When a mix of buyers helps consumers keep more surplus

Why would a market designed to benefit consumers need buyers with different willingness to pay? Because those differences can limit how much a seller can charge its most enthusiastic customers.

In Designing Markets for Screening: Optimal Composition and the Geometry of Surplus, Panagiotis Kyriazis studies this mechanism mathematically. The arXiv preprint, version four, examines a theoretical benchmark rather than measuring outcomes in an actual market: an institution can freely choose the distribution of buyer characteristics before a monopolist sets its offers.

Designing the population before the menu

The seller offers a menu of qualities and prices. Each buyer privately knows their “type”: how much they value an additional unit of quality. The seller knows the population’s distribution of types, but not an individual buyer’s type. Buyers select their preferred offer, allowing the menu to screen them through their choices.

Serving higher-value buyers can also cost more. However, the model assumes their willingness to pay rises faster than the type-dependent marginal cost. Higher types therefore offer greater potential gains from trade. Providing additional quality becomes increasingly costly.

Consumer surplus is the value buyers receive minus their payments. Seller profit is payments minus costs. Adding them gives total surplus; payments merely divide that total between the two sides.

The institution chooses a population to maximize consumer surplus plus a weighted amount of profit. Varying that weight identifies the Pareto frontier: outcomes where neither side can gain without the other losing, across the populations the model permits.

Diversity sustains information rents

When profit receives at least as much weight as consumer surplus, the optimal population consists entirely of the highest feasible type. The seller provides efficient quality—the quality maximizing gains from trade—and extracts all surplus.

When consumers receive greater weight, the optimal market instead combines a continuous range of types with a positive share concentrated at the highest type. All selected buyers are served, and distinct interior types receive distinct qualities. The highest-type group receives efficient quality.

Those top buyers nevertheless retain “information rents”: surplus the seller must leave them so they do not choose cheaper contracts intended for lower types. The lower offers constrain surplus extraction higher up the menu.

The result is not a recommendation to erase screening. In this benchmark, consumer-oriented market design uses screening and product differentiation to sustain rents. Under the paper’s cost-curvature condition, each efficient payoff pair comes from a unique market composition.

Crucially, serving all selected buyers does not mean including everyone from an existing population. The benchmark allows the institution to choose which types appear and in what proportions.

Why the shape of the payoff set matters

The proof works by replacing the distribution-choice problem with a problem over “virtual net values”: quantities that account for both trading gains and the seller’s incentive-related cost of leaving buyers rents. These determine the seller’s quality choices. Carefully constructed changes establish the optimal market’s structure; differential equations and boundary conditions establish uniqueness under the relevant curvature restriction.

With a stronger curvature condition, the analysis identifies maximum consumer surplus at every attainable profit, including profits below the consumer-optimal market’s level.

The full payoff set is convex in two cases: when costs do not depend on buyer type, or when a feasible type generates no gains from trade. Convexity means that intermediate combinations of two attainable payoff pairs are also attainable in a single market. Adding buyers of the no-trade type provides one way to scale both payoffs down proportionally.

Otherwise, type-dependent costs can make the set nonconvex. The paper constructs two attainable outcomes whose intermediate payoff combinations cannot arise in any single market.

Observable segmentation fills such gaps by letting the seller offer separate menus in separately chosen populations. Yet, under the stronger curvature condition, it cannot raise maximum consumer surplus at any given profit. The added possibilities lie on the side associated with suppressing consumer rents, not improving consumers’ best attainable outcome.

Better averages need not mean better treatment

When costs are type-independent, greater consumer orientation shifts the optimal population toward lower valuations while improving quality for a fixed valuation in the shared interior support. Consumer surplus rises, but profit and total surplus fall.

Type-dependent costs can reverse the individual comparison. With sufficiently steep cost increases near the top and a sufficiently high minimum feasible type, greater consumer orientation lowers every above-minimum type’s rent. Average consumer surplus still rises because the population shifts toward higher types, who earn larger rents within either market.

These conclusions depend on freedom to reshape populations. Introducing formation costs changes the incentives; fixing average valuation can permit exclusion and allow segmentation to improve the efficient frontier. The preprint supplies a benchmark for screening’s limits, not a universal prescription for real-world pricing or market access.