How to Price Discriminate When Tariff Size Matters

Abstract

Firms that serve a large market with many diverse consumer types use discriminatory or nonlinear pricing to extract higher revenue, inducing consumers to separate by self-selecting from a large number of tariff options. But the extent of price discrimination must often be tempered by the high costs of devising and managing discriminatory tariffs, including costs of supporting consumers in understanding and making selection from a complex menu of choices. These tariff design trade-offs occur in many industries where firms face many consumer types and each consumer picks the number of units to consume over time. Examples include wireless communication services, other telecom and information technology products, legal plans, fitness clubs, automobile clubs, parking, healthcare plans, and many services and utilities. This paper evaluates alternative ways to price discriminate while accounting for both revenues and tariff management costs. The revenue-maximizing menu of quantity-price bundles can be very (or infinitely) large and hence not practical. Instead, two-part tariffs (2PTs), which charge a fixed entry fee and a per-unit fee, can extract a large fraction of the optimal revenue with a small menu of choices, and they become more attractive once the costs of tariff management are factored in. We show that three-part tariffs (3PTs), which use an additional instrument, the “free allowance,” are an even more efficient way to price discriminate. A relatively small menu of 3PTs can be more profitable than a menu of 2PTs of any size. This 3PT menu can be designed with less information about consumer preferences relative to the menu of two-part tariffs, which, in order to segment customers optimally, needs fine-grained information about preferences. Our analysis reveals a counterintuitive insight that more-complex tariffs need not always be more profitable; it matters whether the complexity is from many choices or more pricing instruments.

Pricing and Public Policy Issues

“…Many companies take the help of latest technologies to access real-time information and to take decisions. They use software to understand and analyze actual customer responses to different pricing schedules (Bagh & Bhargava, 2013). For example, merchants who sell their products on Amazon.com, change their prices regularly, sometimes on a daily or even hourly basis to reflect the demands of customers.…”

Optimal Three-Part Tariff Plans

“…None of these studies, however, calculated the optimal three-part tariff plan. For example, Bagh and Bhargava (2013) analyzed the ability of alternative nonlinear pricing structures to price discriminate. They showed that three-part tariffs are more efficient than two-part tariffs as price-discriminating mechanisms for heterogeneous consumers.…”

Non-linear pricing by convex duality

“…The parameter t for the type of the buyer is assumed to represent the valuation of a potential buyer for the good. The buyer derives a utility equal to t · u(A t ) − p t from acquisition of a quantity A t (allocation to buyer of type t) of the good, where u is a differentiable, strictly concave, strictly increasing function (u The non-linear pricing problem briefly described above occurs in many industries, e.g., wireless communication services, other telecom and technology products, legal plans, fitness clubs, automobile clubs and healthcare plans; see Bagh and Bhargava (2013) for further details. It is part of the general theory of basic static adverse selection problems in economics.…”

“…In this case, one can implement the optimal nonlinear payment schedule by offering a menu of two-part tariffs as discussed in Section 3.5 of Tirole (1990). In a recent paper Bagh and Bhargava (2013) study the efficiency of two and three-part tariffs and show that a relatively small menu of three-part tariffs may be more profitable than a menu of two-part tariffs of any size. In Section 2.3.1 of Bolton and Dewatripont (2004) the solution of the above problem is investigated under the so-called SpenceMirrlees single crossing condition on the utility function u, which helps simplify the problem by reducing the number of constraints considerably.…”