- Email: [email protected]
Distribution, effective demand, and the orthodox macromodel
WILLIAM A. DARITY, JR. WANDA I. MARRERO of Texas at Austin
University
Distribution, Effective Demand, and the Orthodox Macromodel * The ordinary IS-LM framework is revised to incorporate macro-distributional considerations. This permits us to cast a new light on Keynes’ theoretical refutation of the usefulness of cutting money wages in the midst of a depression in a comparative statics context. We demonstrate that a generalized cut in money wages under conditions of complete price flexibility and perfect competition (marginal product factor pricing) can lower the volume of employment. This version of the orthodox macromodel also provides a potential handle on such seemingly elusive concepts as Keynes’ notions of full employment and under-employment equilibrium.
1. Introduction At the beginning of the General Theory Keynes (1936) makes clear his intention of launching a frontal attack on a position he ascribes to the classical school-the view that a generalized cut in money wages will lead to a rise in employment and provide a springboard out of economic depression. For the classicists the ultimate source of the depression’s unemployment crisis was the perceived downward inflexibility of money wages. Although Keynes’ classical colleagues did not generally advocate cutting money wages to solve the unemployment problem, their theoretical perspective suggested that if such a reduction could be achieved the economic system would self-adjust to full employment. On political grounds virtually all agreed that a general wage cut could not be achieved without intolerable social disruption. In the intervening years the translation of Keynes’ analysis into the Hicksian synthesis has led to the widespread opinion that the logic of Keynes’ critique depends on the downward rigidity of money wages. According to this interpretation Keynes did not offer a refutation of the classical position on theoretical grounds ‘The authors are grateful to J.S. Fl emming, Bobbie Horn, Stephen Kirsten Mullen, Lance Taylor, and an anonymous referee for comments drafts. Their remarks impelled us to substantially revise the presentation ideas-hopefully for the better. Journal Copyright
of Macroeconomics,
0
1982
by Wayne
Fall 1981, Vol. State University
3, No. 4, pp. 455-487 Press.
McDonald, on earlier of these
455
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at all. After all, the classicists themselves agreed that the existence of sticky prices of any sort could block the attainment of full employment. Possible keys to the conclusions drawn from the Hicksian synthesis stem from a failure to consider the influence of the distribution of income on aggregate effective demand and a failure to grasp the full scope of Keynes’ concept of unemployment. Aggregate effective demand is, after all, a major centerpiece of the General Theory [Pasinetti (1974)]. Keynes’ two definitions of “involuntary unemployment” also are of special importance and have been a source of controversy [Kahn (1976)]. In Keynes’ (1930) work a direct role for macrodistribution emerged in Chapter 10 of the first volume of his Treatise on Money which featured his use of the famous “widow’s cruse” metaphor.’ But it is in the oft-neglected Chapter 19 of the General Theory, entitled “Changes in Money-Wages, ” where distributional concerns lie beneath his refutation of the efficacy of wage-cutting. It is clear that Keynes was aware of the difference in the response to income changes on the parts of the wage-earner and rentiers who received only profit income. Given these response differentials the ultimate effect of a wage cut on employment could be ambiguous since the wage reduction could adversely affect aggregate demand: . . . whilst no one would wish to deny the proposition that a reduction in money-wages accompanied by the same aggregate effective demand as before will be associated with an increase in employment, the precise question at issue is whether the reduction in money-wages will or will not be accompanied by the same aggregate effective demand as before measured in money, or, at any rate, by an aggregate effective demand which is not reduced in full proportion to the reduction in money-wages . . . [Keynes (1936), pp. 259-601.
To illuminate the problem that Keynes was raising, assume that employment and output are fixed or given. Suppose workers ‘The importance of macrodistribution pervades works ranging from Hobson’s (1902) Imperialism to Kalecki’s (1933) essay on the business cycle to Kaldor’s (1955-6) macroeconomic alternative to the marginal productivity theory of distribution. Paradoxically all of these works can find their roots in the early chapters of Ricardo’s Principles. Keynes’ (1936) development of his aggregate demand and supply apparatus further reveals the continued importance of the functional distribution of income to his analysis.
The Orthodox
Macromodel
receive only wage income and rentiers receive only profit income. Suppose too that workers consume all of their income and rentiers save all of theirs. Obviously a redistribution of income from workers to rentiers will alter the volume of aggregate consumption, lowering it. This redistribution could be attempted by a decrease in money wages across the board, but one would expect employment and output to change in response to the change in the wage rate. The question of the overall impact becomes more complicated. The answer depends on the relative sensitivities of various behavioral relationships to movements of all elements of the system. It would seem that this type of problem is a natural for the Walrasian general equilibrium method. This is precisely the approach which we follow in this paper, amending the orthodox model to accommodate the influences of alterations in income received by each class that follows the money wage disturbance. In principle, the Walrasian method enables us to capture simultaneously all the competing influences on the employment level. We are well aware that the Hicksian synthesis has been viewed by some members of Keynes’ inner circle at Cambridge as a bastardization of his work and has been described by one of them, Joan Robinson (1965), as a restoration of “preKeynesian” thinking. We are not unsympathetic to this critique. Rather, we agree that an analysis replete with an aggregate physical production function, homogeneous capital, an inadequate treatment of the role of uncertainty, and an analysis that ignores Keynes’ rich discussion of the roles of finance and speculation rings as a hollow interpretation of Keynes’ insights. Robinson’s complaints strike long and hard against this entire methodology. However, we imbed distributional considerations in the orthodox macromodel because we want to show precisely how quickly the usual theoretical conclusions about the consequences of a money wage cut can vanish once macrodistribution is introduced. Moreover, we want to serve the heuristic aim of reinforcing the intuitive glimmerings that principles students frequently have when they wonder why their instructor claims output will rise to a permanently higher level when laborers’ take-home pay is lowered. We show that the students’ bewilderment is quite justified. Our version of the orthodox macromodel can be viewed as a straightforward adaption of the one-sector IS-LM system that makes employment fluctuations sensitive to the functional distribution of income. In addition, the model we develop will aid in illuminating the full implications of Keynes’ definitions of less than full employ457
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ment. For Keynes (1936), unemployment meant the existence of “involuntary unemployment” for which he offered two definitions which he treated, in his own words, as “equivalent.” The first definition [(1936), p. 151 he offered was: Men are involuntarily unemployed if, in the event of a small rise in the price of wage-goods relatively to the money-wage, both the aggregate supply of labour willing to work for the current money-wage and the aggregate demand for it at that wage would be greater than the existing volume of employment. Keynes’ (1936, p. 26) second definition
was the following:
In the previous chapter we have given a definition of full employment in terms of the behaviour of labour. An alternative, though equivalent, criterion is that at which we have now arrived, namely a situation in which aggregate employment is inelastic in response to an increase in the effective demand for its output. Clearly these two definitions are not always equivalent. The first requires as a test for the existence of involuntary unemployment the possibility that employment increases as the real wage declines. The second definition, in contrast, requires only that an increase in aggregate effective demand leads to an increase in employment, regardless of what happens to the real wage rate. Although the first definition is consistent with a condition where the labor market fails to clear, it does not have to be limited to such a circumstance. As long as an inflation of consumer goods prices results in a decline in the real wage and both the demand and supply of labor end up higher than at the previous equilibrium, involuntary unemployment by Keynes’ first definition exists. If the wage-goods price rise was engineered by an aggregate demand expansion, the two definitions are equivalent even if the supply and demand for labor are always in equality. All this shall become clearer in what follows. 2. The Model We assume that physical units of a single all-purpose commodity (Y) are produced via a neoclassical aggregate (constant returns to scale) production function by combining labor (N) and a homogeneous nonhuman input (Q) which we will call “machines.” Y is, therefore, both a consumption and investment good. 458
The Orthodox
Macromodel
In the now accepted manner of short period analysis, our world has no technical change and a stationary population size. The stock of machines is given so that physical output is positively related only to the level of employment, subject to diminishing returns to the fixed machine factor. The technology can thus be specified as follows: Y= F(N,Q);
aF
~>O,--g
a2F
Macrodistribution surfaces through the next relationship we postulate, an accounting identity for gross national income. Output in value terms becomes nominal income through a leak-free circular flow and must be divided between the wage bill and profits: PF(N,Q)
= wN + rPQ.
(2)
In (2), w is the money wage rate so that wN is the total wage bill, P is the money price of a unit of output while r is the rate of interest. Under competition and, hence, marginal product factor pricing, r must be equal to the marginal physical product of the machinery. Therefore, r also serves as the’rate of return on machinery, and rPQ constitutes gross money profits. In general, cases could exist where marginal product factor pricing does not apply, where there is a money surplus above and beyond the factor payments. This would open the analysis toward an explanation of the dispensation of this additional surplus by criteria other than marginal productivity. However, to keep this analysis manageable we do not explore these cases. Next, since aggregate demand in a one-sector model is the demand for a single output, we combine consumption and investment demand in a single aggregate private demand function, A. Public expenditure, in our closed economy framework, is captured by government demand, G. Private aggregate demand has the following specification, which separates this model from the usual IS-LM model: A = A(wN
A,>(); A,>A,;
(3)
- T,, rPQ - Tn, r, yM, 9M) ;
A,>O; A,>A,;
A,
A,>O;
A,'O;
(34 W
William
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(3a) indicates that A depends positively on disposable income from wages and profits. T,,, and T, are the taxes on wages and profits respectively. In addition A bears an inverse relationship to the rate of interest, r. This latter separate effect of interest rate changes hinges on the adverse consequences for corporate spending plans of a rise in the price of borrowing. We also assume a positive relationship between private expenditure and cash balances held by wage-earners, yM, and by profit-recipients, qM; y and Q are the shares of total cash balances held by workers and profiteers respectively. These shares are determined institutionally. To the extent that the government also holds cash balances, y and 4 will sum to a positive number smaller than one. Workers may receive some profits if they own and rent capital to corporations. However, the concurrent existence of pure rentiers, corporate-owned capital, and/or retained corporate earnings can all lead to the divergence in marginal propensities to spend out of wages and profits. As (3b) reveals we assume that the marginal propensity to spend out of wages is larger than the marginal propensity to spend out of profits. Similarly, the marginal propensity to spend out of wealth held by wage-recipients exceeds the marginal propensity to spend out of wealth held by profit-recipients. Government demand, public money expenditure, is treated as a pure policy variable (or as exogenous): G=cfi The commodity follows: PF(N,Q)
market
= A(wN
(4)
equilibrium
- T,,rPQ
can then be written
- T,,r,yM,
M) + G .
as
(5)
We turn next to the labor market where we make the following assumptions: The demand for labor is inversely related to the real wage, w/P, positively related to the quantity of real cash balances held by profit-recipients, qM/P, and positively related to the quantity of machinery in place, Q. The supply of labor is positively related to the real wage rate, inversely related to the quantity of real cash balances held by wage-recipients, yM / P, and inversely related to the rate of interest, r. Real cash balances and the interest rate are included in these two functions because of rigorous aggregation from micro founda460
The Orthodox
Macromodel
tions. Our specifications follow a generalization suggested by Patinkin [(1965), p. 2041 in his development of this sort of model: Both the demand and supply functions for labor should actually be presented as dependent on the real value of bond and money holdings as well as on the real wage rate. Furthermore, if we were to permit the firm to vary its input of capital, its demand for labor would depend also on the rate of interest. Finally, a full utility analysis of individual behaviour would show the supply of labor also to depend on this rate. Throughout our analysis we suppress explicit treatment of the bonds market equilibrium, assuming it clears by Walras’ Law. We also exclude the interest rate from the demand for labor function because, in the relevant period, machinery is in place and firms cannot vary the quantity utilized. The negative relationship between real wages and labor demand follows directly from profit-maximization and diminishing returns. The existence of transaction costs for firms can justify our postulated positive relationship between labor demand and cash balances held by profit-recipients. The positive relationship between real wage increases and labor supply stems from the conventional presumption that income effects dominate substitution effects for workers. Reversal of this latter condition would yield a backward-bending labor supply curve. The wealth effects of additional cash balances held by wagerecipients and of increases in the interest rate are assumed to lower the labor supply. The latter relationship implies that we conceive of suppliers of labor as net creditors, although this assumption could be relaxed easily.’ Equilibrium in the labor market dictates:
(6) Nf
Nz>o;
N,D>O;
‘Obviously if we assumed the contrary, rate increase representing a rise in the supply to expand by parallel logic.
