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Equilibrium theory with unbounded consumption sets and non-ordered preferences: Part I. Non-satiation

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  • Won, Dong Chul
  • Yannelis, Nicholas C.

Abstract

A new condition is introduced for the existence of equilibrium for an economy where preferences need not be transitive or complete and the consumption set of each agent need not be bounded from below. The new condition allows us to extend the literature in two ways. First, the result of the paper can cover the case where the utility set for individually rational allocations may not be compact. As illustrated in Page et al. [Page Jr., F.H., Wooders, M.H., Monteiro, P.K., 2000. Inconsequential arbitrage. Journal of Mathematical Economics 34, 439-469], the no arbitrage conditions do not apply to an economy with a non-compact utility set. Second, we generalize the arbitrage-based equilibrium theory to the case of non-transitive preferences.

Suggested Citation

  • Won, Dong Chul & Yannelis, Nicholas C., 2008. "Equilibrium theory with unbounded consumption sets and non-ordered preferences: Part I. Non-satiation," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1266-1283, December.
    • Handle: RePEc:eee:mateco:v:44:y:2008:i:11:p:1266-1283
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    References listed on IDEAS

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    Cited by:

    1. Ha-Huy, Thai & Le Van, Cuong, 2017. "Existence of equilibrium on asset markets with a countably infinite number of states," Journal of Mathematical Economics, Elsevier, vol. 73(C), pages 44-53.
    2. Ha-Huy, Thai & Le Van, Cuong & Nguyen, Manh-Hung, 2016. "Arbitrage and asset market equilibrium in infinite dimensional economies with short-selling and risk-averse expected utilities," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 30-39.
    3. Senda Ounaies & Jean-Marc Bonnisseau & Souhail Chebbi, 2016. "Equilibrium of a production economy with noncompact attainable allocations set," Documents de travail du Centre d'Economie de la Sorbonne 16056r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Oct 2017.
    4. Hervé Crès & Mich Tvede, 2011. "Production externalities: internalization by voting," SciencePo Working papers Main hal-00972983, HAL.
    5. repec:spo:wpmain:info:hdl:2441/eu4vqp9ompqllr09ieq060086 is not listed on IDEAS
    6. Won, Dong Chul & Yannelis, Nicholas C., 2011. "Equilibrium theory with satiable and non-ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 245-250, March.
    7. repec:hal:wpspec:info:hdl:2441/eu4vqp9ompqllr09ieq060086 is not listed on IDEAS
    8. Hervé Crès & Mich Tvede, 2011. "Production externalities: internalization by voting," SciencePo Working papers hal-00972983, HAL.
    9. Hervé Crès & Mich Tvede, 2013. "Production externalities: internalization by voting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(2), pages 403-424, June.
    10. repec:spo:wpecon:info:hdl:2441/eu4vqp9ompqllr09ieq060086 is not listed on IDEAS
    11. Sato Norihisa, 2010. "Existence of Competitive Equilibrium in Unbounded Exchange Economies with Satiation: A Note," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-22, July.
    12. repec:hal:spmain:info:hdl:2441/eu4vqp9ompqllr09ieq060086 is not listed on IDEAS

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