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Existence of equilibria in economies with increasing returns and infinitely many commodities

Author

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  • Jean-Marc Bonnisseau

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Moncef Meddeb

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this paper, we prove the existence of equilibria in a model with infinitely many commodities and where production sets exhibit increasing returns to scale or more general types of non-convexities. We distinguish two cases. In the first, producers follow loss free pricing rules like the average cost or the profit maximizing pricing rule. The second case is devoted to bounded loss pricing rules. In each case, we give an existence result under assumptions which extend those considered in the finite dimensional case. In particular, they are satisfied by a firm with a convex production set which maximizes its profits. We also give a new sufficient condition to have an economically meaningful equilibrium price.

Suggested Citation

  • Jean-Marc Bonnisseau & Moncef Meddeb, 1999. "Existence of equilibria in economies with increasing returns and infinitely many commodities," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00187220, HAL.
    • Handle: RePEc:hal:cesptp:hal-00187220
    DOI: 10.1016/S0304-4068(97)00064-5
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    References listed on IDEAS

    as
    1. 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.
    2. Zame, William R, 1987. "Competitive Equilibria in Production Economies with an Infinite-Dimensional Commodity Space," Econometrica, Econometric Society, vol. 55(5), pages 1075-1108, September.
    3. Florenzano, Monique, 1983. "On the existence of equilibria in economies with an infinite dimensional commodity space," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 207-219, December.
    4. BEWLEY, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," LIDAM Reprints CORE 122, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Paulina Beato, 1982. "The Existence of Marginal Cost Pricing Equilibria with Increasing Returns," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 97(4), pages 669-688.
    6. Bonnisseau, Jean-Marc & Cornet, Bernard, 1988. "Existence of equilibria when firms follow bounded losses pricing rules," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 119-147, April.
    7. 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.
    8. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
    9. Mas-Colell, Andreu & Zame, William R., 1991. "Equilibrium theory in infinite dimensional spaces," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 34, pages 1835-1898, Elsevier.
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    Cited by:

    1. Fuentes, Matías N., 2011. "Existence of equilibria in economies with externalities and non-convexities in an infinite-dimensional commodity space," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 768-776.
    2. Jean-Marc Bonnisseau & Matías Fuentes, 2022. "Increasing returns, externalities and equilibrium in Riesz spaces," Post-Print halshs-03908326, HAL.
    3. Jean-Marc Bonnisseau, 2000. "The Marginal Pricing Rule in Economies with Infinitely Many Commodities," Econometric Society World Congress 2000 Contributed Papers 0262, Econometric Society.
    4. J. M. Bonnisseau & A. Jamin, 2008. "Equilibria with Increasing Returns: Sufficient Conditions on Bounded Production Allocations," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(6), pages 1033-1068, December.
    5. 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.
    6. Jean-Marc Bonnisseau & Matías Fuentes, 2022. "Increasing returns, externalities and equilibrium in Riesz spaces," Working Papers halshs-03908326, HAL.
    7. Jean-Marc Bonnisseau & Matías Fuentes, 2020. "Market Failures and Equilibria in Banach Lattices: New Tangent and Normal Cones," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 338-367, February.

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    More about this item

    Keywords

    General equilibrium; Increasing returns; Infinitely many commodities; Bounded loss pricing rule;
    All these keywords.

    JEL classification:

    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models

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