The Equilibrium Existence Duality

Abstract

We show that with indivisible goods, the existence of competitive equilibrium fundamentally depends on agents' substitution effects, not their income effects. Our equilibrium existence duality allows us to transport results on the existence of competitive equilibrium from settings with transferable utility to settings with income effects. One consequence is that net substitutability-which is a strictly weaker condition than gross substitutability-is sufficient for the existence of competitive equilibrium. Further applications give new existence results beyond the case of (net) substitutes. Our results have implications for auction design.This paper extends and supersedes sections 2-4 of the 2020 working paper "The Equilibrium Existence Duality: Equilibrium with Indivisibilities and Income Effects," by Elizabeth Baldwin, Omer Edhan, Ravi Jagadeesan, Paul Klemperer, and Alexander Teytelboym. extends and supersedes section 5 of that working paper. We thank Federico