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 inputs, 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.
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https://www.researchgate.net/publication/365890801_Correspondence_between_Exploitation_and_Profits_in_General_Neoclassical_Production_Economies
I am not sure that I understand all the arguments and their imports here, but I will try nonetheless to make come comments.
«In mainstream economics, marginal productivity does not determine distribution.»
But it does, under suitably restrictive (and absurd) conditions, which amount to there being a single efficiency maximum.
«The technique consists of a list of the physical inputs and outputs in each industry in which a commodity is produced. [...] inputs are themselves produced commodities, with the exception of (types of) labor and land.»
But that's not "maintream economics", as it is based on two important differences:
* The view of the political economy is that of a set of markets, not as a production process.
* Production somehow "happens" and the inputs and outputs are accounted for in currency.
«And the prices of all commodities are functions of the wage, as well.»
But not *only* of the wage.
«formed out of an interval bounded by right hand and left hand derivatives of the production function»
Here I think I recognize my usual argument that demand and supply schedules, however expressed, should be bands, not lines.
«what would prices be if the wage was at its maximum, where capital does not obtain any accounting profits? These are labor values.»
That is by definition. But does definition make sense even if there are land rents? Or are those excluded by the "capital does not obtain any accounting profits" condition?
What's a sensible reply to that is not clear to me. I guess it is possible to create models in which either outcomes happen.
«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.»
But it is not a theorem, it is a tautology: if one defines the cost of commodities solely as labour, and the only suppliers of labour are workers, then anybody who is not a worker and obtains commodities must be consuming the labour of some worker.
That conclusion is logically contained in the premise. If you uses "defines the cost of commodities solely as beauty" the conclusion becomes that anybody who is ugly and obtains commodities must be exploiting the beauty of someone else.
The whole argument rests on whether the definition of "value" as "labour" for the purpose of cost accounting is meaningful.
There are some critical details here:
* In the original model the labour of slaves and animals is not defined as "value", only that of free person.
* In the original model there is the role of the "reserve army of labour", and phrase about "the hide ... hiding", which suggests that there is an argument relative scarcities.
* As to relative scarcities it has happened in history (e.g. Black Death) that workers have "exploited" the capitalists, which has manifested eventually as a reduction in the amount of capital.
Thanks for the comments. Part of my inspiration for this post was annoyance at some comments on twitter.
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