A three-part tariff refers to a pricing scheme consisting of a fixed fee, a free allowance of units up to which the marginal price is zero, and a positive per-unit price for additional demand beyond that allowance. The three-part tariff and its variations are commonly used in both final-goods and intermediate-goods markets. Recently, the offering of three-part tariffs and the like by dominant firms has become a prominent antitrust issue (e.g., U.S. v. Microsoft Corp. and AMD v. Intel). Existing studies have focused on monopoly models, interpreting the three-part tariff as a price discrimination device. In this paper, I investigate the strategic effects of three-part tariffs in a sequential-move game and offer an equilibrium theory of three-part tariffs in a competitive context. I show that, compared with linear pricing equilibrium and two-part tariff equilibrium, a three-part tariff always strictly increases the dominant firm¡¯s (the leader¡¯s) profit when competing against a rival (the follower) with substitute products, in the absence of usual price discrimination motive. To explore the effects of a three-part tariff on welfare, I further perform comparative statics analysis using general differentiated linear demand system. I show that the competitive effect of a three-part tariff in contrast to linear pricing depends on the degree of substitutability between products: Competition is intensified when two products are more differentiated, yet softened when two products are more substitutable. This is in stark contrast with the competitive scenario posed by a two-part tariff: A two-part tariff always enhances competition and gives the highest total surplus of these three pricing schemes. Moreover, the rival firm always gets hurt in both profit and quantity sale when the dominant firm switches from linear pricing to a two-part tariff, yet it enjoys higher profit when the dominant firm moves from a two-part tariff to the more ornate three-part tariff, despite the fact that its quantity and market share are decreased even further. My findings offer a new perspective on three-part tariffs, a perspective which could help antitrust enforcement agencies distinguish the exclusionary three-part tariff from the pro-competitive one.
We extend the traditional literature on bundling and the burgeoning literature on two-sided markets by presenting a theoretical monopoly model of mixed bundling in the context of the portable video game console market¡ªa prototypical two-sided market. We show that the monopoly platform¡¯s dominant strategy is to offer a mixed bundle rather than pure bundle or no bundle. Deviating from both traditional bundling literature and standard two-sided markets literature, we find that, under mixed bundling, both the standalone console price on the consumer side and the royalty rate on the game developer side are lower than their counterparts under independent pricing equilibrium. In our setting, mixed bundling acts as a price discrimination tool segmenting the market more efficiently as well as functions as a coordination device helping solve ¡°the chicken or the egg¡± problem in two-sided markets. After theoretically evaluating the impact mixed bundling has on prices and welfare, we further test the model predictions with new data from the portable video game console market in the early to middle 2000s, during which Nintendo was a monopolist. We employ a reduced form approach, and find empirical support for all theoretical predictions.
¡°All-Units Discount, Quantity Forcing, and Capacity Constraint¡± with Guofu Tan(Under Review)
An all-units discount (AUD) is a pricing scheme that lowers a buyer's marginal price on every unit purchased when the buyer's purchase exceeds or is equal to a pre-specified threshold. The AUD and its variations are commonly used in both final-goods and intermediate-goods markets. The usual antitrust concern about the AUD and its variations is their potential foreclosure effects when adopted by a dominant firm to compete against a small rival. The existing literature has so far focused on interpreting the AUD as a price discrimination tool, investment incentive program, or rent-shifting instrument.
In this article, we investigate strategic effects of volume threshold based pricing schemes used by a dominant firm in the presence of a smaller, capacity-constrained rival. In particular, we consider a three-stage game in which the dominant firm and its rival make price offers to a buyer sequentially before the buyer purchases. We show that the AUD adopted by a dominant firm leads to a partial foreclosure of a capacity-constrained competitor (and full foreclosure is likely, too, if there are fixed costs) in the sense that the small rival is under-supplied strictly below its capacity and its profit is reduced. This result holds even when the rival has a lower marginal cost. When the rival¡¯s capacity level is in the range of low values, the buyer is worse off under the AUD as compared to linear pricing. The intuition for our findings is that, due to the limited capacity of the rival, the dominant firm has a ¡°captive¡± portion of the buyer's demand and is able to use the AUD to leverage its market power on the ¡°captive¡± portion to the ¡°contestable¡± portion of the demand, much like the tied-in selling strategy in the context of multiple products.
We compare the AUD with a simple scheme called quantity-forcing (QF), which specifies a single quantity and the corresponding payment. We find that, in equilibrium, when the rival's capacity level is in the range of low values, AUD and QF have the same foreclosure effect; however, when the rival's capacity is in the range of high values, the QF has an additional, softening competition effect. We further explore antitrust implications of the AUD and the QF.
Using a game theoretic framework, we show that not only can pay-whatyou-want pricing generate positive profits, but it can also be more profitable than charging a fixed price to all consumers. Further, whenever it is more profitable, it is also Pareto-improving. We derive conditions in terms of two cost parameters, namely the marginal cost of production and the psychological cost of the consumer for paying too little compared to her reference price.