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About the second theorem of welfare economics with stock markets

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This paper discusses necessary optimality conditions for multi-objective optimization problems with application to theSecond 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. Jofr� and J. Rivera Cayupi [A nonconvex separationproperty 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 Université Panthéon-Sorbonne (Paris 1) in its series Cahiers de la Maison des Sciences Economiques with number b06053.

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Length: 19 pages
Date of creation: Jul 2006
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Handle: RePEc:mse:wpsorb:b06053

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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.
  2. Bonnisseau, Jean-Marc & Lachiri, Oussama, 2004. "On the objective of firms under uncertainty with stock markets," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 493-513, August.
  3. 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).
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