Discussion paper

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

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.

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Citation

Baldwin, E, O Edhan, R Jagadeesan, P Klemperer and A Teytelboym (2020), ‘DP14926 The Equilibrium Existence Duality: Equilibrium with Indivisibilities & Income Effects‘, CEPR Discussion Paper No. 14926. CEPR Press, Paris & London. https://cepr.org/publications/dp14926