N+O;
N,S
i.e., workers are price of borrowing,
net
NS,
debtors, an interest could lead the labor
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Finally we consider the money market. The supply of money, like government expenditure, is treated as a pure policy variable. The Keynesian liquidity preference relation L (. . .), depends positively on the two types of disposable income, negatively on the money rate of interest, which captures the opportunity cost of holding money, and positively on existing holdings of cash balances. We consider the marginal demand for cash balances to differ out of wages and profits and to differ out of worker and profiteer wealth. This makes our analysis symmetric with our treatment of commodity demands. For money market equilibrium we have: M = L(wN L,>O;
L, CL,;
- Tw,rPQ
- T,,r,yM,qM)
L,>O;
L,
; L,>O;
(7) L,>O;
(74
L,
VW
The money supply, M, is measured in its own units. With the money market clearing condition introduced, we impose the following inequalities: A, + L,
% 1;
@a)
A, + L,
5 1.
@W
All income received is divided between expenditure on output, held as new cash balances (hoarded), or lent out to earn interest (purchases of bonds). Relations (8a) and (8b) are inequalities to account for the third option. The usual IS-LM framework is a special case of the model developed here. If we set A, = A,, A, = A,, L, = L,, and L, = L, we are back in the old, familiar world where macrodistribution does not matter. The absence of these equalities in our present effort gives the orthodox macromodel a different perspective. Our complete system appears below:
462
PF(N,Q)
= wN + TPQ
PF(N,Q)
= A(wN
- T,,rPQ
(94 - T,,r,yM,qM)
+ G
(9b)
The Orthodox M = L(wN
- T,,rPQ
Macromodel
- T,,r,yM,qM)
In the relevant period of our analysis the machine stock, Q, is fixed. There are four exogenous policy variables: G, M, T,, and T,. The shares of money holdings, y and q, are also given. We are left, therefore, with four equations and four endogenous variables: w, N, P, and r.
3. Preliminary Observations Using our modified version of the orthodox macromodel, we want to explore what happens to the level of employment when there is a general cut in money wages. We want to isolate the conditions under which a wage cut will precipitate a further decline in employment under the most conventional assumptions-perfect price flexibility and perfect competition. This means we assume that marginal product factor pricing applies, although our model is sufficiently general to encompass other types of distributions. However, we want to prove our point in a world where all the conditions obtain that Keynes is thought to have relaxed in arriving at his under-employment equilibrium. Consequently, we arrive at a conception of less than full employment consistent with labor market clearing, a condition assumed under (SC). Keynes’ notion of an under-employment equilibrium makes sense in our model even when there is complete price flexibility. The system can churn out a Walrasian equilibrium where prevailing relative prices yield a level of employment that is not the maximum that potentially could be achieved by Keynes’ criteria. Our specification of the labor demand and supply functions under (6) can help illuminate this point. Under perfect price flexibility and perfect competition there is no reason for the system to always settle at the same wage-price ratio after a disturbance; consequently, the system does not have to restore an original level of employment. In addition, whatever that original level of employment might have been, it is not necessarily full employment in Keynes’ special sense. Keynes’ two definitions of involuntary unemployment can lead to an interpretation of full employment as a situation where a commodity price level has been attained such that a further rise, associated with an increase in aggregate effective demand, will cause the labor market to clear at a lower volume of employment. Keynes had in mind lowering real wages via a commodity 463
William
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price inflation. But in our system employment could actually rise as the real wage rate goes up under some parameterizations. This provides us with a range of possibilities that transcend Keynes’ belief that the real wage must be negatively correlated with the quantity of employment [de Largentaye (1979)]. In the standard IS-LM framework that overlooks macrodistribution, the direct effect of money wage changes is confined to the labor market, while changes in the commodity price level directly influence the labor and money markets. In this model the money wage rate and the commodity price level both exercise direct influence on all three markets-commodity, labor, and money. Consequently, this theory of employment becomes richer than the theory in the ordinary IS-LM framework. With these preliminary observations in mind, we can now examine the comparative statics of the system we present here. We will ask specifically what the effect would be of a small cut in the money wage rate which disturbs a prevailing (not necessarily Keynes’ full employment) equilibrium. Depression level employment does not have to mean here that the labor market fails to clear. Rather, it can mean that the labor market clears at a low level of employment-a level which could be raised with an expansion of demand. Empirically, from the standpoint of this analysis, the relevant measure of cyclical fluctuations would be the employment-population ratio in place of the unemployment rate. It is not necessary to conceive of cyclical swings as disequilibrium or non-market clearing phenomena. Instead cyclical swings can be thought of as movements from one general equilibrium to another, each corresponding to different levels of aggregate demand. We will use a four-quadrant diagrammatic technique to display our results. In the appendix we provide an algebraic presentation of the model.
4. The Diagrams We begin with the labor market drawn in money wageemployment space. Given a commodity price level, in Figure 1 the demand for labor schedule appears as downward sloping in w-N space while the supply schedule appears as upward sloping. The effect of a change in the price level on the two schedules is ambiguous. A rise in the price level, ceteris paribus, lowers the real wage and the real value of wealth, reductions which have 464
The Orthodox
Macromodel
w Labor
Figure 1. market equilibrium
competing effects on both labor demand and supply. Total differentiation of (9c) permits the effect of the price level change on the labor demand and supply to be given as follows: aN” -= ap aNS -= ap
1 (w/P”)
NF
+ (qM/P’)
N,D
;
1 (w/P”)
N; + (TM/P”)
N;
’
(104 (lob)
As long as the real wage effects dominate the wealth effects, the schedules will shift in the conventional manner. An increase in the price of output will shift the demand schedule to the right and the supply schedule to the left. Given our assumption that firms cannot vary their input of machinery, the labor demand will be invariant with respect to a change in the interest rate. Labor supply, however, will decline as the interest rate rises since we treat workers as net creditors. Finally consider the impact of changes in the exogenous
William
A. Darity,
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Derivation
Figure of labor-market
2. clearing
locus
FF
variables. Expansion in the money supply, other things unchanged, will tend to increase the demand for labor as will an autonomous increase in the share of wealth held by profiteers. On the other hand, the labor supply will decline as a consequence of either of these changes due to the positive wealth effect. An autonomous increase in the stock of machinery in place will raise the demand for labor. The concept of full employment we advanced in the previous section can be interpreted clearly with the aid of Figure 2. As the output price is raised, perhaps by raising aggregate demand as Keynes suggested, both the labor demand and supply schedules shift in w-N space. A new equilibrium level of employment corre-
The
Orthodox
Macromodel
sponds to each output price. We can trace out a locus, FF, representing the various equilibrium levels of employment in the labor market associated with each level of the commodity price. Inspection of the locus FF reveals that the maximum level of employment associated with variations in output price correspond to the value of P that generates the equilibrium NF. This is full employment in Keynes’ sense. A further increase in the commodity price can only lower the equilibrium level of employment. There is no reason for the model, in the absence of intervention by policymakers, to generate the price level that will cause the labor market to clear at NF. There is no natural tendency toward full employment in this sense. The system can settle at any level of employment along the FF locus. Which exact level is reached depends on the initial conditions prior to attainment of general equilibrium. We turn next to the gross national income identity which we will trace as a locus (II) in money wage-price level space in Figure 3. The ZZ locus thus provides all combinations of wage rates and output prices that are consistent with the identity when employment (and output) and the rate of interest are constant. The identity locus will appear as a rising schedule in w-P w
P
The
Figure identity
3. locus
II 467
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space, since the slope expression of (2) yields the following partial
aw -= aP
obtained by total differentiation derivative:
1 - @L/P) 1 - [(l -6,)/w]
;
(11)
where 6, is the share of profits in national income and 1 - 6, is the wage share. If we couple our assumption of marginal product factor pricing with an assumption that the production function is characterized by a constant elasticity of substitution, 8, will be a constant. With a variable-elasticity-of-substitution production function the distributional possibilities widen even under perfect competition. The ceteris paribus effect on the II locus of a rise in the volume of employment is given by the following differential:
But under marginal product factor pricing, the numerator in (12) vanishes. Consequently a change in the volume of employment, with other things being unchanged, does not alter the position of the II locus. A similar argument can be made for the effect of an autonomous change in the stock of machinery. However, an increase in the rate of interest in isolation will cause the entire ZZ locus to shift downward to the right. The relevant differential,
aw
= -PQ/N ar
(13)
is clearly negative in sign. Now consider the money market. Our strategy here is to trace out a locus of output prices and interest rates that will clear the market given the level of employment, the wage rate, the money supply, and the tax levels. To determine the slope of this MM locus, which is analogous to the L M schedule, we totally differentiate equation (7a) and perform the appropriate manipulations to obtain the desired partial derivative: 468
The Orthodox
at-=aP
Macromodel
L,rQ LzPQ
+ L,
(14)
*
The expression in (14) is ambiguous in sign. When “income” effects dominate “substitution” effects the MM locus will be negatively sloped in r-P space. When substitution effects are dominant, i.e., when L, is large, the locus will be positively sloped. We will assume that substitution effects are stronger as in Figure 4. The effect of an increase in employment on the MM locus can be determined by examining the following differential: ar -=aN
L,w
LPQ
+ LJ
(15)
’
The sign of (15) is ambiguous, but if substitution effects dominate the MM locus will shift toward the left. A rise in the money wage rate will have consequences similar to an employment increase. An increase in taxes of either type will shift the MM locus in the opposite direction, while an autono-
P
The
money-market
Figure 4. equilibrium
locus
MM 469
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mous rise in either the machine will have consequences similar increases. It is the conflicting effects demand for money that also make supply uncertain. ar -= aM
I. Marrero
stock or the cash balance shares to money wage or employment of interest rate changes on the the result of a rise in the money
(1 - YL, - 9&J
(16)
&i?PQ + L3)
It is reasonable to consider the numerator in (16) as positive, although strong tendencies to hoard could reverse this conclusion when y and 9 are sufficiently large. If the numerator is positive and income effects are strongest then a monetary expansion could actually raise the rate of interest.3 If substitution effects dominate, as we assume, the conventional result is retained that the direct effect of a money supply increase is to lower the interest rate. Finally, we turn to the commodity market to derive an equilibrium locus (YY) in employment-interest rate space. While the MM locus is analogous to the LM curve, the YY locus is analogous to the IS curve. The expression for the slope of the YY locus, under marginal product factor pricing simplifies to: aN
-= ar
A,PQ + (1-A,)w
A3
’
(17)
The sign of (17) also depends on the relative strengths of interest rate income and substitution effects. If a rise in the interest rate precipitates an increase in aggregate private demand, via an increase in income for profit recipients which more than offsets the tendency to purchase bonds rather than the commodity, then the YY locus will slope upward. Otherwise it will slope downward as in Figure 5. Along a single YY locus the money wage rate and the price level are constant. A ceteris paribus rise in the money wage rate will shift the YY locus to the right. This is because
‘The argument by Lance Taylor framework.
