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Linear exchange economies with a continuum of agents

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  • Florenzano, Monique
  • Moreno García, Emma

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 an explicit formula allowing to compute the equilibrium price vector around a so-called "regular" endowment where it is known.

Suggested Citation

  • Florenzano, Monique & Moreno García, Emma, 1996. "Linear exchange economies with a continuum of agents," UC3M Working papers. Economics 3969, Universidad Carlos III de Madrid. Departamento de Economía.
    • Handle: RePEc:cte:werepe:3969
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    References listed on IDEAS

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    1. Gale, David, 1976. "The linear exchange model," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 205-209, July.
    2. Artstein, Zvi, 1979. "A note on fatou's lemma in several dimensions," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 277-282, December.
    3. Dierker, Hildegard, 1975. "Equilibria and core of large economies," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 155-169.
    4. 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).
    5. Cheng, Hsueh-Cheng, 1979. "Linear economies are "gross substitute" systems," Journal of Economic Theory, Elsevier, vol. 20(1), pages 110-117, February.
    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

    Open mapping theorem;

    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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