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

TL;DR

This paper explores the geometric properties of two-variable product production functions in economics by analyzing their associated graph surfaces in isotropic 3-space, focusing on classification based on constant curvature.

Contribution

It introduces a geometric approach to classifying product production functions using isotropic geometry, providing new insights into their structural properties.

Findings

Classification results for graph surfaces with constant curvature

Geometric characterization of product production functions

Insights into the shape and curvature of economic models

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 I^{3}. In particular, we derive several classification results for the graph surfaces of product production functions in I^{3} with constant curvature.