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Core equivalence with differentiated commodities

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  • Greinecker, Michael
  • Podczeck, Konrad

Abstract

This paper presents improved core equivalence results for atomless economies with differentiated commodities in the framework of Ostroy and Zame (1994). Commodity bundles are elements of the space M(K) of signed Borel measures on a compact space K of commodity characteristics. Ostroy and Zame provide two sufficient conditions for core equivalence: It is sufficient that markets are “physically thick”, so that there are many suppliers of every commodity, or that markets are “economically thick”, so that consumers are sufficiently willing to substitute commodities with a similar composition for each other. The sufficient conditions in Ostroy and Zame (1994) all imply that there are “many more agents than commodities”, an idea of Aumann that was formalized and discussed in Tourky and Yannelis (2001) and Greinecker and Podczeck (2016). We generalize the framework in Ostroy and Zame (1994) and weaken their sufficient conditions to not imply the presence of “many more agents than commodities”. In particular, we drop the requirement that K is metrizable from the basic model, the requirement of an uniform bound on endowments from the condition of “physically thick markets”, and the requirement that preferences are weak∗-continuous from the condition of “economically thick markets”. Core equivalence still holds, showing that “many more agents than commodities” are not needed for core equivalence in models of commodity differentiation.

Suggested Citation

  • Greinecker, Michael & Podczeck, Konrad, 2017. "Core equivalence with differentiated commodities," Journal of Mathematical Economics, Elsevier, vol. 73(C), pages 54-67.
  • Handle: RePEc:eee:mateco:v:73:y:2017:i:c:p:54-67
    DOI: 10.1016/j.jmateco.2017.08.005
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    References listed on IDEAS

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    1. Jones, Larry E, 1984. "A Competitive Model of Commodity Differentiation," Econometrica, Econometric Society, vol. 52(2), pages 507-530, March.
    2. Mas-Colell, Andreu, 1975. "A model of equilibrium with differentiated commodities," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 263-295.
    3. Konrad Podczeck, 2003. "Core and Walrasian equilibria when agents' characteristics are extremely dispersed," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(4), pages 699-725, November.
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    7. Ezra Einy & Diego Moreno & Benyamin Shitovitz, 2005. "Competitive and core allocations in large economies with differential information," Studies in Economic Theory, in: Dionysius Glycopantis & Nicholas C. Yannelis (ed.), Differential Information Economies, pages 173-183, Springer.
    8. 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.
    9. Michael Greinecker & Konrad Podczeck, 2016. "Edgeworth’s conjecture and the number of agents and commodities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 93-130, June.
    10. 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.
    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. Laura Angeloni & V. Martins-da-Rocha, 2009. "Large economies with differential information and without free disposal," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 263-286, February.
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