Thursday, October 12, 2023

MARX BOOK DAY FOURTEEN

As we have seen, Smith, Ricardo, Mill, and Marx and their many lesser compatriots wrote their works of political economy with little or no mathematical elaboration. The sophisticated mathematical economists who returned to that tradition in the 1960s, 1970s, and 1980s brought to bear on it the powerful tools of linear algebra and associated branches of mathematics. For a while in the late 1970s and early 1980s I was content simply to read book after book, following the arguments given by the authors and deepening my own understanding of the classical tradition of political economy. But after I had plowed through two or three thousand pages of mathematical economics, several things began to dawn on me.

 

First of all, as I have struggled very hard to make clear, the central theme of Marx’s analysis of capitalism is that it is thoroughgoingly mystified. It portrays the marketplace as a realm, in Marx’s wonderful phrase, of Freedom, Equality, Property, and Bentham, whereas the truth is that is a thoroughly mystified misrepresentation of the reality of capitalism, which is a realm of exploitation and domination. But in the formal reconstructions of the arguments of the classical political economists, none of this mystification appears. The equations are precise, transparent, and – as one author after another demonstrates – essentially correct. The labor value of the physical surplus in each system is in fact equal precisely, mathematically, to the surplus labor extracted from the labor inputs. What is more – and this will be gone into in considerable detail later on – it is even possible to demonstrate that in an extremely important subset of all the possible cases, the money profit appropriated by all of the capitalists in the system can be derived from that surplus labor value.

 

In my attempt to make the modern formal reconstructions of classical political economy available to an audience not familiar with linear algebra, I constructed little corn – iron models like System C with variables for the amount of corn, the amount of iron, the labor value of corn, the labor value of iron, the price of corn, the price of iron, the wage rate and the profit rate. But in the books I was reading, the authors did not bother with such elementary examples. It was page after page of matrices with variables like a1, a2, … an and such.

 

One day, as I was working my way through a page of mathematics, a thought occurred to me. “I have been asking how much labor is required, directly or indirectly, to produce a unit of iron. That is the labor value of a unit of iron. I wonder how much corn is required, directly or indirectly, to produce a unit of iron.  What is the corn value of a unit of iron?”

 

THE CORN VALUE OF A UNIT OF IRON!  What on earth are you talking about! There is no such thing as the corn value of a unit of iron. This is the LABOR theory of value, for God sake!”  But then I thought to myself, “Why can’t I calculate the corn value of a unit of iron?”

 

“Well,” I asked myself, “is that question even meaningful? How do I know that the amount of corn required directly or indirectly to produce a unit of iron is always a positive number? And since there is nothing special about corn in relation to iron, the question I am really asking is whether any input into production can serve as the basis for such a question."

 

Nobody in all of the books I had read had ever even hinted at such a question, but by this point I had acquired sufficient familiarity with the mathematics so that, with very little difficulty, I was able to prove the following proposition: So long as there is a physical surplus anywhere in the system of any of the inputs into the system (restricting myself, of course, to inputs that are required directly or indirectly in all lines of production, which excludes luxury products like theology books), all of the ai values in the system will be positive quantities of the input ai.

 

Fairly quickly, with very little difficulty, I was able to demonstrate that all the propositions Marx and his predecessors had asserted regarding labor values could be demonstrated equally well for corn values, iron values, or a–values, indeed for any input a required directly or indirectly in all lines of production.

 

But this, I reflected, striking though it might be, was irrelevant to Marx’s argument, because that argument dependent on the distinction between labor-power and labor, and there was certainly no distinction to be drawn between corn–power and corn, or iron–power and iron, or, in the general case, ai–power and ai.

 

And then I realized something enormously important, something that, so far as I could tell, no one else had ever thought before me. The distinction between labor–power and labor seemed to be an essential part of Marx’s argument in Capital but there was no symbol in the formal mathematical reconstructions of Marx’s argument in Capital that corresponded to the concept of labor–power!

