Chichilnisky, Graciela and Kalman, P.J. (1978): An extension of comparative statics to a general class of optimal choice models. Published in: Some Aspects of the Foundations of General Equilibrium Theory: The Posthumous Papers of Peter J. Kalman No. 159 (1978): pp. 125.

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Abstract
We study properties of the solutions to a parametrized constrained optimization problem in Hilbert spaces. A special operator is studied which is of importance in economic theory; sufficient conditions are given for its existence, symmetry, and negative semidefiniteness. The techniques used are calculus on Hilbert spaces and functional analysis.
Item Type:  MPRA Paper 

Original Title:  An extension of comparative statics to a general class of optimal choice models 
Language:  English 
Keywords:  Hilbert spaces; maximization; optimization; SlutskyHicksSamuelson; semidefiniteness; symmetry, operators 
Subjects:  C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C68  Computable General Equilibrium Models 
Item ID:  8092 
Depositing User:  Graciela Chichilnisky 
Date Deposited:  04. Apr 2008 06:33 
Last Modified:  01. Mar 2015 02:35 
References:  K.J. ARROW, E. W. BARANKIN, AND D. BLACKWELL., Admissible points in convex sets, in "Contributions to the Theory of Games" (H. W. Kuhn and A.W. Tucker, Eds.), Vol. II, pp. 8792, Princeton Univ. Press, Princeton, N.J., 1953. K. J. Arrow and F. H. Hahn, "General Competitive Analysis," HoldernDay, San Francisco, 1971. M. S. BERGER, Generalized differentiation and utility functionas for commodity spaces of arbitrary dimensions, in "Preferences, Utility and Demand" (J. Chipman, L. Hurqicz, M. Richeter, and H. Sonnenschein, Eds.), Harcourt, Brace, Jovanovich, New York, 1971. G. CHICHILNISKY, Nonlinear functional analysis and optimal economic growth, J. Math. Anal. Vol. 61 (1977), 490503. Chichilnisky, G . and P, J . Kalman, "An Application of Functional Analysis to Models of Efficient Allocation of Economic Resources", Working Paper, Harvard University, 1976 . G. CHICHILNISKY AND P. J. KALMAN, Properties of critical points and operators in economics, J. Anal. Appl. 57 (1977) 241297. L. COURT, Entrepreneurial and consumer demand theories for commodity spectra, Parts I, II, Econometrica 9 (April, July, Oct. 1941), 241297. N. DUNFORD AND J. SCHWARTZ, "Linear Operators," Interscience, New York, 1966. P. KALMAN, Theory of consumer behavior when prices enter the utility function, Econometrica (Oct. 1968). P. J. Kalman and M. Intriligator, Generalized comparative statics with applications to consumer theory and producer theory, International Economics Review 14 (1973). L. V. KANTOROVICH AND G. P. AKILOV, "Functional Analysis in Normed Spaces," Pergamon Press and Macmillian Co., New York, 1964. S. LANG, "Differential Manifolds," Series in Mathematics, AddisonWesley, Reading, Mass., 1972. D. G. LUENBERGER, "Optimization by vector space methods," Wiley, New York, 1969. F. RIESZ AND B. SZNAGY, "Functional Analysis," Unger, New York, 1955. P. A. Samuelson, "The Foundations of Economic Analysis," Harvard University Press, Cambridge, Mass., 1947. S. SMALE, An infinite dimensional version of Sard's theorem, Amer. J. Math. 87 (1965), 861866. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/8092 