A characterization of homogeneous production functions using the ratio of average to marginal costs

Abstract

This paper states a theorem that characterizes homogeneous production functions
in terms of the ratio of average to marginal costs. The theorem claims that a
production function is homogeneous of degree k if and only if the ratio of average
costs to marginal costs is constant and equal to k. In order to prove the theorem
two lemmas -with theoretical value of their own- are demonstrated before hand:
the first one establishes that a production function is homogeneous of degree k if
and only if its elasticity of scale is k; the second one determines the conditions on
the production function under which any input vector can be an optimum, for some
choice of the price vector and the level of production.