DP14926 The Equilibrium Existence Duality: Equilibrium with Indivisibilities & Income Effects

Author(s): Elizabeth Baldwin, Omer Edhan, Ravi Jagadeesan, Paul Klemperer, Alex Teytelboym
Publication Date: June 2020
JEL(s): C62, D11, D44
Programme Areas: Financial Economics, Industrial Organization
Link to this Page: cepr.org/active/publications/discussion_papers/dp.php?dpno=14926

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. We also extend the "demand types" classification of valuations to settings with income effects and give necessary and sufficient conditions for a pattern of substitution effects to guarantee the existence of competitive equilibrium.