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NOW AVAILABLE ON YOUTUBE: LECTURES ON THE THOUGHT OF KARL MARX. To view the lectures, go to YouTube and search for Robert Paul Wolff Marx."





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Thursday, April 8, 2021

PART VII THE IRONY HITS THE MATH

 

My Interpretation of the Thought of Karl Marx

 

Part Seven: The Irony Hits the Math

 

So Marx was wrong. The distinction between labor and labor power is not the key to understanding both the exploitation that lies at the heart of capitalism. But he is clearly right that the workers are exploited. Furthermore, he is clearly right when he claims that capitalism misrepresents itself as a system founded upon freedom for all including the workers. And he is right that capitalism manages both the mystify itself and, unlike the church, even to conceal the fact of this mystification so that both workers and capitalists and the economists who analyze their doings imagine wrongly that what goes on in the capitalist marketplace is free of the clouds of mystery that surround the altar and the throne.

 

It was also clear to me that the sophisticated mathematical reinterpretations of the classical school of Political Economy, while they were an enormous analytical advance on the arguments of Marx or Ricardo, completely failed to capture the mystifications of capitalism or the irony in the description of capitalism as a system of “free markets.” So I put to myself a question: is there some way of revising the mathematical analysis so that it preserves the power and clarity that had been achieved by the modern reinterpreters of the classical school while at the same time, in some manner of speaking, introducing the irony into the equations? No one had ever asked this question before, so far as I could tell. Indeed, no one had ever conceived it to be a question one could ask. But I had an idea.

 

Let us for a moment clear away the equations and ask what Marx is telling us about the situation in which 19th-century English workers found themselves. He is telling us that by a long historical process the workers have been deprived of control over their own labor, they have been deprived of the tools of their labor, they have been deprived even of the skills which they use in their labor.  As part of what Marx memorably called “the reserve army of the unemployed,” the workers are compelled to accept the wages that the capitalists offer and to labor in the factories in the manner and under the conditions dictated by their employers. They do not have land on which they can grow their own food if they choose not to accept employment in the factories. They do not have looms or forges, spinning jennies or lathes. They have only their own bodies which day after day they apply to the tools and raw materials presented to them by their employers.

 

Now, in a free market, a competitive market, a capitalist market – so all the classical Political Economists agreed -- there is a single ruling rate of profit which is adjusted and regulated by the free choices that capitalists make to move their capital from sector to sector in pursuit of the largest return on their investment. If a capitalist who owns a factory that weaves woolen cloth observes that capitalists in the furniture business make a higher rate of return (and, let us recall, that in the classical school perfect information is assumed), then over time and with some adjustment that capitalist can cash in his investment in the woolen factory and shift it with to a furniture factory. To be sure, this is not a switch that can be made overnight for there is a problem with what is called “fixed capital,” but over time and more or less bumpily, the capital gets transferred to the new sphere of production. This has the double effect of increasing the amount of woolen cloth available in the market and decreasing the amount of furniture available for sale. Changes in the relative size of demand and supply alter the prices at which these goods sell which in turn reduces somewhat the rate of return in the cloth industry and increases it in the furniture industry. So by an unceasing series of such individual capitalist decisions and actions the profit rate is perpetually equilibrated. This is the familiar picture painted by Ricardo and his lesser contemporaries. The system of price equations representing the operations of a capitalist economy provides a mathematical model for this story of what goes on in the normal functioning of capitalism.

 

Now, since capitalism represents itself – or, more precisely, misrepresents itself – as a system in which the workers must be understood as producers of a commodity, labor, on a par with the furniture producer and the woolen cloth producer, a mathematical model of this economy must include an equation for the labor producing sector. Like all the other equations, this equation must include a profit markup.

 

Thus far the mystification. Ah, but the labor producers, unlike the furniture producers and the cloth producers, cannot shift their capital to a different line of production when they observe that it pays a higher rate of return, for their capital is nothing other than their bodies and the only way they can cash in their investment in their bodies is by… cashing it in, which is to say dying. This is nothing against capitalism, of course. Capitalism places no legal or other constraint on the choices of the workers. It is just an unfortunate metaphysical accident, perhaps laid at the door of Descartes if someone must be blamed, that the workers’ body and soul are inseparable this side of the grave.

 

Suppose we were to write a system of equations for an economy in which the workers genuinely are treated as free petty commodity producers of the commodity labor. And suppose we were to express mathematically this unfortunate constraint on the workers’ ability to move their capital into other lines of production, thus in a manner of speaking – and only in a manner of speaking – building the ironic treatment of capitalism as a free market system into the equations.  Well, because of the unfreedom of those condemned to produce labor, the rate of return in that sector may not be equal to the rate of return in the other sectors and so it must be represented by a different variable, which in my new system of equations I arbitrarily decided would be ρ or rho. What mathematical conclusions could we then draw?

 

Without troubling you overly with the mathematics, and, I might say, hardly surprisingly, it turns out that the total profit appropriated in the system by all of the capitalists exactly equals the profit forgone by the workers on their capital – their bodies – by the fact that they cannot shift that capital about in pursuit of a better rate of return and hence are forced to sell their output below what would otherwise be its equilibrium price. (Those who wish to see all of this demonstrated mathematically can take a look at my essay A Critique and Reinterpretation of Marxist Labor Theory of Value, archived and accessible by the link at the top of this page.)  In the world Marx was looking at rho was effectively zero.

