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Advances in Mathematical Economics pp 113–153Cite as

Set-valued optimization in welfare economics

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Part of the book series: Advances in Mathematical Economics ((MATHECON,volume 13))

Abstract

This paper mainly concerns applications of advanced techniques of variational analysis and generalized differentiation to nonconvex models of welfare economics with finite-dimensional and infinite-dimensional commodity spaces. We pay special attention to establishing new relationships between necessary conditions in multiobjective/set-valued optimization and appropriate extensions of the second fundamental theorem of welfare economics to nonconvex economies with general preference relations. The variational approach developed in this paper allows us to obtain new necessary conditions for various types of local optimal solutions to constrained multiobjective problems and to derive from them new versions of the second welfare theorem applied to Pareto as well as weak, strict, and strong Pareto optimal allocations of nonconvex economies under certain qualification conditions developed in the paper. We also establish relationships of the latter conditions with some versions of Mas-Colell’s uniform properness.

Received: September 27, 2009

Revised: October 19, 2009

JEL classification: D6

Mathematics Subject Classification (2000): 90A14

Research of this author was partly supported by the US National Science Foundation under grant DMS-0603846.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Northern Michigan University, Marquette, MI, 481855, USA

    Truong Q. Bao

  2. Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA

    Boris S. Mordukhovich

Authors
  1. Truong Q. Bao
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  2. Boris S. Mordukhovich
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Correspondence to Boris S. Mordukhovich .

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Editors and Affiliations

  1. Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-0041, Japan

    Shigeo Kusuoka (Professor) (Professor)

  2. Department of Economics, Keio University, 2-15-45 Mita, Minato-ku, Tokyo, 108-8345, Japan

    Toru Maruyama (Professor) (Professor)

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Bao, T.Q., Mordukhovich, B.S. (2010). Set-valued optimization in welfare economics. In: Kusuoka, S., Maruyama, T. (eds) Advances in Mathematical Economics. Advances in Mathematical Economics, vol 13. Springer, Tokyo. https://doi.org/10.1007/978-4-431-99490-9_5

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