Chen, Bang-Yen On some geometric properties of quasi-sum production models. (English) Zbl 1243.39019 J. Math. Anal. Appl. 392, No. 2, 192-199 (2012). 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 \(f(\mathbf x) = F(h_1(x_1)+ \dots +h_n(x_n))\) (cf. J. Aczél and 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. Cited in 12 Documents MSC: 39B52 Functional equations for functions with more general domains and/or ranges 39B22 Functional equations for real functions 91B38 Production theory, theory of the firm 90B30 Production models Keywords:production function; quasi-linear production function; quasi-sum production model; Gauss-Kronecker curvature; flat space Citations:Zbl 0858.39013 PDF BibTeX XML Cite \textit{B.-Y. Chen}, J. Math. Anal. Appl. 392, No. 2, 192--199 (2012; Zbl 1243.39019) Full Text: DOI OpenURL References: [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 [2] Chen, B.-Y., On some geometric properties of \(h\)-homogeneous production function in microeconomics, Kragujevac J. math., 35, 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 [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, 3, 225-250, (1961) [7] Hicks, J.R., Theory of wages, (1932), Macmillan London [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, 1, 113-125, (2010) · Zbl 1224.62143 [11] Chen, B.-Y., Pseudo-Riemannian geometry, \(\delta\)-invariants and applications, (2011), World Scientific Hackensack, NJ · Zbl 1245.53001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.