Equilibrium and matching under price controls

The paper considers a one-to-one matching with contracts model in the presence of price controls. This set-up contains two important streams in the matching literature, those with and those without monetary transfers, as special cases and allows for intermediate cases with some restrictions on the monetary transfers that are feasible. An adjustment process that ends with a stable outcome is presented, thereby proving the existence of stable outcomes. The process contains the deferred acceptance algorithm of Gale and Shapley 1962 and the approximate auction mechanism of Demange, Gale, and Sotomayor 1986 as special cases. The paper presents a notion of competitive equilibrium, called Drze equilibrium, for this class of models, an extension of the concept as developed by Drze 1975 for economies with divisible commodities subject to price controls. It is shown that Drze equilibrium allocations are equivalent to allocations induced by stable outcomes. One implication is the existence of Drze equilibria. Another implication is the equivalence of a competitive equilibrium concept and the concept of stable outcomes that is valid with and with- out monetary transfers as well as when monetary transfers are limited.