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Equations on the Derivatives of an Initial Endowment-Competitive Equilibrium Mapping for an Exchange Economy

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  • Williams, Steven R.

    (U of Illinois at Urbana-Champaign)

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    Abstract

    Consider an exchange economy with n traders and k goods. Suppose that there exists C2 mappings p(middot) and x (middot) that specify for each initial endowment w of the k goods to the n traders a price vector p(w) and a vector of net trades x(w) that define a competitive equilibrium. Three systems of determinant equations are derived that the derivatives of p(middot) and x(middot) necessarily satisfy regardless of the underlying preferences that determine these mappings. Each of the three systems of equations fundamentally reflects the interaction among traders in the competitive mechanism.

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    File URL: http://www.business.illinois.edu/Working_Papers/papers/02-0110.pdf
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    Bibliographic Info

    Paper provided by University of Illinois at Urbana-Champaign, College of Business in its series Working Papers with number 02-0110.

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    Date of creation: May 2002
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    Handle: RePEc:ecl:illbus:02-0110

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    Web page: http://www.business.uiuc.edu/Working_Papers/Main.asp
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    1. Sonnenschein, Hugo, 1972. "Market Excess Demand Functions," Econometrica, Econometric Society, vol. 40(3), pages 549-63, May.
    2. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
    3. John H. Nachbar, 2002. "General Equilibrium Comparative Statics," Econometrica, Econometric Society, vol. 70(5), pages 2065-2074, September.
    4. Mas-Colell, Andreu, 1977. "On the equilibrium price set of an exchange economy," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 117-126, August.
    5. Saari, Donald G., 1984. "A method for constructing message systems for smooth performance functions," Journal of Economic Theory, Elsevier, vol. 33(2), pages 249-274, August.
    6. Chen, Pengyuan, 1992. "A lower bound for the dimension of the message space of the decentralized mechanisms realizing a given goal," Journal of Mathematical Economics, Elsevier, vol. 21(3), pages 249-270.
    7. Donald J. Brown & Rosa L. Matzkin, 1995. "Testable Restrictions on the Equilibrium Manifold," Cowles Foundation Discussion Papers 1109, Cowles Foundation for Research in Economics, Yale University.
    8. Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
    9. Sonnenschein, Hugo, 1973. "Do Walras' identity and continuity characterize the class of community excess demand functions?," Journal of Economic Theory, Elsevier, vol. 6(4), pages 345-354, August.
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