My success at downloading the 1981 article, "A Critique and Reinterpretation of Marx's Labor Theory of Value" has made it possible for me to incorporate portions of it into this narrative, rather than trying to recreate its argument de novo. I will omit completely the mathematics, relying on interested readers to find their way to that article for the hairy details. [I am pretty thrilled by the fact that forty-five of you have already done so!]
The problem, just to repeat myself, is to find some way of modeling the anomalous condition of the workers in a capitalist economy so that this anomaly makes its way into the mathematics rather than serving merely as an extraneous story that Marx tells while doing his economic analysis. My strategy is to ask what happens in our model if the producers of one of the inputs into production have imposed on them quite arbitrarily the constraint that they, unlike their fellow capitalists, are unable to shift their investment from sector to sector in search of the highest available rate of return. After analyzing mathematically what happens to prices in that peculiar case, I then give Marx's reasons for believing that labor producers, which is to say workers, do indeed suffer under that constraint. We shall see that everything Marx wants to say about exploitation can be captured by this maneuver, and can be demonstrated to be what in fact happens in a capitalist economy, all without invoking a supposed distinction between labor and labor power.
Here is what I say in my 1981 article:
We have been looking at the consequences that flow, in our model, from the imposition of some exogenous constraint on the ability of producers in one sector to earn the going rate of return on the value of capital invested. Since the mechanism that insures a uniform rate of return is the free flow of capital from sector to sector -- capitalists shifting their capital out of sectors yielding a relatively low return and into sectors yielding a relatively high return -- our exogenous constraint must consist of some impediment to the flow of capital into or out of the industry in question.
Now, I should like to suggest that this is precisely the proper way to construe labor in a capitalist economy. This is not, of course, the way in which labor is treated either by Ricardo and the neo-Ricardians or by the neo-classical school. Sraffa and his followers treat labor as a non-reproduced resource, the amount of which is given for a given economic system. Indeed, the total quantity of labor available to the system is one of the normalizing constraints on the system, in Sraffa's analysis. But this is clearly not the way in which Marx thinks of the matter. Labor power is described by him as a commodity, and a commodity, technically speaking, is a good produced for the purpose of exchange on the market in such a manner as to be characterizable as having been produced by abstract, socially necessary labor. (What this means, among other things, is that there is a competitive market for the commodity that drives out inefficient means of production, and so on.) Like all other commodities, labor power has a natural price, toward which its market price tends.
So we must render labor power, in a model of a capitalist economy, as a produced commodity, and insofar as we restrict ourselves to the simplification of single-product industries, we must identify one of the industries in our model as the labor industry -- that is, the industry producing labor power for ex-change on the market. Precisely at this point, as Marx is at great pains to make clear, the whole superstructure of liberal bourgeois philosophy and political theory and law is introduced to justify the treatment of labor power as a commodity. Workers are treated in law, in ideology, and in philosophy as small producers, petty entrepreneurs who bring their product, like any other capitalists, to the market and exchange it for the products of other capitalists' enterprises. Their fixed capital is their bodies, which --according to classical liberal philosophy and jurisprudence -- they own. Their circulating capital is the fund they spend for food and clothing. Assuming that they live at the level of bare subsistence, the worker-capitalists are not likely to hire labor services (although they may be forced to go to a doctor from time to time). Hence, all their capital will be constant capital, none of it will be variable capital, to use Marx's terminology.
Why are the workers unable to move their capital freely to sectors paying a higher rate of return? The simple answer, of course, is that their fixed capital is their bodies and their circulating capital is the food they eat to stay alive. A steel producer who finds the return in steel declining can, given a long enough period of time, cash in his investment and shift his capital to clothing, rental housing, or luxury appliances. The worker who notices the absence of any significant rate of return on her capital investment, and who, like any prudent capitalist, wishes to shift to a more profitable line, will find it necessary to separate herself ("alienate herself," to use the technical legal term) from her body. And by a quite unfortunate metaphysical accident -- which, however, can scarcely be blamed on capitalism itself! -- she is unable to survive that particular liquidation of her investment!
It will be objected that workers are not really petty capitalists. Just so. But the objection entirely misses the point of Marx's analysis. The workers must be made to appear as petty capitalists, in law, in political philosophy, and in the formal theory of political economy. A political economy that fails to model the essential mystification and ideological self-deception of capitalist economic, political, and legal relationships will be an inadequate theory of capitalism. An adequate political economy must capture that feature as false, in order to be true to the reality and to the appearance of capitalism.
We have here a very strange requirement indeed. We need a formal model of an ironic, dialectical relationship between appearance and reality. The trouble with other attempts to capture Marx's meaning is that they are either literary renderings, which preserve the irony and the intricate interrelation between appearance and reality, but without the formal structure that will allow us to calculate the magnitudes of the relevant variables; or else they are formal models, like the Sraffa model, that lose entirely the element of mystification and self-deception. If we agree with Marx that capitalism has its own mad logic, then we will search for a model that embodies both the logic and the madness of capitalism. I suggest that the correct way to begin this process is to treat the workers as though they were petty entrepreneurs, producers, producing a commodity-labor power-for the market, and then capture the inner madness of this way of thinking of them by stipulating that they, alone among all capitalists, are unable to shift their capital about from sector to sector.