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An extension of comparative statics to a general class of optimal choice models


  • Chichilnisky, Graciela
  • Kalman, P.J.


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.

Suggested Citation

  • Chichilnisky, Graciela & Kalman, P.J., 1978. "An extension of comparative statics to a general class of optimal choice models," MPRA Paper 8092, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:8092

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    References listed on IDEAS

    1. Kalai, Ehud & Schmeidler, David, 1977. "Aggregation Procedure for Cardinal Preferences: A Formulation and Proof of Samuelson's Impossibility Conjecture," Econometrica, Econometric Society, vol. 45(6), pages 1431-1438, September.
    2. Graciela Chichilnisky, 1982. "Social Aggregation Rules and Continuity," The Quarterly Journal of Economics, Oxford University Press, vol. 97(2), pages 337-352.
    3. Chichilnisky, Graciela & Heal, Geoffrey, 1983. "Necessary and sufficient conditions for a resolution of the social choice paradox," Journal of Economic Theory, Elsevier, vol. 31(1), pages 68-87, October.
    4. Graciela Chichilnisky, 1980. "Continuous Representation of Preferences," Review of Economic Studies, Oxford University Press, vol. 47(5), pages 959-963.
    5. Chichilnisky, Graciela, 1982. "The topological equivalence of the pareto condition and the existence of a dictator," Journal of Mathematical Economics, Elsevier, vol. 9(3), pages 223-233, March.
    6. Graciela Chichilnisky, 1981. "Existence and Characterization of Optimal Growth Paths Including Models with Non-Convexities in Utilities and Technologies," Review of Economic Studies, Oxford University Press, vol. 48(1), pages 51-61.
    7. Chichilnisky, Graciela, 1982. "Structural instability of decisive majority rules," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 207-221, January.
    8. Chichilnisky, Graciela, 1980. "Social choice and the topology of spaces of preferences," MPRA Paper 8006, University Library of Munich, Germany.
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    More about this item


    Hilbert spaces; maximization; optimization; Slutsky-Hicks-Samuelson; semidefiniteness; symmetry; operators;

    JEL classification:

    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models


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