Economic Theory Seminar Series - Bing Liu (University of Queensland)

Title: The Shape and Size of Nonlinear Pricing Menus

Abstract: Why do firms use nonlinear tariffs with rising, falling, or zero marginal prices, and why do some offer a single bundle while others offer finely differentiated menus? This paper develops a unified framework with piecewise-linear buyer utility to explain both tariff shape and menu size. Under virtual richness, marginal valuations at endogenous cutoffs determine whether optimal marginal prices rise or fall. A two-dimensional extension shows how positive dependence between per-unit value and satiation generates quantity premiums, while negative dependence generates discounts. The paper also characterizes the extremes of menu size without imposing the standard single-crossing condition. Relative-value monotonicity yields pure grand bundling; group-wise threshold crossing and virtual dominance yield maximal screening. Under grand bundling, more quantity-intensive participants receive strictly less consumer surplus. When capacity is endogenous, expanding the feasible quantity set can induce the monopolist to over-provide than the first best. Finally, the two extreme screening regimes can coexist within a single optimal menu. If satiation (d(v)) is nonincreasing in (v) and maximum surplus (s(v)=v d(v)) is at most single-peaked, there exists an optimal mechanism with at most three regions: non-service, minimal screening through all-you-can-eat bundles, and maximal screening through all-you-can-pay bundles. Thus, zero marginal pricing and full extraction of consumer surplus can arise from non-single-crossing preferences.