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Competitive equilibrium for indivisible objects

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  • Yang, Yi-You

Abstract

We study an exchange economy with indivisible objects that may not be substitutes for each other, and we introduce the p-substitutability condition, a relaxation of the gross substitutes condition of Kelso and Crawford (1982), in which a parameter vector p is adopted to permit complicated types of complementarity. We prove that for any economy E, there exists a corresponding vector p^{E} such that the p^{E}-substitutability condition is sufficient to guarantee the existence of a competitive equilibrium, and that the largest competitive price of each object is equal to its contribution to the social welfare. Our approach relies on a classification result that partitions economies into disjoint similarity classes such that whenever a similarity class contains an economy with an equilibrium, each economy in this class also has an equilibrium.

Suggested Citation

  • Yang, Yi-You, 2013. "Competitive equilibrium for indivisible objects," MPRA Paper 57637, University Library of Munich, Germany, revised 28 Jul 2014.
  • Handle: RePEc:pra:mprapa:57637
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    References listed on IDEAS

    as
    1. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    2. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    3. Jos A.M. Potters & Anita van Gellekom & Hans Reijnierse, 2002. "Verifying gross substitutability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(4), pages 767-776.
    4. Hatfield, John William & Kojima, Fuhito, 2010. "Substitutes and stability for matching with contracts," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1704-1723, September.
    5. Ning Sun & Zaifu Yang, 2006. "Equilibria and Indivisibilities: Gross Substitutes and Complements," Econometrica, Econometric Society, vol. 74(5), pages 1385-1402, September.
    6. Ma, Jinpeng, 1998. "Competitive Equilibrium with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 82(2), pages 458-468, October.
    7. Bikhchandani, Sushil & Mamer, John W., 1997. "Competitive Equilibrium in an Exchange Economy with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 74(2), pages 385-413, June.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Indivisibility; equilibrium; gross substitutability; p-substitutability;
    All these keywords.

    JEL classification:

    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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