Matching and Money

ABSTRACTWe analyze the implications of financial or other budget constraints in a model of matching with contracts. We assume that agents' preferences satisfy the net substitutability condition: i.e, if a price of a good increases, then minimizing the cost of obtaining a given level of utility would lead buyers (resp. sellers) to buy (resp. sell) more (resp. less) of other goods. The net substitutability condition coincides with gross substitutability if agents' preferences are quasilinear, but is strictly weaker otherwise. If agents have sufficient incomes for hard budget constraints not to bind, stable outcomes exist and coincide with competitive equilibrium outcomes. Otherwise, competitive equilibria can fail to exist, but stable outcomes exist and coincide with quasiequilibrium outcomes. Stable outcomes are at least weakly Pareto-efficient, but do not form a lattice and do not satisfy a Lone Wolf (or Rural Hospitals) Theorem. Our results suggest a new scope for sealed-bid auctions and matching with budget constraints.