How To Attack Marx's Theory Of Value

Figure 1: Capitalism

1.0 Introduction

Before one can criticize a theory, one must first restate it. I take Marx to have:

1. Developed a theory of value as an aid to demonstrating that returns to propertied classes exist only through the exploitation of labor.
2. Argued that:
• The net national product, when evaluated at labor values, is equal to the net national product, when evaluated at prices of production.
• The total labor value of the commodities expropriated by the propertied classes is equal to the total exchange value of these same commodities, when evaluated at prices of production.
• The rate of profits in the system of labor values is equal to the rate of profits in the system of prices of production.

I take Matias Vernengo, Fabio Petri, and others to be arguing¹ over whether or not one must accept (2) to defend the conclusion in (1) that labor is exploited. In particular, many of those working with formalizations of a revived classical theory of value and distribution seem to defend (1) while noting that, in general, all three invariants in (2) cannot hold.

2.0 An Empirical Sraffian Defense of the Invariants

I start with another defense of the invariants, closer to Sraffa and different from the defenses that Petri argues cannot stand. Consider large aggregates of commodities mentioned in the invariants: the capital stock used throughout the economy, net national income, the total of all wage goods, luxury consumption bought by the capitalists out of their income, etc. One might expect an individual commodity to be highly capital-intensive² or labor-intensive. But would not such extreme cases average out in these aggregates? So cannot one assume, as a first approximation at least, that such aggregates have an average capital intensity, in some sense?

Sraffa's standard commodity formalizes this argument. The standard commodity is a commodity of average capital intensity for the production technology expressed in the ruling Leontief input-output matrix. Consider the circulating capital case, in which:

• All production processes produce one commodity as an output, and
• Abstract, homogeneous labor is the only non-produced input for all production processes.

Furthermore, assume that net national output consists of the standard commodity and that wages are measured in units of the standard commodity. Then all of Marx's invariants hold. Labor value accounting seems to be prior to and revealing of fundamental features of value and distribution under capitalism.³

I have a question about this approach. It seems to introduce an empirical element into Marxism where neither Marx nor his followers might accept such an element⁴. Are claims about exploitation of the worker being the source of profits dependent on how close the composition of national output is to that of the standard commodity? Would the truth or falsity of these claims be altered by technological innovations or change in consumption patterns that result in some aggregate becoming more or less capital-intensive?

3.0 The Fundamental Theorem of Marxism

I here consider another rationale for paying attention to labor value accounting, while accepting that all three invariants cannot be expected to hold in general. I refer to the so-called fundamental theorem of Marxism, that profits are positive in the system of prices of production if and only if labor is exploited.

The theorem is perfectly valid in the circulating capital case. But Ian Steedman, quite some time ago, produced an example with fixed capital in which profits are positive even though surplus value is negative⁵. Mishio Morishima's reaction was to redefine labor values in the case of joint production⁶. My reaction to this redefinition is much like Petri's to the New Interpretation and the Temporal Single System Interpretation (TSSI). It seems to retain Marx's invariants as uninteresting tautologies while muddying up how labor value accounting can be explanatory of price phenomena⁷.

4.0 Rectangular Input-Output Matrices

I next want to consider a more fundamental mathematical objection to the surplus approach, at least as reconstructed by Sraffa. Under what cases might the Leontief matrix corresponding to prices of production turn out to be non-square⁸? In other words, when might the number of cost-minimizing processes be more or less than the number of produced commodities? Under these cases, a unique standard commodity does not exist. If the number of processes is less than the number of commodities, the system does not yield a solution for prices of production, given the wage. Furthermore, if the number of processes is more than the number of commodities, the system does not provide a degree of freedom for distribution.

First, consider cases when requirements for use become more important because of the lack of enough processes to specify prices of production, given the wage. Suppose inputs into production include more than one non-produced input (for example, labor and different kinds of land). And suppose the marginal land⁹ happens to be fully employed (that is, not in excess supply). Then the marginal land may have a positive rent¹⁰. Prices of production now have, at least, a second degree of freedom.

At a switch point, the number of cost-minimizing processes is one more than the number of produced commodities. Michael Mandler imposes an arbitrary assumption that labor markets clear in one example. This assumption then results in distribution being fixed at a switch point in the example.

I believe there are other cases of rectangular Leontief input output matrices associated with joint production. The golden rule of growth considers smoothly expanding growth paths in which:

• Prices of production prevail, and
• The rate of profits equals the rate of growth.

As I understand it, a theorem about the Von Neumann model states that the cost-minimizing technique yields a square matrix along such a path. So, I guess, rectangular matrices can arise along such a growth path when the rate of profits differs from the rate of growth.

5.0 Conclusion

I have considered above different ways of complicating the story even more. My conclusion is that Marxist political economy should remain a live and exciting field of scholarly research.

Footnotes

1. The argument extends to what other aspects of Marx's thought depends on labor value accounting. For example, does his doctrine of commodity fetishism still retain an interest without such accounting? How about the distinction between classical and vulgar political economy? I have trouble seeing how historical materialism is implicated in these discussions.
2. As measured by labor values or by prices of production at a given rates of profits, for example.
3. Notice how under this reading, Sraffa's book, unlike, arguably, the Cambridge Capital Controversies, is not confined to an internal critique of neoclassical theory. By reconstructing classical and Marxist economic theory, Sraffa puts forward an (unmet) external critique of neoclassical theory.
4. I am not saying that Marxist economics cannot be empirically tested or does not have empirical implications. A lot of work has been performed looking at how close labor values and prices of production are to actual prices. And Marx directs one to look at struggles over wages, variations in the quality of wage goods, struggles over the length of the working day and working conditions, the formation of industrial reserve army, etc.
5. Gustavo Lucas and Franklin Serrano have recently commented on Steedman's example.
6. Under joint production, the output of some production processes consists of more than one commodity. Fixed capital and non-produced land-like natural resources can be analyzed as special cases of joint production.
7. John Roemer has proposed an even more radical definition of exploitation, using game theory concepts and, I guess, dropping labor value accounting.
8. One can consult the work of, for example, Christian Bidard, Michael Mandler, and Bertram Schefold to find quite different perspectives on these issues.
9. Which kind of land is marginal is determined endogenously.
10. I am not at all sure that this corresponds to the case of Marx's absolute rent. Anyways, if one accepts the existence of another degree of freedom here, has one located another potential contradiction between Volumes 1 and 3 of Capital?