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On Core-Walras (Non-)Equivalence for Economies with a Large Commodity Space

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Abstract

Addressing a question raised by Tourky and Yannelis (1998), we show that given any non-separable Banach space as commodity space and giben any atomless measure space of agents, there is an economy fulfilling the usual standard assumptions but having a core allocation not supportable as a Walrasion equilibrium, and in fact, having no Walrasian equilibria at all. We shall also consider the framework of economies with weakly compact consuption sets as developed by Khan and Yannelis (1991). We prove that in this setting the core of an economy with a measure space of traders is non-empty, regardless of wheter or not the commodity space is separable. On the other hand, we show that when the commodity space contains weakly compact subsets that are non-separable, than, again, there are atomless economies for which core-Walras equivalence fails. Thus, in particular, for very large commodity spaces the notion of the core seems to be more robust than that of a Walrasian equilibrium.

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  • Konrad Podczeck, 2001. "On Core-Walras (Non-)Equivalence for Economies with a Large Commodity Space," Vienna Economics Papers vie0107, University of Vienna, Department of Economics.
    • Handle: RePEc:vie:viennp:vie0107
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    1. Konard Podczeck, 1997. "Markets with infinitely many commodities and a continuum of agents with non-convex preferences (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(3), pages 385-426.
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    More about this item

    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
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General

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