Aggregate demand curves: Static and dynamic

Aggregate demand curves: Static and dynamic

DAVID J. SMYlH Louisiana State Unioersity Baton Rouge, Louisiana Aggregate Demand Curves: Static and Dynamic* The correct treatment of aggregate...

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DAVID J. SMYlH Louisiana

State

Unioersity

Baton

Rouge,

Louisiana

Aggregate Demand Curves: Static and Dynamic* The correct treatment of aggregate demand curves has been a topic of debate in recent articles. The present paper defends the conventional derivation and interpretation of the aggregate demand schedule. It shows that the critics have failed to distinguish clearly between aggregate demand curves appropriate for comparative statics analysis and dynamic aggregate demand curves that shift from period to period

1. Introduction The conventional aggregate demand schedule is derived by changing the price level in an IS/LM system. This yields the desired or planned level of expenditure, the effective demand for goods, at different price levels. In recent articles Rabin and Birch (1982) and Hall and Treadgold (1982) argue that the curve so derived is not the economy’s effective demand curve for goods. The present paper rebuts the Rabin and Birch (RB) and Hall and Treadgold (HT) criticisms, arguing that they fail to distinguish between static and dynamic aggregate demand schedules. ’

2. The RB and HT Analyses In Figure 1, AD is the aggregate demand schedule and AS is the aggregate supply schedule. The supply of labor depends on the

*I have benefitted from comments on an earlier version of this paper (Smyth 1983) by Malcolm Treadgold and P.H. Hall, as well as those by Alan Rabin and Alan Woodfield. The responsibility for the final version is mine alone. ‘Two other recent criticisms of the aggregate demand curve are Perry (1981) and Henry and Woodfield (1985). The Hall and Woodfield article led to an exchange-Owen (1987), Dalziel (1987), and Henry and Woodfield (1987). Ftao (1986) is a critique of some aspects of HT, and Hall and Treadgold (1987) is a reply to Ftao. To keep the present paper focused, discussion will be limited to the RB and HT papers.

of Macroeconomics, Winter 1989, Vol. Journal Copyright 6 1989 by Louisiana State University 0164-0704/89/$1.50

11, No. Press

1, pp.

133-140

133

Daoid J Smyth AS

P

L

0

Y, v,=T Figure

Y 1.

real wage rate, so AS is vertical.2 Equilibrium output is P and the equilibrium price level is P. RB, HT, and I all agree that, with price level, P, and output, Y, AD represents the volume of real desired or planned expenditure, or effective demand for goods. But suppose the price level is Pr. What then? RB (1982, 236) write . . . suppose the economy is represented by . . . a point on the AS curve but off the AD curve. Given price level P1, actual income (output) is represented by Y2. The goods market is not in equilibrium since the economy is not on the AD curve. Thus . . . [Y,] represents the economy’s desired expenditure on (effective demand for) goods . . . assuming that output (income) is equal to Y1. But in this case, output is given by Y2! Hence the economy’s effective demand for goods cannot be [Y,].” The HT (1982, 39) argument The AD curve indicates that at mand will be at a level of Y1 if the usual assumption that firms’ the AS schedule indicates that output actually supplied will be

is the following. . . . [PI] . . . aggregate deoutput is at Y1. However, on supply plans are carried out, at price level . . . [P,] . . . at . . . [Y,]. ”

‘RB and HT draw similar figures. They assume that the supply of labor depends on the money wage rate so the AS curve is upward sloping, not vertical. HT (1982, 38, 44) refer to the possibility of a perfectly elastic (horizontal) AS curve until full employment output is reached; however, it is not possible to derive such a curve horn profit-maximizing behavior-for a proof, see Holmes and Smyth (1974).

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Aggregate

Demand

Curves

Hence, as Y, differs from Y,, planned expenditure will differ from YL. The RB and HT arguments are similar. Both sets of authors are led to conclude that excess supply for goods cannot be represented by AS minus AD at any price level because planned expenditure will diverge from the AD line (RB 1982, 236; HT 1982, 40). There are two problems with the RB and HT analyses. First, they plug the value of Y = YZ into the aggregate demand curve. Second, it is assumed that output is determined on the AS schedule. These cause RB and HT to be confused about the distinction between static (equilibrium) and dynamic (disequilibrium) analyses. 3. Disequilibrium in the AS-AD Model Inserting the value of Y = Ye into the aggregate demand curve involves a misinterpretation of what the AD curve is. Except in equilibrium, at price level P and output level Y, the AD curve does not tell us what expenditure and output actually are. The AD curve is a static one. It asks the question: What level of expenditure and output will clear the IS/LM markets at different price levels? For these markets to be cleared simultaneously, it is necessary that planned expenditure and output be equal. At price level P1 the level of expenditure and output that clears the IS/LM markets is Y,. Whether output is Y1 or not depends on the position of the aggregate supply curve. Given the AS curve in Figure 1, output may or may not be at level Y1. Certainly Y, is not an equilibrium position where the IS/LM and labor markets are simultaneously cleared. But it is a feasible disequilibrium position with the IS/LM markets in equilibrium and the labor market in disequilibrium so that the system as a whole is in disequilibrium. To know what output is with price level P1 we have to tell some story about how the economic system behaves in disequilibrium. RB and HT develop essentially the same story. However, they are misled in two ways. They do not realize that many other stories are possible and that their choice of story has implications for the static AD curve. The RB and HT stories run like this. At price level P1 actual output is given by planned output YZ. Y, is greater than Yi. So income is not Y1 and hence expenditure differs from Y,.3 This is a 3According to RB (1982, (1982, 39) does not constrain

237), e ff ec t’ we demand will lie between effective demand in this way.

