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Zbl 1243.39019
Chen, Bang-Yen
On some geometric properties of quasi-sum production models. (English)
[J] J. Math. Anal. Appl. 392, No. 2, 192-199 (2012). ISSN 0022-247X

Summary: A production function $f$ is called quasi-sum if there are continuous strict monotone functions $F$, $h_{1},\dots ,h_{n}$ with $F>0$ such that $f(\bold x) = F(h_1(x_1)+ \dots +h_n(x_n))$ (cf. {\it J. Aczél} and {\it G. Maksa} [J. Math. Anal. Appl. 203, No. 1, 104--126 (1996; Zbl 0858.39013)]). A quasi-sum production function is called quasi-linear if at most one of $F$, $h_{1},\dots ,h_{n}$ 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 terms of the graph of $f$. Moreover, we completely classify quasi-sum production functions whose production hypersurfaces have vanishing Gauss-Kronecker curvature.

MSC 2000:: *39B52 Functional equations for functions with more general domains
39B22 Functional equations for real functions
91B38 Production theory etc.
90B30 Production models

Keywords: production function; quasi-linear production function; quasi-sum production model; Gauss-Kronecker curvature; flat space

Citations: Zbl 0858.39013

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