Production functions

The orthodox theory of the firm makes the strong assumption that it is always possible to specify a function, the so-called production function, which expresses the maximum volume of physical output that can be obtained from all technically feasible combinations of physical inputs, given the prevailing level of freely available technical knowledge about the relationship between inputs and output. It is customary to classify the inputs into more or less homogeneous classes, which ought to carry the labels “man-hours,” “machine-hours,” and “acres-per-year,” and not “labor,” “capital,” and “land,” because the inputs in question are supposed to be flow and not stock variables. On the further convenient assumption that the microproduction function so defined is smoothly differentiable and the strictly necessary assumption that the firm is profit maximizing (no value being placed on the psychic income of entrepreneurs), the theory then proceeds to derive the input demand functions as inverse forms of the marginal productivity equations. If factor and product markets are competitive, firms will hire workers, machines, and space until wage rates, machine rentals, and land rentals are equal to their respective marginal value or marginal revenue products.

If the supplies of these factor services are exogenously determined, this theory may be said to “determine” wage and rental rates. For the firm, it would be truer to say that factor prices “determine” marginal products than that marginal products “determine” factor prices.