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Extended second welfare theorem for nonconvex economies with infinite commodities and public goods

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Advances in Mathematical Economics

Part of the book series: Advances in Mathematical Economics ((MATHECON,volume 14))

Abstract

This paper is devoted to the study of nonconvex models of welfare economics with public goods and infinite-dimensional commodity spaces. Our main attention is paid to new extensions of the fundamental second welfare theorem to the models under consideration. Based on advanced tools of variational analysis and generalized differentiation, we establish appropriate approximate and exact versions of the extended second welfare theorem for Pareto, weak Pareto, and strong Pareto optimal allocations in both marginal price and decentralized price forms.

Research of this author was partly supported by the US National Science Foundation under grant DMS-0603846, DMS-1007132 and by Australian Research Council under grant DP-12092508.

Received: April 12, 2010

Revised: June 28, 2010

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Notes

  1. 1.

    The second author gratefully acknowledges numerous discussions with Ali Khan on the subject of this paper and other issues of general equilibrium theory. We also thanks the referee for his/her careful reading the paper and helpful remarks.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Benedict College, Columbia, SC, 29204, USA

    Aychiluhim Habte

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

    Boris S. Mordukhovich

Authors
  1. Aychiluhim Habte
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  2. Boris S. Mordukhovich
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Correspondence to Aychiluhim Habte .

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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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Habte, A., Mordukhovich, B.S. (2011). Extended second welfare theorem for nonconvex economies with infinite commodities and public goods. In: Kusuoka, S., Maruyama, T. (eds) Advances in Mathematical Economics. Advances in Mathematical Economics, vol 14. Springer, Tokyo. https://doi.org/10.1007/978-4-431-53883-7_5

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