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A Unified Perspective on Resource Allocation : Limited Arbitrage is Necessary and Sufficient for the Existence of a Competitive Equilibrium, the Core and Social Choice

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  • CHICHILNISKY , Graciela

    ()
    (Columbia University,)

Abstract

Different forms of resource allocation-by markets, cooperative games, and by social choice are unified by one condition, limited arbitrage, which is defined on the endowments and the preferences of the traders of an Arrow Debreu economy. Limited arbitrage is necessary and sufficient for the existence of a competitive equilibrium in economies with or without short sales, and with finitely or infinitely many markets. The same condition is also necessary and sufficient for the existence of the core, for resolving Arrow's paradox on choices of large utility values, and for the existence of social choice rules which are continuous, anonymous and respect unanimity, thus providing a unified perspective on standard procedures for resource allocation. When limited arbitrage does not hold, social diversity of various degrees is defined by the properties of a topological invariant of the economy, a family of cohomology rings CH defined on a family of cones which are naturally associated with it. CH has additional information about the resource allocation properties of subsets of traders in the economy and of the subeconomies which they span.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 1995027.

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Date of creation: 01 Apr 1995
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Handle: RePEc:cor:louvco:1995027

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Cited by:
  1. Fleurbaey, Marc & Suzumura, Kotaro & Tadenuma, Koichi, 2002. "Arrovian Aggregation in Economic Environments: How Much Should We Know About Indifference Surfaces?," Discussion Papers 2002-10, Graduate School of Economics, Hitotsubashi University.
  2. Page, F.H. & Wooders, M.H., 1995. "The partnered core of an economy," Discussion Paper 1995-55, Tilburg University, Center for Economic Research.
  3. Chichilnisky, Graciela, 1996. "Markets with endogenous uncertainty: theory and policy," MPRA Paper 8612, University Library of Munich, Germany.
  4. Graciela Chichilnisky, 1996. "Markets And Games: A Simple Equivalence Among The Core, Equilibrium And Limited Arbitrage," Metroeconomica, Wiley Blackwell, vol. 47(3), pages 266-280, October.
  5. Monteiro, Paulo K. & Page, Frank Jr. & Wooders, Myrna Holtz, 1997. "Arbitrage, equilibrium, and gains from trade: A counterexample," Journal of Mathematical Economics, Elsevier, vol. 28(4), pages 481-501, November.
  6. Graciela Chichilnisky, 1998. "The knowledge revolution," The Journal of International Trade & Economic Development, Taylor & Francis Journals, vol. 7(1), pages 39-54.
  7. Chichilnisky, Graciela, 1997. "Limited arbitrage is necessary and sufficient for the existence of an equilibrium," Journal of Mathematical Economics, Elsevier, vol. 28(4), pages 470-479, November.

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