Do not cite, unless favorably.
James G. Devine
Professor of Economics
University Hall (Rm. 4227)
Loyola Marymount University
One LMU Drive, Suite 4200
Los Angeles, CA 90045-2659 USA
office phone: 310/338-2948; FAX: 310/338-1950
January 7, 2004
A. purpose: to explain Marx’s concept of exploitation using an equilibrium model with neoclassical production function exhibiting constant returns to scale, operated by a representative agent under competitive conditions.
1. Despite the obvious fallacies of this kind of model, the point is that if a flower can grow in such sterile soil, the flower must be robust: it adds evidence for the validity of Marx’s theory of exploitation.
2. The assumption is that an even more realistic model would be consistent with the Marxian theory.
3. This outline only discusses the graphs used in the main paper. The math is left out.
B. the two key elements making the model different from the pure neoclassical model are the dropping of Say’s Law and the introduction of variable effort, with effort rising with the cost of job loss and the size of the reserve army of labor (unemployment).
1. These two assumptions interact and reinforce each other: dropping Say’s Law (following Marx or Keynes) implies that involuntary unemployment is normal, while that unemployment motivates people to work to produce a surplus-product (to accept being exploited).
2. In addition, the model assumes an independent investment function, while technology is putty-clay, and a “wage curve” determines real wages (from Blanchflower and Oswald).**
a) The first is a necessary component of the Keynesian rejection of Say’s Law.
b) The second represents part of this paper’s distinction between the short and longer “runs.”
c) The last is a representation of one interpretation of Marx’s idea of the reserve army of labor.
C. Overview: Charts I through III represent short-term determination of the levels of profits and wages, while Chart IV represents the longer-term processes which determine the operations of the labor-power market in the neoclassical/Marxian model. (Below, click on the Chart name to see the diagram.)
1. Chart I represents the neoclassical case, in which operations of the labor-power market under Say’s “Law” determines not only profits and wages but the level of employment and output.
2. Chart II and Chart III drop Say’s Law, so that the level of employment is determined by effective demand (the sales constraint), which is taken as given.
3. Chart IV represents the longer-term determination of the level of employment by the interaction between profitability and accumulation.
Chart I: the Short-Run Labor-Power Market, under Say’s Law.
D. Chart I shows the simple neoclassical case, with the shaded area representing profits and overhead. Unlike the standard neoclassical model, it includes the role of variable labor effort (Marx’s distinction between labor-power sold and labor actually done).
1. It also shows that an increase in worker effort is not sufficient to imply exploitation, since it also causes a rise in equilibrium wages.
2. In my discussion, the pure neoclassical model is used as a baseline. It is assumed to represent a non-exploitative case.
E. Chart II drops Say’s Law and the wage curve, showing two elements of my model. (For simplicity, overhead is assumed to equal zero.)
1. The sales constraint represents limited aggregate demand, while the wage curve function determines real wages.
a) The latter need not be upward-sloping for my model to work.
b) Many see the sales constraint as upward-sloping (in that higher wages correspond to higher spending). However, in the short run consumer credit breaks this link. Further, in the model it is shifts of this curve, not its slope, that are important.
Chart II: the Short-Run Labor-Power Market without Say’s Law
2. This simple model shows a very simple version of the Keynesian idea of an unemployment equilibrium. One major thing that’s missing here – and in the entire paper – is the role of money and other nominal assets.
3. The graph also suggests that dropping of Say’s Law is insufficient to show Marxian exploitation. The economy could be in equilibrium at point B, with the wage rate equal to the marginal product of labor. Though this point is not developed in the current version of full paper, it seems that this case would be unlikely to have exploitation. In addition to dropping Say’s Law, we must have either unemployment depressing real wages relative to productivity or unemployment motivating further effort.
F. Chart III shows the effects of increased effort by workers (assumed to occur), which here can lead to increased profits. There are three separate effects.
1. the first effect is a rise in productivity and the MPL, which all else constant raises profits.
2. but for given aggregate effective demand (D), the demand for workers falls, hurting profits.
3. the decline of wages along the wage curve function (WCF) raises profits.
Chart III: Variable Effort without Say’s Law
G. Endogenous effort. In Chart IV, the level of effort is endogenized, made a function of the level of employment and wages.
H. Determination of the rate of profit by employment. The model of Charts II and III has a major implication, for the derivation of the relationship between profitability and employment.
1. As unemployment rises – and employment falls – we see that these conflicting effects (and similar) imply the upside-down U shaped ρ curve shown in Chart IV. (Some additional assumptions are made: see the longer version of this paper.) The profit rate (r) rises and then falls as employment falls. These changes occur due to changes in effective demand, taken as given in deriving this curve.
a) r rises due to increased realization of surplus-value (the Keynesian region).
b) r falls due to a wage squeeze on profits and decreased effort (the Marxian region).
2. The model is incomplete, so we need to turn to:
I. Determination of the level of employment by the expected rate of profit. It is argued at length in the main paper that a rise in expected profitability raises the rate of accumulation, which raises the level of employment (L). Further, it is argued that the accumulation curve (g) is not horizontal, for reasons that add realism to the model.
Chart IV: Profitability and Accumulation.
J. Equilibrium in Chart IV results from the combination of the ρ and accumulation (g), where the latter is assumed to rise with the expected rate of profit.
1. equilibrium occurs where the actual rate of profit (determined by ρ) equals the expected rate of profit. This determines both the level of employment (L) and the actual rate of profit (r).
2. only those equilibria where the g line cuts the ρ curve from below are stable. The arrows between the curves indicate the direction of disequilibrium dynamics.
3. Note that the model in this outline ignores a lot of relevant cases such as business cycles and depressions. It assumes that there is only one stable equilibrium, at high levels of demand (i.e., in the Marxian region).
4. interestingly, a purely neoclassical model (with a horizontal g curve) would have any profits bid away by unlimited accumulation. The Marxian equilibrium requires that accumulation not be unlimited, i.e., be deterred by falling expected profit rates.
* This was presented at the Allied Social Sciences Associations (URPE) convention on January 4, 2004. A very early version of this paper was presented at the ASSA/URPE convention on January 7, 1995. Thanks to Barkley Rosser, Gil Skillman, and Michael Reich for their comments on earlier drafts of this paper and to Pat Shanahan for help with the math. Special thanks to Roberto Veneziani for his innumerable comments on earlier drafts, which improved this paper immeasurably. Thanks also to Ismael Hossein-Zadeh for his comments on the longer version of this paper, even though I have not yet incorporated them into this manuscript. Of course, all flaws, whether cosmetic or fundamental, are my fault alone.
** For references, see the longer version of this paper.