SIGMA-OPTIMALITY AND FAIRNESS

Consistency between Pareto optimality and no envy requires some assump tions on the structure of the set of Pareto optimal allocations. Here we prove that sigma-optimality-a concept first introduced by Campbell in his 1988 paper is a sufficient condition. Campbell proved the equiv alence between sigma-optimality and price equilibrium. Using a differe ntiability approach we also give a simple proof of that result.