 

And there you have it. In a simple model that abstracts for the moment from any number of complications that in a fully developed theory would of course have to be taken care of, you can see transparently the real root of capitalism’s exploitation of workers, an exploitation, Marx makes clear over hundreds of pages, that was grounded in a long historical process leading from late feudalism to the capitalism of 19th century England.

 

This is just a beginning, quite obviously, but it is I think a good beginning for it places center stage in all of its complexity Marxist conception of the essence of capitalism and of the combination of theoretical and literary devices required to capture that complexity. Tomorrow I will say just a bit about how to develop this theory in order to make it come closer to fitting the reality of the capitalism we know today.

9 comments:

marcel proust said...

1) He is telling us that by a long historical process the workers have been deprived of control over their own labor, they have been deprived of the tools of their labor, they have been deprived even of the skills which they use in their labor.

When had they had all this: control over their own labor, the tools of their labor, or even any skills? As serfs during the feudal era? As peasants during the period between the Black Death and Industrial Revolution? Perhaps further back during the Roman Empire or the Roman Republic, or when various Celts and Germans dominated most of the European landmass? Certainly you can (almost) always find small numbers of urban or manorial workers who had skills and perhaps owned their own tools, but it is not evident to me that more than a small fraction were ever in command of their own labor. Imagining otherwise strikes me as akin to positing some long ago golden age.



2) A comment on the following passage (not reprinted in full)

Ah, but the labor producers, unlike the furniture producers and the cloth producers, cannot shift their capital to a different line of production when they observe that it pays a higher rate of return, ... I arbitrarily decided would be ρ or rho.

This calls to mind both the abbreviated version of one of Keynes's most famous quotes, "In the long run we are all dead" (full quotation here, and Malthus's analysis. Without yet having read A Critique, the logical rejoinder is that the difference between the rate of profit in "the labor sector" and all other sectors is merely a short run, out of equilibrium, phenomenon which is corrected in the long run by the shrinking of the sector (thus my mention of Malthus above). NB, I wrote "logical response"; like many arguments in economics, it is not limited by considerations of realism.

Perhaps more to the point: In the absence of technological progress, would not the falling rate of profit (in all other sectors) fall in the long run to the rate of profit in the labor sector? As the rate of profit falls, and the labor sector shrinks, providing ever fewer workers to the rest of the economy, all (non-labor) sectors not only shrink as well (because of fewer available workers) but become ever more concentrated until there is at last only one firm in the whole economy. one single gigantic monopoly owned by a single family or individual who no longer has a base of customers that can afford the goods at a price which allows for a profit?

marcel proust said...

Correction of a typo in my previous comment.

short run, out of equilibrium, phenomenon which is corrected in the long run by the shrinking of the LABOR sector (thus my mention of Malthus above).

Eric said...

Prof Wolff, having watched your Youtube lecture series that convered this material, I have been able to follow along. However, I'm wondering whether you might consider choosing a different symbol for this blog to represent the labor value variable. Perhaps τ or λ (I realize λ is used for a different value in your published article). As your post from yesterday currently shows up, the following is (I think) potentially a bit confusing for someone who does not consult the published article, as the displayed versions for your "Greek letter l" and the number 1 used by blogger.com/blogspot.com appear to be almost indistinguishable (at least with the web browsers, fonts, & platform I am using—my eyes aren't as good as they used to be)

Quoting from your post:

If we use the Greek letter l for labor value or quantity of embodied labor with subscripts indicating whether we are talking about the labor value of corn or the labor value of iron ...

100 + 2lc+ 10li = 300lc

...

(100w + 2pc+ 10pi)(1 + π) = 300pc

_______

That first equation is showing up on my screen as nearly identical to:

100 + 21c + 101i = 3001c

(except that I am able to see the subscripts as actual subscripts)


If you were to substitute τ instead, the first equation might be easier for some readers to understand:

100 + 2τc + 10τi = 300τc?

Jerry Brown said...

Marcel Proust, it seems to me that anyone who can make any finished product out of raw materials has skills even if it is a loaf of bread from grain you have grown. Growing things is a skill. Peasants had skills. A factory system tends to break up the production process into limited skill subsets and while it may be more efficient in some ways and end up with more total product your workers are likely to be skilled in only a small part of the production of a product. So they lost their skills , or at least the ability to use them.



Eric said...

Following on what Jerry Brown said, on a more macro level, the same is true with the capitalist transformation of the economic capacities of colonial possessions. The Caribbean region was self-sufficient prior to the arrival of the Europeans. As the economic output of the islands were reoriented to mainly produce single crops for export to Europe, eg sugar (or its derivative, rum), the islands lost their self-sufficiency and became wholly dependent on their colonial masters for not only finished manufactures whose production required more advanced technology than held by the islands but also almost all products other than those primary crops. This same process was repeated across the colonial world, throughout the Americas and Africa, and many of the former colonial states still have not escaped from this dependency.

Atanu Dey said...

Prof Wolff:

You write, "If a capitalist who owns a factory that weaves woolen cloth observes that capitalists in the furniture business make a higher rate of return (and, let us recall, that in the classical school perfect information is assumed), then over time and with some adjustment that capitalist can cash in his investment in the furniture factory and shift it with to a cloth factory."

I guess you mean that the capitalist would shift out of the cloth business and into the furniture business.

Regards.

Robert Paul Wolff said...

Yes, of course. Thank you my bad. I will fix it. Getting old, alas.

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