Adv. Math. Econ. 14, 93–126 (2011)

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

Aychiluhim Habte^{1} and Boris S. Mordukhovich ^{3} ^{4} ^{2}

1 Department of Mathematics and Computer Science, Benedict College, Columbia, SC 29204, USA (e-mail: habtea@benedict.edu)

2 Department of Mathematics, Wayne State University, Detroit, MI 48202, USA (e-mail: aa1086@wayne.edu)

Received: April 12, 2010 Revised: June 28, 2010

JEL classification: D06

Mathematical Subject Classification (2010): 90A14, 49J52

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.

Key words: welfare economics, public goods, Pareto optimal allocations, second welfare theorem, variational analysis, generalized differentiation, extremal principle

3Research 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.

4The 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.