 

Let me say that again. In the formal mathematical reconstructions of Marx’s argument, there were symbols for corn, iron, and all the other inputs into production, there was a symbol for labor with units of hours, weeks, years, or whatever, there were symbols for the prices of the inputs into production, for the labor values of the inputs into production, there were symbols for the wage and for the profit-rate.  But there was no symbol for labor–power. That term played a central role in Marx’s argument in Capital but played no role at all in the formal reconstruction of his argument.

 

My first thought was, So, Marx was wrong.  But then I thought, He wasn’t wrong.  He understood, in a way that nobody before him really had, that capitalism depended on the existence of a large mass of propertyless men and women who were compelled, if they wanted to live, to sell their labor as though it were a commodity.  As Marx said in chapter 6, “For the conversion of his money into capital, therefore, the owner of money must meet in the market with the free labourer, free in the double sense, that as a free man he can dispose of his labour-power as his own commodity, and that on the other hand he has no other commodity for sale, is short of everything necessary for the realisation of his labour-power.”

 

The question I faced was precisely this: How could I represent formally in the equations both the reality of exploitation and the appearance of free equality? How could I introduce the mystification into the equations, as it were?  The labor/labor–power distinction was Marx’s unsuccessful effort to solve this problem, but his fundamental insight into what was happening in capitalism was, I was convinced, absolutely correct.

 

Tomorrow I will explain the solution I came up with, a solution which I published forty-two years ago.

 

 

25 comments:

  1. The professor has correctly pointed out a number of times now that Marx “understood, in a way that nobody before him really had, that capitalism depended on the existence of a large mass of propertyless men and women who were compelled, if they wanted to live, to sell their labor as though it were a commodity.”

    When you think about it, this is extraordinary. Because isn’t this insight available even to the most middle-class (and therefore most thoroughly indoctrinated into the mystifications of Capital) 16-year-old in his or her first summer job? It is—or ought to be—perfectly obvious that the lowest-paid laborers, the dishwashers and busboys, are essential and are working just as hard as anyone else, and yet are only making enough to put gas in the car to get to work.

    And while for middle-class kids the summer job is meant to serve mostly as an object lesson (“stay in school or you’ll be washing dishes when you’re 30”), this doesn’t change the nature of the work, nor the labor relation, nor the obviousness of Marx’s insight.

    So it must have been that Marx’s predecessors, those gentlemen, were either somehow simply unfamiliar with labor and laborers (which seems unlikely) or they had somehow contrived to push this image out of their consciousness, in order to not see this large mass of humanity and be discomfited by it.

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  2. Couldn't be at the same time the realm of freedom, equality and property and Bentham and of
    exploitation and domination?

    It just depends on whose point of view we're talking about, but one point of view isn't more
    "real" than the other.

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  3. Re: the peculiar sort of “freedom” available to the great mass of workers, in law we have the notion of “freedom of contract”, which had been banished, temporarily it seems, by the New Deal. That is, workers are “free” to enter into a notional “contract” with their employers. This contract has some funny provisions in it (for one thing it is for at-will employment), and sure it may seem just a bit one-sided, but it’s a contract, so everything is hunky-dory and there is nothing to complain about. So which of these interpretations is more real: that this is a bona fide contract, or that this contractual interpretation is just so much bullshit?

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  4. Wrt John Pillette's remark, it just so happens that in the just published New Left Review Perry Anderson discusses the role of power in relation to law. The piece is primarily about "international law," a topic that has come up in this blog on several occasions, but he does include some observations on the role of power in domestic law too. His remarks in both cases will no doubt arouse chagrin in those who take law to be the be all and end all.

    It's here: https://newleftreview.org/issues/ii143/articles/perry-anderson-the-standard-of-civilization

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  5. The point of view of the capitalist is just as "real" as the point of view of Marx's hypothetical class conscious worker.

    The capitalist point of view is so real that they've kept the fucking system operating for
    about 250 years now (Wealth of Nations published in 1776) and convinced most of humanity that their point of view is the "real" one.

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  6. Ha ha ha! Well, the exact numbers on just who is convinced, and who is forced to go along (while muttering “e pur se muove” sotto voce), and who makes a point of not thinking about it are a little hard to come by. But it’s the people who inhabit and constitute the delusional op-ed-o-sphere that seem to me to be the most contemptible.

