Competitive Equilibria in Matching Models with Financial Constraints

We consider the one-to-one two-sided matching with contracts model in which buyers face financial constraints. In this model there is a stable outcome, but not necessarily a competitive equilibrium as defined in the standard way. We propose a new equilibrium notion, quantity-constrained competitive equilibrium (QCCE) that allows buyers to form rational expectations on the lack of supply when their financial constraints are binding. We show the existence of QCCEs and establish the equivalence among QCCE outcomes, stable outcomes, and core outcomes. We also analyze the existence of QCCEs with uniform prices, the lattice property of QCCEs, and the rural hospital theorem of QCCEs. We finally examine the relation between models with financial constraints and models with price controls

The Structure of Equilibria in Trading Networks with Frictions

Several structural results for the set of competitive equilibria in trading networks with frictions are established: The lattice theorem, the rural hospitals theorem, the existence of side-optimal equilibria, and a group-incentive-compatibility result hold with imperfectly transferable utility and in the presence of frictions. While our results are developed in a trading network model, they also imply analogous (and new) results for exchange economies with combinatorial demand and for two-sided matching markets with transfers