About the second theorem of welfare economics with stock markets

Jean-Marc Bonnisseau and Oussama Lachiri ()
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Oussama Lachiri: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

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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.

Keywords: non-smooth analysis; extremal principle; Multi-objective optimization; non-convex programming; first-order necessary conditions; Second Theorem of Welfare Economics; programmation non-convexe; principe d'extremalité; deuxième théorème de l'économie du bien-être; Optimisation multi-critère; conditions nécessaires du premier ordre; analyse non-différentiable (search for similar items in EconPapers)
Date: 2006-06
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00118822
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Citations: View citations in EconPapers (1)

Published in 2006

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Related works:
Working Paper: About the second theorem of welfare economics with stock markets (2006)
Working Paper: About the second theorem of Welfare economics with stock markets (2006)
Working Paper: About the second theorem of Welfare economics with stock markets (2006)
Working Paper: About the second theorem of welfare economics with stock markets (2006)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-00118822

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