470
produced here is similar, although simpler, (1979) in his Latin American structuralist
than the one developed version of the IS-LM
The Orthodox
Figure The
commodities-market
aN -= aw
5. equilibrium
locus
A,N
YY
(18)
(1-A,)w
is always positive in sign given our assumption than unity. The effect of a price rise on the position market equilibrium locus is determined by:
A,rQ - F(NQ)
aN -= aP
Macromodel
(1-A,)w
;
that A, is smaller of the commodity
(19)
which is unambiguously negative. This means that the YY locus will shift leftward as the price level rises. An increase in taxes of either type will have a similar effect on the YY locus. Next consider the impact of an increase in government money expenditure (or pure fiscal policy): aN -= ac
1 (1 - A,)ti
’
(20) 471
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Equation (20) is a simple government expenditure multiplier which is, as usual, larger as the marginal propensity to spend out of wages is larger. The effect of pure fiscal policy would be to shift the YY locus to the right. As for the direct outcome of a monetary expansion the pertinent differential is: arv -= aM
?IA, + 4, (1 - A,)w
’
Gw
Again the YY locus will shift to the left after a monetary expansion. The same consequences also follow from ceteris paribus increases in either of the cash balance shares, y and q. With all four of the equations in the system given geometric form, the model can now be displayed in full via a four quadrant diagram in Figure 6. Here we draw the MM and YY loci under the condition that substitution effects of interest rate changes are more potent than income effects. The four quadrant diagram enables us to combine all the graphs developed above into a single picture. Moreover, this enables us to consider the simultaneous causation in operation in the model since there are no ceteris paribus effects when the full system is considered. The system appears in “general equilibrium” in Figure 6. Simultaneously all markets clear and the identity relation is satisfied. The configuration values of the endogenous variables-r *, P “, w “, and N *-provide a solution for the system. But as we emphasized earlier, N *, the equilibrium level of employment, need not be Keynes’ “full employment” level. The system might come to rest at an under-employment equilibrium. If N * is less than N F, it would be possible to raise employment still higher if, for example, the commodity price level could be raised by an increase in demand.
5. The Effects of a Money Wage Cut Our development of this variant of the ordinary IS-LM framework was motivated by our concern with the theoretical consequences of an across-the-board wage cut. The diagram we presented in Figure 6 provides us with a direct route toward a theoretical investigation of the outcome of just such a policy measure. Refer to Figure 7 where we present a possible outcome in a comparative statics exercise. Suppose we begin from a (in our 472
The Orthodox
General
Macromodel
Figure 8. equilibrium
special sense) less-than-full employment general equilibrium. Suppose further an across-the-board cut in money wages is mandated overnight that lowers the money wage rate from w * to w ‘. The immediate effect will be a withdrawal of labor services by workers who move down their labor supply schedule. The volume of employment falls, constrained from the supply side. The lower money wage rate implies a lower price level moving along the ZZ locus, which will induce laborers to raise their work effort and employers to reduce their demand for laborers. The NS schedule starts to shift to the left in quadrant Z while the ND schedule starts to shift to the right. The final outcome will depend on what happens in the money and commodity markets to mediate the magnitude of the labor market schedule shifts. We display a case where the money wage cut ultimately works its way through to a lower level of employment, N. The shift in 473
William
A. Darity,
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I’
I
u* s---B Y’ ---I I’
A
I
+--J++ I
I
I r .---
I I
* r mm---
M
\
Comparative
statics
1
Figure 7. of a money wage
M’
cut,
possible
case
the MM locus to M’M’ is due to the combined effects of the money wage cut and the initial employment decline. The shift in the YY locus to Y’Y’ is similarly based upon the assumption that the effect of the wage cut dominates the price level decline. We end up with a lower money wage rate, a lower interest rate, a lower commodity price level, and a lower level of employment. The entire economy has downshifted. The possibility of a fall in employment after a wage cut is not strictly dependent upon the postulated shifts in the MM and YY loci. Readers are welcome to convince themselves by playing with the diagram if they are still in doubt. Nevertheless, our central result is obvious: A wage cut in a world with flexible prices and perfect competition will not necessarily result in an adjustment of relative prices that will lead back to the original level of 474
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Macromodel
employment, let alone a higher level of employment. In fact, if N * were less than full employment, in the sense advanced here, the Figure 7 case represents a situation where the money wage cut merely aggravates the crisis. Of course, the classicists, like most contemporary economists, lacked a notion of less than full employment when the labor market clears. They only conceived of the theoretical validity of a generalized wage cut from a set of initial circumstances where there is excess supply in the labor market. Our model speaks directly to the case of classical involuntary unemployment in Figure 8. Suppose, for example, there is an initial unemployment in the fixed wage t; > w * so that involuntary customary sense exists. Lowering the money wage is deflationary, which is apparent once more from moving down the ZZ schedule.
I’ I -
W
----I---/II N
i I I I I
I I
*
Y y’
I I I
I
I
I
--m--e
-
me
%Y Y’
\
M’
II
Potential
consequences
of
money
Figure 8. wage cut: classical model
involuntary
M unemployment
475
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A. Darity,
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However, since employment was constrained from the demand side, the initial effect of the wage cut will be to raise employment. Still there is no a priori reason for employment ultimately to rise when all the simultaneous effects work their way through the system. The central problem is that the joint decline in the money wage rate and the price level leaves unclear what happens to the critical labor market variable, the real wage rate. If the drop is nearly equiproportionate, a la Keynes, the system will not reach the market-clearing level of employment merely by a marginal cut in money wages. The money wage cannot fall continuously toward W0 without generating other effects throughout the system that cause the labor demand and supply schedules to shift. There is no reason for the shifts to bring about self-adjustment to labor market clearing. In fact, employment may remain largely unchanged, say at fi in Figure 8.
6. Some Famous Special Cases Hicks (1937) in his pioneering essay where he sought to graft the General Theory onto Walrasian theory contended that an interest inelastic money demand function is the major feature of the classical system that Keynes repudiated. This is a highly questionable interpretation of Keynes’ break with the classicists. Nevertheless, it is still of interest to examine what effects a wage cut will have in Hicks’ “classical” system once the system is amended to incorporate distributional considerations. After all the classical system provided the theoretical basis for the wage cut policy in the first place. There are two possible interpretations of Hicks’ classical case in our system. One interpretation is that the substitution effect is eliminated or L, = 0. This means that the MM locus will be negatively sloped in r-P space. Due to the distributional considerations the money demand function will still be interest elastic, and Hicks’ classical results will not obtain. A second interpretation states that interest rate changes have no effect on liquidity preference whatsoever so that L, = L, = 0. This means that the MM schedule will appear as a vertical locus in quadrant four of Figure 6. Changes in the quantity of money can no longer directly alter the rate of interest. How the YY locus shifts matters in determining the direction of change in employment since a wage rate decline precipitates a commodity price fall, Employment can still fall as the result 476
The
Orthodox
Macromodel
of a wage reduction. Unlike the conventional IS-L M framework the commodity market still matters in determining the level of employment, although the money demand function is interest-rate insensitive. Even with the strong condition L, = L, = 0, Hicks’ classical results do not emerge with macrodistribution. Another special case that has generated interest among socalled Keynesians, rather than with Keynes himself, is the now-venerable liquidity trap which Hicks treated as the antithesis of the classical case.4 This is the case which arises when the money demand function is infinitely interest elastic. This means that the MM locus will be horizontal in quadrant three of Figure 6. However, this does not mean that the interest rate is pegged because a cut in money wages and the accompanying change in employment will cause the MM locus to shift up or down depending, once again, upon the relative strengths of all the effects. A third special case that the Keynesians have promoted is the interest-inelastic investment demand function. This generalizes to interest-insensitivity of private expenditure. Again there are two possible interpretations. The weaker case is one where the substitution effects of interest rate changes vanish, or A, = 0. In this situation the YY locus will be positively sloped as in Figure 5. But insofar as monetary changes affect the interest rate, there is no dichotomy because the interest rate still operates through the incomes of profit recipients. Obviously, monetary changes also have a direct effect on aggregate demand via the real balance effects. Under the more stringent interpretation we would have A, = A, = 0 which implies that the YY locus will be vertical in the third quadrant of Figure 6. Interest rate changes could only influence employment so long as the labor supply varies in response to interest variations, presumably a weak effect. Next, we consider Kalecki’s case (1971) where all wages are consumed, a case where A, = 1. Under marginal product factor pricing the expression in (18) becomes infinitely large and the YY
‘In fact Keynes [(1936), p. 2071 did not think much of the empirical relevance of the liquidity trap: “There is the possibility that, after the rate of interest has fallen to a certain level, liquidity-preference may become virtually absolute in the sense that almost everyone prefers cash to holding a debt which yields so low a rate of interest. In this event the monetary authority would have lost effective control over the rate of interest. But whilst this limiting case might become practically important in the future, I know of no example of it hitherto.” 477
William
A. Da&y,
Jr. and Wanda I. Marrero
locus highly unstable. Simultaneously if A, = 1 then L i = 0 from inequality (8a). As (15) reveals, this means variations in either the money wage rate or the volume of employment will not cause shifts in the MM locus. The money market thus becomes a stable anchor in a world where there are dramatic fluctuations in aggregate demand.
