Efficiency and income redistribution in the single-peaked preferences model with several commodities

We consider the problem of allocating m infinitely divisible commodities among agents with single-peaked preferences. We propose a variation on the Mas–Colell’s Walrasian solution with slacks to characterize the efficient allocations. Our solution allows us to associate with each efficient allocation an income redistribution. We prove that the original solution proposed by Mas–Colell is the efficient selection which requires an income redistribution where the maximum payoff and the maximum subsidy are smallest. This generalizes a derivation of the Uniform Rule by Schummer and Thomson.