Heterodox
In mainstream economics, marginal productivity does not determine distribution. Furthermore, every correct proposition of marginal productivity theory is consistent, under competitive conditions, with Marx's claim that workers are exploited by capitalists. Assume technology is given, the economy is in a stationary state, and one knows what technique is chosen. (Ludwig von Mises called a stationary state an 'evenly rotating economy'.) The technique consists of a list of the physical inputs and outputs in each industry in which a commodity is produced. Following convention, I call such a list in a given industry, a process. I assume the chosen technique is cost-minimizing. Furthermore, inputs are themselves produced commodities, with the exception of (types of) labor and land. Under
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In mainstream economics, marginal productivity does not determine distribution. Furthermore, every correct proposition of marginal productivity theory is consistent, under competitive conditions, with Marx's claim that workers are exploited by capitalists.
Assume technology is given, the economy is in a stationary state, and one knows what technique is chosen. (Ludwig von Mises called a stationary state an 'evenly rotating economy'.) The technique consists of a list of the physical inputs and outputs in each industry in which a commodity is produced. Following convention, I call such a list in a given industry, a process. I assume the chosen technique is cost-minimizing. Furthermore, inputs are themselves produced commodities, with the exception of (types of) labor and land.
Under the assumptions of, say, certain models of circulating capital, pure fixed capital, or extensive rent, the cost-minimizing technique is a function of the real wage. One can generalize the model, to have multiple types of labor input, say 'unskilled' and 'skilled' labor. And the prices of all commodities are functions of the wage, as well.
I like a discrete description of technology. For each industry, the processes for producing the output commodity can be described by a production function that approximates a continuously differentiable production function. The value of the marginal product of labor is not found by multiplying the price of the output commodity by the derivative of the production function. Rather, it is, at least at non-switch points, formed out of an interval bounded by right hand and left hand derivatives of the production function. And the wage is equal to the marginal product of labor in these models in this sense; it lies within the appropriate bounds.
In an example of the reswitching of techniques, the same cost-minimizing technique can be cost-minimizing for two non-overlapping intervals of wages. In both intervals, the real wage is equal to the marginal product of labor in the above sense. Yet the same physical flows of inputs and outputs between industries and to consumers can be consistent with these ranges. Workers might not get higher wages because they have raised their (marginal) productivity in some physical sense. Rather, through some sort of class struggle they have won higher wages. And this may result in a tendency for the economy to approach a steady state where these higher wages are consistent with the same marginal physical products.
One can do labor-value accounting with the cost-minimizing technique. Given that technique, what would prices be if the wage was at its maximum, where capital does not obtain any accounting profits? These are labor values. In Leontief input-output analysis, they are also known as employment multiplers. One can evaluate the value of the capital goods used up in production with these labor values. Likewise, one can calculate the labor value of the commodities represented by the wage and by the surplus product obtained by capitalists. If and only if the wage is less than its maximum, the labor value of the net output is more than the labor value represented by wages. This is exploitation, as Marx defined it. And it obtains in these sort of models as a matter of mathematics; Nobuo Okishio christened this the fundamental theorem of Marxism.