In a Kelso-Crawford job matching framework, we consider arbitrary constraints imposed on sets of doctors that hospitals can hire. Constraints preserve the substitutes condition if and only if they are "generalized interval constraints,'' slightly generalizing "interval constraints'' that specify minimum and maximum numbers of doctors allowed. Given the substitutes condition, a mild assumption ensures existence of competitive equilibria; equilibrium salaries form a lattice; a rural hospital theorem holds. We study comparative statics about changing interval constraints, and also show that instead of compelling hospitals to obey interval constraints, the government can entice them through subsidy and taxation.

Joint work with Ning Sun and Ning (Neil) Yu.