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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.
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    1. M. Ali Khan & Metin Uyanik, 2021. "The Yannelis–Prabhakar theorem on upper semi-continuous selections in paracompact spaces: extensions and applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 799-840, April.

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