Solutions to homogeneous Monge-Ampere equations of homothetic functions and their applications to production models in economics

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(x) = F((h(x(1),, x(n))), where F is a monotonically increasing function and h is a homogeneous function of any degree d not equal 0. In this paper, we classify homothetic functions satisfying the homogeneous Monge-Ampere equation. Several applications to production models in economics will also be given. (C) 2013 Elsevier Inc. All rights reserved.