The Success of the Cobb-Douglas Production Function Is An Illusion

Abstract

The Cobb-Douglas production function (the C-D function) is believed to have successfully validated and consolidated the marginal productivity theory of income distribution (MPTID) and the aggregate production function (APF). However, this paper discovers that this success is an illusion. It demonstrates neither the partial derivatives of the C-D function are as believed to be the marginal productivities of production factors nor its homogeneity is as believed to be a technical result of the constant returns to scale (CRS). Without these believed theoretical contents, the C-D function is further shown to be just a mathematical transformation of the national income identity. It is in fact not a production function as it does not truly summarize any productive behavior or technological relationships. The illusion should have been one of the reasons why the mainstream macro models, of which the C-D function alike is one of the cornerstones, have been struggling with the identification problems and failed to foresee the GFC. Methodologically, the illusion is a result of grafting dynamic data upon the static concept of marginal productivity and confusing the concept of CRS with the fact that the sum of all factor’s income shares must equal 1.

Keywords: Validity of Cobb-Douglas production function, marginal productivity theory of income distribution, aggregate production function, homogeneity, constant returns to scale

JEL Classification: E23, E25, E13, E12