On the minimality of quasi‐sum production models in microeconomics

Abstract

Historically, the minimality of surfaces is extremely important in mathematics, and the study of minimal surfaces is a central problem, which has been widely concerned by mathematicians. Meanwhile, the study of the shape and the properties of the production models is a great interest subject in economic analysis. The aim of this paper is to study the minimality of quasi‐sum production functions as graphs in a Euclidean space. We obtain minimal characterizations of quasi‐sum production functions with two or three factors as hypersurfaces in Euclidean spaces. As a result, our results also give a classification of minimal quasi‐sum hypersurfaces in dimensions two and three.

Classification of quasi‐product production models with minimal isoquants

“…In (17), we take the partial derivative with respect to the variable x n and obtain after some simplifications that…”

“…Among geometric properties of production functions, those related to Gauss curvature and mean curvature of the corresponding production hypersurfaces are of primary interest. In particular, the minimality of quasi-sum production models was investigated by Du et al [17], the authors establishing the classification of minimal quasi-sum production hypersurfaces for Dimensions 2 and 3. Recently, Luo and Wang [18] extended the classification of minimal hypersurfaces to the case of quasi-product production models.…”