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original papers : Uniqueness of Arrow-Debreu and Arrow-Radner equilibrium when utilities are additively separable

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  • Rose-Anne Dana
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    Abstract

    This survey paper has three purposes: We first present in finite dimension, different approaches to the problem of uniqueness of Arrow-Debreu equilibrium when agents have additively separable utilities. We then study how, in the specific framework of a two period contingent good economy the results obtained generalize to infinite dimension. We consider economies where agents' consumption space is $L^p_+ (\mu)\; 1 \leq p \leq \infty$ and agents' utilities are additively separable. Lastly, we show that in some restricted settings, some results may be used to prove uniqueness of Arrow-Radner equilibria when there are incomplete financial markets.

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    Bibliographic Info

    Article provided by Springer in its journal Review of Economic Design.

    Volume (Year): 6 (2001)
    Issue (Month): 2 ()
    Pages: 155-173

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    Handle: RePEc:spr:reecde:v:6:y:2001:i:2:p:155-173

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    1. Timothy J Kehoe & David K Levine, 1985. "Comparative Statics and Perfect Foresight in Infinite Horizon Economies," Levine's Working Paper Archive 1873, David K. Levine.
    2. Magill, Michael & Shafer, Wayne, 1991. "Incomplete markets," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 30, pages 1523-1614 Elsevier.
    3. Polterovich, Victor & Mityushin, Leonid, 1978. "Criteria for Monotonicity of Demand Functions," MPRA Paper 20097, University Library of Munich, Germany.
    4. Mas-Colell, Andreu & Zame, William R., 1991. "Equilibrium theory in infinite dimensional spaces," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 34, pages 1835-1898 Elsevier.
    5. Greenberg, Joseph, 1977. "An Elementary Proof of the Existence of a Competitive Equilibrium with Weak Gross Substitutes," The Quarterly Journal of Economics, MIT Press, vol. 91(3), pages 513-16, August.
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