Isotropic geometry of graph surfaces associated with product production functions in economics

Abstract

A production function is a mathematical formalization in economics which denotes the relations between the output generated by a firm, an industry or an economy and the inputs that have been used in obtaining it. In this paper, we study the product production functions of 2 variables in terms of the geometry of their associated graph surfaces in the isotropic $3-$space $\mathbb{I}^{3}$. In particular, we derive several classification results for the graph surfaces of product production functions in $\mathbb{I}^{3}$ with constant curvature.