Y, and

Y,; HT

135

David J. Smyth particular dynamic scenario, but only one of an infinite number that are possible. Moreover, it begs a lot of questions. For instance, if expenditure is less than Y2, inventories must accumulate. Do firms entirely ignore this? Or do they allow for it in the next period and produce less than is determined by AS? It is clear that we are in the midst of a dynamic story but one that is incomplete. The particular stories told by RB and HT have expenditure with price level P1 diverging from Yr. This is a disequilibrium expenditure level with IS/LM markets not in equilibrium. It does not represent a point on an AD curve. The AD curve as usually drawn is correct. What RB and HT have represented is a particular point on a particular dynamic AD curve. There are an infinite number of these dynamic AD curves corresponding to the infinite number of possible dynamic assumptions about disequilibrium behavior. Just because the IS/LM markets are in disequilibrium at price level P1 and output Y2 does not mean that they will not be in equilibrium at price level P1 and output Y,. For there to be equilibrium in the IS and LM markets expenditure and output (planned and actual) must be equal. But these values need not be the same as the output (planned and actual) on the supply side.4 Clearly, then, Y, - Yi does indeed measure excess supply at price level Pi. It is the difference between the output that will clear the labor market at price level P, and the output that will clear the IS/LM markets at price level P,. We may then make the standard Walrasian assumption that the percentage change in the price level is proportional to excess demand for goods, given at price PI by -(Yz - Y,) = Y1 - Y,. What disequilibrium assumption should we make to determine the level of output? The assumption that Y is given on the AS curve made by RB and HT is a strange one that is not common 4A special case of the RB and HT analyses, and one described by HT, is Rowan’s (1975, 394-95) aggregate demand schedule. Rowan’s curve is derived from a standard aggregate supply and demand framework with two modifications. First, the nominal wage rate is taken to be given. Second, output from the aggregate demand schedule is substituted into AD. The resulting schedule obtained by Rowan lies between the AD and AS schedules and is upward sloping for prices less than the price level at which the aggregate supply schedule becomes vertical (because all labor is employed). However, what Rowan views as an aggregate demand schedule is not really one; Rowan’s schedule shows the disequilibrium values of expenditures at different price levels given his dynamic assumptions of fixed nominal wages and output determined on the AS schedule. Note that Rowan makes no other dynamic assumptions; for instance, the unintended inventory accumulation or decumulation resulting from differences between output and expenditure does not affect output.

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Demand

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in the literature. One possibility, usually associated with the Walrasian adjustment process, is the “principle of voluntary exchange” or “short side of the market” assumption by which output is determined by the lesser of supply or demand-see, for instance, Barro and Grossman (1976). Here, with price level PI, output would be given by Yi. The second type of approach is firmly rooted in the tradition of Marshall (1920) and Hicks (1939). Output and price level are determined by dynamic short-period supply and demand curves which shift from period to period. In any period the intersection of these short-run curves generates “temporary equilibria.” Shifts in the dynamic short-period curves may occur through patterns of time lags (as the result, for instance, of adjustment costs). Or the curves may shift as the result of divergences between expected and actual prices and through stochastic terms as in the rational expectations literature. With such dynamic processes in operation in general disequilibrium, output will be neither Y2 nor Y,.5

4. An Illustration of Static and Dynamic Aggregate Demand Curves It may be helpful to present an example of the temporary equilibrium approach. Suppose that we have the following very simple log-linear dynamic system, where 2, Y, P and P are the logarithms of expenditure, output (= income), the price level, and the expected price level, respectively, and t subscripts indicate time periods 2, = a0 + alY,-, + azP, , Y, = P + b,(P, - P;) ) Y, = 2, .

O 0.

a,
(1) (2) (3)

‘In their analysis, RB (1982, 236) go part of the way toward the latter approach when they write that “for each level of income there would be a unique effective demand curve. Thus there exists a whole family of effective demand curves (one for each level of income).” However, there is a much wider range of curves for price level Pr than they suggest (because they apply the constraint Y, = YJ. Also, they do not make the crucial distinction that these are short-period demand curves that shift from period to period, not the long-run, static, aggregate demand schedule that does not shift from period to period, which determines the equilibrium price level and output.

