Geometric Characterizations of Quasi-Product Production Models in Economics

Abstract

In this work, we investigate quasi-product production functions
taking the form:
$$L(x_1,\ldots,x_n)=F\big(\prod _{i=1}^nf_i(x_i)\big).$$
We get a simple geometric classification of quasi-product production
functions via studying geometric properties of their associated
graphs in Euclidean spaces. Moreover precisely, if their
corresponding graphs are flat spaces, a complete classification of
quasi-product production functions with an arbitrary number of
inputs is obtained.