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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 existence of equilibrium in a measure-theoretic general equilibrium (MGE) model with production, bads, and comprehensive externalities. These features are jointly essential for modeling perfect competition in which emissions of production byproducts impose harm on agents. We show that, when bads and externalities are modeled in an economically natural way, equilibrium exists. This yields the first existence theorem with bads for MGE models, the benchmark for perfect competition, overcoming Hara (2005)'s nonexistence example. The proof uses nonstandard analysis, which provides a systematic technique to extend results for finite to infinite models.

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, revised May 2026.
    • 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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