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Non-existence of weakly Pareto optimal allocations

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  • Foivos Xanthos

    (University of Alberta)

Abstract

In this paper, we improve a characterization of the Riesz decomposition property, obtained in Aliprantis et al. (J Math Econ 92:55–76, 2000). As an application of this result, we show that the existence of weakly Pareto optimal allocations in some economic models is equivalent to the finite dimensional nature of the commodity space. This result enables us to give a characterization of infinite dimensional $$C(K)$$ C ( K ) spaces in terms of general equilibrium theory.

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  • Foivos Xanthos, 2014. "Non-existence of weakly Pareto optimal allocations," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(2), pages 137-146, October.
    • Handle: RePEc:spr:etbull:v:2:y:2014:i:2:d:10.1007_s40505-014-0044-6
    DOI: 10.1007/s40505-014-0044-6
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    1. Aliprantis, Charalambos D. & Brown, Donald J., 1983. "Equilibria in markets with a Riesz space of commodities," Journal of Mathematical Economics, Elsevier, vol. 11(2), pages 189-207, April.
    2. Aliprantis, Charalambos D. & Florenzano, Monique & Tourky, Rabee, 2004. "General equilibrium analysis in ordered topological vector spaces," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 247-269, June.
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    6. Charalambos Aliprantis & Rabee Tourky, 2009. "Equilibria in incomplete assets economies with infinite dimensional spot markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 221-262, February.
    7. Yannelis, Nicholas C. & Zame, William R., 1986. "Equilibria in Banach lattices without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 15(2), pages 85-110, April.
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    Cited by:

    1. Xanthos, Foivos, 2014. "A note on the equilibrium theory of economies with asymmetric information," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 1-3.
    2. Basile, Achille & Graziano, Maria Gabriella & Papadaki, Maria & Polyrakis, Ioannis A., 2017. "Cones with semi-interior points and equilibrium," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 36-48.
    3. Maurizio Chicco & Anna Rossi, 2015. "Existence of Optimal Points Via Improvement Sets," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 487-501, November.

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    More about this item

    Keywords

    General equilibrium theory; Infinite dimensional commodity spaces; Pareto optimality; Riesz decomposition property;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

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