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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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    1. Allouch, Nizar, 2002. "An equilibrium existence result with short selling," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 81-94, April.
    2. 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.
    3. Dana, Rose-Anne & Le Van, Cuong & Magnien, Francois, 1999. "On the Different Notions of Arbitrage and Existence of Equilibrium," Journal of Economic Theory, Elsevier, vol. 87(1), pages 169-193, July.
    4. PageJr., Frank H. & Wooders, Myrna H. & Monteiro, Paulo K., 2000. "Inconsequential arbitrage," Journal of Mathematical Economics, Elsevier, vol. 34(4), pages 439-469, December.
    5. Gale, D. & Mas-Colell, A., 1979. "Corrections to an equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 297-298, December.
    6. Chichilnisky, Graciela, 1995. "Limited Arbitrage Is Necessary and Sufficient for the Existence of a Competitive Equilibrium with or without Short Sales," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 79-108, January.
    7. Shafer, Wayne J., 1976. "Equilibrium in economies without ordered preferences or free disposal," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 135-137, July.
    8. 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.
    9. Martins-da-Rocha, V. Filipe & Monteiro, Paulo K., 2009. "Unbounded exchange economies with satiation: How far can we go?," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 465-478, July.
    10. Loomes, Graham & Starmer, Chris & Sugden, Robert, 1991. "Observing Violations of Transitivity by Experimental Methods," Econometrica, Econometric Society, vol. 59(2), pages 425-439, March.
    11. Grether, David M & Plott, Charles R, 1979. "Economic Theory of Choice and the Preference Reversal Phenomenon," American Economic Review, American Economic Association, vol. 69(4), pages 623-638, September.
    12. Yannelis, Nicholas C., 1987. "Equilibria in noncooperative models of competition," Journal of Economic Theory, Elsevier, vol. 41(1), pages 96-111, February.
    13. Yannelis, Nicholas C. & Prabhakar, N. D., 1983. "Existence of maximal elements and equilibria in linear topological spaces," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 233-245, December.
    14. Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 9-15, March.
    15. Page Jr., Frank H. & Wooders, Myrna Holtz, 1996. "A necessary and sufficient condition for the compactness of individually rational and feasible outcomes and the existence of an equilibrium," Economics Letters, Elsevier, vol. 52(2), pages 153-162, August.
    16. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
    17. Page, Frank Jr., 1987. "On equilibrium in Hart's securities exchange model," Journal of Economic Theory, Elsevier, vol. 41(2), pages 392-404, April.
    18. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-1418, November.
    19. Hart, Oliver D., 1974. "On the existence of equilibrium in a securities model," Journal of Economic Theory, Elsevier, vol. 9(3), pages 293-311, November.
    20. D. Won & G. Hahn & N. Yannelis, 2008. "Capital market equilibrium without riskless assets: heterogeneous expectations," Annals of Finance, Springer, vol. 4(2), pages 183-195, March.
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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. Hervé Crès & Mich Tvede, 2011. "Production externalities: internalization by voting," SciencePo Working papers Main hal-00972983, HAL.
    4. 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.
    5. repec:hal:wpspec:info:hdl:2441/eu4vqp9ompqllr09ieq060086 is not listed on IDEAS
    6. 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.
    7. repec:spo:wpecon:info:hdl:2441/eu4vqp9ompqllr09ieq060086 is not listed on IDEAS
    8. repec:hal:spmain:info:hdl:2441/eu4vqp9ompqllr09ieq060086 is not listed on IDEAS
    9. repec:spo:wpmain:info:hdl:2441/eu4vqp9ompqllr09ieq060086 is not listed on IDEAS
    10. 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.

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