7. Policy Measures Finally, we want to examine the implications of three policy measures that might be taken if it is believed that the prevailing level of employment, N”, is too low. These are policy measures ultimately advanced in place of a money wage cut. First, pure fiscal policy might be attempted-an expansion of public expenditure-which will shift the YY schedule to the left in Figure 6. This will put upward pressure on commodity prices. Employment can rise if Keynes’ full employment threshold (where a further increase in the price level cannot raise employment) has not already been reached. Second, a monetary expansion might be attempted which will shift the MM locus to the right in the third quadrant of Figure 6. This will put downward pressure on interest rates and upward pressure on prices as aggregate demand expands. Again the eventual effect on output depends upon whether the system is still at a stage where inflation can buy more employment. Third, consider a redistribution of income so that the profit share, 6+ is lower at the prevailing level of employment and output. This was Hobson’s (1902) prescription for “depression in trade.” If 6, falls the ZZ locus in the second quadrant of Figure 6 will shift to the right which implies a higher price level must accompany the prevailing wage rate. The higher price level implies shifts in the labor demand and supply schedules, as well as the commodity market equilibrium locus, that could work towards a higher level of employment. Thus, the redistribution strategy also becomes a means of inflating the economy. For all three of these latter strategies, inflation of commodity prices is the doorway advocated out of depression. This was the essence of Keynes’ policy position [Klein (1947)]. The version of the orthodox macromodel advanced here provides a clear theoretical basis for such a policy position and a theoretical basis for rejection of money-wage cuts as a cure for unemployment. 478
The Orthodox
Macromodel
Appendix This appendix presents the algebra of the model developed in the preceding pages. Logarithmic differentiation coupled with marginal product factor pricing permits us to rewrite the system under (9) as follows, where hatted variables are logarithmic rates of change: (A. la)
- (1 - 6,)ii, + (1 - 6,)P - 6,; = 0 ; C = -A,(1
- 6,);
+ (1 - A,&,)p
+ (1 - A,)(1
- 6,)ti (A. lb)
- [A, + (A, / PQ)l 62 ; R=(+-
uS)l; + VP- up ;
D = L,m,i;,
+ L,m,p
(A.lc)
+ L,m,A
+ IL, + CL,/ PQ)Im,;. The new symbols
are defined
(A. Id) below:
6, = W’QIJ’F(N,Q)l ; (I- 6,) = [wNIPFW,Q)I ; C = -(l
- A,)&,0
+ gd - A, t,f,
- A&,
+ (~4 + qA,)M ti + r&M Q&P 1 q; ?+ PFW,Q) PF(NTQ) PFW, Q) G g = PF(N,Q) v-(a~-a~)+(u+J~);
t, s ;
Tw PF(N>
Q)
(A.2a)
;
t,=
T,
PF(N,Q)
(A-) (A.2c)
’ (A.2d)
(A.2f)
479
A. Darity,
William
Jr. and
D E [l - L,y
- L,5q]
+ Lpmlnfv
rPQ
mm =-----
Wanda
d - L,m,,Q^
- L,yq
M’
+ L,mtwfw
- L,q$;
WN
m
I. Marrero
=-. w-M’
m
@.%d
T SU) tw M;
Err
mhr
T
(A.2h) M
’
Solving the system under (A.l) for G, p, fi, and r^yields the following reduced form equations: W-0
=
(1 - A,)(1
- g,.,) L,
1
mnR
+ (1 - 6,) $
I
A3 - (1 - A,) PQ
+ h,L,m, + L,m,
(1 - 6,)az]
[6,V-
+ (1 - A,)(1 P-c =
-0
- 6,)[(1
- U
-
(1 - 6J 2
I
C
- 8,)~;
- A,)(1
- L,mn
R
(1 - 6,) -
(L,m,
- S-V] D
. J-’
;
(A.3a)
+ L,m,)k
mm
1 R
s,(l - %,)A, + (1 - %)A,
+ km,
- (1 - 6,) $a-
R - L,m,
[(l - 8,)~:
C + (1 - A,)(1
- 6,)[(1
I
+ bf
- u;)fLl
+ (a:,r*’
= {-(I
- A,)(1
+ L,m,(l 480
a;)6,]
D
* J-’
- 6,)“(L,m,
- %)I(1
-A,%)
- sJu,S (A.3b)
; + L,m,)R - A,(1
- S,)] R
The Orthodox - L, m,(l
- s$Ja;
+ (1 - A,)(1
- a,D) c
- 6J2(a,S
L3
L,--m,
PQ +
- a;)~}
A3
-mm+
Macromodel
. J-’
;
(A.3c)
8,
PQ
>
A3
L3 6,m,
PQ
PQ
> 1
L.--A,--
R
+ h [L,m, - A,L,mAIR
+ US, (L,m,
+ 6, kc
+ (1 - 8,) [A,(1 [(C
+ A,(1
C
- UXL ,mw + L,m,)
- (US,- ut)L,m,l
- k
1
+ L,mJ
- 6,)
- d)U - 6,)V]
C
-
D
+ (1 - A2SJ]
u;D
A,%,)
. J-’
;
(A.3d)
1 where
J is given
below:
J = (1 - 6,)(uS,
--u~)[L,mw(A2+$>,.
481
William
A. Da&y,
Jr. and Wanda I. Marrero
. I(1 - A,)(1
- 6,,)L,m,
- (1 - A,G,)L,m,]
+ [(l - s,,cr,” + S,(u~ - a;)
~310 - kJL,m, .
+ 6, (a; -
(A.4)
It is immediately apparent in a system this complicated that changes in any of the exogenous variables G, M, Tw, Tn, y, or 9, will have ambiguous effects on the endogenous variables w, P, T, or N. The variable that is of special interest to us is the volume of employment. To make any precise claims we must make some assumptions about the relative magnitudes of some of the parameters in the model. In the discussion in the main text the diagram in Figure 6 was drawn on the assumption that substitution effects of interest rate changes are stronger than income effects. In the limiting case this would mean A, = L, = 0. If we make such an assumption here fi simplifies to:
>1
4 PQ
+L,-mu
hm R + G-L,m,R
+ (1 - 6,)
(u,S - a:) 2
m, + azL,m,
[
482
C I
+ SW[(cry - al)
- (0,” - a:)]
+ (1 - &,)[A,(1
- 6,) + l]u;D
L,m,C
The Orthodox
Macromodel
- fL rcuT-a’;‘)+A,(14,)V]D where
J is now
unambiguously
J = (1 - 6,)(a$
positive:
- a:)
L,m, [
hn PQ
La + (1 - A,)(1 - 6,) po m, - 6, [(l
- 8,)Ui
+ 6, (a:
- ul)(l
+ s,(uf
1
- us)]
- 6,) L ,rn=
L,mw
64.6)
.
Now we can consider some comparative statics exercises under = L, = 0. First, consider the impact on our assumption that A, employment of an expansion in government spending:
afl aC
--=
I
(l-6.J
[
(uz-ui)$m,
+ a_ [(UT - Us)
- (U,S - a:)]
+ u,SL,mw
L,m,
1
. g . J-’
.
(A.7)
The stronger the responsiveness of liquidity preference to interest rate variations and the weaker the propensity to hoard out of income from wages the more positive the effect of government money expenditure on employment, i.e., if IL,1 is large and L, is small. A strong desire for liquidity on the part of wage recipients could lead to a case where increased government expenditure might even lower employment. Next consider the direction of the effect of a monetary expansion on employment.
483
William
A. Da&y,
Jr. and Wanda I. Marrero
)1
A3 +L,-m, PQ
6, (u;-u;)
+(1-&J
(+&$a[
+ a: L,m,
I
(YA,+qAs)M+6rn PFW,Q)
- (US, - u,D)L ,mw
+ (1 - 6J [
(-/A. + qA,)M
PFW,Q)
(ai - u3
$
I
Cl-
[
(ur-4
1 YL, - qL,)
+ (1 - %J [A,(1 - 6,) + 11o,s(l - YL, - qL,) - 6, [(cry - CT;, + A,0
- UVl(l
- YL, - qL,)
. I-‘.
L4.8)
Like (A.7) the sign of (A.8) is ambiguous. As long as L, is fairly large while L, is small and as long as the interest elasticity of the supply of labor, a:, is fairly small, it would be reasonable to assert that the expression in (A.8) is positive. What about an overnight increase in machine stock? The direction of this effect is given by the following expression:
A3 m, 6, 0,” - iS,L,m,u,D > I PQ
+ L, -
484
The Orthodox
- (1 - 6,)
(ai - a:)
Macromodel
zrnm
[
+ uiL,m,
(1 - A,)6,
+ 6, [(af
- as)
I
- (+
1
a:)
- (1 - 6,)
L,%U(l - A,)S,
(a$ - a:)
-$a-
[ - (1 - 6,)[A,(l
1
L,m,
- 6,) + l] uiL,m,
+6,rcuf- UT) + A,(1
- 6,)V]
L,m,
. J-’
.
(A.9
Expression (A.9) is plainly ambiguous in sign, It is more likely to take the anticipated, positive sign the larger the interest elasticity of the labor supply. Keynes’ full employment might be interpreted as a case where changes in the key variables at policymakers’ disposal no longer raise employment, a condition where:
afi aN -=-=ad an2
aA ati =-co. a?, af,
(A.lO)
But the question that initially prompted our interest in these matters was the effect of a small cut in money wages on employment in a world where macrodistribution matters. Still assuming A, = L, = 0, dividing (A.3d) by (A.3a) yields the elasticity of employment with respect to a money wage change:
+L,-mm,
A3 PQ
>1 6,
R + G,L,m,R
485
William
A. Da&y,
Jr. and Wanda I. Marrero
+ 6, [(cry - as) - (al - a:)]
+ (1 - 6J[A,(l
- STkc *
- 6,) + l]u;D
a;) + A,(1
(1 - A,)(1
- 6,,)‘-
-6JV]
[6-V-
+ (1 - A,)(1
D
L3 PQ
m-R
(1-tin)%-1 + L,m,
L,m,C
(1 - 6,)0~]
- a=)[(1 - 8,)~;
1 R
C
- hnV] D
.
(A.ll)
Even with A, = L, = 0 the expression in (A.11) is still intractable as to the sign of the elasticity. Lowering money wages may raise or may lower employment, which has been our main point. Finally, one might want to explore the comparative statics of a money wage cut when the system begins with classical involuntary unemployment as in Figure 8. In this case we would treat our system as constrained from the demand side of the labor market. We would only need to replace equation (A.9c) with
N=ND
and that 486
work through the expression
(A. 12)
the analysis again. We can assure the reader for the elasticity of employment as a whole
The
with respect to the money wage rate will sign as the expression in (A. 11). Received: November, Final version received:
1979 January,
Orthodox
Macromodel
be just as uncertain
in
1981
References de Largentaye,
Jean. “A Note on The General Theory of Employment, Money. ” Journal of PostKeynesian Economics 1 (Spring 1979): 6-15. Hicks, John. “Mr. Keynes and the Classics: A Suggested Interpretation” Econometrica 5 (April 1937): 147-59. Hobson, J.A. Imperialism: A Study. London: George Allen and Unwin, 1902. Kahn, R.F. “Unemployment As Seen By the Keynesians.” In The Concept and Measurement of Znvoluntary Unemployment, G.D.N. Worswick, ed. London: George Allen and Unwin, 1976. Kaldor, Nicholas. “Alternative Theories of Distribution.” Review of Economic Studies 23 (1955-56): 83-100. Kalecki, Michal. “Outline of a Theory of the Business Cycle.” In Selected Essays on the Dynamics of the Capitalist Economy, M. Kalecki, ed. Cambridge: Cambridge University Press, 1971. Keynes, J.M. A Treatise on Money: Volume I, The Pure Theory of Money. London: Macmillan and Company, 1930. Keynes, J.M. The General Theory of Employment, Interest and Money. London: Macmillan and Company, 1936. Klein, Lawrence. The Keynesian Revolution. New York: The Macmillan Company, 1947. Pasinetti, Luigi. “The Economics of Effective Demand.” In L. Pasinetti, Growth and Income Distribution. Cambridge: Cambridge University Press, 1974. Ricardo, David. The Principles of Political Economy and Taxation. London: J.M. Dent and Sons, 1973. Robinson, Joan. “Pre-Keynesian Theory After Keynes,” Australian Economic Papers 3 (June-December 1964): 25-35. Taylor, Lance. “IS-LM in the Tropics.” In Economic Stabilization in Developing Countries, William R. Klein and Sidney Weintraub, eds. Washington D.C.: The Brookings Institution, 1981. Interest,
and
487
University
Distribution, Effective Demand, and the Orthodox Macromodel * The ordinary IS-LM framework is revised to incorporate macro-distributional considerations. This permits us to cast a new light on Keynes’ theoretical refutation of the usefulness of cutting money wages in the midst of a depression in a comparative statics context. We demonstrate that a generalized cut in money wages under conditions of complete price flexibility and perfect competition (marginal product factor pricing) can lower the volume of employment. This version of the orthodox macromodel also provides a potential handle on such seemingly elusive concepts as Keynes’ notions of full employment and under-employment equilibrium.
