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Existence of Competitive Equilibrium in Unbounded Exchange Economies with Satiation: A Note

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  • Sato Norihisa

    ()

    (Waseda University)

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    Abstract

    In this note, we extend the result of Sato (2010) to economies with unbounded-from-below choice sets: we prove the existence of a competitive equilibrium (to be exact, a quasi-equilibrium) by assuming boundary satiation introduced in Sato (2010) and the strong compactness of the individually rational utility set introduced in Martins-da-Rocha and Monteiro (2009). As a result, we obtain a new equilibrium existence theorem that can be applied to the case in which choice sets are unbounded from below and satiation occurs only inside the set of individually rational feasible choices. We also investigate the relationships between boundary satiation and some other conditions concerning satiation provided in the literature.

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    File URL: https://www.degruyter.com/view/j/bejte.2010.10.1/bejte.2010.10.1.1689/bejte.2010.10.1.1689.xml?format=INT
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    Article provided by De Gruyter in its journal The B.E. Journal of Theoretical Economics.

    Volume (Year): 10 (2010)
    Issue (Month): 1 (July)
    Pages: 1-22

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    Handle: RePEc:bpj:bejtec:v:10:y:2010:i:1:n:30
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    1. Allouch, Nizar & Le Van, Cuong, 2008. "Walras and dividends equilibrium with possibly satiated consumers," Journal of Mathematical Economics, Elsevier, vol. 44(9-10), pages 907-918, September.
    2. repec:hal:journl:halshs-00101189 is not listed on IDEAS
    3. Nguyen, Manh-Hung & Ha-Huy, Thai, 2010. "No unbounded arbitrage, weak no market arbitrage and no arbitrage price system conditions; Equivalent conditions," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 128-131, January.
    4. Allouch, Nizar & Le Van, Cuong & Page, Frank Jr., 2002. "The geometry of arbitrage and the existence of competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 38(4), pages 373-391, December.
    5. Allouch, Nizar & Le Van, Cuong & Page, Frank Jr., 2006. "Arbitrage and equilibrium in unbounded exchange economies with satiation," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 661-674, September.
    6. repec:hal:journl:halshs-00241543 is not listed on IDEAS
    7. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-1418, November.
    8. Lars Tyge Nielsen, 1989. "Asset Market Equilibrium with Short-Selling," Review of Economic Studies, Oxford University Press, vol. 56(3), pages 467-473.
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    Cited by:

    1. Jürgen Eichberger & Klaus Rheinberger & Martin Summer, 2014. "Credit risk in general equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(2), pages 407-435, October.

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