Some characterizations on isoquants of homogeneous and quasi-sum production functions in microeconomics

Abstract

Production function is an important concept in neoclassical economics and of great significance in economics and management. In the theory of geometric variations, the minimality of surfaces describes the optimal solutions of energy equations. Due to the nature of minimum energy, beautiful shape and stable structure, the theory of minimal surfaces is widely utilized in the fields of engineering, architecture, physics and molecular chemistry. In this article, we investigate homogeneous production functions and quasi-sum production functions with minimal isoquants, which solves two problems proposed by Neacşu et al. After meticulous calculations, the complete classifications of homogeneous production functions and quasi-sum production functions are reached. The research results interestingly indicate that homogeneous production functions with minimal isoquants are closely related to harmonic functions, which is a classical concept in mathematics and have widely applications.