1. Introduction At the beginning of the General Theory Keynes (1936) makes clear his intention of launching a frontal attack on a position he ascribes to the classical school-the view that a generalized cut in money wages will lead to a rise in employment and provide a springboard out of economic depression. For the classicists the ultimate source of the depression’s unemployment crisis was the perceived downward inflexibility of money wages. Although Keynes’ classical colleagues did not generally advocate cutting money wages to solve the unemployment problem, their theoretical perspective suggested that if such a reduction could be achieved the economic system would self-adjust to full employment. On political grounds virtually all agreed that a general wage cut could not be achieved without intolerable social disruption. In the intervening years the translation of Keynes’ analysis into the Hicksian synthesis has led to the widespread opinion that the logic of Keynes’ critique depends on the downward rigidity of money wages. According to this interpretation Keynes did not offer a refutation of the classical position on theoretical grounds ‘The authors are grateful to J.S. Fl emming, Bobbie Horn, Stephen Kirsten Mullen, Lance Taylor, and an anonymous referee for comments drafts. Their remarks impelled us to substantially revise the presentation ideas-hopefully for the better. Journal Copyright
of Macroeconomics,
0
1982
by Wayne
Fall 1981, Vol. State University
3, No. 4, pp. 455-487 Press.
McDonald, on earlier of these
455
William
A. Darity,
Jr. and Wanda I. Marrero
at all. After all, the classicists themselves agreed that the existence of sticky prices of any sort could block the attainment of full employment. Possible keys to the conclusions drawn from the Hicksian synthesis stem from a failure to consider the influence of the distribution of income on aggregate effective demand and a failure to grasp the full scope of Keynes’ concept of unemployment. Aggregate effective demand is, after all, a major centerpiece of the General Theory [Pasinetti (1974)]. Keynes’ two definitions of “involuntary unemployment” also are of special importance and have been a source of controversy [Kahn (1976)]. In Keynes’ (1930) work a direct role for macrodistribution emerged in Chapter 10 of the first volume of his Treatise on Money which featured his use of the famous “widow’s cruse” metaphor.’ But it is in the oft-neglected Chapter 19 of the General Theory, entitled “Changes in Money-Wages, ” where distributional concerns lie beneath his refutation of the efficacy of wage-cutting. It is clear that Keynes was aware of the difference in the response to income changes on the parts of the wage-earner and rentiers who received only profit income. Given these response differentials the ultimate effect of a wage cut on employment could be ambiguous since the wage reduction could adversely affect aggregate demand: . . . whilst no one would wish to deny the proposition that a reduction in money-wages accompanied by the same aggregate effective demand as before will be associated with an increase in employment, the precise question at issue is whether the reduction in money-wages will or will not be accompanied by the same aggregate effective demand as before measured in money, or, at any rate, by an aggregate effective demand which is not reduced in full proportion to the reduction in money-wages . . . [Keynes (1936), pp. 259-601.
To illuminate the problem that Keynes was raising, assume that employment and output are fixed or given. Suppose workers ‘The importance of macrodistribution pervades works ranging from Hobson’s (1902) Imperialism to Kalecki’s (1933) essay on the business cycle to Kaldor’s (1955-6) macroeconomic alternative to the marginal productivity theory of distribution. Paradoxically all of these works can find their roots in the early chapters of Ricardo’s Principles. Keynes’ (1936) development of his aggregate demand and supply apparatus further reveals the continued importance of the functional distribution of income to his analysis.
The Orthodox
Macromodel
receive only wage income and rentiers receive only profit income. Suppose too that workers consume all of their income and rentiers save all of theirs. Obviously a redistribution of income from workers to rentiers will alter the volume of aggregate consumption, lowering it. This redistribution could be attempted by a decrease in money wages across the board, but one would expect employment and output to change in response to the change in the wage rate. The question of the overall impact becomes more complicated. The answer depends on the relative sensitivities of various behavioral relationships to movements of all elements of the system. It would seem that this type of problem is a natural for the Walrasian general equilibrium method. This is precisely the approach which we follow in this paper, amending the orthodox model to accommodate the influences of alterations in income received by each class that follows the money wage disturbance. In principle, the Walrasian method enables us to capture simultaneously all the competing influences on the employment level. We are well aware that the Hicksian synthesis has been viewed by some members of Keynes’ inner circle at Cambridge as a bastardization of his work and has been described by one of them, Joan Robinson (1965), as a restoration of “preKeynesian” thinking. We are not unsympathetic to this critique. Rather, we agree that an analysis replete with an aggregate physical production function, homogeneous capital, an inadequate treatment of the role of uncertainty, and an analysis that ignores Keynes’ rich discussion of the roles of finance and speculation rings as a hollow interpretation of Keynes’ insights. Robinson’s complaints strike long and hard against this entire methodology. However, we imbed distributional considerations in the orthodox macromodel because we want to show precisely how quickly the usual theoretical conclusions about the consequences of a money wage cut can vanish once macrodistribution is introduced. Moreover, we want to serve the heuristic aim of reinforcing the intuitive glimmerings that principles students frequently have when they wonder why their instructor claims output will rise to a permanently higher level when laborers’ take-home pay is lowered. We show that the students’ bewilderment is quite justified. Our version of the orthodox macromodel can be viewed as a straightforward adaption of the one-sector IS-LM system that makes employment fluctuations sensitive to the functional distribution of income. In addition, the model we develop will aid in illuminating the full implications of Keynes’ definitions of less than full employ457
William
A. Darity,
Jr. and Wanda I. Marrero
ment. For Keynes (1936), unemployment meant the existence of “involuntary unemployment” for which he offered two definitions which he treated, in his own words, as “equivalent.” The first definition [(1936), p. 151 he offered was: Men are involuntarily unemployed if, in the event of a small rise in the price of wage-goods relatively to the money-wage, both the aggregate supply of labour willing to work for the current money-wage and the aggregate demand for it at that wage would be greater than the existing volume of employment. Keynes’ (1936, p. 26) second definition
was the following:
In the previous chapter we have given a definition of full employment in terms of the behaviour of labour. An alternative, though equivalent, criterion is that at which we have now arrived, namely a situation in which aggregate employment is inelastic in response to an increase in the effective demand for its output. Clearly these two definitions are not always equivalent. The first requires as a test for the existence of involuntary unemployment the possibility that employment increases as the real wage declines. The second definition, in contrast, requires only that an increase in aggregate effective demand leads to an increase in employment, regardless of what happens to the real wage rate. Although the first definition is consistent with a condition where the labor market fails to clear, it does not have to be limited to such a circumstance. As long as an inflation of consumer goods prices results in a decline in the real wage and both the demand and supply of labor end up higher than at the previous equilibrium, involuntary unemployment by Keynes’ first definition exists. If the wage-goods price rise was engineered by an aggregate demand expansion, the two definitions are equivalent even if the supply and demand for labor are always in equality. All this shall become clearer in what follows. 2. The Model We assume that physical units of a single all-purpose commodity (Y) are produced via a neoclassical aggregate (constant returns to scale) production function by combining labor (N) and a homogeneous nonhuman input (Q) which we will call “machines.” Y is, therefore, both a consumption and investment good. 458
The Orthodox
Macromodel
In the now accepted manner of short period analysis, our world has no technical change and a stationary population size. The stock of machines is given so that physical output is positively related only to the level of employment, subject to diminishing returns to the fixed machine factor. The technology can thus be specified as follows: Y= F(N,Q);
aF
~>O,--g
a2F
Macrodistribution surfaces through the next relationship we postulate, an accounting identity for gross national income. Output in value terms becomes nominal income through a leak-free circular flow and must be divided between the wage bill and profits: PF(N,Q)
= wN + rPQ.
(2)
In (2), w is the money wage rate so that wN is the total wage bill, P is the money price of a unit of output while r is the rate of interest. Under competition and, hence, marginal product factor pricing, r must be equal to the marginal physical product of the machinery. Therefore, r also serves as the’rate of return on machinery, and rPQ constitutes gross money profits. In general, cases could exist where marginal product factor pricing does not apply, where there is a money surplus above and beyond the factor payments. This would open the analysis toward an explanation of the dispensation of this additional surplus by criteria other than marginal productivity. However, to keep this analysis manageable we do not explore these cases. Next, since aggregate demand in a one-sector model is the demand for a single output, we combine consumption and investment demand in a single aggregate private demand function, A. Public expenditure, in our closed economy framework, is captured by government demand, G. Private aggregate demand has the following specification, which separates this model from the usual IS-LM model: A = A(wN
A,>(); A,>A,;
(3)
- T,, rPQ - Tn, r, yM, 9M) ;
A,>O; A,>A,;
A,
A,>O;
A,'O;
(34 W
William
A. Darity,
Jr. and Wanda I. Marrero
(3a) indicates that A depends positively on disposable income from wages and profits. T,,, and T, are the taxes on wages and profits respectively. In addition A bears an inverse relationship to the rate of interest, r. This latter separate effect of interest rate changes hinges on the adverse consequences for corporate spending plans of a rise in the price of borrowing. We also assume a positive relationship between private expenditure and cash balances held by wage-earners, yM, and by profit-recipients, qM; y and Q are the shares of total cash balances held by workers and profiteers respectively. These shares are determined institutionally. To the extent that the government also holds cash balances, y and 4 will sum to a positive number smaller than one. Workers may receive some profits if they own and rent capital to corporations. However, the concurrent existence of pure rentiers, corporate-owned capital, and/or retained corporate earnings can all lead to the divergence in marginal propensities to spend out of wages and profits. As (3b) reveals we assume that the marginal propensity to spend out of wages is larger than the marginal propensity to spend out of profits. Similarly, the marginal propensity to spend out of wealth held by wage-recipients exceeds the marginal propensity to spend out of wealth held by profit-recipients. Government demand, public money expenditure, is treated as a pure policy variable (or as exogenous): G=cfi The commodity follows: PF(N,Q)
market
= A(wN
(4)
equilibrium
- T,,rPQ
can then be written
- T,,r,yM,
M) + G .
as
(5)
We turn next to the labor market where we make the following assumptions: The demand for labor is inversely related to the real wage, w/P, positively related to the quantity of real cash balances held by profit-recipients, qM/P, and positively related to the quantity of machinery in place, Q. The supply of labor is positively related to the real wage rate, inversely related to the quantity of real cash balances held by wage-recipients, yM / P, and inversely related to the rate of interest, r. Real cash balances and the interest rate are included in these two functions because of rigorous aggregation from micro founda460
The Orthodox
Macromodel
tions. Our specifications follow a generalization suggested by Patinkin [(1965), p. 2041 in his development of this sort of model: Both the demand and supply functions for labor should actually be presented as dependent on the real value of bond and money holdings as well as on the real wage rate. Furthermore, if we were to permit the firm to vary its input of capital, its demand for labor would depend also on the rate of interest. Finally, a full utility analysis of individual behaviour would show the supply of labor also to depend on this rate. Throughout our analysis we suppress explicit treatment of the bonds market equilibrium, assuming it clears by Walras’ Law. We also exclude the interest rate from the demand for labor function because, in the relevant period, machinery is in place and firms cannot vary the quantity utilized. The negative relationship between real wages and labor demand follows directly from profit-maximization and diminishing returns. The existence of transaction costs for firms can justify our postulated positive relationship between labor demand and cash balances held by profit-recipients. The positive relationship between real wage increases and labor supply stems from the conventional presumption that income effects dominate substitution effects for workers. Reversal of this latter condition would yield a backward-bending labor supply curve. The wealth effects of additional cash balances held by wagerecipients and of increases in the interest rate are assumed to lower the labor supply. The latter relationship implies that we conceive of suppliers of labor as net creditors, although this assumption could be relaxed easily.’ Equilibrium in the labor market dictates:
(6) Nf
Nz>o;
N,D>O;
‘Obviously if we assumed the contrary, rate increase representing a rise in the supply to expand by parallel logic.
