Twentieth Century Developments on the Transformation Problem

A group of economists led by the "Anglo-Italians," Piero Sraffa and Luigi Passinetti, directed effort to the solution of the "transformation problem." In their later work, they drew on matrix algebra and the input-output analysis developed by Wassily Leontieff. (Leontieff, who had studied economics at the University of Leningrad before moving to the United States, was partly inspired in his work by Marx' chapters on machinery and the labor theory. However, Input-Output analysis was mainly aimed at practical applications, and continues to be widely used in applied economics). The question was: given the labor input requirements per unit of output, both direct and indirect, can we find a rate of exploitation, rate of profit, and system of relative prices that all work together? As it turns out, there is not just one solution to that problem -- there are infinitely many, each with a different wage and corresponding rate of exploitation and profits.

And that's a problem. One wants just one solution, not a whole universe of them! Marx' idea was to reason from the given rate of exploitation to the rate of profit and so to the relative prices and labor values -- but we are still trying to figure out: which rate of exploitation to begin with?

Here is my distillation of a good deal of Marxist thinking on this subject: the average worker's "standard of living," that is, the "cost of production of labor," is whatever history has made it at a specific time. It is the product of many influences: scarcity of resources, struggles over political power and regulation, bargaining power, unions and cartels. Once we know this cost of production of labor, we know the competitive wage for an average worker (in terms of the goods and services it will buy) and from that we can derive both the rate of exploitation and (subsequently) the rate of profits.

The purpose of Marxist theory, after all, is to understand capitalist dynamics. For that purpose, we need to understand were the economy will go from the state it is now in, not from some hypothetical state. And the state it is now in is well defined. The objective of a capitalist is to increase his profits, and to do that, he must increase the rate of exploitation, s/v. Roughly speaking, there are four ways to do that.

Increase labor productivity

In other words, introduce technological innovations. This increases s/v by increasing the output from a given input of labor. However, it usually requires an increase c relative to v, which cuts v/(v+c) and thus limits its short-run impact. In the long run, innovations can be imitated and the competition for labor is increased, so that either (1) the standard of living of the average worker, and so the wage cost, increases, or (2) the socially necessary labor time and the price of output declines. Thus, in the long run, innovation is self-denying. But the fact that innovation raises profits in the short run is the great reason why capitalism (at its best) has been a very dynamic system.

Push workers' standards of living down

That is, cut the purchasing power of wages, either directly or with raises that lag behind inflation.

Lengthen the working day

This forces the working people to supply more input for the same pay. It was a major capitalist strategy in Marx' time, and the source of a great deal of agitation, strikes, violence, and political reform. This is limited, of course, in that there is an upper limit of about 16 hours per day.

Make working conditions worse

Although we have not mentioned working conditions before -- and they don't come up separately when we think in terms of v, c, and s -- requiring workers to make more effort, risk their lives and limbs more often, take fewer breaks and go home more tired and weakened can cut some nonlabor cost, lowering c, and so increasing profits. This works very much like lengthening the working day, and Marx discussed this a good deal in some of the informal sections of Capital.

From a particular time, the direction of the economy will be the overall result of these forces. This direction determines the standard of living of the working class, and thus the starting point for the next round of change. In this way, the path of the capitalist system over decades is determined. This path isn't unique or perfectly predictable, and that should not be a surprise. The search for a unique solution to "the transformation problem" is a search for a "unilinear path of development," and as critics of Marxism have often pointed out, there is no unilinear path of development. But perhaps we can understand the actual path, where it will lead and how political and economic events influence it, by thinking in terms of surplus-value.

Monopoly Capital