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Differentiability of Equilibria for Linear Exchange Economies

Author

Listed:
  • J. M. BONNISSEAU

    (Université de Paris 1)

  • M. FLORIG

    (Université de Paris 1)

  • A. JOFRÉ

    (Universidad de Chile)

Abstract

The purpose of this paper is to study the differentiability properties of equilibrium prices and allocations in a linear exchange economy when the initial endowments and utility vectors vary. We characterize an open dense subset of full measure of the initial endowment and utility vector space on which the equilibrium price vector is a real analytic function, hence infinitely differentiable function. We provide an explicit formula to compute the equilibrium price and allocation around a point where it is known. We also show that the equilibrium price is a locally Lipschitzian mapping on the whole space. Finally, using the notion of the Clarke generalized gradient, we prove that linear exchange economies satisfy a property of gross substitution.

Suggested Citation

  • J. M. Bonnisseau & M. Florig & A. Jofré, 2001. "Differentiability of Equilibria for Linear Exchange Economies," Journal of Optimization Theory and Applications, Springer, vol. 109(2), pages 265-288, May.
    • Handle: RePEc:spr:joptap:v:109:y:2001:i:2:d:10.1023_a:1017558204399
    DOI: 10.1023/A:1017558204399
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    References listed on IDEAS

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    1. J. M. Bonnisseau & M. Florig & A. Jofré, 2001. "Continuity and Uniqueness of Equilibria for Linear Exchange Economies," Journal of Optimization Theory and Applications, Springer, vol. 109(2), pages 237-263, May.
    2. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702.
    3. Jouini, Elyes, 1993. "The graph of the Walras correspondence : The production economies case," Journal of Mathematical Economics, Elsevier, vol. 22(2), pages 139-147.
    4. repec:dau:papers:123456789/5639 is not listed on IDEAS
    5. Gale, David, 1976. "The linear exchange model," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 205-209, July.
    6. Cheng, Hsueh-Cheng, 1979. "Linear economies are "gross substitute" systems," Journal of Economic Theory, Elsevier, vol. 20(1), pages 110-117, February.
    7. 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. J. M. Bonnisseau & M. Florig & A. Jofré, 2001. "Continuity and Uniqueness of Equilibria for Linear Exchange Economies," Journal of Optimization Theory and Applications, Springer, vol. 109(2), pages 237-263, May.
    2. Gaël Giraud & Dimitrios Tsomocos, 2010. "Nominal uniqueness and money non-neutrality in the limit-price exchange process," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 303-348, October.
    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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