Demand functions and reflexivity

Polyrakis, IA

dc.contributor.author	Polyrakis, IA	en
dc.date.accessioned	2014-03-01T01:28:07Z
dc.date.available	2014-03-01T01:28:07Z
dc.date.issued	2008	en
dc.identifier.issn	0022-247X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18711
dc.subject	Bases for cones	en
dc.subject	Budget sets	en
dc.subject	Cones	en
dc.subject	Demand functions	en
dc.subject	Reflexive Banach spaces	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mathematics	en
dc.subject.other	EXISTENCE	en
dc.title	Demand functions and reflexivity	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.jmaa.2007.04.079	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.jmaa.2007.04.079	en
heal.language	English	en
heal.publicationDate	2008	en
heal.abstract	In the theory of ordered spaces and in microeconomic theory two important notions, the notion of the base for a cone which is defined by a continuous linear functional and the notion of the budget set are equivalent. In economic theory the maximization of the preference relation of a consumer on any budget set defines the demand correspondence which at any price vector indicates the preferred vectors of goods and this is one of the fundamental notions of this theory. Contrary to the finite-dimensional economies, in the infinite-dimensional ones, the existence of the demand correspondence is not ensured. In this article we show that in reflexive spaces (and in some other classes of Banach spaces), there are only two classes of closed cones, i.e. cones whose any budget set is bounded and cones whose any budget set is unbounded. Based on this dichotomy result, we prove that in the first category of these cones the demand correspondence exists and that it is upper hemicontinuous. We prove also a characterization of reflexive spaces based on the existence of the demand correspondences. (C) 2007 Elsevier Inc. All rights reserved.	en
heal.publisher	ACADEMIC PRESS INC ELSEVIER SCIENCE	en
heal.journalName	Journal of Mathematical Analysis and Applications	en
dc.identifier.doi	10.1016/j.jmaa.2007.04.079	en
dc.identifier.isi	ISI:000253172100055	en
dc.identifier.volume	338	en
dc.identifier.issue	1	en
dc.identifier.spage	695	en
dc.identifier.epage	704	en