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Existence of an Equilibrium in Arrowian Markets for Consumption Externalities

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Abstract

We study the existence of quasi-equilibria and equilibria for pure exchange economies with consumption externalities and Arrowian markets with personalized Lindahl prices. We provide example showing first that quasi-equilibria of the externality economy fail to exist under assumptions guaranteeing existence for economies without externalities. We show that the externality economy has identical equilibrium allocations of an appropriately defined constant returns to scale production economy without externalities. We exploit this equivalence to map sufficient conditions for the existence of quasi equilibria and equilibria of the production economy into sufficient conditions of the pure exchange economy with externalities, thereby unveiling suitable irreducibility conditions and survival conditions

Suggested Citation

  • Jean-Marc Bonnisseau & Elena L. del Mercato & Paolo Siconolfi, 2022. "Existence of an Equilibrium in Arrowian Markets for Consumption Externalities," Documents de travail du Centre d'Economie de la Sorbonne 22007, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:22007
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    1. 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.
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    More about this item

    Keywords

    Consumption externalities; markets for externalities; existence of an equilibrium; irreducibility and survival;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D62 - Microeconomics - - Welfare Economics - - - Externalities

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