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Tuesday, May 6, 2014


I understand that several Marxist economists are preparing a response to my critique of Marx's labor theory of value, but while they are at it, let me drop the other shoe.  I have said many times that I think Marx is correct in asserting that capitalism rests on the exploitation of the working class [which class includes more of us than you might imagine.]  I have also referred to my published essay, "A Critique and Reinterpretation of Marx's Labor Theory of Value," accessible via the link at the top of this blog to  But thus far, I have only summarized my critique.  What is my reinterpretation?  Let me see whether I can do this without any math.

If you look at the labor value equations one can write from the specification of an economy's inputs and outputs in each line of production, you can easily identify the labor inputs because the letter l or the Greek letter λ is used to identify them.  But that is just a labeling convention.  Suppose the labor inputs were represented simply by aq, so that one could not tell from the notation which were the labor inputs.  Where in the formal structure of the equations does Marx capture the distinction, supposedly unique to labor, between labor and labor power?   The answer, presumably, is that labor inputs are put into the equations at full value, as it were -- one unit of labor counts for one -- whereas the iron, corn, and other inputs in the labor value equations are put into the equations at their discounted values, which is to say discounted by their labor values.  The key to all of Marx's conclusions is that the labor inputs are entered at full value, supposedly because "labor is the substance of value."

But this is a classic example of what is correctly called begging the question.  People defending Marx say that the correctness of Marx's mathematical claims [such as the claim that commodities exchange at their labor values] proves that labor is the substance of value.  But to prove those mathematical claims, they construct equations that assume that labor is the substance of value [so that they enter the labor inputs at full value.]  By showing formally that all of Marx's claims for labor values can be replicated for corn values or iron values, I demonstrated that Marx failed to establish his fundamental claim that labor is the substance of value.

But Marx's fundamental intuition about capitalism really is correct.  What he needs [and we as well] is some alternative formal interpretation of that intuition that, when embodied in a set of equations, does in fact identify labor as different from all other inputs, not by a mere notational convention, but by the structure of the equations.

An obvious but wrong answer is that labor is a direct input into every production process whereas no other input can make that claim.  But that is a mistake, the full unpacking of which would take me more time and lead us all deeper into the weeds than I think it wise to venture here.  Let me just say this:  If we restrict ourselves to inputs that are directly or indirectly required in all lines of production, then my mathematical refutation of the claim that labor is the substance of value is correct.  For example, food is required by workers, so it is indirectly required in all lines of production.  [Trust me, it is not a satisfactory reply to point out that no particular food is required by all workers.  I go into this in my article.]

In my essay, I offer an answer.  I do not claim it is the necessarily right answer, just that it captures what Marx has to say about labor and workers, and it yields all the desired mathematical results.  Frankly, I hoped that when I laid my idea out in my essay, some Marxist with much more mathematical ability than I would pick it up and develop it into a robust theory, as they say.  But since no one read the essay, so far as I can tell, that never happened.  Oh well, four hundred years from now, someone writing the early history of the emergence of socialism in the bowels of capitalism [or in the womb, if that sounds better] may hit on my essay when doing a search in whatever takes the place of the cloud, and I will at last get some respect.  Sigh.]

Here is the essence of my idea without all the linear algebra I laboriously worked up to give it an aura of respectability.  Marx says two things about capitalism, among many others, that we can use as keys to an alternative analysis.  The first is that workers are historically robbed of their access to and control over the means of production, until at last they have nothing but their ability to work, their labor, and are forced to sell that labor for a wage.  The second is that in the mystified and ideologically encoded rationalization of capitalism, workers are treated as commodity producers, on a par with all other commodity producers, who enter the free market and strike a free bargain for the "commodity" with buyers -- which is to say, with employers.  How can we model this historically unequal and conceptually mystified situation in the equations of a capitalist economy?

My suggestion was this:  Together with all the price equations defining the price per unit output of iron, corn, and so forth, add an equation for the "industry that produces labor.”   Now, in all the price equations there is a profit markup represented by the expression (1+π).  By hypothesis, competition and the movement of capital from sector to sector in pursuit of the highest possible rate of profit results in the establishment if a single economy-wide profit rate.   So, Ricardo and Marx [and other economists] claim, investment in iron, in corn, in cars, or in hats will produce the same rate of profit on the value of the invested capital.  If a capitalist is making 4% in hats when coat manufacturers are making 6%, he will pull his capital out of hats and put it in coats.  Shifts in output, intersecting with market demand, will move prices, which will move the profit rate, until everyone in hats, coats, or any other sector is making the same rate of return.

But though we talk about workers as producers of the commodity labor, they and they alone are unable to move their capital into other lines of production if their return is inadequate, because their "capital" is their bodies, and as the saying goes, for them to "cash in" their capital is to die!  So the system of equations must actually have two rates of return:  One is (1+π) for everyone but the labor producing sector.  The other, which we may call r, will appear as the factor (1+r) in the labor producing sector.  And it is quite possible that r will be zero even when π is quite substantial.

Now, this is really an odd way of talking, or indeed, of calculating, but it captures perfectly the ironic structure of capitalism, which talks as though workers were petty capitalists while really treating them as expropriated propertyless victims of exploitation.  [My book, Moneybags Must Be So Lucky discusses at length the deeper significance of the role of irony in Marx's economic writings.]

What is the consequence of the fact that the labor producers cannot move their "capital" in pursuit of a return on their "investment"?  The simple answer, easily demonstrated mathematically, is that the prices they pay for their "inputs"  [which is to say their food, clothing, and shelter] are driven up above their "labor values."  What is more, the extra amount they are thus forced to pay for their food, clothing, and shelter exactly equals the profit reaped by the capitalists in the system.

Now, the virtue of this novel and unfamiliar way of modeling what is going on is that the anomalous condition of the workers, and thus of labor, is built into the formal structure of the price equations and is not simply a just so story told as an accompaniment of the equations.

This way of modeling the economy also allows us to analyze the "relative exploitation" whereby those high up on the income pyramid exploit those lower down even while they in turn are being exploited by those who control capital.

Well, I assume that I have now lost all but the most indefatigable of you, so I shall go back to playing FreeCell and searching databases for charitable foundations.


Jerry Fresia said...

I would have to re-read everything a few times before I could comment intelligently on your contribution. But what strikes me about the math factor is its bias. For example, Marx's great insight here is his distinction between labor power and labor. Enter alienation. But mathematically alienated labor and labor are the same (no?). Which brings me back to Piketty: what's different? Ans: the data. Reminds me of the time I was in therapy explaining how my father, upon his return from work, would inspect carefully how I happened to mow the grass that day. The therapist noted that he needed empirical evidence to justify his feelings. So where does Marx's wonderful distinction between labor as human emancipation and alienated labor fit into any of these calculations? It seems that once we take that step into math, which may be necessary for determining what's behind prices, the early Marx drops out.

Robert Paul Wolff said...

well, I spent two books trying to show that the early Marx does not "drop out" when you capture his insights properly in a formal analysis, right up to showing how the ironic voice of Marx finds a place in the equations.

Jerry Fresia said...

Ironic voice in the equations. This is great stuff. There's so much to read!