On the non existence of envy-free and egalitarian-equivalent allocations in economies with indivisibilities

Abstract

We consider economies with indivisible goods (houses, jobs) and one infinitely divisible good. An allocation is envy-free if no agent prefers someone else's consumption to his own. An allocation is egalitarian-equivalent if there is a reference bundle that every agent finds indifferent to his consumption. We show that in such economies there may be no allocation that is both egalitarian-equivalent and envy-free.