Chichilnisky, Graciela and Kalman, P.J. (1979): Comparative statics and dynamics of optimal choice models in Hilbert spaces. Published in: Journal of Mathematical Analysis and Applications , Vol. 70, No. No. 2 (August 1979): pp. 490504.

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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 and non linear functional analysis on Hilbert spaces.
Item Type:  MPRA Paper 

Original Title:  Comparative statics and dynamics of optimal choice models in Hilbert spaces 
Language:  English 
Keywords:  Hilbert spaces; optimization; operator; parametrized constrained maximization; comparative statics; Slutky; Hicks; Samuelson; matrix; Hilbert; Euclidean spaces; optimal growth; dynamic models; growth; manifold; constrained optimization 
Subjects:  C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C61  Optimization Techniques; Programming Models; Dynamic Analysis 
Item ID:  8001 
Depositing User:  Graciela Chichilnisky 
Date Deposited:  31. Mar 2008 05:33 
Last Modified:  18. Feb 2013 03:19 
References:  K. J. Arrow and F. H. Hahn, "General Competitive Analysis," HoldernDay, San Francisco, 1971. 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. 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. 61 (1977), 490503. 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, 1958. P. J. Kalman and M. Intriligator, Generalized comparative statics with applications to consumer theory and producer theory, International Economics Review 14 (1973). P. KALMAN, Theory of consumer behavior when prices enter the utility function, Econometrica (Oct. 1968). L. V. KANTOROIVICH 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., 972. 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:  http://mpra.ub.unimuenchen.de/id/eprint/8001 