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 - 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.

Keywords: Multi-objective optimization; extremal principle; non-smooth analysis; non-convex programming; first-order necessary conditions; Second Theorem of Welfare Economics. (search for similar items in EconPapers)
Date: 2006-07
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Working Paper: About the second theorem of welfare economics with stock markets (2006)
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