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Properties of critical points and operators in economics

Author

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  • Chichilnisky, Graciela
  • Kalman, P.J.

Abstract

The study of the local characteristics of equilibrium positions generated by the constrained maximization of some criterion functions (such as utility, profit, cost, etc.) goes back to Antonelli's paper [2] of 1886. Certain local properties have been proved to be particularly fruitful for economic theory since the early works of Slutsky, Hicks, and Samuelson [9]; they have been formulated in terms of a matrix of "compensated" terms and they concern the properties of partial derivatives of the demand function in some neighborhood of the equilibrium. We now discuss this matrix and its applications.

Suggested Citation

  • Chichilnisky, Graciela & Kalman, P.J., 1977. "Properties of critical points and operators in economics," MPRA Paper 7976, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:7976
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    File URL: https://mpra.ub.uni-muenchen.de/7976/1/MPRA_paper_7976.pdf
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    References listed on IDEAS

    as
    1. Chichilnisky, Graciela & Kalman, Peter J, 1978. "Comparative Statics of Less Neoclassical Agents," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 19(1), pages 141-148, February.
    2. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-392, May.
    3. Kalman, Peter J & Intriligator, Michael D, 1973. "Generalized Comparative Statics with Applications to Consumer Theory and Producer Theory," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(2), pages 473-486, June.
    4. Kalman, Peter J & Dusansky, Richard & Wickstrom, Bengt-Arne, 1974. "On the Major Slutsky Properties When Money Is the Sole Medium of Exchange," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(3), pages 718-728, October.
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    Cited by:

    1. M. Hossein Partovi & Michael R. Caputo, 2006. "A Complete Theory Of Comparative Statics For Differentiable Optimization Problems," Metroeconomica, Wiley Blackwell, vol. 57(1), pages 31-67, February.

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    More about this item

    Keywords

    Antononelli; Slutsky; Hicks; Samuelson; equilibrium; contstrained maximization; maximization; matrix; compensated; economic theory; Slutsky-Hicks-Samuelson equation; utility analysis; demand; optimization; topological; topology;
    All these keywords.

    JEL classification:

    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • B1 - Schools of Economic Thought and Methodology - - History of Economic Thought through 1925
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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