Supporting weakly Pareto optimal allocations in infinite dimensional nonconvex economies
type: Item
instance of: scholarly article
title: Supporting weakly Pareto optimal allocations in infinite dimensional nonconvex economies
zbMATH Open document ID: 1108.91052
author: Monique Florenzano
author: Pascal Gourdel
author: Alejandro Jofre
published in: Economic Theory
publication date: 2006-11-29T00:00:00Z
review text: Recalling, that the interest for nonconvex economies (arising on the production side as well as on the consumption side) is an old interest in Economics, the authors prove for such economies in the infinite dimensional case (i.e., there are infinitely many commodities) new versions of the second wellfare theorem. To get an equilibrium notion they apply first order optimality conditions written in terms of normal cones (to the preferred and production sets). There are three points, which are especially interesting in this paper: First, the authors use an abstract version of subdifferentials (in Banach spaces) to get different notions of normal cones and discuss the connections to Joffe's, Mordukhovich's and Clarke's subdifferential. Second, they apply a viscous separation theorem [compare \textit{J. M. Borwein} and \textit{A. Jofré}, Math. Methods Oper. Res. 48, 169--179 (1998; Zbl 0935.49008)] which was obtained with help of Ekeland's variational principle. Third, the preferences need not be transitive or complete nor are there monotonicity assumptions. Finally it is worth noticing, that the authors discuss and compare carefully the different assumptions of this paper and show, that -- applied to the convex case -- their results contain the usual second wellfare theorem (when the stated properness assumptions are replaced by interiority conditions).
Mathematics Subject Classification ID: 91B54
Mathematics Subject Classification ID: 91B52
Mathematics Subject Classification ID: 58E17
Mathematics Subject Classification ID: 49K27
zbMATH DE Number: 5076542
zbMATH Keywords: second welfare theorem
zbMATH Keywords: nonconvex economies
zbMATH Keywords: viscous separation
zbMATH Keywords: properness assumptions
zbMATH Keywords: normal cones
reviewed by: Alfred Göpfert
MaRDI profile type: Publication
full work available at URL: s00199-005-0033-y
OpenAlex ID: W2083268302
Wikidata QID: Q56552749
cites work: Q3993194
cites work: Edgeworth and Walras equilibria of an arbitrage-free exchange economy
cites work: The Second Welfare Theorem with Nonconvex Preferences
cites work: Q4070950
cites work: Valuation equilibrium and Pareto optimum in non-convex economies
cites work: A nonconvex separation property in Banach spaces
cites work: VALUATION EQUILIBRIUM AND PARETO OPTIMUM
cites work: Éléments maximaux des préordres partiels sur les ensembles compacts
cites work: Pareto Optimality in Non-Convex Economies
cites work: Approximate Subdifferentials and Applications. I: The Finite Dimensional Theory
cites work: Approximate subdifferentials and applications II
cites work: Approximate subdifferentials and applications 3: the metric theory
cites work: Q4524521
cites work: Q4524523
cites work: Ioffe's normal cone and the foundations of welfare economics: The infinite dimensional theory
cites work: Pareto optimal allocations of nonconvex economies in locally convex spaces
cites work: The Price Equilibrium Existence Problem in Topological Vector Lattices
cites work: Q3815822
cites work: Q4389637
cites work: An abstract extremal principle with applications to welfare economics
cites work: The extremal principle and its applications to optimization and economics
cites work: Nonsmooth sequential analysis in Asplund spaces
cites work: Equilibria in vector lattices without ordered preferences or uniform properness
cites work: Generalized Directional Derivatives and Subgradients of Nonconvex Functions
cites work: Quasi-Equilibria in Markets with Non-Convex Preferences
cites work: A new approach to the limit theorem on the core of an economy in vector lattices
cites work: The limit theorem on the core of a production economy in vector lattices with unordered preferences
DOI: 10.1007/S00199-005-0033-Y
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description: scientific article; zbMATH DE number 5076542