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The index theorem for a GEI economy when the degree of incompleteness is even

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  • Momi, Takeshi

Abstract

The purpose of this paper is to present a method to compute the index in an incomplete market economy. We show that generically in endowments and the asset structure the index theorem holds when the deficiency of markets, S-J, is even. The result is based on the indices of homotopies which have been presented for computation of an equilibrium in incomplete market economies.

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  • Momi, Takeshi, 2003. "The index theorem for a GEI economy when the degree of incompleteness is even," Journal of Mathematical Economics, Elsevier, vol. 39(3-4), pages 273-297, June.
    • Handle: RePEc:eee:mateco:v:39:y:2003:i:3-4:p:273-297
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    1. Demarzo, Peter M. & Eaves, B. Curtis, 1996. "Computing equilibria of GEI by relocalization on a Grassmann manifold," Journal of Mathematical Economics, Elsevier, vol. 26(4), pages 479-497.
    2. Brown, Donald J & DeMarzo, Peter M & Eaves, B Curtis, 1996. "Computing Equilibria When Asset Markets Are Incomplete," Econometrica, Econometric Society, vol. 64(1), pages 1-27, January.
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    4. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, October.
    5. Donald J. Brown & Peter M. Demarzo & B. Curtis Eaves, 1996. "Computing Zeros of Sections of Vector Bundles Using Homotopies and Relocalization," Mathematics of Operations Research, INFORMS, vol. 21(1), pages 26-43, February.
    6. Dierker, Egbert, 1972. "Two Remarks on the Number of Equilibria of an Economy," Econometrica, Econometric Society, vol. 40(5), pages 951-953, September.
    7. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    8. W. Hildenbrand & H. Sonnenschein (ed.), 1991. "Handbook of Mathematical Economics," Handbook of Mathematical Economics, Elsevier, edition 1, volume 4, number 4.
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    Cited by:

    1. Covarrubias, Enrique, 2013. "The number of equilibria of smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 263-265.
    2. Predtetchinski, Arkadi, 2006. "A new proof of the index formula for incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 626-635, August.
    3. Momi, Takeshi, 2012. "Failure of the index theorem in an incomplete market economy," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 437-444.
    4. Philippe Bich, 2006. "On the orientability of the asset equilibrium manifold," Post-Print halshs-00287677, HAL.
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