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Note on the Core-Walras Equivalence Problem when the Commodity Space is a Banach Lattice

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Abstract

The core-Walras equivalence problem for an atomless economy is considered in the commodity space setting of Banach lattices. In particular, necessary and sufficient conditions on the commodity space in order for core-Walras equivalence to hold are established. In general, these conditions can be regarded as implying that an economy with a continuum of agents has indeed "many more agents than commodities". However, it turns out that there are special commoditiy spaces in which core-Walras equivalence holds for every atomless economy satisfying certain standard assumptions, but in which an atomless economy does not have the meaning of there being "many more agents than commodities."

Suggested Citation

  • Konrad Podczeck, 2003. "Note on the Core-Walras Equivalence Problem when the Commodity Space is a Banach Lattice," Vienna Economics Papers 0307, University of Vienna, Department of Economics.
  • Handle: RePEc:vie:viennp:0307
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    File URL: http://homepage.univie.ac.at/Papers.Econ/RePEc/vie/viennp/vie0307.pdf
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    1. Rustichini, Aldo & Yannelis, Nicholas C., 1991. "Edgeworth's conjecture in economies with a continuum of agents and commodities," Journal of Mathematical Economics, Elsevier, vol. 20(3), pages 307-326.
    2. Ostroy, Joseph M & Zame, William R, 1994. "Nonatomic Economies and the Boundaries of Perfect Competition," Econometrica, Econometric Society, vol. 62(3), pages 593-633, May.
    3. Tourky, Rabee & Yannelis, Nicholas C., 2001. "Markets with Many More Agents than Commodities: Aumann's "Hidden" Assumption," Journal of Economic Theory, Elsevier, vol. 101(1), pages 189-221, November.
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    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D41 - Microeconomics - - Market Structure, Pricing, and Design - - - Perfect Competition

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