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, h(1), ... , h(n) with F > 0 such that f (x) = F (h(1) (x(1)) + ... + h(n)(x(n))) (cf. Aczel and Maksa (1996)[1]). A quasi-sum production function is called quasi-linear if at most one of F, h(1), ... , h(n) is a nonlinear function. For a production function!, the graph of f is called the production hypersurface off. In this paper, we obtain a very simple necessary and sufficient condition for a quasi-sum production function f to be quasi-linear in terms of graph of f. Moreover, we completely classify quasi-sum production functions whose production hypersurfaces have vanishing Gauss-Kronecker curvature. (C) 2012 Elsevier Inc. All rights reserved.