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Existence of an upper hemi-continuous and convex-valued demand sub-correspondence

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  • Scapparone, Paolo

Abstract

In this paper we show that a strictly open, non-saturated and acyclically convex preference relation admits an extension which is ordered by inclusion (a weaker property than regularity), strictly open, locally non saturated and convex; in turn, this result permits to prove the existence of an upper hemi-continuous and convex-valued demand sub-correspondence. By directly applying standard fixed-point techniques to these sub-correspondences, it is therefore possible to demonstrate the existence of general economic equilibrium even if consumers’ preference relations are not regular.

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  • Scapparone, Paolo, 2015. "Existence of an upper hemi-continuous and convex-valued demand sub-correspondence," Mathematical Social Sciences, Elsevier, vol. 75(C), pages 123-129.
  • Handle: RePEc:eee:matsoc:v:75:y:2015:i:c:p:123-129
    DOI: 10.1016/j.mathsocsci.2015.03.004
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    1. Bossert, Walter & Sprumont, Yves, 2003. "Efficient and non-deteriorating choice," Mathematical Social Sciences, Elsevier, vol. 45(2), pages 131-142, April.
    2. Demuynck, Thomas, 2009. "A general extension result with applications to convexity, homotheticity and monotonicity," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 96-109, January.
    3. Paolo Scapparone, 1999. "Existence of a convex extension of a preference relation," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 22(1), pages 5-11, March.
    4. Bridges, Douglas S., 1983. "A numerical representation of preferences with intransitive indifference," Journal of Mathematical Economics, Elsevier, vol. 11(1), pages 25-42, January.
    5. Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, vol. 10(3), pages 403-404, June.
    6. Mas-Colell, Andrew, 1974. "An equilibrium existence theorem without complete or transitive preferences," Journal of Mathematical Economics, Elsevier, vol. 1(3), pages 237-246, December.
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