A Second Welfare Theorem in a Non-convex Economy: The Case of Antichain-convexity

Maria Carmela Ceparano and Federico Quartieri

MPRA Paper from University Library of Munich, Germany

Abstract: We introduce the notion of an antichain-convex set to extend Debreu (1954)'s version of the second welfare theorem to economies where either the aggregate production set or preference relations are not convex. We show that (possibly after some redistribution of individuals' wealth) the Pareto optima of some economies which are marked by certain types of non-convexities can be spontaneously obtained as valuation quasi-equilibria and equilibria: both equilibrium notions are to be understood in Debreu (1954)'s sense. From a purely structural point of view, the mathematical contribution of this work is the study of the conditions that guarantee the convexity of the Minkowski sum of finitely many possibly non-convex sets. Such a study allows us to obtain a version of the Minkowski\Hahn-Banach separation theorem which dispenses with the convexity of the sets to be separated and which can be naturally applied in standard proofs of the second welfare theorem; in addition (and equally importantly) the study allows to get a deeper understanding of the conditions on the single production sets of an economy that guarantee the convexity of their aggregate.

Keywords: Second Theorem of Welfare Economics; Non-convex Economies; Chain-convexity and Antichain-convexity; Separation Theorem; Convex Sum of Non-convex Sets. (search for similar items in EconPapers)
JEL-codes: C02 C60 D51 D61 (search for similar items in EconPapers)
Date: 2018-06-21
References: Add references at CitEc
Citations:

Downloads: (external link)
https://mpra.ub.uni-muenchen.de/87531/1/MPRA_paper_87531.pdf original version (application/pdf)

Related works:
Journal Article: A second welfare theorem in a non-convex economy: The case of antichain-convexity (2019)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:87531

Access Statistics for this paper

More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Joachim Winter ().