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A note on continuously decomposed evolving exchange economies

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  • Marco Lehmann-Waffenschmidt

Abstract

It is routine to demonstrate in the exchange economy framework that small changes of individual preferences and endowments always result in small changes of the derived excess demand functions as one should expect. Though being as desirable for reasons of the consistency of the whole approach, however, a precise proof of the converse direction so far is still open to question. The present paper shows that it is actually true. We use a decomposition method for aggregate excess demand functions developed by Mas-Colell which is derived from the well-known decomposition method developed by Sonnenschein and perfected by Debreu and Mantel. Our result fills in a notorious gap in the line of economic justification usually given for this decomposition, or disaggregation, method in that comparative static analysis would be restricted if the decomposition of excess demand functions would not be continuous. Copyright Physica-Verlag 2006

Suggested Citation

  • Marco Lehmann-Waffenschmidt, 2006. "A note on continuously decomposed evolving exchange economies," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 14(3), pages 289-298, September.
    • Handle: RePEc:spr:cejnor:v:14:y:2006:i:3:p:289-298
    DOI: 10.1007/s10100-006-0005-8
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    References listed on IDEAS

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    1. Bottazzi, Jean-Marc & Hens, Thorsten, 1996. "Excess Demand Functions and Incomplete Markets," Journal of Economic Theory, Elsevier, vol. 68(1), pages 49-63, January.
    2. Mas-Colell, Andreu, 1977. "On the equilibrium price set of an exchange economy," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 117-126, August.
    3. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, January.
    4. Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
    5. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
    6. Allen, Beth, 1981. "Utility perturbations and the equilibrium price set," Journal of Mathematical Economics, Elsevier, vol. 8(3), pages 277-307, October.
    7. A. P. Kirman & K. J. Koch, 1986. "Market Excess Demand in Exchange Economies with Identical Preferences and Collinear Endowments," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(3), pages 457-463.
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    More about this item

    Keywords

    Continuous decomposition; Aggregate excess demand; C63; D11; D50;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General

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