Geodesic
Hessian Determinants of Composite Functions With Applications for Production Functions in Economics
Kragujevac Journal of Mathematics, Tome 38 (2014) no. 2, p. 259

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B.-Y. Chen [7] derived an explicit formula for the Hessian determinants of composite functions defined by $f=F(h_1(x_1)+\cdots+h_n(x_n))$. In this paper, we introduce a new formula for the Hessian determinants of composite functions of the form \[ f=F(h_1(x_1)\times\cdots\times h_n(x_n)) \] Several applications of the new formula to the well-known Cobb-Douglas production functions in economics are also given.
Classification : 91B38 15A15
Keywords: Hessian matrix, Hessian determinant, production function, generalized Cobb-Douglas production function, composite function 
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     author = {M. E. Aydin and D. M. Ergut},
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M. E. Aydin; D. M. Ergut. Hessian Determinants of Composite Functions With Applications for Production Functions in Economics. Kragujevac Journal of Mathematics, Tome 38 (2014) no. 2, p. 259 . http://geodesic.mathdoc.fr/item/KJM_2014_38_2_a3/