Solutions to homogeneous Monge–Ampère equations of homothetic functions and their applications to production models in economics

Abstract

In economics, homothetic functions are production functions whose marginal technical rate of substitution is homogeneous of degree zero. Mathematically, a homothetic function is a function of the form $f(\mathbf{x})=F(h(x_1,\dots ,x_n))$, where F is a monotonically increasing function and h is a homogeneous function of any degree $d\ne 0$. In this paper, we classify homothetic functions satisfying the homogeneous Monge–Ampère equation. Several applications to production models in economics will also be given.