137

David J. Smyth In Equation (1) expenditure depends on lagged income and the price level; it is a dynamic aggregate demand curve. Equation (2) is a dynamic aggregate supply function in which the deviation of output from its equilibrium level is proportional to the unexpected price change, I’, - Pf. In (3) we make the assumption of short-run market clearing. Full equilibrium in the IS/LM markets requires that Y, = Yt-i = Z,, yielding the static aggregate demand schedule: a0 + 2,

Correspondingly,

=

a2Pt

l-al

the static aggregate

’ supply

schedule

Y, = P

is (5)

because equilibrium on the supply side requires P, = P:. Solving (4) and (5) gives full equilibrium values of output and price level as Y and [(l - a,)y - ao]/a,, respectively. The temporary equilibrium value of output and expenditure is obtained by solving Equations (l), (2), and (3). It is y, =

b

Ia0

- a,P + alblY,-,

+ azblPf (6)

b, - a2 The temporary

equilibrium P, =

price level is

a, - P + alY,-, + b,P,” b, - a2

*

(7)

RB and HT obtain their aggregate demand curve by imposing the condition that output be equal to Y. Substituting Y,-i = Y in (1) yields their aggregate demand schedule: 2, = a0 + a,P + a,P, .

(8)

Now if we assume market clearing, 2, = Y, = Y and the temporary equilibrium values of Y, and Pt are Y and P, respectively, the equilibrium values, so (8) has no meaning outside of equilibrium. If the assumption of market clearing is abandoned, so that 2, 138

Aggregate

Demand

Curves

then (8) is a dynamic aggregate demand # P in disequilibrium, schedule. As 2, # Y,, the stock of inventories will accumulate or be depleted making the assumption Y, = Y implausible-it implies that firms do not worry about what happens to their inventories. Moreover, some assumption must be made to determine I’,. This example makes clear the fundamental difficulty with the RB and HT exercises. They insist on substituting a particular value of output into a dynamic aggregate demand curve and confuse the result with a static aggregate demand curve.

5. Conclusion The RB and HT analyses are invalid because they misinterpret the nature and role of the AD curve. If the system is in equilibrium and the AS or AD curves shift, we can use the AD curve in conjunction with the AS curve to work out what the new equilibrium output and price level will be. If the system is not in equilibrium, then the IS/LM subsystem or the labor market, or both, are in disequilibrium. Dynamic assumptions are necessary to analyze disequilibrium behavior. RB and HT make one particular assumption and then incorrectly identify the disequilibrium locus of points as an AD curve. Problems of interpretation of aggregate demand and supply models can be avoided if economic analysts make the clear distinction between static and dynamic analyses. Receioed:

Final

May

version:

1985

June

1988

References Barro, R. J., and H.I. Grossman. Money, Employment and Znflation. Cambridge: Cambridge University Press, 1976. Dalziel, P.C. “Aggregate Demand Curves in Macroeconomic Theory: Comment.” New Zealand Economic Papers 21 (1987): 10511. Hall, P.H., and M.L. Treadgold. “Aggregate Demand Curves: A Guide to Use and Abuse.” Australian Economic Papers 21 (June 1982): 37-48. -. “Alternative Aggregate Demand Functions in MacroecoAustralian Economic Papers 26 (Denomics: Some Comments.” cember 1987): 337-88. Henry, K., and A. Woodfield. “Aggregate Demand Curves in Mac139

David J Smyth roeconomic

Some Curiously Antipodean Controversies.” Papers 19 (1985): 21-34. -. “Aggregate Demand Curves in Macroeconomic Theory: Reply.” New Zealand Economic Papers 21 (1987): 113-16. Hicks, J.R. Value and Capital. 2d ed. London: Oxford University Press, 1939. Holmes, J.M., and D. J. Smyth. “The Aggregate Supply of Output and a Constant Price Level.” De Economist, no. 2 (1974): 16166. Marshall, A. Principles of Economics. 8th ed. London: Macmillan and Co., Ltd., 1920. Owen, P.D. “Aggregate Demand Curves in General-Equilibrium Macroeconomic Models: Comparisons with Partial-Equilibrium Microeconomic Demand Curves.” New Zealand Economic Papers 21 (1987): 97-104. Perry, L.J. “Aggregate Demand Analysis: A Neglected Issue.” Discussion Paper No. 61, School of Economics, University of New South Wales, Canberra, Australia, 1983. Rabin, A., and D. Birch. “A Clarification of the IS Curve and the Aggregate Curve.” Journal of Macroeconomics 4 (Spring 1982):

New Zealand

Theory:

Economic

233-38. Rao, B.B. “Alternative Aggregate Demand Functions in Macroeconomics.” Australian Economic Papers 25 (December 1986): 26164. Rowan, D.C. Output, Inflation and Growth: An Zntroduction to Macroeconomics. South Melbourne, Australia: Macmillan, 1975. Smyth, D. J. “The Use of Aggregate Demand Curves.” Working Paper, Wayne State University, Detroit, Michigan, March 1983. Mimeo.

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