Designing Markets for Screening: Optimal Composition and the Geometry of Surplus

Abstract

We characterize the structure of market compositions that generate Pareto efficient outcomes and the geometry of the surplus set in a screening model with type-dependent costs. Maximizing principal or total surplus concentrates the market at the highest type, with all surplus extracted. Agent-oriented optima instead use, rather than suppress, screening: all agents in the market are served, there is no bunching, and a positive share of agents have the highest type and are served efficiently. Separation is valuable even under agent surplus maximization because it propagates information rents. Under a mild cost-curvature condition, each Pareto efficient outcome is implemented by a unique market. Under a stronger cost-curvature condition, the surplus set is convex whenever values are private, or types with no gains from trade can be included in the market. We characterize all surplus outcomes in these cases. Without such types and with type-dependent costs, the surplus set can be nonconvex. Market segmentation generates the missing outcomes but does not increase the maximum agent surplus at any level of principal surplus. We also derive comparative statics along the Pareto frontier and with respect to value-cost co-movement, distinguishing changes in market composition from changes in individual allocations and rents.