment is highly durable equipment and housing are affected by changes in interest rates. Another area, where the interest rates have a greater influence is inventory investment or stocks held by the firms. Even here, there is chance of firms passing on the increased cost of interest in the form of higher prices on the products they produce.
