MARX BOOK DAY FIFTEEN

The central mystification of capitalism, Marx argued, is the representation of propertyless workers as legally free commodity producers exchanging their “product,” their labor, with the producers of corn and iron and wheat and cloth in a market free of all traditional constraints, both legal and customary. In order to capture this mystification formally in the equations representing a capitalist system, I had to find a way to treat labor both as a commodity like any other and also as not really a commodity at all, and I had to do this in such a way as to explain quantitatively as well as qualitatively the origin of the profit gained by the capitalists.

 

Let us recall the assumptions underlying the systems of equations by means of which the modern mathematical economists formalized the arguments of the classical political economists.  They made a series of behavioral and knowledge assumptions about the capitalists that allowed them to posit the existence of a single profit rate throughout the economy. Capitalists sought a maximum return on their invested capital, and they knew what rate was being gained by capitalists in all sectors of the economy, they were unconstrained by law, by tradition, or by sentiment as they moved their capital from sector to sector, seeking the greatest possible return.

 

A woolen cloth producer gaining 4% on his invested capital who saw that the producers of carriage wheels were making 7% would shift his capital from woolen cloth to carriage wheels.  This took some time, of course, because some of his capital was frozen in looms and spinning jennys which were no use in making carriage wheels.  But in time he would make the shift. This would reduce the quantity of woolen cloth being brought to market, and drive up the price. The carriage wheels he started to make would be added to those already in the market and drive down their price. By the “higgling and jiggling of the marketplace,” in Adam Smith’s felicitous phrase, a single economy wide profit rate would emerge.

 

But the workers were unable to respond in this way to market signals. By a metaphysical misfortune, which could of course in no way be blamed on capitalism, their fixed capital was their bodies. In order to cash in their fixed capital and switch it to a more profitable line of production, they would have to – cash it in, which is to say, die.

 

To capture this situation in the equations in such a way as to represent both the reality and the illusion of capitalism, I decided to introduce a new variable, standing for the rate of return in the labor sector. The Greek letter π was already being used for the profit rate gained by the capitalists, so I chose the Greek letter ρ to represent the profit earned, if there was any, in the labor industry.

 

Marx, observing the situation in mid-19^th century England, saw that there were a large number of displaced peasants who had streamed into the big cities looking for work. He described them in a famous phrase as “the reserve army of the unemployed.” Their desperation kept ρ at zero – which is to say, the workers were barely making enough to stay alive.

 

From an analytical point of view, it was now easy to see that the workers were compelled to buy their food, clothing, and shelter at inflated prices. I was able to demonstrate mathematically that the sum total of these inflated portion of those prices was exactly equal to the total profit gained in the other sectors of the economy. Since the workers were the great mass of the population, and since capitalists were driven endlessly to increase their profits – “accumulate, accumulate, that is Moses and the prophets to the capitalists” as Marx put it – the workers were the final consumers of most of the output of the system.

 

Thus, without introducing the faulty distinction between labor-power and labor, I could answer the question that Marx had posed to the classical political economists – whence profit? – In such a way as both to give a correct mathematically precise answer and also to capture the mystification that underlies all capitalist systems.

 

I wrote this all up complete with the mathematical demonstrations and in 1981 published it in Philosophy and Public Affairs. I was, as you can imagine, rather pleased with myself. I had identified for the very first time a fundamental problem in Marx’s account of capitalism – the fact that all of the propositions he asserted about labor value could be demonstrated for corn value, iron value, or wool value. 

 

AND THEN DISASTER STRUCK.

 

John Roemer, the most mathematically sophisticated Marxist in America, pointed out in a comment to the Journal that Josep Vegara, a Professor of Economics at Barcelona, had published essentially the same theorem in 1979 in a book entitled economía política y modelos multisectoriales.  I was heartbroken.  Such things do not happen in Philosophy [because we so rarely prove anything].  Still and all, the theoretical elaboration that followed the statement and proof of the theorem is quite original, but I doubt that anyone has ever taken note of it.  A word of advice to my readers;  If you prove an exciting theorem in theoretical economics, do not publish it in a Philosophy journal.