On Some Geometric Properties of Quasi-sum Production Models

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