On Core-Walras (Non-) Equivalence for Economies with a Large Commodity Space
AbstractAddressing 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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Bibliographic InfoPaper provided by University of Vienna, Department of Economics in its series Vienna Economics Papers with number 0107.
Date of creation: May 2001
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Find related papers by 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 and Pricing - - - Perfect Competition
- D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
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- 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.
- Konard Podczeck, 1997. "Markets with infinitely many commodities and a continuum of agents with non-convex preferences (*)," Economic Theory, Springer, vol. 9(3), pages 385-426.
- Tourky, R. & Yannelis, N.C., 1998. "Market with Many More Agents than Commodities," Department of Economics - Working Papers Series 652, The University of Melbourne.
- Filipe Martins-da-Rocha, V., 2003. "Equilibria in large economies with a separable Banach commodity space and non-ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 39(8), pages 863-889, November.
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