Job Matching under Constraints

Studying job matching in a Kelso-Crawford framework, we consider arbitrary constraints imposed on sets of doctors that a hospital can hire. We characterize all constraints that preserve the substitutes condition (for all revenue functions that satisfy the substitutes condition), a critical condition on hospitals’ revenue functions for well-behaved competitive equilibria. A constraint preserves the substitutes condition if and only if it is a “generalized interval constraint,” which specifies the minimum and maximum numbers of hired doctors, forces some hires, and forbids others. Additionally, “generalized polyhedral constraints” are precisely those that preserve the substitutes condition for all “group separable” revenue functions. (JEL C78, D47, I11, J23, J41, J44)