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 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.
Using a game theoretic framework, we show that not only can pay-what-you-want (PWYW) 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.
The paper makes the
following contributions to the existing literature. First, we endogenize the choice
of pricing strategies—PWYW vs. fixed price. Thus rather than solely focusing
on the profitability of PWYW pricing, we evaluate its profitability vis-a-vis
uniform pricing. To the best of our knowledge this has not been done so far theoretically.
Second, we specify consumer utility to account for both economic and
behavioral considerations. We show that when marginal cost is low and behavioral
considerations are strong, then PWYW pricing can exploit the deadweight
loss present under the uniform price to gain additional profit at the cost of serving
some free riders. Therefore, PWYW pricing can be more profitable than charging
a fixed price especially when the marginal cost is low and the deadweight loss is
high. Third, we demonstrate PWYW pricing is more attractive when the cost of price setting is considerable or the market size is small.
We consider second-degree price discrimination for two types of consumers. When the net-of-cost valuation functions cross at least once at some positive quantity, it is always optimal to serve both types of consumers. Moreover, the type with the higher valuation peak always gets the socially efficient quantity. The sufficient and necessary condition for the overall efficiency is the peak of each type's net-of-cost valuation is above the other type's net-of-cost valuation at that peak quantity. For two general linear demands, we quantify the degree of efficiency, upward and downward distortions.
All-units discounts (AUD) are pricing schemes that lower 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 related conditional rebates are commonly used in both final-goods and intermediate-goods markets. Although the existing literature has thus far focused on interpreting the AUD as a price discrimination tool, investment incentive program, or rent-shifting instrument, the antitrust concerns on the AUD and related conditional rebates are often their plausible exclusionary effects.
In this article, we investigate strategic effects of volume-threshold based AUD used by a dominant firm in the presence of a capacity-constrained rival. We find that the AUD always increase the dominant firm’s profits, sales volume and market share over linear pricing or two-part tariff. At the same time, the AUD adopted by a dominant firm lead to “partial foreclosure” of an equally or more efficient rival, in the sense that the rival’s profit, sales volume and market share are strictly reduced, as compared to linear pricing. The buyer’s surplus and total surplus could be either lower or higher under AUD, depending on the rival's capacity level relative to the demand size. The intuition for our findings is that, due to the limited capacity of the rival, the dominant firm, that has a “captive” portion of the buyer’s demand in the context of a single product, is able to use the AUD to leverage its market power on the “captive” to “competitive” portion of the demand, much like the tied-in selling strategy in the context of multiple products. Our analysis applies to other similar settings in which the dominant firm has some “captive” market when it offers “must-carry” brands or a wider range of products.
We investigate competition between stock exchanges that choose the number of trading platforms to establish and the fee structure on each platform. U.S. exchanges compete for order flow by setting “make” fees for limit orders and “take” fees for market orders. When traders can quote continuous prices, the manner in which exchanges divide the total fee between makers and takers is irrelevant, because traders can choose prices that perfectly counteract any division of the fee. In such a case, order flow will simply consolidate to the platform with the lowest total fee. The one-cent minimum tick size constraints imposed by SEC Rule 612 (Minimum Pricing Increment) to traders prevent perfect neutralization and also destroy mutually agreeable trades at price levels that range within a tick. These frictions create both scope and incentive for an exchange to establish multiple platforms with different fee structures in order to engage in second-degree price discrimination, and lead to mixed-strategy equilibria with positive profits for intrinsically identical competing platforms, rather than to zero-fee, zero-profit Bertrand equilibrium. We show that price discrimination via platforms with differing fee structures can Pareto-improve social welfare in the presence of tick-size constraints. These theoretical results rationalize the diversity of fee structures, the frequent fee adjustments, and the proliferations of stock exchanges that have been observed empirically.
Vertical Probabilistic Selling: the Role of Consumer Anticipated Regret. with Lin Liu and Dongyuan Zhan(Under Review)
This paper studies vertical probabilistic selling (mixing products with different qualities) when firms compete, and consumers have different abilities to anticipate the potential post-purchase regret raised by the possibility of obtaining the inferior products. We show that, when consumers have either no or full ability to anticipate the regret, probabilistic selling emerges only when the product differentiation between firms is intermediate. However, when consumers have partial ability to anticipate the regret, probabilistic selling will arise more often and yield higher profit compared with the previous two cases. This is due to the ¡°reverse quality discrimination¡±: the perceived quality of the random product becomes non-increasing in consumer type. Such reverse discrimination can increase product differentiation at competition margin and, meanwhile, maintain sufficient attractiveness of the random product for infra-marginal consumers. Nevertheless, consumers¡¯ perceived quality of the random product is not fully reversed in the full anticipation case, and this mutes the benefits from the ¡°reverse quality discrimination.¡± Thus, the profit of probabilistic selling is not monotone in consumers¡¯ ability to anticipate regret. Accordingly, the random product provider prefers consumers to anticipate the regret partially, but not fully. In addition, the probabilistic selling always benefits its provider, but may hurt the competitor.
Under pay-what-you-want (PWYW) pricing, each consumer has total control over the price she wants to pay, which could potentially result in negative profits for the firm. In the standard Bertrand competition, two identical firms earn zero profits when they both charge the uniform price. We show that when one firm deviates and uses PWYW pricing, both firms could earn positive profits in equilibrium, breaking the so-called Bertrand trap. Although behavioral concerns are the driving factors for voluntary payments under PWYW, they may not always help the viability of PWYW pricing in the presence of competition.