Abstract In markets for indivisible resources such as workers and objects, subsidy and taxation for an agent may depend on the set of acquired resources and prices. This paper investigates how such transfer policies interfere with the substitutes condition, which is critical for market equilibrium existence and auction mechanism performance among other important issues. For environments where the condition holds in the absence of policy intervention, we investigate which transfer policies preserve the substitutes condition in various economically meaningful settings, establishing a series of characterisation theorems. For environments where the condition may fail without policy intervention, we examine how to use transfer policies to re-establish it, finding exactly when transfer policies based on scales are effective for that purpose. These results serve to inform policymakers, market designers, and market participants of how transfer policies may impact markets, so more informed decisions can be made.

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)