2013년 1월 31일 목요일

[발췌] Aggregate Supply and Demand: An Explanation of Chapter III of the General Theory


지은이: Paul Wells
출처: The Canadian Journal of Economics and Political Science, vol. 28, No. 4 (Nov. 1962), pp. 585-590

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In Chapter III of The General Theory of Employment, Interest and Money Keynes provides the reader with two conceptually different and unrelated summaries of his short-run theory of employment. He expresses these two brief accounts in terms of three macroeconomic relations:
  • an aggregate demand function that is the sum of consumer and investment spending;
  • an aggregate supply function that states the proceeds entrepreneurs must obtain from the sale of output if a given level of employment is to be maintained; and
  • what we may call an "expected proceeds" function that relates the receipts entrepreneurs expect to receive from the sale of output to the volume of employment necessary to produce the output. 

Because Keynes does not show explicitly the connection between his two summaries, and because he employs two relations that today seem still to puzzle many economists, students of the General Theory are likely to find this important chapter difficult, if not impossible, to understand. This is highly unfortunate, for we aim to show that this chapter constitutes a very eloquent and valuable epitome of Keynes's short-run theory of employment.

I. Keynes's First Summary

The first of Keynes's brief accounts runs as follows:
It follows that in a given situation of technique, resources and factor cost per unit of employment, the amount of employment, both in each individual and industry and in the aggregate, depends on the amount of proceeds which the entrepreneurs expect to receive from the corresponding output. For entrepreneurs will endeavour to fix the amount of employment at the level which they expect to maximise the excess of the proceeds over the factor cost.
  Let Z be the aggregate supply price of the output from employing N men, the relationship between Z and N being written Z=Φ(N), which can be called the ^Aggregate Supply Function^. Similarly, let D be the proceeds which entrepreneurs expect to receive from te employment of N men, the relationship between D and N being written D=f(N) , which can be called the ^Aggregate Demand Function^.
  Now if for a given value of N the expected proceeds are greater than the aggregate supply price, i.e. if D is greater than Z, there will be an incentive to entrepreneurs to increase employment beyond N and, if necessary, to raise costs by competing with one another for the factors of production, up to the value of N for which Z has become equal to D. Thus the volume of employment is given by the point of intersection between the aggregate demand function and the aggregate supply function; for it is at this point that the entrepreneurs' expectation of profits will be maximised.[1]

To understand this passage we need to attach definite meanings to Keynes's aggregate supply function, Z=Φ(N), and to D=f(N), which Keynes calls, unluckily, an "aggregate demand" function, but which we shall call an "expected proceeds" function so as not to confuse this relation with the sum of consumer and investment spending.

1. ^The aggregate supply function^ is a relation between employment, N, and a sum of money receipts, Z, that states the aggregate revenues entrepreneurs must receive from the sale of output if they are to maintain a given level of employment. This function ^does not^ state the actual receipts entrepreneurs do receive from the sale of output that results from a given level of employment; it simply expresses, for each volume of employment, the minimal receipts which must be forthcoming to support various levels of employment.

To establish the exact relation between employment and the necessary receipts entrepreneurs must obtain we need to assume that: (a) the problem of aggregation has been solved, (b) perfect competition exists, (c) a given money wage rate w obtains, (d) varying amounts of X, final output measured in real terms, are produced with a fixed amount of capital equipment together with varying amounts of labour. Thus the short run aggregate production function may be written as X=X(N). In addition we shall make the customary assumptions[2] concerning the shape of this function, namely, that X'>0, X''<0, and X'''=0.

Under conditions of perfect competition firms adjust their rates of output until marginal cost, w/X', equals the per-unit price of output, P. Thus we have the following microeconomic equilibrium condition holding for all firms in the economy.

(1.1) P = w/X'

Multiplying both sides of this equation by X, total physical output of the final good produced by all firms in the economy, gives us the corresponding macroeconomic equilibrium condition.

(1.2) PX = (w/X')X

Since the product PX is simply the sum total of all expenditures on final output, and is, in equilibrium, equal to Z, the sume of money receipts necessary to support the amount of employment necessary to produce an output X, we may rewrite equation (1.2) as

(1.3) Z = (w/X') X

This equation states the necessary sum of money, Z, entrepreneurs must receive if they are to maintain a rate of output X. The relation we seek to define, however is between the variable Z and N, not between Z and X. To find this relation we replace X in equation (1.3) by Xbar N, where Xbar denotes the average productivity of labour. Thus Xbar N is simply the total output produced by a given amount of labour N. This substitution yields the exact form of Keynes's elusive aggregate supply function.

(1.4) Z = (w Xbar)/X' N

This equation states the minimal proceeds, Z, entrepreneurs must earn from the sale of output if the established level of employment, N, is to be maintained. If the actual receipts accruing to entrepreneurs exceeds (falls short of) Z, then employment will rise (fall) until equation (1.4) satisfied. 

Because Xbar/X', the elasticity of output with respect to employment, ^decreases^ as employment increases,[3] this relation is drawn, Figure 1, convex to the abscissa. This means that in order for higher levels of employment to be established proportionately larger increments in expenditure and receipts are necessary. An additional property of this function is that it is not defined for points beyond Nf (Figure 1), the size of the labour force

2. ^The expected proceeds function^ states that the proceeds, D, entrepreneurs expect to realize from the sale of output resulting from the employment of a certain amount of labour. These proceed are simple the product of the price expected by entrepreneurs, P~, and the physical output they produce, X. If we assume that the expected price is a diminishing function of output, then both P~ and X, and their product D, are functions of the level of employment. This function is concave to the absissa (Figure 1) because of diminishing marginal returns in production and because of the assumed inverse relation between the expected price and employment. Thus, in the minds of entrepreneurs, given increments in employment produce constantly decreasing additions to expected proceeds.

From the definitions we have give these two relations, and from the implicit assumptions of Keynes that expected proceeds will equal realized revenues, it follows that ^expected^ profits will be maximized if sufficient labour is employed to equate expected proceeds, D, to the aggregate supply of output, Z. For if D = Z, the P~X = (w/X')X, and the expected price will equal the marginal cost of production. Thus the intersection of these two curves at point a(Figure 1) illustrates the expected equilibrium level of employment, Ne, according to the first of Keynes's two summaries. As can be seen from the diagram this equilibrium is stable barring changes in any of the parameters of the system. At a higher(lower) level of employment, marginal cost would exceed (fall short of) the expected price and entrepreneurs would make the appropriate adjustment in their rates of output.

Strangely enough, in this account of his theory of employment Keynes makes no direct use of one of his major contributions to economic theory, The Principle of Effective Demand, for in this summary the unknowns are simply employment, output, and expected proceeds. The relations necessary to determine their equilibrium values are the aggregate supply function, the production function, and the price expectations of entrepreneurs.


II. The Second Summary

Keynes expresses his second summary in the forms of five separate points. They are:
(... ...)
(... ...)

From the above two summaries we may conclude that Chapter III of the General Theory teaches us, contrary to many of the popularized accounts of this book, that ^expectations^ and ^supply^, as well as demand, play important roles in Keynes's short run theory of employment. Though one may agree with Patinkin's oft-repeated charge that Keynesian economics "overlooks the supply side of the commodity market"[6] it is clear that the General Theory does not.[7]

[7] Additional support for this conclusion is to be found in chapters 20 and 21 of the General Theory, and in H. Neisser, "Keynes's Aggregate Supply Function: Further Comments," Economic Journal, LXXI, 850-2.

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