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A Dual Characterization of Pareto Optimality

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  • Aldo Montesano

    (Bocconi University)

Abstract

According to Pareto’s definition, an allocation is optimal if there is no other feasible allocation that is at least as good for all individuals and better for some individuals. This definition is currently adopted in economics as a condition of efficiency, that is, no waste of resources. Consequently, the relation between maximization of utilities and minimization of resources has to be studied. This paper examines the duality between these two problems. Assumptions currently adopted in economics, such as continuity of functions, convexity of sets, absence of externalities and divisibility of goods, are not introduced. Equivalence is established between ‘Pareto maximal allocations’ and ‘Pareto efficient allocations’ (that is, allocations generating a utility vector unreachable with a smaller resource vector). The duality between utilities and resources allows to measure the social loss caused by inefficiency in terms of a quantity of resources. Moreover, the introduction of the ‘social welfare function’ and its dual concept, ‘the social requirement function’, allows an extension of the Gossen–Menger loss principle. Finally, the implications of duality between utilities and resources are considered with respect to the notion of Potential-Pareto-Dominance.

Suggested Citation

  • Aldo Montesano, 2018. "A Dual Characterization of Pareto Optimality," Italian Economic Journal: A Continuation of Rivista Italiana degli Economisti and Giornale degli Economisti, Springer;Società Italiana degli Economisti (Italian Economic Association), vol. 4(1), pages 153-188, March.
    • Handle: RePEc:spr:italej:v:4:y:2018:i:1:d:10.1007_s40797-017-0061-3
    DOI: 10.1007/s40797-017-0061-3
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    References listed on IDEAS

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    1. Balasko, Yves, 1979. "Budget-constrained Pareto-efficient allocations," Journal of Economic Theory, Elsevier, vol. 21(3), pages 359-379, December.
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    More about this item

    Keywords

    Pareto optimality; Efficiency; Distributable surplus; Social loss; Social welfare; Potential-Pareto-Dominance;
    All these keywords.

    JEL classification:

    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • B41 - Schools of Economic Thought and Methodology - - Economic Methodology - - - Economic Methodology

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