The Simple Keynesian Model of Income Determination

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Introduction The model introduced here is the Simple Keynesian Model of Income Determination. The principle tool of analysis in this model is the aggregate 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 certain assumptions on which 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 curve is perfectly elastic). 2

Determination of Equilibrium Output It is important to know the meaning of aggregate demand. Simply stated, aggregate demand is the total 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

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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 no. The concept of aggregate demand is in the exante sense. 4

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.5

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 output. 6

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).

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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, 00

AD = A+ b Y

C=a+bY AI 0; fi < 045

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. r is the interest rate. 46

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)

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r0 Investment Function

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The investment function allowing for the effect of income. Let the initial income level be Y0 , is the initial rate of interest be r0 and the investment function be f(Y0). If investment is strictly a function of the rate of interest, a rise in the rate of interest will reduce investment to I1. However, if income rises to Y1, the entire investment demand function shifts to the right and becomes f (Y1). Consequently, at interest rate r1 the level of investment becomes I2. Therefore, both the rate of interest and investment are higher than before. 48

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 will make funds available. 49

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 to spend for investment. 50

Marginal 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 efficiency of investment. 51

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 enterprises 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 marginalefficiency-ofinvestment schedule.52

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.53

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 yield high rates of return. 54

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.55

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.56

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 on expectations and forecasts of future events. 57

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 pay for themselves in three to five years. 58

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.59

However, it may not be that effective. If the interest rates are raised very steeply, they definitely affect inventory stocks held by the business sector. The Indian experience shows the same situation in recent times.

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