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Market Failures and Equilibria in Banach Lattices: New Tangent and Normal Cones

Author

Listed:
  • Jean-Marc Bonnisseau

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Matías Fuentes

    (UNSAM - Universidad Nacional de San Martin)

Abstract

In this paper, we consider an economy with infinitely many commodities and market failures such as increasing returns to scale and external effects or other regarding preferences. The commodity space is a Banach lattice possibly without interior points in the positive cone in order to include most of the relevant commodity spaces in economics. We propose a new definition of the marginal pricing rule through a new tangent cone to the production set at a point of its (non-smooth) boundary. The major contribution is the unification of many previous works with convex or non-convex production sets, smooth or non-smooth, for the competitive equilibria and for the marginal pricing equilibria, with or without external effects, in finite-dimensional spaces as well as in infinite-dimensional spaces. In order to prove the existence of a marginal pricing equilibria, we also provide a suitable properness condition on non-convex technologies to deal with the emptiness of the interior of the positive cone.

Suggested Citation

  • Jean-Marc Bonnisseau & Matías Fuentes, 2020. "Market Failures and Equilibria in Banach Lattices: New Tangent and Normal Cones," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02344270, HAL.
    • Handle: RePEc:hal:cesptp:halshs-02344270
    DOI: 10.1007/s10957-019-01593-w
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    Cited by:

    1. Jean-Marc Bonnisseau & Matías Fuentes, 2022. "Increasing returns, externalities and equilibrium in Riesz spaces," Post-Print halshs-03908326, HAL.
    2. Jean-Marc Bonnisseau & Matías Fuentes, 2022. "Increasing returns, externalities and equilibrium in Riesz spaces," Working Papers halshs-03908326, HAL.
    3. Jean-Marc Bonnisseau & Matías Fuentes, 2024. "Marginal pricing equilibrium with externalities in Riesz spaces," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(1), pages 1-27, August.

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