Competitive equilibria in matching models with financial constraints

We consider a matching with contracts model in which buyers face financial constraints. In this model, a competitive equilibrium may fail to exist. We therefore propose the new notion of quantity-constrained competitive equilibrium (QCCE). At a QCCE, buyers form expectations about the expected supply of trades. A buyer may expect that a trade is not to be supplied if the corresponding financial constraint is binding. We show the existence of QCCEs via a dynamic process that updates prices and quantity constraints, the equivalence between QCCE outcomes and stable outcomes, and some other properties of QCCEs like the lattice property.