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.
