On some geometric properties of quasi-sum production models

A production function ff is called quasi-sum if there are continuous strict monotone functions F,h1,…,hnF,h1,…,hn with F>0F>0 such that f(x)=F(h1(x1)+⋯+hn(xn)) (cf. Aczél and Maksa (1996) [1]). A quasi-sum production function is called quasi-linear if at most one of F,h1,…,hnF,h1,…,hn is a nonlinear function. For a production function ff, the graph of ff is called the production hypersurface of ff. In this paper, we obtain a very simple necessary and sufficient condition for a quasi-sum production function ff to be quasi-linear in terms of graph of ff. Moreover, we completely classify quasi-sum production functions whose production hypersurfaces have vanishing Gauss–Kronecker curvature.