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On some geometric properties of quasi-sum production models. (English) Zbl 1243.39019
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.

39B52Functional equations for functions with more general domains and/or ranges
39B22Functional equations for real functions
91B38Production theory, theory of the firm (economics)
90B30Production models
Full Text: DOI
[1] Aczél, J.; Maksa, G.: Solution of the rectangular $m{\times}$n generalized bisymmetry equation and of the problem of consistent aggregation, J. math. Anal. appl. 203, 104-126 (1996) · Zbl 0858.39013 · doi:10.1006/jmaa.1996.0369
[2] Chen, B. -Y.: On some geometric properties of h-homogeneous production function in microeconomics, Kragujevac J. Math. 35, No. 3, 343-357 (2011) · Zbl 1289.91107
[3] Vilcu, A. D.; Vilcu, G. E.: On some geometric properties of the generalized CES production functions, Appl. math. Comput. 218, 124-129 (2011) · Zbl 1231.91278
[4] Vilcu, G. E.: A geometric perspective on the generalized cobb--Douglas production functions, Appl. math. Lett. 24, 777-783 (2011) · Zbl 1208.91076 · doi:10.1016/j.aml.2010.12.038
[5] Cobb, C. W.; Douglas, P. H.: A theory of production, Amer. econom. Rev. 18, 139-165 (1928)
[6] Arrow, K. J.; Chenery, H. B.; Minhas, B. S.; Solow, R. M.: Capital-labor substitution and economic efficiency, Rev. econom. Stat. 43, No. 3, 225-250 (1961)
[7] Hicks, J. R.: Theory of wages, (1932)
[8] Allen, R. G.; Hicks, J. R.: A reconsideration of the theory of value, pt. II, Economica 1, 196-219 (1934)
[9] B.-Y. Chen, Classification of h-homogeneous production functions with constant elasticity of substitution, Tamkang J. Math. (in press).
[10] Losonczi, L.: Production functions having the CES property, Acta math. Acad. paedagog. Nyházi. (N.S.) 26, No. 1, 113-125 (2010) · Zbl 1224.62143
[11] Chen, B. -Y.: Pseudo-Riemannian geometry, ${\delta}$-invariants and applications, (2011) · Zbl 1245.53001