Equilibrium Existence Duality

We analyze how income effects influence competitive equilibria in markets for indivisible goods. To do so, we develop an "Equilibrium Existence Duality" that allows us to transport results on the existence of equilibrium from transferable utility economies to settings with income effects. As an application, we show that the net substitutability of units of indivisibles—which is a strictly weaker condition than their gross substitutability—ensures the existence of equilibria. More generally, we illustrate how the nature of the effects of compensated price changes on demand—as opposed to the effects of uncompensated price changes—determine whether equilibrium exists with indivisible goods.

Authors: Elizabeth Baldwin (Oxford), Ravi Jagadeesan (Harvard, visiting Simons), Paul Klemperer (Oxford), Alexander Teytelboym (Oxford, visiting Simons)