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Market failures and equilibria in Banach lattices

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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 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 or 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 new properness condition on technologies

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  • Jean-Marc Bonnisseau & Matías Fuentes, 2018. "Market failures and equilibria in Banach lattices," Documents de travail du Centre d'Economie de la Sorbonne 18037, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:18037
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    1. Alberto A. Pinto & Elvio Accinelli Gamba & Athanasios N. Yannacopoulos & Carlos Hervés-Beloso (ed.), 2016. "Trends in Mathematical Economics," Springer Books, Springer, number 978-3-319-32543-9, October.
    2. Bonnisseau, Jean-Marc & Meddeb, Moncef, 1999. "Existence of equilibria in economies with increasing returns and infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 287-307, April.
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    5. Bonnisseau, Jean-Marc & Medecin, Jean-Philippe, 2001. "Existence of marginal pricing equilibria in economies with externalities and non-convexities," Journal of Mathematical Economics, Elsevier, vol. 36(4), pages 271-294, December.
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    8. Bonnisseau, Jean-Marc & Cornet, Bernard, 1990. "Existence of Marginal Cost Pricing Equilibria in Economies with Several Nonconvex Firms," Econometrica, Econometric Society, vol. 58(3), pages 661-682, May.
    9. Bonnisseau, Jean-Marc & Cornet, Bernard, 1990. "Existence of Marginal Cost Pricing Equilibria: The Nonsmooth Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(3), pages 685-708, August.
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    More about this item

    Keywords

    Marginal pricing rule; Banach lattices; Market failures; Properness; General equilibrium;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D62 - Microeconomics - - Welfare Economics - - - Externalities

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