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About the second theorem of welfare economics with stock markets

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Author Info
Jean-Marc Bonnisseau () (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I)
Oussama Lachiri () (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I)

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Abstract

This paper discusses necessary optimality conditions for multi-objective optimization problems with application to the Second Theorem of Welfare Economics. We use the extremal principle, since we consider non-convex sets non-smooth functions. Particularly, we develop a slight generalization of the main result of A. Jofré and J. Rivera Cayupi [A nonconvex separation property and some applications, Math. Program. 108 (2006) 37-51], which allows more flexibility in a stochastic economy with production and stock market. Formally, we define a stock market equilibrium through the necessary optimality conditions at a constrained Pareto optimal allocation. We show that the Second Theorem of Welfare Economics holds in a two-period framework. But, by mean of an example, we show that this later result is no longer true for multi-period economies.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00118822_v1.

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Date of creation: Jul 2006
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Handle: RePEc:hal:cesptp:halshs-00118822_v1

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Related research
Keywords: Multi-objective optimization; extremal principle; non-smooth analysis; non-convex programming; first-order necessary conditions; Second Theorem of Welfare Economics.;

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  1. Grossman, Sanford J & Hart, Oliver D, 1979. "A Theory of Competitive Equilibrium in Stock Market Economies," Econometrica, Econometric Society, vol. 47(2), pages 293-329, March. [Downloadable!] (restricted)
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  2. Cornet, B., 1986. "The second welfare theorem in nonconvex economies," CORE Discussion Papers 1986030, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Jean-Marc Bonnisseau & Oussama Lachiri, 2004. "On the objective of firms under uncertainty with stock markets," Cahiers de la Maison des Sciences Economiques b04122, Université Panthéon-Sorbonne (Paris 1). [Downloadable!]
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