The model itself can be found in the essay that I have deposited in box.net. For those of you who choose not to look at it there, suffice it to say that the central idea is to model the workers' production of labor as an industry, on a par with all the others, in which however there is a rate of return that is distinct from the rate of return in the other industries of the economy. Because the workers cannot shift their "capital" into other lines of production, they are unable to capture a portion of the higher rate of return being offered there. Hence their rate of return, if indeed it rises above zero [which is to say, if the workers can manage to do better than mere subsistence], will always be lower than the society wide profit rate. Analytically, what this means is that whereas they are compelled to sell their "product" [their labor] at its labor value, they must buy their inputs [their food, clothing, and shelter] at prices above their labor value. This has the effect of transferring away to the producers of those wage goods a portion of the labor value produced by the workers. Not surprisingly, it is easy to show that the quantity of value this transferred away from the workers by forcing them to pay higher prices just exactly equals the value of the physical surplus generated in the economy and also exactly equals the money profit earned by the capitalists. If this does not seem intuitively obvious, reflect on the fact that in an economy hell-bent on expansion ["Accumulate, accumulate. That is Moses and the Prophets."], the consumers of final goods are the workers. The consumption of the parsimonious, pious, Puritanical capitalists is negligible -- there are, after all, very few of them relative to the workers.
Let us stand off a bit from the detail of the model and reflect on what our analysis has taught us. According to Marx, the central craziness (Verrücktheit, he calls it) of capitalism is the fact that the capacity to labor, to transform nature purposefully and artfully in the service of human need, is treated in the marketplace as a commodity. This absurdity has its historical roots in the separation of the working class from the means of production. It is, under capitalism, the root and source of exploitation, which, technically speaking, is the extraction from a factor of production of more value than is embodied or contained within it.
Thus far, I follow Marx completely. His insight is, in my judgment, correct, as are the essential elements of his historical account. (The two other fundamental crazinesses of capitalism, to which Marx devotes equal attention, are the emergence of money and capital as objectively real social forms, and the existence of internal crises of over-production. I cannot spend as much space here as would be required to deal with those "contradictions," although a fully adequate reconstruction of Marx's political economy must deal with both in such a manner as to establish their relationship to the treatment of labor power as a commodity.)
Marx locates exploitation in the sphere of production, not in the sphere of circulation (behind the factory door, not in the sunlit market), and identifies exploitation with the extraction of surplus labor-time from the workers. His principal analytic maneuver is the distinction between labor and labor power, and his most powerful justification for the labor theory of value is its success, in conjunction with that distinction, in identifying the precise source and quantity of surplus value extracted by the capitalists in the process of production. Marx's analysis of exploitation is incorrect, as we have seen. But his central insight is perfectly correct: the root of exploitation, and the source of surplus value, is the treatment of labor power as a produced commodity.
However, exploitation does not take place in the sphere of production; nor does it take place in the sphere of circulation. Rather, the extraction of the surplus from the workers takes place in the interaction between the spheres of production and circulation. To be precise, the extraction of the surplus comes about through the fact that the workers are forced to sell their product (labor power) at its labor value, but must purchase the non-labor inputs into their production process (that is, their food, clothing, and shelter) at prices driven above their values. Capitalists are able to earn the economy-wide rate of profit because they are able to shift their capital into or out of lines of production according to whether the short-term, or market profit-rate is above or below the natural or economy-wide profit rate. The anomalous status of workers prohibits them from shifting their "capital" about in search of a higher rate of return, and the existence of a reserve army of the unemployed effectively drives the rate of return in the labor-producing industry down to zero.
In Capital, Marx represents the workers, with bitter irony, as suffering exploitation because of the sheer metaphysical accident that their product happens to be capable of creating exchange value when it is consumed as a use value. In short, Marx says that the workers can be exploited because labor is the substance of value. The truth, not surprisingly, is the exact opposite: labor is the substance of value because the workers can be exploited!
To put the same point somewhat differently, the distinguishing logical feature of labor in a formal model of a capitalist economy is not that it must be chosen as numeraire, for that is simply false; nor that commodities, at their natural prices, exchange in proportion to the quantities of labor directly or indirectly required for their production, for that too is false. The distinguishing logical feature of labor in a capitalist economy is that the industry producing it does not in general earn the uniform rate of return on the value of capital invested. Any notational system which contains within it enough in the way of formal differentiation to permit an adequate representation of the formal structure of capitalism will preserve this logical peculiarity. It makes no difference whether we use the Greek letter lambda to signify that we are representing labor. What matters is that the logical, or formal, relationships between labor and the other elements of a capitalist economy be modeled in our formal system. So long as this condition is met, the formal structure we set out will be adequate to serve as the basis for an analysis of exploitation consonant with Marx's central insights.
There is a very great deal more to be said about the implications of this analysis, of course, and I simply cannot impose upon my little band of readers to that extent. But it is worth saying a few things to connect this analysis with the situation we confront in contemporary capitalist society, which differs in important respects from the world Marx was writing about.
Marx treated all labor as essentially interchangeable [referring on occasion to skilled labor as simply a "multiple" of unskilled labor.] This makes it possible for us to model capitalism as having a single labor-producing sector with a single "rate of return," ρ. He believed that historical forces were inexorably destroying the traditions of skilled labor, replacing it with semi-skilled machine tending labor. Indeed, this homogenization of labor, he thought, was the condition for the development of a unified proletariat. It was, on the side of labor, the counterpart, he thought, to the progressive absorption of small capitals into big capitals, leading eventually to a confrontation between big capital and organized labor.
But the reality, one hundred fifty years after the publication of Capital, is different. We see a segmented labor sector with seemingly permanent distinctions between unskilled, semi-skilled, and skilled labor. To model this situation properly we would need to introduce a number of distinct labor producing sectors, each with its own capital requirements [most notably in the form of education, resulting in what Gary Becker called human capital.] As Samuel Bowles and Herb Gintis showed many years ago in a fascinating journal article, this situation leads to what they called "relative exploitation." That is to say, capital exploits labor, and skilled labor relatively exploits unskilled labor.
All of this, in a quite natural way, can be understood as resulting from the different degrees of freedom with which workers in one or another of these "labor industries" can shift their "capital" so as to capture a larger share of the surplus. Intuitively, an unskilled worker who manages to acquire some post-secondary education acquires "capital" that allows her to shift to a different line of labor production without "cashing in" her body by dying. She has capital other than her body that can actually be transferred to a different line of labor production. It remains the case that she is exploited, and hence that the return that she earns on her capital is lower than the return on money capital earned by capitalists. But she does manage to appropriate some portion of the social surplus, which enables her to live markedly better than those in the unskilled labor sector. Not surprisingly, once she has made that transition, she does not retain either a subjective sense of solidarity with her former comrades nor an objective community of interest that could serve as the basis for the successful organizing of a united labor front.
By means of a formal analysis, I have managed to introduce the odd notion of a formal model capturing and encapsulating the mystification and false consciousness of capitalist economy and society. This takes us part of the way to an explanation of Marx's highly unusual language in Capital, the puzzle with which I started, but to complete my explanation, I must now spend some time talking directly about language. So tomorrow we take leave for a bit of economics and linear algebra and turn to English Metaphysical Poetry of the seventeenth century. You humanists can breathe a sigh of relief.