The equilibrium existence duality: equilibrium with indivisibilities & income effects

Working paper

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.

Authors: Baldwin, E; Klemperer, P; Teytelboym, A; Jagadeesan, O

• Publication status: Published
• Publisher: University of Oxford
• Series: Department of Economics Discussion Paper Series
• Publication date: 2020-06-17
• Paper number: 912