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arXiv · 1307.0399

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

Bang-Yen Chen
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Abstract

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

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Bang-Yen Chen. 2013-07-05. Solutions to homogeneous Monge-Ampère equations of homothetic functions and their applications to production models in economics. https://arxiv.org/abs/1307.0399

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