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Existence of Equilibria in Large Competitive Markets with Bads, Production and Comprehensive Externalities

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  • Robert M. Anderson
  • Haosui Duanmu
  • M. Ali Khan
  • Metin Uyanik

Abstract

This paper establishes the existence of equilibrium in an economy with production and a continuum of consumers, each of whose incomplete and price-dependent preferences are defined on commodities they may consider deleterious, bads which cannot be freely disposed of, and each of whom takes into account the productions of all firms and the consumptions of all other consumers. This result has proved elusive since Hara (2005) presented an example of an atomless measure-theoretic exchange economy with bads (but no externalities) that has no equilibrium. The result circumvents Hara's example by showing that, in the presence of bads and externalities, natural economic considerations imply an integrable bound on the consumption of bads. The proofs make an essential use of nonstandard analysis, and the novel techniques we offer to handle comprehensive externalities expressed as an equivalence class of integrable functions may be of independent methodological interest.

Suggested Citation

  • Robert M. Anderson & Haosui Duanmu & M. Ali Khan & Metin Uyanik, 2025. "Existence of Equilibria in Large Competitive Markets with Bads, Production and Comprehensive Externalities," Papers 2511.00478, arXiv.org.
    • Handle: RePEc:arx:papers:2511.00478
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    References listed on IDEAS

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    1. Anderson, Robert M. & Duanmu, Haosui & Khan, M. Ali & Uyanik, Metin, 2022. "On abstract economies with an arbitrary set of players and action sets in locally-convex topological vector spaces," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    2. Grodal, Birgit, 1974. "A note on the space of preference relations," Journal of Mathematical Economics, Elsevier, vol. 1(3), pages 279-294, December.
    3. Hart, Oliver D. & Kuhn, Harold W., 1975. "A proof of the existence of equilibrium without the free disposal assumption," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 335-343, December.
    4. Ali Khan, M., 1976. "Oligopoly in markets with a continuum of traders: An asymptotic interpretation," Journal of Economic Theory, Elsevier, vol. 12(2), pages 273-297, April.
    5. Gay, Antonio, 1979. "A note on Lemma 1 in Bergstrom's `how to discard "free disposability" at no cost'," Journal of Mathematical Economics, Elsevier, vol. 6(2), pages 215-216, July.
    6. Greenberg, Joseph & Shitovitz, Benyamin & Wieczorek, Andrzej, 1979. "Existence of equilibria in atomless production economies with price dependent preferences," Journal of Mathematical Economics, Elsevier, vol. 6(1), pages 31-41, March.
    7. Anderson, Robert M. & Duanmu, Haosui & Ghosh, Aniruddha & Khan, M. Ali, 2024. "On existence of Berk-Nash equilibria in misspecified Markov decision processes with infinite spaces," Journal of Economic Theory, Elsevier, vol. 217(C).
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