N+O;
N,S
i.e., workers are price of borrowing,
net
NS,
debtors, an interest could lead the labor
461
William
A. Da&y,
Jr. and Wanda I. Marrero
Finally we consider the money market. The supply of money, like government expenditure, is treated as a pure policy variable. The Keynesian liquidity preference relation L (. . .), depends positively on the two types of disposable income, negatively on the money rate of interest, which captures the opportunity cost of holding money, and positively on existing holdings of cash balances. We consider the marginal demand for cash balances to differ out of wages and profits and to differ out of worker and profiteer wealth. This makes our analysis symmetric with our treatment of commodity demands. For money market equilibrium we have: M = L(wN L,>O;
L, CL,;
- Tw,rPQ
- T,,r,yM,qM)
L,>O;
L,
; L,>O;
(7) L,>O;
(74
L,
VW
The money supply, M, is measured in its own units. With the money market clearing condition introduced, we impose the following inequalities: A, + L,
% 1;
@a)
A, + L,
5 1.
@W
All income received is divided between expenditure on output, held as new cash balances (hoarded), or lent out to earn interest (purchases of bonds). Relations (8a) and (8b) are inequalities to account for the third option. The usual IS-LM framework is a special case of the model developed here. If we set A, = A,, A, = A,, L, = L,, and L, = L, we are back in the old, familiar world where macrodistribution does not matter. The absence of these equalities in our present effort gives the orthodox macromodel a different perspective. Our complete system appears below:
462
PF(N,Q)
= wN + TPQ
PF(N,Q)
= A(wN
- T,,rPQ
(94 - T,,r,yM,qM)
+ G
(9b)
The Orthodox M = L(wN
- T,,rPQ
Macromodel
- T,,r,yM,qM)
In the relevant period of our analysis the machine stock, Q, is fixed. There are four exogenous policy variables: G, M, T,, and T,. The shares of money holdings, y and q, are also given. We are left, therefore, with four equations and four endogenous variables: w, N, P, and r.
3. Preliminary Observations Using our modified version of the orthodox macromodel, we want to explore what happens to the level of employment when there is a general cut in money wages. We want to isolate the conditions under which a wage cut will precipitate a further decline in employment under the most conventional assumptions-perfect price flexibility and perfect competition. This means we assume that marginal product factor pricing applies, although our model is sufficiently general to encompass other types of distributions. However, we want to prove our point in a world where all the conditions obtain that Keynes is thought to have relaxed in arriving at his under-employment equilibrium. Consequently, we arrive at a conception of less than full employment consistent with labor market clearing, a condition assumed under (SC). Keynes’ notion of an under-employment equilibrium makes sense in our model even when there is complete price flexibility. The system can churn out a Walrasian equilibrium where prevailing relative prices yield a level of employment that is not the maximum that potentially could be achieved by Keynes’ criteria. Our specification of the labor demand and supply functions under (6) can help illuminate this point. Under perfect price flexibility and perfect competition there is no reason for the system to always settle at the same wage-price ratio after a disturbance; consequently, the system does not have to restore an original level of employment. In addition, whatever that original level of employment might have been, it is not necessarily full employment in Keynes’ special sense. Keynes’ two definitions of involuntary unemployment can lead to an interpretation of full employment as a situation where a commodity price level has been attained such that a further rise, associated with an increase in aggregate effective demand, will cause the labor market to clear at a lower volume of employment. Keynes had in mind lowering real wages via a commodity 463
William
A. Darity,
Jr. and Wanda I. Marrero
price inflation. But in our system employment could actually rise as the real wage rate goes up under some parameterizations. This provides us with a range of possibilities that transcend Keynes’ belief that the real wage must be negatively correlated with the quantity of employment [de Largentaye (1979)]. In the standard IS-LM framework that overlooks macrodistribution, the direct effect of money wage changes is confined to the labor market, while changes in the commodity price level directly influence the labor and money markets. In this model the money wage rate and the commodity price level both exercise direct influence on all three markets-commodity, labor, and money. Consequently, this theory of employment becomes richer than the theory in the ordinary IS-LM framework. With these preliminary observations in mind, we can now examine the comparative statics of the system we present here. We will ask specifically what the effect would be of a small cut in the money wage rate which disturbs a prevailing (not necessarily Keynes’ full employment) equilibrium. Depression level employment does not have to mean here that the labor market fails to clear. Rather, it can mean that the labor market clears at a low level of employment-a level which could be raised with an expansion of demand. Empirically, from the standpoint of this analysis, the relevant measure of cyclical fluctuations would be the employment-population ratio in place of the unemployment rate. It is not necessary to conceive of cyclical swings as disequilibrium or non-market clearing phenomena. Instead cyclical swings can be thought of as movements from one general equilibrium to another, each corresponding to different levels of aggregate demand. We will use a four-quadrant diagrammatic technique to display our results. In the appendix we provide an algebraic presentation of the model.
4. The Diagrams We begin with the labor market drawn in money wageemployment space. Given a commodity price level, in Figure 1 the demand for labor schedule appears as downward sloping in w-N space while the supply schedule appears as upward sloping. The effect of a change in the price level on the two schedules is ambiguous. A rise in the price level, ceteris paribus, lowers the real wage and the real value of wealth, reductions which have 464
The Orthodox
Macromodel
w Labor
Figure 1. market equilibrium
competing effects on both labor demand and supply. Total differentiation of (9c) permits the effect of the price level change on the labor demand and supply to be given as follows: aN” -= ap aNS -= ap
1 (w/P”)
NF
+ (qM/P’)
N,D
;
1 (w/P”)
N; + (TM/P”)
N;
’
(104 (lob)
As long as the real wage effects dominate the wealth effects, the schedules will shift in the conventional manner. An increase in the price of output will shift the demand schedule to the right and the supply schedule to the left. Given our assumption that firms cannot vary their input of machinery, the labor demand will be invariant with respect to a change in the interest rate. Labor supply, however, will decline as the interest rate rises since we treat workers as net creditors. Finally consider the impact of changes in the exogenous
William
A. Darity,
Jr. and Wanda I. Marrero
Derivation
Figure of labor-market
2. clearing
locus
FF
variables. Expansion in the money supply, other things unchanged, will tend to increase the demand for labor as will an autonomous increase in the share of wealth held by profiteers. On the other hand, the labor supply will decline as a consequence of either of these changes due to the positive wealth effect. An autonomous increase in the stock of machinery in place will raise the demand for labor. The concept of full employment we advanced in the previous section can be interpreted clearly with the aid of Figure 2. As the output price is raised, perhaps by raising aggregate demand as Keynes suggested, both the labor demand and supply schedules shift in w-N space. A new equilibrium level of employment corre-
The
Orthodox
Macromodel
sponds to each output price. We can trace out a locus, FF, representing the various equilibrium levels of employment in the labor market associated with each level of the commodity price. Inspection of the locus FF reveals that the maximum level of employment associated with variations in output price correspond to the value of P that generates the equilibrium NF. This is full employment in Keynes’ sense. A further increase in the commodity price can only lower the equilibrium level of employment. There is no reason for the model, in the absence of intervention by policymakers, to generate the price level that will cause the labor market to clear at NF. There is no natural tendency toward full employment in this sense. The system can settle at any level of employment along the FF locus. Which exact level is reached depends on the initial conditions prior to attainment of general equilibrium. We turn next to the gross national income identity which we will trace as a locus (II) in money wage-price level space in Figure 3. The ZZ locus thus provides all combinations of wage rates and output prices that are consistent with the identity when employment (and output) and the rate of interest are constant. The identity locus will appear as a rising schedule in w-P w
P
The
Figure identity
3. locus
II 467
William
A. Da&y,
Jr. and Wanda I. Marrero
space, since the slope expression of (2) yields the following partial
aw -= aP
obtained by total differentiation derivative:
1 - @L/P) 1 - [(l -6,)/w]
;
(11)
where 6, is the share of profits in national income and 1 - 6, is the wage share. If we couple our assumption of marginal product factor pricing with an assumption that the production function is characterized by a constant elasticity of substitution, 8, will be a constant. With a variable-elasticity-of-substitution production function the distributional possibilities widen even under perfect competition. The ceteris paribus effect on the II locus of a rise in the volume of employment is given by the following differential:
But under marginal product factor pricing, the numerator in (12) vanishes. Consequently a change in the volume of employment, with other things being unchanged, does not alter the position of the II locus. A similar argument can be made for the effect of an autonomous change in the stock of machinery. However, an increase in the rate of interest in isolation will cause the entire ZZ locus to shift downward to the right. The relevant differential,
aw
= -PQ/N ar
(13)
is clearly negative in sign. Now consider the money market. Our strategy here is to trace out a locus of output prices and interest rates that will clear the market given the level of employment, the wage rate, the money supply, and the tax levels. To determine the slope of this MM locus, which is analogous to the L M schedule, we totally differentiate equation (7a) and perform the appropriate manipulations to obtain the desired partial derivative: 468
The Orthodox
at-=aP
Macromodel
L,rQ LzPQ
+ L,
(14)
*
The expression in (14) is ambiguous in sign. When “income” effects dominate “substitution” effects the MM locus will be negatively sloped in r-P space. When substitution effects are dominant, i.e., when L, is large, the locus will be positively sloped. We will assume that substitution effects are stronger as in Figure 4. The effect of an increase in employment on the MM locus can be determined by examining the following differential: ar -=aN
L,w
LPQ
+ LJ
(15)
’
The sign of (15) is ambiguous, but if substitution effects dominate the MM locus will shift toward the left. A rise in the money wage rate will have consequences similar to an employment increase. An increase in taxes of either type will shift the MM locus in the opposite direction, while an autono-
P
The
money-market
Figure 4. equilibrium
locus
MM 469
William
A. Darity,
Jr. and
Wanda
mous rise in either the machine will have consequences similar increases. It is the conflicting effects demand for money that also make supply uncertain. ar -= aM
I. Marrero
stock or the cash balance shares to money wage or employment of interest rate changes on the the result of a rise in the money
(1 - YL, - 9&J
(16)
&i?PQ + L3)
It is reasonable to consider the numerator in (16) as positive, although strong tendencies to hoard could reverse this conclusion when y and 9 are sufficiently large. If the numerator is positive and income effects are strongest then a monetary expansion could actually raise the rate of interest.3 If substitution effects dominate, as we assume, the conventional result is retained that the direct effect of a money supply increase is to lower the interest rate. Finally, we turn to the commodity market to derive an equilibrium locus (YY) in employment-interest rate space. While the MM locus is analogous to the LM curve, the YY locus is analogous to the IS curve. The expression for the slope of the YY locus, under marginal product factor pricing simplifies to: aN
-= ar
A,PQ + (1-A,)w
A3
’
(17)
The sign of (17) also depends on the relative strengths of interest rate income and substitution effects. If a rise in the interest rate precipitates an increase in aggregate private demand, via an increase in income for profit recipients which more than offsets the tendency to purchase bonds rather than the commodity, then the YY locus will slope upward. Otherwise it will slope downward as in Figure 5. Along a single YY locus the money wage rate and the price level are constant. A ceteris paribus rise in the money wage rate will shift the YY locus to the right. This is because
‘The argument by Lance Taylor framework.
