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On the Maximal Domain Theorem

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  • Yang, Yi-You

Abstract

The maximal domain theorem by Gul and Stacchetti (J. Econ. Theory 87 (1999), 95-124) implies that for markets with indivisible objects and sufficiently many agents, the set of gross substitutable preferences is a largest set for which the existence of a competitive equilibrium is guaranteed, and hence no relaxation of the gross substitutability can ensure the existence of a competitive equilibrium. However, we note that there is a flaw in their proof, and give an example to show that a claim used in the proof may fail to be true. We correct the proof and sharpen the result by showing that even there are only two agents in the market, if the preferences of one agent are not gross substitutable, then gross substitutable preferences can be found for another agent such that no competitive equilibrium exists. Moreover, we introduce the new notion of implicit gross substitutability, which is weaker than the gross substitutability condition and is still sufficient for the existence of a competitive equilibrium when the preferences of some agent are monotone.

Suggested Citation

  • Yang, Yi-You, 2015. "On the Maximal Domain Theorem," MPRA Paper 67265, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:67265
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    References listed on IDEAS

    as
    1. Ning Sun & Zaifu Yang, 2006. "Equilibria and Indivisibilities: Gross Substitutes and Complements," Econometrica, Econometric Society, vol. 74(5), pages 1385-1402, September.
    2. Ma, Jinpeng, 1998. "Competitive Equilibrium with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 82(2), pages 458-468, October.
    3. Hara, Chiaki, 2005. "Bargaining set and anonymous core without the monotonicity assumption," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 545-556, August.
    4. Bevia, Carmen & Quinzii, Martine & Silva, Jose A., 1999. "Buying several indivisible goods," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 1-23, January.
    5. 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.
    6. 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.
    7. Manelli, Alejandro M, 1991. "Monotonic Preferences and Core Equivalence," Econometrica, Econometric Society, vol. 59(1), pages 123-138, January.
    8. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
    9. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    10. Chiaki Hara, 2005. "Existence of Equilibria in Economies with Bads," Econometrica, Econometric Society, vol. 73(2), pages 647-658, March.
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    More about this item

    Keywords

    Competitive equilibrium; gross substitutability; indivisibility;
    All these keywords.

    JEL classification:

    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D6 - Microeconomics - - Welfare Economics
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

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