Friday, April 03, 2015

How To And How Not To Attack Marx's Economics

1.0 Introduction

I am currently reading John Roemer's Free to Lose. I thought I would outline some areas where Marx can be criticized on economic theory, as well as some areas where I do not think he is not so vulnerable. (I do not think I had previously absorbed Roemer's theory of the emergence of classes from an analysis of reproducible equilibrium. But then the Roemer work I know the best is Analytical Foundations of Marxian Economic Theory, which may predate this explanation.) Another motivation is irritation with a series of post here.

2.0 Labor Theory of Prices

For purposes of this post, I put aside the question of whether prices tend to be proportional to labor values. I think Marx rejected this theory, including in the first volume of Capital. He says so, for example, in this passage:

"From the foregoing investigation, the reader will see that this statement only means that the formation of capital must be possible even though the price and value of a commodity be the same; for its formation cannot be attributed to any deviation of the one from the other. If prices actually differ from values, we must, first of all, reduce the former to the latter, in other words, treat the difference as accidental in order that the phenomena may be observed in their purity, and our observations not interfered with by disturbing circumstances that have nothing to do with the process in question. We know, moreover, that this reduction is no mere scientific process. The continual oscillations in prices, their rising and falling, compensate each other, and reduce themselves to an average price, which is their hidden regulator. It forms the guiding star of the merchant or the manufacturer in every undertaking that requires time. He knows that when a long period of time is taken, commodities are sold neither over nor under, but at their average price. If therefore he thought about the matter at all, he would formulate the problem of the formation of capital as follows: How can we account for the origin of capital on the supposition that prices are regulated by the average price, i. e., ultimately by the value of the commodities? I say 'ultimately,' because average prices do not directly coincide with the values of commodities, as Adam Smith, Ricardo, and others believe." -- Karl Marx, Capital, V. 1 (last footnote in Chapter V.)

I take "average price" in the above passage to be referring to what has also been called "such classical terms as 'necessary price', 'natural price', or 'price of production'" (Piero Sraffa, PCMC: p. 9). And Marx is saying that prices of production do not correspond to labor values, even though he is abstracting from this distinction in the first volume of Capital. Others have also asserted that a contradiction in Marx cannot be found here:

"Writers ... like E. Bohm-Bawerk have asserted that there is a contradiction between the analyses of Volumes I and III which is certainly not to be found there unless one reads into them an interpretation different from that which Marx repeatedly emphasized." -- William J. Baumol, "The Transformation of Values: What Marx 'Really' Meant (An Interpretation)" (, V. 12, N. 1 (Mar. 1974): pp. 51-62,
3.0 Heterogeneous Labor Activities

Employees perform many distinct activities in laboring under the direction of capital. I do not think this observation is sufficient, in itself, to hinder the development of a theory organized around labor values. Consider jobs provided by supposedly unskilled labor, such as stocking shelves in a supermarket or working behind the counter in a fast food restaurant. These sort of jobs are often treated as homogenous, both by workers and employers. Workers in one or other such job can transition among them easily enough in times of high employment.

What are jobs that require vastly different levels or types of skills? I do not think this is a problem for Marx as long as relative wages can be treated as stable:

"We suppose labor to be uniform in quality or, what amounts to the same thing, we assume any differences in quality to have been previously reduced to equivalent differences in quantity so that each unit of labor receives the same wage." -- Piero Sraffa, (1960: p. 10).

As far as I can tell, this is a common position among the classical economists, with Adam Smith providing an early explanation of wage differentials.

A problem can arise here, however. Suppose some skills are acquired through an investment, such as paying for higher education. Perhaps there is a tendency for skilled workers to make decisions based on anticipated rates of return. Then, just as Wicksell effects express the dependence of the price of capital goods on distribution, so relative wages would vary with distribution. And labor values would be dependent on prices. One could then express labor value as a vector of different quantities of different types of non-competing workers. But would the assumption that the economy hangs together - e.g., all commodities are basic - work in this case? Or one could make the claim that even skilled labor is heavily produced in the household and outside of firms run for profits. And, thus, calculations of rates of return for acquisition of many skills for the worker are empirically unimportant. (I think I take this objection, as well as the first response, from Ian Steedman.)

