Reswitching, Recurrence, And The Incoherence Of The Marginal Productivity Theory Of Distribution

Blair Fix argues that economists argue in a circle in putting forth the marginal productivity theory of distribution. I know that there is no such consistent theory anyways. It occurs to me that process recurrence, as well as the reswitching of techniques, can be used to demonstrate this inconsistency.

Suppose you completely know the technique being used in an economy to produce its output. And, which is even more impossible, you know all other possible techniques. I am thinking of a technique being specified with something like a Leontief input-output matrix, in physical terms. Assume, counterfactually, that all these techniques exhibit constant returns to scale. With these assumptions, you know the physical marginal product of each input into production, whether it is previously produced or not. (In my favorite way of specifying technology, marginal products are typically intervals, not derivatives.)

The reswitching of techniques shows that one cannot necessarily uniquely map from technology and the technique in use to the functional distribution of income. Wages, for example, are not determined by the marginal product of labor. With reswitching, the same technique is adopted for different (ranges of) wages, with other techniques being cost-minimizing in-between. For both ranges in which the technique is adopted, the same inputs are used in each industry, per unit output. Productivity and marginal products are the same, in physical terms. Yet the value of marginal products, in price terms, can be vastly different. How then can the price of factors of production be said to be determined by marginal productivity?

The same argument applies at the level of a single industry. Suppose the process in use to provide the output of an industry is known. Likewise, all other processes that may be used in that industry, at the given level of technology, is assumed known. With process recurrence, the process in use is adopted at different levels of wages, with other processes being cost-minimizing in-between. Once again, one can see that the prices of factor inputs are not determined by marginal productivity.

Process recurrence is more general than the reswitching of techniques. Reswitching implies recurrence, but recurrence can happen without reswitching. Arrigo Opocher and Ian Steedman have further generalized recurrence to individual coefficients of production. As I understand it, he amount of iron ore required as input per ton steel produced by the steel industry can recur without the whole process of production recurring in the steel industry.

Anyways, no competent economist nowadays accepts the marginal productivity theory of distribution. But many economists might teach incoherent nonsense to students, all the same.