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  7. In the (schematic) model of Capital v. 1, workers "own" the commodity labor-power and have to sell it in order to live.

    They appear to be selling it in an open sunlit marketplace under conditions of "equality," but according to Marx that is an illusion because it masks the reality that, acc to Marx, labor-power creates more value than it contains, so to speak, and that the capitalist appropriates that extra value. (RPW agrees w Marx that workers are exploited in some more than colloquial sense of the word "exploitation" but disagrees w Marx on the details of how they are exploited.)

    Marx's notion of exploitation is technical rather than colloquial, and so, contrary to John Pillette's first comment, it has only a very attenuated connection, if any, to a teenager working a menial summer job for pocket money. Phenomenologically the kid may feel exploited in the colloquial sense but he probably doesn't even fit into Marx's schematic model: the teenager is working for pocket money or extra cash, not selling his labor-power in order to survive.

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  8. james wilson
    Thx for ref to Perry Anderson article, which appears to be open access at the moment though maybe I didn't scroll down far enough in it. He refers close to the beginning to the Treaty of Westphalia, which is a common and minor error: no such thing as the treaty (singular) of Westphalia. Rather two main treaties comprising the Peace of Westphalia. Still, in an article critiquing int'l law, it's not the kind of thing one wants to lead off with.

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  9. I don’t know why Anderson in his NLR piece omits the North American decision that established that the “merciless Indian savages” were uncivilized and therefore had to go, but I remember reading it in law school and chuckling to myself over its laughably tendentious reasoning. I don’t remember the name of it, but the reasoning was more-or-less identical to the cases he cites. This being law school, there was no discussion of the implications arising therefrom …

    Otherwise, OF COURSE there can be no comparison between the grubby imperialism of say Belgium in the Congo and the United States’ selfless efforts to make the world a better place. These efforts may go a teensy bit, ah … awry … sometimes, but our hearts are in the right place. Theirs are not. I’m sorry but this is SCIENCE. Some peoples just happen to be “exceptional”.

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  10. John Pillette

    I don’t think anyone seriously believes that US efforts “to make the world a better place” is because we’re more noble than anyone else. We do it because it’s in our interest to do it. The Marshall Plan was sold to Congress that way. So was the occupation of Japan. What was the “grubby imperialism” in that? Ditto billions of $$ in foreign aid to developing countries. You can add tariff preferences for imports from developing countries. In fact, you are absolutely right in saying, “OF COURSE there can be no comparison between the grubby imperialism of Belgium in the Congo.” There sure as hell can’t.

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  11. Don't you have to distinguish between how policies were sold to Congress and other powerful interests and how they were sold to the general public. Another distinction would have to be drawn between the various elements of foreign aid, at least some of it being tied to American advantage of various sorts both material and political?

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  12. American foreign policy is indeed a very mixed bag … one the one hand, we have the Marshall plan, on the other hand we have Iraq and Libya (and a few other examples). I’ll leave it to some Steven Pinker type to finish the P&L statement and calculate the exact degree of grubbiness and/or virtue.

    As for who “seriously” believes in our *mission civilatrice* it seems like most of the crew who writes for the NYT and the Atlantic, as well as all of the talking heads on TV. Kayfabe? Sincerely held belief? Who knows, but either way it’s certainly a mystification of what’s really going on.

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  13. anon

    The policies were sold to Congress and the public in ways that appealed to interests, which were many: employment for Americans; profits for Americans; concern for the suffering Europe; pictures of starving kids. It was no joke. We were told not to waste food—“think of the starving children in Europe.” Returning GI’s who were in the Army of Occupation came told vivid stories of what like was like in Europe. (My father was one of them.) The winter of 1946/7 was one of the coldest on record in Europe and people had little or no heat and little food.

    No victor had ever done what the US did after WWII—in allied countries like France and Britain, or in enemy countries like Germany and Italy, as well as Japan—although I think there wasn’t as much economic aid to Japan.

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