Equilibria in Matching Markets with Soft and Hard Liquidity Constraints

We consider a matching with contracts model in the presence of liquidity constraints on the buyers side. Liquidity constraints can be either soft or hard. A convergent sequence of economies with increasingly stringent soft liquidity constraints is an economy with hard liquidity constraints at the limit. The limit of a corresponding convergent sequence of competitive equilibria may fail to be a competitive equilibrium in the limit economy. We establish limit results of two alternative notions of competitive equilibrium, quantity-constrained competitive equilibrium and expectational equilibrium, which do not suffer from such discontinuity problems. The implications of these limit results are discussed.