Regular distributive efficiency and the distributive liberal social contract

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 elicit 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 . The property obtains 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 non-satiation 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 consists of the allocations that are unanimously weakly preferred to the initial market equilibrium and that maximize, in the set of attainable allocations, weighted sums of individual interdependent utilities derived from suitable vectors of positive weights of ℝn ++. Its relative interior is a simply connected smooth manifold of dimension n-1 whenever the initial market equilibrium is not Pareto-efficient relative to individual interdependent preferences.