470
produced here is similar, although simpler, (1979) in his Latin American structuralist
than the one developed version of the IS-LM
The Orthodox
Figure The
commodities-market
aN -= aw
5. equilibrium
locus
A,N
YY
(18)
(1-A,)w
is always positive in sign given our assumption than unity. The effect of a price rise on the position market equilibrium locus is determined by:
A,rQ - F(NQ)
aN -= aP
Macromodel
(1-A,)w
;
that A, is smaller of the commodity
(19)
which is unambiguously negative. This means that the YY locus will shift leftward as the price level rises. An increase in taxes of either type will have a similar effect on the YY locus. Next consider the impact of an increase in government money expenditure (or pure fiscal policy): aN -= ac
1 (1 - A,)ti
’
(20) 471
William
A. Darity,
Jr. and
Wanda
I. Marrero
Equation (20) is a simple government expenditure multiplier which is, as usual, larger as the marginal propensity to spend out of wages is larger. The effect of pure fiscal policy would be to shift the YY locus to the right. As for the direct outcome of a monetary expansion the pertinent differential is: arv -= aM
?IA, + 4, (1 - A,)w
’
Gw
Again the YY locus will shift to the left after a monetary expansion. The same consequences also follow from ceteris paribus increases in either of the cash balance shares, y and q. With all four of the equations in the system given geometric form, the model can now be displayed in full via a four quadrant diagram in Figure 6. Here we draw the MM and YY loci under the condition that substitution effects of interest rate changes are more potent than income effects. The four quadrant diagram enables us to combine all the graphs developed above into a single picture. Moreover, this enables us to consider the simultaneous causation in operation in the model since there are no ceteris paribus effects when the full system is considered. The system appears in “general equilibrium” in Figure 6. Simultaneously all markets clear and the identity relation is satisfied. The configuration values of the endogenous variables-r *, P “, w “, and N *-provide a solution for the system. But as we emphasized earlier, N *, the equilibrium level of employment, need not be Keynes’ “full employment” level. The system might come to rest at an under-employment equilibrium. If N * is less than N F, it would be possible to raise employment still higher if, for example, the commodity price level could be raised by an increase in demand.
5. The Effects of a Money Wage Cut Our development of this variant of the ordinary IS-LM framework was motivated by our concern with the theoretical consequences of an across-the-board wage cut. The diagram we presented in Figure 6 provides us with a direct route toward a theoretical investigation of the outcome of just such a policy measure. Refer to Figure 7 where we present a possible outcome in a comparative statics exercise. Suppose we begin from a (in our 472
The Orthodox
General
Macromodel
Figure 8. equilibrium
special sense) less-than-full employment general equilibrium. Suppose further an across-the-board cut in money wages is mandated overnight that lowers the money wage rate from w * to w ‘. The immediate effect will be a withdrawal of labor services by workers who move down their labor supply schedule. The volume of employment falls, constrained from the supply side. The lower money wage rate implies a lower price level moving along the ZZ locus, which will induce laborers to raise their work effort and employers to reduce their demand for laborers. The NS schedule starts to shift to the left in quadrant Z while the ND schedule starts to shift to the right. The final outcome will depend on what happens in the money and commodity markets to mediate the magnitude of the labor market schedule shifts. We display a case where the money wage cut ultimately works its way through to a lower level of employment, N. The shift in 473
William
A. Darity,
Jr. and Wanda I. Marrero
I’
I
u* s---B Y’ ---I I’
A
I
+--J++ I
I
I r .---
I I
* r mm---
M
\
Comparative
statics
1
Figure 7. of a money wage
M’
cut,
possible
case
the MM locus to M’M’ is due to the combined effects of the money wage cut and the initial employment decline. The shift in the YY locus to Y’Y’ is similarly based upon the assumption that the effect of the wage cut dominates the price level decline. We end up with a lower money wage rate, a lower interest rate, a lower commodity price level, and a lower level of employment. The entire economy has downshifted. The possibility of a fall in employment after a wage cut is not strictly dependent upon the postulated shifts in the MM and YY loci. Readers are welcome to convince themselves by playing with the diagram if they are still in doubt. Nevertheless, our central result is obvious: A wage cut in a world with flexible prices and perfect competition will not necessarily result in an adjustment of relative prices that will lead back to the original level of 474
The Orthodox
Macromodel
employment, let alone a higher level of employment. In fact, if N * were less than full employment, in the sense advanced here, the Figure 7 case represents a situation where the money wage cut merely aggravates the crisis. Of course, the classicists, like most contemporary economists, lacked a notion of less than full employment when the labor market clears. They only conceived of the theoretical validity of a generalized wage cut from a set of initial circumstances where there is excess supply in the labor market. Our model speaks directly to the case of classical involuntary unemployment in Figure 8. Suppose, for example, there is an initial unemployment in the fixed wage t; > w * so that involuntary customary sense exists. Lowering the money wage is deflationary, which is apparent once more from moving down the ZZ schedule.
I’ I -
W
----I---/II N
i I I I I
I I
*
Y y’
I I I
I
I
I
--m--e
-
me
%Y Y’
\
M’
II
Potential
consequences
of
money
Figure 8. wage cut: classical model
involuntary
M unemployment
475
William
A. Darity,
Jr. and Wanda I. Marrero
However, since employment was constrained from the demand side, the initial effect of the wage cut will be to raise employment. Still there is no a priori reason for employment ultimately to rise when all the simultaneous effects work their way through the system. The central problem is that the joint decline in the money wage rate and the price level leaves unclear what happens to the critical labor market variable, the real wage rate. If the drop is nearly equiproportionate, a la Keynes, the system will not reach the market-clearing level of employment merely by a marginal cut in money wages. The money wage cannot fall continuously toward W0 without generating other effects throughout the system that cause the labor demand and supply schedules to shift. There is no reason for the shifts to bring about self-adjustment to labor market clearing. In fact, employment may remain largely unchanged, say at fi in Figure 8.
6. Some Famous Special Cases Hicks (1937) in his pioneering essay where he sought to graft the General Theory onto Walrasian theory contended that an interest inelastic money demand function is the major feature of the classical system that Keynes repudiated. This is a highly questionable interpretation of Keynes’ break with the classicists. Nevertheless, it is still of interest to examine what effects a wage cut will have in Hicks’ “classical” system once the system is amended to incorporate distributional considerations. After all the classical system provided the theoretical basis for the wage cut policy in the first place. There are two possible interpretations of Hicks’ classical case in our system. One interpretation is that the substitution effect is eliminated or L, = 0. This means that the MM locus will be negatively sloped in r-P space. Due to the distributional considerations the money demand function will still be interest elastic, and Hicks’ classical results will not obtain. A second interpretation states that interest rate changes have no effect on liquidity preference whatsoever so that L, = L, = 0. This means that the MM schedule will appear as a vertical locus in quadrant four of Figure 6. Changes in the quantity of money can no longer directly alter the rate of interest. How the YY locus shifts matters in determining the direction of change in employment since a wage rate decline precipitates a commodity price fall, Employment can still fall as the result 476
The
Orthodox
Macromodel
of a wage reduction. Unlike the conventional IS-L M framework the commodity market still matters in determining the level of employment, although the money demand function is interest-rate insensitive. Even with the strong condition L, = L, = 0, Hicks’ classical results do not emerge with macrodistribution. Another special case that has generated interest among socalled Keynesians, rather than with Keynes himself, is the now-venerable liquidity trap which Hicks treated as the antithesis of the classical case.4 This is the case which arises when the money demand function is infinitely interest elastic. This means that the MM locus will be horizontal in quadrant three of Figure 6. However, this does not mean that the interest rate is pegged because a cut in money wages and the accompanying change in employment will cause the MM locus to shift up or down depending, once again, upon the relative strengths of all the effects. A third special case that the Keynesians have promoted is the interest-inelastic investment demand function. This generalizes to interest-insensitivity of private expenditure. Again there are two possible interpretations. The weaker case is one where the substitution effects of interest rate changes vanish, or A, = 0. In this situation the YY locus will be positively sloped as in Figure 5. But insofar as monetary changes affect the interest rate, there is no dichotomy because the interest rate still operates through the incomes of profit recipients. Obviously, monetary changes also have a direct effect on aggregate demand via the real balance effects. Under the more stringent interpretation we would have A, = A, = 0 which implies that the YY locus will be vertical in the third quadrant of Figure 6. Interest rate changes could only influence employment so long as the labor supply varies in response to interest variations, presumably a weak effect. Next, we consider Kalecki’s case (1971) where all wages are consumed, a case where A, = 1. Under marginal product factor pricing the expression in (18) becomes infinitely large and the YY
‘In fact Keynes [(1936), p. 2071 did not think much of the empirical relevance of the liquidity trap: “There is the possibility that, after the rate of interest has fallen to a certain level, liquidity-preference may become virtually absolute in the sense that almost everyone prefers cash to holding a debt which yields so low a rate of interest. In this event the monetary authority would have lost effective control over the rate of interest. But whilst this limiting case might become practically important in the future, I know of no example of it hitherto.” 477
William
A. Da&y,
Jr. and Wanda I. Marrero
locus highly unstable. Simultaneously if A, = 1 then L i = 0 from inequality (8a). As (15) reveals, this means variations in either the money wage rate or the volume of employment will not cause shifts in the MM locus. The money market thus becomes a stable anchor in a world where there are dramatic fluctuations in aggregate demand.
