A Characterization of Egalitarian Equivalence

Consider a solution (an allocation rule) for an economy which satisfies the following criteria: (1) Pareto efficiency, (2) monotonicity, in the sense that if the set of attainable allocations of the economy becomes larger then the solution makes no consumer worse-off, (3) a weak and primitive notion of fairness with respect to some commodity, say commodity h, in the sense that in an exchange economy in which the aggregate endowment consists only of commodity h, the solution is equal division. We show that in the class of economies which includes non-convex technologies the only such solution is egalitarian equivalence with respect to commodity h. It is also shown that this characterization of egalitarian equivalence holds in convex exchange economies if we add a weak version of a positive association requirement.