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Application of functional analysis to models of efficient allocation of economic resources

Author

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  • Chichilnisky, Graciela
  • Kalman, P. J.

Abstract

The present paper studies existence and characterization of efficient paths in infinite-horizon economic growth models: the method used is based on techniques of nonlinear functional analysis on Hilbert spaces developed earlier by Chichilnisky. Necessary and sufficient conditions are given for the existence of positive competitive price systems in which the efficient programs maximize present value and intertemporal profit. Approximation of these competitive price systems by strictly positive ones with similar properties is studied. A complete characterization is also given f a class of welfare functions (nonlinear operators defined on consumption paths) for continuity in a weighted L2-norm.

Suggested Citation

  • Chichilnisky, Graciela & Kalman, P. J., 1979. "Application of functional analysis to models of efficient allocation of economic resources," MPRA Paper 8004, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:8004
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    File URL: https://mpra.ub.uni-muenchen.de/8004/1/MPRA_paper_8004.pdf
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    References listed on IDEAS

    as
    1. McFadden, Daniel, 1975. "An example of the non-existence of Malinvaud prices in a tight economy," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 17-19, March.
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    Cited by:

    1. Chichilnisky, Graciela & Gruenwald, Paul F., 1995. "Existence of an optimal growth path with endogenous technical change," Economics Letters, Elsevier, vol. 48(3-4), pages 433-439, June.
    2. Chichilnisky, Graciela, 2009. "Avoiding extinction: equal treatment of the present and the future," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy (IfW), vol. 3, pages 1-25.
    3. Abramovich, Y A & Aliprantis, C D & Zame, W R, 1995. "A Representation Theorem for Riesz Spaces and Its Applications to Economics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(3), pages 527-535, May.
    4. Joël Blot & Bertrand Crettez, 2004. "On the smoothness of optimal paths," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 27(1), pages 1-34, August.
    5. Graciela Chichilnisky, 1996. "An axiomatic approach to sustainable development," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(2), pages 231-257, April.
    6. Charalambos Aliprantis & Kim Border & Owen Burkinshaw, 1996. "Market economies with many commodities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 19(1), pages 113-185, March.

    More about this item

    Keywords

    Hilbert spaces; existence theorems; functional analysis; applied mathematics;

    JEL classification:

    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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