Screening Frontiers

Abstract

A principal screens an agent with an arbitrary set of allocations $X$. The agent's values for the allocations are comonotonic. A subset of allocations $X^{\ast }\subseteq X$ is a surplus-elasticity frontier if (i) any other allocation has a demand curve that is pointwise lower and less elastic than that of some allocation in $X^{\ast }$ and (ii) the allocations in $X^{\ast }$ can be ordered in terms of their demand curves such that a higher demand curve is more inelastic. We show that any surplus-elasticity frontier is an optimal menu. Moreover, if the incremental demand curves along the frontier are also ordered by their elasticities, then the frontier remains optimal even if randomization is allowed. The frontier is agnostic to type distributions and redistributive welfare weights---the same menu remains optimal for a broad class of objectives, yielding a decomposition between menu design and optimal pricing. Under the same incremental-elasticity condition, a generalized notion of the frontier is not only sufficient but also necessary for this robust optimality. As applications, we derive new results on optimal bundling, taxation, sequential screening, selling information, and regulating a data-rich monopolist.

75 pages, 6 figures