Optimal Nonlinear Pricing by a Dominant Firm Under Competition
47 Pages Posted: 14 Jan 2019 Last revised: 10 Oct 2019
Date Written: October 10, 2019
We consider a nonlinear pricing problem faced by a dominant firm which competes with a capacity-constrained minor firm for a downstream buyer who may purchase the product from the firms under complete information. Specifically, we analyze a three-stage game in which the dominant firm offers a general tariff first and then the minor firm responds with a per-unit price, followed by the buyer choosing her purchases. By establishing an equivalence between the subgame perfect equilibrium of our asymmetric competition game and the optimal mechanism in a “virtual” principal-agent model, we characterize the dominant firm's optimal nonlinear tariff, which exhibits convexity and yet can display quantity discounts. Our analysis provides a rationale for nonlinear pricing under competition in the absence of private information: The dominant firm can use unchosen offers to constrain its rival’s possible deviations and extract more surplus from the buyer. Antitrust implications are also discussed.
Keywords: Optimal Nonlinear Pricing, Complete Information, Capacity Constraint, Partial Foreclosure
JEL Classification: L13, L42, K21
Suggested Citation: Suggested Citation