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Linear exchange economies with a continuum of agents

Author

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  • Monique Florenzano

    (CNRS-CERMSEM, Université de Paris 1, Boulevard de l'Hôpital 112, 75647 Paris Cedex 13, France Departamento de Economía e Historia Económica, Facultad de Economía y Empresa, Universidad de Salamanca, Edificio F.E.S. Campus Miguel de Unamuno, 37007 Salamanca, Spain)

  • Emma Moreno-García

    (CNRS-CERMSEM, Université de Paris 1, Boulevard de l'Hôpital 112, 75647 Paris Cedex 13, France Departamento de Economía e Historia Económica, Facultad de Economía y Empresa, Universidad de Salamanca, Edificio F.E.S. Campus Miguel de Unamuno, 37007 Salamanca, Spain)

Abstract

The purpose of this paper is to study how the equilibrium prices vary with respect to the initial endowments in a linear exchange economy with a continuum of agents. We first state the model and give conditions of an increasing strength for existence, uniqueness and continuity of equilibrium prices. Then, if we restrict ourselves to economies with essentially bounded initial endowments and if we assume that there is, from the point of view of preferences, only a finite number of types of agents, we show that, on an open dense subset of the space of initial endowments, the equilibrium price vector is an infinitely differentiable function of the initial endowments. The proof of this claim is based on a formula allowing to compute the equilibrium price vector around a so-called "regular" endowment where it is known.

Suggested Citation

  • Monique Florenzano & Emma Moreno-García, 2001. "Linear exchange economies with a continuum of agents," Spanish Economic Review, Springer;Spanish Economic Association, vol. 3(4), pages 253-272.
    • Handle: RePEc:spr:specre:v:3:y:2001:i:4:p:253-272
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    References listed on IDEAS

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    1. Bonnisseau, J.M. & Joffre, A., 1994. "Equilibrium Manifold for Linear Exchange Economies," Papiers d'Economie Mathématique et Applications 94.87, Université Panthéon-Sorbonne (Paris 1).
    2. Gale, David, 1976. "The linear exchange model," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 205-209, July.
    3. Dierker, Hildegard, 1975. "Equilibria and core of large economies," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 155-169.
    4. Cheng, Hsueh-Cheng, 1979. "Linear economies are "gross substitute" systems," Journal of Economic Theory, Elsevier, vol. 20(1), pages 110-117, February.
    5. Artstein, Zvi, 1979. "A note on fatou's lemma in several dimensions," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 277-282, December.
    6. Eaves, B. Curtis, 1976. "A finite algorithm for the linear exchange model," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 197-203, July.
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    Cited by:

    1. Jean-Marc Bonnisseau & Michael Florig, 2003. "Existence and optimality of oligopoly equilibria in linear exchange economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(4), pages 727-741, November.
    2. Gaël Giraud, 2004. "The limit-price exchange process," Cahiers de la Maison des Sciences Economiques b04118, Université Panthéon-Sorbonne (Paris 1).
    3. M. Florig, 2004. "Equilibrium Correspondence of Linear Exchange Economies," Journal of Optimization Theory and Applications, Springer, vol. 120(1), pages 97-109, January.

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    More about this item

    Keywords

    Linear utilities; indirect utility function; Walrasian equilibrium; atomless economies;
    All these keywords.

    JEL classification:

    • D59 - Microeconomics - - General Equilibrium and Disequilibrium - - - Other
    • D49 - Microeconomics - - Market Structure, Pricing, and Design - - - Other
    • D00 - Microeconomics - - General - - - General
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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