On the minimality of quasi-sum production models in microeconomics

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.