Geometric characterizations of quasi-product production models in economics

In this work, we investigate quasi-product production functions taking the form: L(x1,..., xn) = F (Πn,i=1 fi(xi)). 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.