Three Paradoxes with The Cobb-Douglas Production Function

Abstract

The output elasticities of inputs seem all about what an applied researcher is concerned with. The Cobb-Douglas production functions formulae possess the convenient property that the exponents of inputs readily represent the output elasticities of inputs such that the sum of these exponents reveal whether there are increasing, constant or decreasing returns to scale. However, there are also some inconveniencies with this type of production functions. In this paper we will investigate three of them. First of all, the short run marginal cost functions obtained from the Cobb-Douglas type of production functions can be both convex and concave depending on the magnitude of the technical coefficient of labor input. Unfortunately, this awkward behavior cannot be explained with the economic theory. Secondly, when the variable input labor with a given level of Technical productivity is complemented with a once-and-for-all increase in the amount of physical capital input, the labor becomes more and more productive as the usage of labor increases. This clearly stands in contrast with the Law of Diminishing Marginal Returns. Finally, we find ever-increasing returns to ‘Technical productivity of labor’, keeping the amounts of labor and physical capital constant, which is again surprising.

Key words: paradox; convex and concave marginal costs; Cobb-Douglas production function; increasing rate of return to Technical productivity of labor.

JEL classification: D2, D3, D4.

DOI: 10.7176/EJBM/11-1-12