A Dual Characterization of Pareto Optimality

Aldo Montesano

Italian Economic Journal: A Continuation of Rivista Italiana degli Economisti and Giornale degli Economisti, 2018, vol. 4, issue 1, No 6, 153-188

Abstract: 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.

Keywords: Pareto optimality; Efficiency; Distributable surplus; Social loss; Social welfare; Potential-Pareto-Dominance (search for similar items in EconPapers)
JEL-codes: B41 D61 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s40797-017-0061-3

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