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Non-Atomic Economies and the Boundaries of Perfect Competition

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  • Joseph M. Ostroy

    (UCLA)

  • William R. Zame

    (UCLA)

Abstract

The distinction between nonatomicity and thick markets as the source of perfect competition is examined. The authors construct a model of an imperfectly competitive economy with a nonatomic continuum of traders and a continuum of differentiated commodities for which Walrasian equilibria exist. The failure of perfect competition is identified in two ways: individuals can affect prices and the core is strictly larger than the set of Walrasian allocations. By contrast, it is shown that, when markets are physically or economically thick (or both), then individuals cannot typically affect prices and the core always coincides with the set of Walrasian allocations. Copyright 1994 by The Econometric Society.

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Bibliographic Info

Paper provided by UCLA Department of Economics in its series UCLA Economics Working Papers with number 502R.

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Date of creation: 01 Sep 1991
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Handle: RePEc:cla:uclawp:502r

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  1. Ostroy, Joseph M, 1984. "A Reformulation of the Marginal Productivity Theory of Distribution," Econometrica, Econometric Society, vol. 52(3), pages 599-630, May.
  2. Jones, Larry E, 1984. "A Competitive Model of Commodity Differentiation," Econometrica, Econometric Society, vol. 52(2), pages 507-30, March.
  3. Zame, William R, 1987. "Competitive Equilibria in Production Economies with an Infinite-Dimensional Commodity Space," Econometrica, Econometric Society, vol. 55(5), pages 1075-1108, September.
  4. Simon, Leo K & Zame, William R, 1990. "Discontinuous Games and Endogenous Sharing Rules," Econometrica, Econometric Society, vol. 58(4), pages 861-72, July.
  5. Gretsky, Neil E & Ostroy, Joseph M & Zame, William R, 1992. "The Nonatomic Assignment Model," Economic Theory, Springer, vol. 2(1), pages 103-27, January.
  6. Dixit, Avinash K & Stiglitz, Joseph E, 1975. "Monopolistic Competition and Optimum Product Diversity," The Warwick Economics Research Paper Series (TWERPS) 64, University of Warwick, Department of Economics.
  7. Hart, Oliver D, 1979. "Monopolistic Competition in a Large Economy with Differentiated Commodities," Review of Economic Studies, Wiley Blackwell, vol. 46(1), pages 1-30, January.
  8. Dubey, Pradeep & Mas-Colell, Andreau & Shubik, Martin, 1980. "Efficiency properties of strategies market games: An axiomatic approach," Journal of Economic Theory, Elsevier, vol. 22(2), pages 339-362, April.
  9. Jones, Larry E., 1983. "Existence of equilibria with infinitely many consumers and infinitely many commodities : A theorem based on models of commodity differentiation," Journal of Mathematical Economics, Elsevier, vol. 12(2), pages 119-138, October.
  10. Bewley, Truman F, 1973. "The Equality of the Core and the Set of Equilibria in Economies with Infinitely Many Commodities and a Continuum of Agents," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(2), pages 383-94, June.
  11. Donald J. Brown & Charalambos Aliprantis & Owen Burkinshaw, 1985. "Edgeworth Equilibria," Cowles Foundation Discussion Papers 756R, Cowles Foundation for Research in Economics, Yale University.
    • Aliprantis, Charalambos D & Brown, Donald J & Burkinshaw, Owen, 1987. "Edgeworth Equilibria," Econometrica, Econometric Society, vol. 55(5), pages 1109-37, September.
  12. Jaskold Gabszewicz, Jean & Vial, Jean-Philippe, 1972. "Oligopoly "A la cournot" in a general equilibrium analysis," Journal of Economic Theory, Elsevier, vol. 4(3), pages 381-400, June.
  13. Pascoa Mario Rui, 1993. "Noncooperative Equilibrium and Chamberlinian Monopolistic Competition," Journal of Economic Theory, Elsevier, vol. 60(2), pages 335-353, August.
  14. Mas-Colell, Andreu, 1986. "The Price Equilibrium Existence Problem in Topological Vector Lattice s," Econometrica, Econometric Society, vol. 54(5), pages 1039-53, September.
  15. Romer, Paul M, 1987. "Growth Based on Increasing Returns Due to Specialization," American Economic Review, American Economic Association, vol. 77(2), pages 56-62, May.
  16. Artstein, Zvi, 1979. "A note on fatou's lemma in several dimensions," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 277-282, December.
  17. Yannelis, Nicholas C. & Zame, William R., 1986. "Equilibria in Banach lattices without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 15(2), pages 85-110, April.
  18. Novshek, William & Sonnenschein, Hugo, 1978. "Cournot and Walras equilibrium," Journal of Economic Theory, Elsevier, vol. 19(2), pages 223-266, December.
  19. Young, Allyn A., 1928. "Increasing Returns and Economic Progress," History of Economic Thought Articles, McMaster University Archive for the History of Economic Thought, vol. 38, pages 527-542.
  20. Mas-Colell, Andreu, 1975. "A model of equilibrium with differentiated commodities," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 263-295.
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Citations