7. Policy Measures Finally, we want to examine the implications of three policy measures that might be taken if it is believed that the prevailing level of employment, N”, is too low. These are policy measures ultimately advanced in place of a money wage cut. First, pure fiscal policy might be attempted-an expansion of public expenditure-which will shift the YY schedule to the left in Figure 6. This will put upward pressure on commodity prices. Employment can rise if Keynes’ full employment threshold (where a further increase in the price level cannot raise employment) has not already been reached. Second, a monetary expansion might be attempted which will shift the MM locus to the right in the third quadrant of Figure 6. This will put downward pressure on interest rates and upward pressure on prices as aggregate demand expands. Again the eventual effect on output depends upon whether the system is still at a stage where inflation can buy more employment. Third, consider a redistribution of income so that the profit share, 6+ is lower at the prevailing level of employment and output. This was Hobson’s (1902) prescription for “depression in trade.” If 6, falls the ZZ locus in the second quadrant of Figure 6 will shift to the right which implies a higher price level must accompany the prevailing wage rate. The higher price level implies shifts in the labor demand and supply schedules, as well as the commodity market equilibrium locus, that could work towards a higher level of employment. Thus, the redistribution strategy also becomes a means of inflating the economy. For all three of these latter strategies, inflation of commodity prices is the doorway advocated out of depression. This was the essence of Keynes’ policy position [Klein (1947)]. The version of the orthodox macromodel advanced here provides a clear theoretical basis for such a policy position and a theoretical basis for rejection of money-wage cuts as a cure for unemployment. 478
The Orthodox
Macromodel
Appendix This appendix presents the algebra of the model developed in the preceding pages. Logarithmic differentiation coupled with marginal product factor pricing permits us to rewrite the system under (9) as follows, where hatted variables are logarithmic rates of change: (A. la)
- (1 - 6,)ii, + (1 - 6,)P - 6,; = 0 ; C = -A,(1
- 6,);
+ (1 - A,&,)p
+ (1 - A,)(1
- 6,)ti (A. lb)
- [A, + (A, / PQ)l 62 ; R=(+-
uS)l; + VP- up ;
D = L,m,i;,
+ L,m,p
(A.lc)
+ L,m,A
+ IL, + CL,/ PQ)Im,;. The new symbols
are defined
(A. Id) below:
6, = W’QIJ’F(N,Q)l ; (I- 6,) = [wNIPFW,Q)I ; C = -(l
- A,)&,0
+ gd - A, t,f,
- A&,
+ (~4 + qA,)M ti + r&M Q&P 1 q; ?+ PFW,Q) PF(NTQ) PFW, Q) G g = PF(N,Q) v-(a~-a~)+(u+J~);
t, s ;
Tw PF(N>
Q)
(A.2a)
;
t,=
T,
PF(N,Q)
(A-) (A.2c)
’ (A.2d)
(A.2f)
479
A. Darity,
William
Jr. and
D E [l - L,y
- L,5q]
+ Lpmlnfv
rPQ
mm =-----
Wanda
d - L,m,,Q^
- L,yq
M’
+ L,mtwfw
- L,q$;
WN
m
I. Marrero
=-. w-M’
m
@.%d
T SU) tw M;
Err
mhr
T
(A.2h) M
’
Solving the system under (A.l) for G, p, fi, and r^yields the following reduced form equations: W-0
=
(1 - A,)(1
- g,.,) L,
1
mnR
+ (1 - 6,) $
I
A3 - (1 - A,) PQ
+ h,L,m, + L,m,
(1 - 6,)az]
[6,V-
+ (1 - A,)(1 P-c =
-0
- 6,)[(1
- U
-
(1 - 6J 2
I
C
- 8,)~;
- A,)(1
- L,mn
R
(1 - 6,) -
(L,m,
- S-V] D
. J-’
;
(A.3a)
+ L,m,)k
mm
1 R
s,(l - %,)A, + (1 - %)A,
+ km,
- (1 - 6,) $a-
R - L,m,
[(l - 8,)~:
C + (1 - A,)(1
- 6,)[(1
I
+ bf
- u;)fLl
+ (a:,r*’
= {-(I
- A,)(1
+ L,m,(l 480
a;)6,]
D
* J-’
- 6,)“(L,m,
- %)I(1
-A,%)
- sJu,S (A.3b)
; + L,m,)R - A,(1
- S,)] R
The Orthodox - L, m,(l
- s$Ja;
+ (1 - A,)(1
- a,D) c
- 6J2(a,S
L3
L,--m,
PQ +
- a;)~}
A3
-mm+
Macromodel
. J-’
;
(A.3c)
8,
PQ
>
A3
L3 6,m,
PQ
PQ
> 1
L.--A,--
R
+ h [L,m, - A,L,mAIR
+ US, (L,m,
+ 6, kc
+ (1 - 8,) [A,(1 [(C
+ A,(1
C
- UXL ,mw + L,m,)
- (US,- ut)L,m,l
- k
1
+ L,mJ
- 6,)
- d)U - 6,)V]
C
-
D
+ (1 - A2SJ]
u;D
A,%,)
. J-’
;
(A.3d)
1 where
J is given
below:
J = (1 - 6,)(uS,
--u~)[L,mw(A2+$>,.
481
William
A. Da&y,
Jr. and Wanda I. Marrero
. I(1 - A,)(1
- 6,,)L,m,
- (1 - A,G,)L,m,]
+ [(l - s,,cr,” + S,(u~ - a;)
~310 - kJL,m, .
+ 6, (a; -
(A.4)
It is immediately apparent in a system this complicated that changes in any of the exogenous variables G, M, Tw, Tn, y, or 9, will have ambiguous effects on the endogenous variables w, P, T, or N. The variable that is of special interest to us is the volume of employment. To make any precise claims we must make some assumptions about the relative magnitudes of some of the parameters in the model. In the discussion in the main text the diagram in Figure 6 was drawn on the assumption that substitution effects of interest rate changes are stronger than income effects. In the limiting case this would mean A, = L, = 0. If we make such an assumption here fi simplifies to:
>1
4 PQ
+L,-mu
hm R + G-L,m,R
+ (1 - 6,)
(u,S - a:) 2
m, + azL,m,
[
482
C I
+ SW[(cry - al)
- (0,” - a:)]
+ (1 - &,)[A,(1
- 6,) + l]u;D
L,m,C
The Orthodox
Macromodel
- fL rcuT-a’;‘)+A,(14,)V]D where
J is now
unambiguously
J = (1 - 6,)(a$
positive:
- a:)
L,m, [
hn PQ
La + (1 - A,)(1 - 6,) po m, - 6, [(l
- 8,)Ui
+ 6, (a:
- ul)(l
+ s,(uf
1
- us)]
- 6,) L ,rn=
L,mw
64.6)
.
Now we can consider some comparative statics exercises under = L, = 0. First, consider the impact on our assumption that A, employment of an expansion in government spending:
afl aC
--=
I
(l-6.J
[
(uz-ui)$m,
+ a_ [(UT - Us)
- (U,S - a:)]
+ u,SL,mw
L,m,
1
. g . J-’
.
(A.7)
The stronger the responsiveness of liquidity preference to interest rate variations and the weaker the propensity to hoard out of income from wages the more positive the effect of government money expenditure on employment, i.e., if IL,1 is large and L, is small. A strong desire for liquidity on the part of wage recipients could lead to a case where increased government expenditure might even lower employment. Next consider the direction of the effect of a monetary expansion on employment.
483
William
A. Da&y,
Jr. and Wanda I. Marrero
)1
A3 +L,-m, PQ
6, (u;-u;)
+(1-&J
(+&$a[
+ a: L,m,
I
(YA,+qAs)M+6rn PFW,Q)
- (US, - u,D)L ,mw
+ (1 - 6J [
(-/A. + qA,)M
PFW,Q)
(ai - u3
$
I
Cl-
[
(ur-4
1 YL, - qL,)
+ (1 - %J [A,(1 - 6,) + 11o,s(l - YL, - qL,) - 6, [(cry - CT;, + A,0
- UVl(l
- YL, - qL,)
. I-‘.
L4.8)
Like (A.7) the sign of (A.8) is ambiguous. As long as L, is fairly large while L, is small and as long as the interest elasticity of the supply of labor, a:, is fairly small, it would be reasonable to assert that the expression in (A.8) is positive. What about an overnight increase in machine stock? The direction of this effect is given by the following expression:
A3 m, 6, 0,” - iS,L,m,u,D > I PQ
+ L, -
484
The Orthodox
- (1 - 6,)
(ai - a:)
Macromodel
zrnm
[
+ uiL,m,
(1 - A,)6,
+ 6, [(af
- as)
I
- (+
1
a:)
- (1 - 6,)
L,%U(l - A,)S,
(a$ - a:)
-$a-
[ - (1 - 6,)[A,(l
1
L,m,
- 6,) + l] uiL,m,
+6,rcuf- UT) + A,(1
- 6,)V]
L,m,
. J-’
.
(A.9
Expression (A.9) is plainly ambiguous in sign, It is more likely to take the anticipated, positive sign the larger the interest elasticity of the labor supply. Keynes’ full employment might be interpreted as a case where changes in the key variables at policymakers’ disposal no longer raise employment, a condition where:
afi aN -=-=ad an2
aA ati =-co. a?, af,
(A.lO)
But the question that initially prompted our interest in these matters was the effect of a small cut in money wages on employment in a world where macrodistribution matters. Still assuming A, = L, = 0, dividing (A.3d) by (A.3a) yields the elasticity of employment with respect to a money wage change:
+L,-mm,
A3 PQ
>1 6,
R + G,L,m,R
485
William
A. Da&y,
Jr. and Wanda I. Marrero
+ 6, [(cry - as) - (al - a:)]
+ (1 - 6J[A,(l
- STkc *
- 6,) + l]u;D
a;) + A,(1
(1 - A,)(1
- 6,,)‘-
-6JV]
[6-V-
+ (1 - A,)(1
D
L3 PQ
m-R
(1-tin)%-1 + L,m,
L,m,C
(1 - 6,)0~]
- a=)[(1 - 8,)~;
1 R
C
- hnV] D
.
(A.ll)
Even with A, = L, = 0 the expression in (A.11) is still intractable as to the sign of the elasticity. Lowering money wages may raise or may lower employment, which has been our main point. Finally, one might want to explore the comparative statics of a money wage cut when the system begins with classical involuntary unemployment as in Figure 8. In this case we would treat our system as constrained from the demand side of the labor market. We would only need to replace equation (A.9c) with
N=ND
and that 486
work through the expression
(A. 12)
the analysis again. We can assure the reader for the elasticity of employment as a whole
The
with respect to the money wage rate will sign as the expression in (A. 11). Received: November, Final version received:
1979 January,
Orthodox
Macromodel
be just as uncertain
in
1981
References de Largentaye,
Jean. “A Note on The General Theory of Employment, Money. ” Journal of PostKeynesian Economics 1 (Spring 1979): 6-15. Hicks, John. “Mr. Keynes and the Classics: A Suggested Interpretation” Econometrica 5 (April 1937): 147-59. Hobson, J.A. Imperialism: A Study. London: George Allen and Unwin, 1902. Kahn, R.F. “Unemployment As Seen By the Keynesians.” In The Concept and Measurement of Znvoluntary Unemployment, G.D.N. Worswick, ed. London: George Allen and Unwin, 1976. Kaldor, Nicholas. “Alternative Theories of Distribution.” Review of Economic Studies 23 (1955-56): 83-100. Kalecki, Michal. “Outline of a Theory of the Business Cycle.” In Selected Essays on the Dynamics of the Capitalist Economy, M. Kalecki, ed. Cambridge: Cambridge University Press, 1971. Keynes, J.M. A Treatise on Money: Volume I, The Pure Theory of Money. London: Macmillan and Company, 1930. Keynes, J.M. The General Theory of Employment, Interest and Money. London: Macmillan and Company, 1936. Klein, Lawrence. The Keynesian Revolution. New York: The Macmillan Company, 1947. Pasinetti, Luigi. “The Economics of Effective Demand.” In L. Pasinetti, Growth and Income Distribution. Cambridge: Cambridge University Press, 1974. Ricardo, David. The Principles of Political Economy and Taxation. London: J.M. Dent and Sons, 1973. Robinson, Joan. “Pre-Keynesian Theory After Keynes,” Australian Economic Papers 3 (June-December 1964): 25-35. Taylor, Lance. “IS-LM in the Tropics.” In Economic Stabilization in Developing Countries, William R. Klein and Sidney Weintraub, eds. Washington D.C.: The Brookings Institution, 1981. Interest,
and
487