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Walrasian equilibrium theory with and without free-disposal: theorems and counterexamples in an infinite-agent context

Author

Listed:
  • Robert M. Anderson

    (University of California)

  • Haosui Duanmu

    (University of California
    Harbin Institute of Technology)

  • M. Ali Khan

    (Johns Hopkins University)

  • Metin Uyanik

    (University of Queensland)

Abstract

This paper provides four theorems on the existence of a free-disposal equilibrium in a Walrasian economy: the first with an arbitrary set of agents with compact consumption sets, the next highlighting the trade-offs involved in the relaxation of the compactness assumption, and the last two with a countable set of agents endowed with a weighting structure. The results generalize theorems in the antecedent literature pioneered by Shafer–Sonnenschein in 1975, and currently in the form taken in He–Yannelis 2016. The paper also provides counterexamples to the existence of non-free-disposal equilibrium in cases of both a countable set of agents and an atomless measure space of agents. One of the examples is related to one Chiaki Hara presented in 2005. The examples are of interest because they satisfy all the hypotheses of Shafer’s 1976 result on the existence of a non-free-disposal equilibrium, except for the assumption of a finite set of agents. The work builds on recent work of the authors on abstract economies, and contributes to the ongoing discussion on the modelling of “large” societies.

Suggested Citation

  • Robert M. Anderson & Haosui Duanmu & M. Ali Khan & Metin Uyanik, 2022. "Walrasian equilibrium theory with and without free-disposal: theorems and counterexamples in an infinite-agent context," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 387-412, April.
    • Handle: RePEc:spr:joecth:v:73:y:2022:i:2:d:10.1007_s00199-021-01395-0
    DOI: 10.1007/s00199-021-01395-0
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    References listed on IDEAS

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    Cited by:

    1. Rabah Amir & Bernard Cornet & M. Ali Khan & David Levine & Edward C. Prescott, 2022. "Special Issue in honor of Nicholas C. Yannelis – Part II," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 377-385, April.
    2. Niccolò Urbinati, 2023. "The Walrasian objection mechanism and Mas-Colell’s bargaining set in economies with many commodities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(1), pages 45-68, July.
    3. Yang, Jian, 2022. "A Bayesian nonatomic game and its applicability to finite-player situations," Journal of Mathematical Economics, Elsevier, vol. 102(C).

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    More about this item

    Keywords

    Exchange economy; Walrasian equilibrium; Discontinuous preferences; Free-disposal; Arbitrary set; Externalities; Bads;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • Q51 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Valuation of Environmental Effects

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