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Cited by:
  1. Podczeck, K., 2005. "On core-Walras equivalence in Banach lattices," Journal of Mathematical Economics, Elsevier, vol. 41(6), pages 764-792, September.
  2. Green, Edward J. & Zhou, Ruilin, 2010. "Perfectly competitive bilateral exchange without discounting," Journal of Monetary Economics, Elsevier, vol. 57(2), pages 121-131, March.
  3. José Penalva, 2000. "Full insurance, asymmetric information and genetic testing," Economics Working Papers 461, Department of Economics and Business, Universitat Pompeu Fabra.
  4. Konrad Podczeck, 2003. "On Core-Walras Equivalence in Banach Spaces when Feasibility is defined by the Pettis Integral," Vienna Economics Papers 0403, University of Vienna, Department of Economics.
  5. Louis Makowski & Joseph M. Ostroy, 1991. "The Margin of Appropriation and an Extension of the First Theorem of Welfare Economists," UCLA Economics Working Papers 629, UCLA Department of Economics.
  6. Suzuki, Takashi, 2013. "Core and competitive equilibria of a coalitional exchange economy with infinite time horizon," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 234-244.
  7. Monteiro, Paulo Klinger & Araújo, Aloísio Pessoa de & Martins-da-Rocha, Victor Filipe, 2003. "Equilibria in security markets with a continuum of agents," Economics Working Papers (Ensaios Economicos da EPGE) 513, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  8. 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.
  9. Campion, Maria J. & Candeal, Juan C. & Indurain, Esteban, 2006. "The existence of utility functions for weakly continuous preferences on a Banach space," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 227-237, March.
  10. Araujo, Aloisio & Martins-da-Rocha, Victor-Filipe & Monteiro, Paulo K., 2004. "Equilibria in reflexive Banach lattices with a continuum of agents," Economics Papers from University Paris Dauphine 123456789/6273, Paris Dauphine University.
  11. Podczeck, K., 2004. "On Core-Walras equivalence in Banach spaces when feasibility is defined by the Pettis integral," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 429-463, June.
  12. Hervés-Beloso, Carlos & Moreno-Garci­a, Emma, 2008. "Competitive equilibria and the grand coalition," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 697-706, July.
  13. Herves-Beloso, Carlos & Moreno-Garcia, Emma & Nunez-Sanz, Carmelo & Rui Pascoa, Mario, 2000. "Blocking Efficacy of Small Coalitions in Myopic Economies," Journal of Economic Theory, Elsevier, vol. 93(1), pages 72-86, July.
  14. Bernard Cornet & V. F. Martins-Da-Rocha, 2005. "Fatou¡¯S Lemma For Unbounded Gelfand Integrable Mappings," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200503, University of Kansas, Department of Economics, revised Feb 2005.
  15. Hervés-Estévez, Javier & Moreno-García, Emma, 2012. "Some remarks on restricted bargaining sets," MPRA Paper 39385, University Library of Munich, Germany, revised 10 Jun 2012.
  16. Gretsky, Neil E. & Ostroy, Joseph M. & Zame, William R., 1999. "Perfect Competition in the Continuous Assignment Model," Journal of Economic Theory, Elsevier, vol. 88(1), pages 60-118, September.

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