Substitute a particular physical product for an agricultural crop, and the concept, it would seem, can be extended to manufacturing.

The production function for a particular plant species would be understood to have a real, objective basis in biochemistry, and could be assumed to be similar for all specimens of the same species. From such data one can hope to identify and describe mathematically a function linking the flow of output to the amounts of various inputs, and the rapidity with which the incremental product declines with additional doses, holding other inputs constant. The incremental (marginal) products of these different inputs can be measured through controlled experiment, varying the amount of one input while everything else is held constant. The yield of a plant (output) can be thought of as dependent on the quantities of a variety of inputs: water, fertilizer, sunlight, for example. The concept of a production function is best understood in the context of an agricultural experiment station. To be fair, the study offers some of both. Actually, he argues, it’s a history not of the function itself, which predates Cobb and Douglas, but a method for estimating its parameters using ordinary least squares, to wit, regressing the log of an output measure on a constant and logs of labor and physical capital inputs. Jeff Biddle has written an intellectual history of the Cobb-Douglas production function. Field, Professor of Economics, Santa Clara University. Cambridge: Cambridge University Press, 2020. Progress through Regression: The Life Story of the Empirical Cobb-Douglas Production Function. Progress through Regression: The Life Story of the Empirical Cobb-Douglas Production Function Author(s):

Cobb douglas function