Semistrictly quasiconcave approximation and an application to general equilibrium theory

We show how to approximate, in the sense of continuous convergence, a quasiconcave function with a sequence of semistrictly quasiconcave functions. This allows extending former existence results of equilibria for pure exchange economies when the preferences of the agents allow for local points of sa...

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Published in:	Journal of mathematical analysis and applications Vol. 428; no. 1; pp. 445 - 456
Main Authors:	Lucchetti, Roberto, Milasi, Monica
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01-08-2015
Subjects:	Equilibrium Exchange economy Free-disposal economy Quasiconcave functions Semistrictly quasiconcave functions Quasiconcave functions Exchange economy Free-disposal economy Equilibrium Semistrictly quasiconcave functions
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Abstract	We show how to approximate, in the sense of continuous convergence, a quasiconcave function with a sequence of semistrictly quasiconcave functions. This allows extending former existence results of equilibria for pure exchange economies when the preferences of the agents allow for local points of satiation, and existence results of free disposal equilibria for economies with production.
AbstractList	We show how to approximate, in the sense of continuous convergence, a quasiconcave function with a sequence of semistrictly quasiconcave functions. This allows extending former existence results of equilibria for pure exchange economies when the preferences of the agents allow for local points of satiation, and existence results of free disposal equilibria for economies with production.
Author	Milasi, Monica Lucchetti, Roberto
Author_xml	– sequence: 1 givenname: Roberto surname: Lucchetti fullname: Lucchetti, Roberto email: roberto.lucchetti@polimi.it organization: Department of Mathematics, Politecnico di Milano, Italy – sequence: 2 givenname: Monica orcidid: 0000-0001-7441-7771 surname: Milasi fullname: Milasi, Monica email: mmilasi@unime.it organization: Department of Mathematics and Computer Science, Università di Messina, Italy
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Keywords	Quasiconcave functions Exchange economy Free-disposal economy Equilibrium Semistrictly quasiconcave functions
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References	Allouch, Le Van (br0020) 2009; 45 Villanacci, Zenginobuz (br0120) 2012; 147 (br0070) 1982 Donato, Milasi, Vitanza (br0080) 2014 Allouch, Le Van (br0010) 2008; 44 Lucchetti (br0090) 2006 Benedetti, Donato, Milasi (br0040) 2013; 2013 Sato (br0110) 2010; 46 Arrow, Debreu (br0030) 1954; 22 Debreu (br0060) 1996 Cass, Siconolfi, Villanacci (br0050) 2001; 36 Milasi (br0100) 2013; 57 Sato (10.1016/j.jmaa.2015.03.019_br0110) 2010; 46 Donato (10.1016/j.jmaa.2015.03.019_br0080) 2014 Lucchetti (10.1016/j.jmaa.2015.03.019_br0090) 2006 Cass (10.1016/j.jmaa.2015.03.019_br0050) 2001; 36 Arrow (10.1016/j.jmaa.2015.03.019_br0030) 1954; 22 Debreu (10.1016/j.jmaa.2015.03.019_br0060) 1996 (10.1016/j.jmaa.2015.03.019_br0070) 1982 Milasi (10.1016/j.jmaa.2015.03.019_br0100) 2013; 57 Allouch (10.1016/j.jmaa.2015.03.019_br0010) 2008; 44 Allouch (10.1016/j.jmaa.2015.03.019_br0020) 2009; 45 Benedetti (10.1016/j.jmaa.2015.03.019_br0040) 2013; 2013 Villanacci (10.1016/j.jmaa.2015.03.019_br0120) 2012; 147
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SubjectTerms	Equilibrium Exchange economy Free-disposal economy Quasiconcave functions Semistrictly quasiconcave functions
Title	Semistrictly quasiconcave approximation and an application to general equilibrium theory
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