4.0 Labor Values Dependent on Choice of Technique

I take labor values as being found from the processes used in production, as expressed in a Leontief input-output matrix and labor coefficients. The components of such matrices and vectors are given in physical units. The analysis of the choice of technique shows that the cost-minimizing technique varies with distribution. So, here too, labor values depend on prices, instead of vice-versa.

Here one could object that the choice of technique is a highly artificial problem, of interest primarily for an internal critique of neoclassical economics. In actuality, firms do not have a choice at any time of processes from a pre-existing menu. Rather technology evolves as a non-reversible process in historical time.

5.0 Volume III Invariants Cannot All Hold

In the above, I have been concentrating mostly on objections to the premises of Marx's economic theory. Let me consider a conclusion. According to Marx, accounting in labor values allows one to identify certain invariants that hold for the economy as a whole. For example, the sum of labor values for gross outputs of industry is equal to the sum of gross outputs, evaluated at prices of production. And the sum of surplus value across industry is equal to the sum of profits. According to Marx, the competition under which prices of production are formed redistributes total surplus values into aliquot quantities distributed to each industry.

Under the traditional analyses of prices of production, Marx was just wrong. For an arbitrary numéraire, not all invariants can simultaneously hold.

Four answers have been given to this issue. I do not think highly of traditional Marxists who argue that one or the other invariant should be given preference. Typically, such arguments are presented with a lot of Hegelian terminology. I find intriguing the argument that all invariants can hold if one adopts Sraffa's standard commodity as the numéraire. Duncan Foley and Gerard Duménil have proposed the new interpretation, organized around the concept of the Monetary Expression of Labor Value (MELT). As I understand it, the new interpretation makes Marx's claims too much a matter of an accounting tautology for my taste. Finally, there is the Temporal Single System Interpretation (TSSI), which I associate mainly with Alan Freeman and Andrew Kliman, although, I guess, they work with many more scholars. Of course, more invariants can be made to hold if you interpret the theory to have many more degrees of freedom.

6.0 Exploitation of Corn

A theorem in the analysis of prices of production states that the rate of profit is positive if and only if labor is exploited. Exploitation here has a technical definition; it is not an ethical concept. From John Roemer, I learn that one can argue that Marx had both ideas in mind.

Anyways, from the same analysis, one can show that same theorem holds for any commodity (that is basic or in the workers' consumption basket?). So why focus on labor? Answers have been given that deal with matters not in the math at this level of abstraction. Workers, unlike owners of commodities sold as means of production, must be brought under the direction of the capitalists when they hire them. Furthermore, the agreements laborers strike are, at best, incomplete contracts. Not all activities that the workers will be expected to perform in given situations can be prespecified. Furthermore, often some will be unpleasant, and a tug-of-war can arise between the worker and the capitalist's representative in the workplace.

Whatever you think of these rationales for focusing on the exploitation of labor, the issue of working conditions seems like a perennial concern.

7.0 Falling Rate of Profit

I do not have much to say about the theory of the falling rate of profit. I think Marx was mistaken here, but recall this is a volume 3 theory, never published in Marx's lifetime. I am aware of Marx's account of countervailing tendencies. (How is this a theory, if no explanation is given why one tendency should predominate?) And, as usual, theorists in the TSSI tradition disagree.

9.0 Outside the Theory of Value and Distribution

Such a brief overview, compared to the thousands of pages Marx wrote, and the many ways scholars and followers have read (parts of?) this work, obviously cannot cover all issues. I have said nothing about historical materialism, for instance. If this theory is read as mandating economic determinism, with no possibility of the superstructure shaping the evolution of the economic base, I, like many others, think the theory is wrong.

