Existence of an equilibrium in incomplete markets with discrete choices and many markets

We define and prove the existence of an equilibrium for Bewley-style models of heterogeneous agents in incomplete markets with discrete and continuous choices. Our sample model also features endogenous price volatility across many markets (locations) but still has a steady state equilibrium with a finite-dimensional state space. Our proof of existence uses Kakutani's Fixed Point Theorem and does not require the set of households that are indifferent between two discrete choices to be measure zero.