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About the second theorem of welfare economics with stock markets

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Abstract

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. Jofré 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

Suggested Citation

  • Jean-Marc Bonnisseau & Oussama Lachiri, 2006. "About the second theorem of welfare economics with stock markets," Cahiers de la Maison des Sciences Economiques b06053, Université Panthéon-Sorbonne (Paris 1).
    • Handle: RePEc:mse:wpsorb:b06053
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    File URL: https://halshs.archives-ouvertes.fr/halshs-00118822
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    1. 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.
    2. Cornet, B., 1986. "The second welfare theorem in nonconvex economies," LIDAM Discussion Papers CORE 1986030, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. 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.
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    Cited by:

    1. Egbert Dierker, 2015. "A multiperiod Drèze rule," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 129-151, October.

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    More about this item

    Keywords

    Multi-objective optimization; extremal principle; non-smooth analysis; non-convex programming; first-order necessary conditions; Second Theorem of Welfare Economics;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • D60 - Microeconomics - - Welfare Economics - - - General

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