Nor have I said anything much about many of Marx's analyses that can be developed independently of the theory of value and distribution. For example, I like to set out Volume 2 models of simple and expanded reproduction in terms of prices of production. Whether or not Richard Goodwin's theory of the business cycle is Marxist or is descriptive of some capitalist economies at some time seems to be independent of Marx's theory of value. And Marx had many other analyses of concrete situations that might or not be worthwhile. For example, in Volume 1, he presented the introduction in Great Britain of laws regulating maximum hours of work as addressing what we would now call a prisoner's dilemma. Each mill owner would like to work their employees until their health breaks, fire them, and then hire refreshed workers. But if all mill owners are doing this for wokers from a young age, no large population of such refreshed workers will exist in the locality. So the owners need such laws after a certain level of development.

I suppose I should say something about the theory of monopoly. I do not see why prices of production cannot be developed with different markups in different industries. I may not be familiar enough with the literature, but it is my impression that many accounts of markup pricing do not take into account constraints arising from the inter-industry flows emphasized in Sraffian theory and empirical work in Leontief input-output analysis. Furthermore, markups cannot be so high in a viable economy that demands total more than the net output of a viable economy. (A theory of cost-push inflation can arise here.) This is not to say that I do not think those exploring administered, full-cost, or markup pricing are not looking at something empirically important.

And Marx had many detailed empirical observations, including claims about how feudalism evolved into capitalism. I cannot address such matters of history. Finally, I have said nothing above about the sociology of economics. I think the above is quite enough for one post.


LK said...

On (3) I think you badly underestimate how heterogeneous labour presents a terrible aggregation problem for Marx's homogeneous abstract socially necessary labour time units.

How does one aggregate the work of surgeon, mathematician, lawyer, bricklayer, or janitor? You have a problem here almost as bad as aggregating interpersonal subjective utilities.

Not to mention: why aren't slaves or animals considered to be capable of creating value?

Ian Wright said...

Hi Robert,

When you say, "I find intriguing the argument that all invariants can hold if one adopts Sraffa's standard commodity as the numéraire", what work are you referring to here?


Robert Vienneau said...

Ian, I've written up the mathematics here, for example. I think of this as echoing John Eatwell's Mr. Sraffa's Standard Commodity and the Rate of Exploitation (1975). Since Sraffa's papers have been opened up to scholars, some have found a similar take on Marx in them. Riccardo Bellofiore is the economist that springs to my mind on this issue.

Part of the point of Chapter 1 of Capital is the raise the question of how all commodities come to be treated as commensurable under capitalism. It sounds crazy to reduce all those sorts of concrete labors to one common measure. Yet that is what happens in the market.

Emil Bakkum said...

It is. May I make three comments? Concerning the TSSI: even in a system with simple reproduction the TSSI predicts a continuous change of the labor values of the products. This is caused by the continuous value transformation, and the redistribution among industries. Of course this may be happening, but nonetheless it is strange. Concerning the transformation problem: the Leninists denied that it exists (perhaps they still do). I get the impression that they argue that equilibrium prices do not exist in capitalism. The economy is dynamic, and always out of balance, and in addition the labor productivity is always changing. Then obviously the model of Bortkiewicz is irrelevant. it also means that the theory of Marx can not be formalized. She is just a supposition, a hypothesis. Concerning the falling rate of profit: it seems that according to Keynes eventually capital will become abundant (with respect to labor), and thus its price will fall. This is a reasonable assumption. So if you replace the profit rate by the interest rate, Marx may be right.

Ian Wright said...

Thanks for the post and the pointers to your article, and also Eatwell's. You're referring to the fact that Marx's invariants are true IF the economy is in standard proportions. I thought you were indicating the existence of a stronger result.

As I point out here Sraffa's standard commodity is really a proxy or indirect reference to a generalization of the classical measure of labour cost. All Marx's invariants hold when we measure real costs in terms of this more general measure.