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Optional. Optimization

If information about the constraints and the objective to be achieved is available, it is possible (in theory) to calculate the optimal allocation.

Leonid V. Kantorovich , 1912-1986

Mathematical Methods of Organizing and Planning Production , https://www.jstor.org/stable/2627082 �The Best Use of Economic Resources , https://archive.org/details/bestuseofeconomi0000kant

George Dantzig, 1914-2005

Linear Programming and Extensions

3 of 4

Dantzig: Prices and the simplex algorithm

The problem of the entrepreneur and the labor theory of value.

Linear Programming and Extensions (ed. 1963), https://www.rand.org/pubs/reports/R366.html

Optional.

Optimization Review

Prices play the role of values, of Lagrange multipliers, as in the school of optimization.

The value (the Lagrange multiplier) of a thing is the rate at which the objective sought to be achieved increases upon the introduction of a small amount of the thing.

And in this sense, values are more than the exchange rate, and can even exist in economies where there are no exchanges, like Robinson's Island.

The value of a thing on Robinson's island is the rate at which Robinson's "subjective utility" would increase if he had a small amount more of that thing.
The value of something to a capitalist entrepreneur is the rate at which his profits would increase if he had a small amount more of that thing.

Therefore, entrepreneurs will sell those things whose value (the profit they generate for them ) is less than the price offered in the market. And therefore, entrepreneurs will buy those things whose value (the profit they generate for them) is greater than the price they have to pay for them.

But the optimization school could not determine the objective for which the allocation should be established; it studied the problem abstractly, without specifying a goal. In capitalist systems, the objective is profit, as is clear from a prospective objectivist perspective.
Nor did it always know how to analyze the integration of exchanges in the allocation process, nor the interrelation between the various allocation units through the market, as well as the path toward general equilibrium. In capitalist systems, multiple constrained maximization problems must be posed for each firm, but these are linked by the market.