Working Paper BETA #2010-01

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Title : The Aggregation of Individual Distributive Preferences through the Distributive Liberal Social Contract : Normative Analysis.

Author(s) : Jean Mercier-Ythier

Abstract : We consider abstract social systems of private property, made of n individuals endowed with non-paternalistic interdependent preferences, who interact through exchanges on competitive markets and Pareto-efficient lumpsum transfers. The transfers follow from a distributive liberal social contract defined as a redistribution of initial endowments such that the resulting market equilibrium allocation is both Pareto-efficient relative to individual interdependent preferences, and unanimously weakly preferred to the initial market equilibrium. We notably elicit two global properties of Pareto-efficient redistribution in smooth differentiable social systems of the type above. The first one is the separability of allocation and distribution: Pareto-efficient redistribution leaves unaltered the role of market prices in the coordination of market exchanges, as expressed, notably, by the existence and efficiency properties of competitive equilibrium. The second one is the global structure of the set of Pareto-efficient allocations: its relative interior is a simply connected smooth manifold of dimension n-1, homeomorphic to the relative interior of the unit-simplex of Rn. Both properties obtain under three suitable conditions on the partial preordering of Pareto associated with individual interdependent preferences, which essentially state that: the social utility functions built from weighted sums of individual interdependent utilities, by means of arbitrary positive weights, exhibit a property of differentiable nonsatiation and some suitably defined property of inequality aversion; and individuals have diverging views on redistribution, in some suitable sense, at (inclusive) distributive optima. The set of market equilibrium allocations associated with the transfers of the inclusive distributive liberal social contracts then consists of the maxima, in the set of attainable allocations unanimously weakly preferred to the initial market equilibrium, of the weighted sums of individual interdependent utilities derived from arbitrary vectors of positive weights of R++ n. Its relative interior is a simply connected smooth manifold of dimension n-1 whenever the initial market equilibrium is not Paretoefficient relative to individual interdependent preferences. It is shown, finally, that the liberal social contract’s inclusive solutions for redistribution, so characterized, maximize a family of social welfare functionals that verify Arrow’s non-dictatorship axiom and Sen’s liberty axiom for the social systems to which it applies.

Key-words : Walrasian equilibrium; Pareto-efficiency; liberal social contract; social preferences; social choice; allocation; distribution.

JEL Classification : A10, A12, A13, D02, D31, D41, D51, D60-64, D70, D71, D78, H10, H11, H21, H23, H41, H42, H44, H53, I30, I38, P10, P11, P14, P16, P35, Z13.