Research

Publications

[1] Strategic Effects of Three-Part Tariffs under Oligopoly, International Economic Review (2013)

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.

[2] Mixed Bundling in Two-Sided Markets in the Presence of Installed Base Effects, with Tim Derdenger, Management Science (2013)

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—a 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.

[3] Pay-What-You-Want Pricing: Can It Be Profitable? with Jose Fernandez and Babu Nahata, Journal of Behavioral and Experimental Economics (2015)

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.

[4] The Degree of Distortions under Second-Degree Price Discrimination, with Babu Nahata, Economics Letters (2015)

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.

[5] Discrete Pricing and Market Fragmentation: a Tale of Two-Sided Markets, with Chen Yao and Mao Ye, American Economic Review (Papers and Proceedings) (2017)

This paper is motivated by an institutional detail of stock market trading: tick size constraint, which requires quotes to be on a discrete pricing grid. Our findings suggest that this discrete pricing leads to two-sided pricing; whereas continuous pricing results in only one-sided pricing. Such discreteness gives rise to endogenous vertical differentiation among platforms, which can explain market fragmentation in the US stock exchange industry.

[6] All-Units Discounts: Leverage and Partial Foreclosure in Single-Product Markets, with Guofu Tan, Canadian Competition Law Review (2017)

We present an exclusionary theory of all-units discounts schemes. These schemes offer a per-unit discount to all units purchased if the customer's purchase reaches a pre-specified quantity threshold. We demonstrate that when a dominant firm competes with a capacity-constrained rival, it is possible for the dominant firm to use all-units discounts to leverage its market power in the non-contestable portion to influence the contestable portion of the demand in single-product markets and to partially foreclose the small rival. Our theory suggests that pricing below cost is not necessary for all-units discounts schemes to be exclusionary and that a standard price-cost test may not be useful in assessing the exclusionary effects of all-units discounts. We advocate a rule of reason approach based on a comprehensive analysis of market structure, the nature of discount programs, exclusionary effects, efficiency, and the welfare consequences of these practices.

[7] All-Units Discounts as a Partial Foreclosure Device, with Guofu Tan and Adam Chi Leung Wong, RAND Journal of Economics (2018)

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.

[8] Market Foreclosure, Output and Welfare under Second-Degree Price Discrimination, with Babu Nahata, Economics Bulletin (2018)

We compare second-degree price discrimination with uniform pricing using two linear demands, with and without the Spence-Mirrlees condition. We find that second-degree price discrimination can result in a welfare-enhancing market foreclosure (one market is excluded under second-degree price discrimination when both markets would be served under uniform pricing) because the resulting foreclosure can increase both the total output and the total surplus. Moreover, the total surplus under second-degree price discrimination could also be lower without the foreclosure. Our results are in stark contrast with the well-known results related to output and welfare effects under third-degree price discrimination.

[9] Why Discrete Price Fragments U.S. Stock Exchanges and Disperses Their Fee Structures, with Chen Yao and Mao Ye, Review of Financial Studies (2019) (Solicited by RFS)

We propose a theoretical model to explain two salient features of the U.S. stock exchange industry: (i) sizable dispersion and frequent changes in stock exchange fees; and (ii) the proliferation of stock exchanges offering identical transaction services, highlighting the role of discrete pricing. Exchange operators in the United States compete for order flow by setting “make” fees for limit orders (“makers”) and “take” fees for market orders (“takers”). When traders can quote continuous prices, the manner in which operators divide the total fee between makers and takers is irrelevant because traders can choose prices that perfectly counteract any fee division. If such is the case, order flow consolidates on the exchange with the lowest total fee. The one-cent minimum tick size imposed by the U.S. Securities and Exchange Commission’s Rule 612(c) of Regulation National Market Systems for traders prevents perfect neutralization and eliminates mutually agreeable trades at price levels within a tick. These frictions (i) create both scope and incentive for an operator to establish multiple exchanges that differ in fee structure in order to engage in second-degree price discrimination; and (ii) lead to mixed-strategy equilibria with positive profits for competing operators, rather than to zero-fee, zero-profit Bertrand equilibrium. Policy proposals that require exchanges to charge one side only or to divide the total fee equally between the two sides would lead to zero make and take fees, but the welfare effects of these two proposals are mixed under tick size constraints.

[10] Asymmetry in Capacity and the Adoption of All-Units Discounts, with Guofu Tan and Adam Chi Leung Wong, International Journal of Industrial Organization (2019)

In many abuse of dominance antitrust cases, the dominant firm adopts pricing schemes involving all-units discounts, whereas its smaller competitors often use simple linear pricing. We provide a game-theoretic justification for the observed asymmetry in pricing practices by studying a model in which a firm with full capacity faces a capacity-constrained rival. The asymmetry in capacity between the firms, which gives rise to the captive market, allows the dominant firm to take advantage of the quantity commitment through all-units discounts while the capacity-constrained rival is induced to offer simple linear pricing.

[11] Zombie Firms and Employment Growth: Protection or Exclusion? with Xingzhi Xiao and Weiguang Zhang, Management World  (《管理世界》) (2019)

The effect of the existence of zombie firms on the stability of employment makes local governments have the motivation to relax their disposal, but the actual effects and subsequent impacts need to be further explored. From the perspective of employment growth, this paper first constructs the market equilibrium model to infer the influence of zombie firms on employment and the theoretical logic of overcapacity formation. Then, based on the data of Chinese industrial firms from 1998 to 2013 to do empirical testing, which shows that zombie firms have a significant crowding out effect on the employment growth of normal firms, and the effect has been strengthened through two channels: corporate financing constraints and firms entering or exiting barriers. Further analysis found that zombie firms not only inhibits the potential employment opportunities of normal firms but also has a crowding effect on the incumbent workers. The proportion of zombie firms significantly inhibits the expansion of normal firms scale, and relatively enhances the welfare and wages of zombie firms, thus the spontaneous flow of employers has been hindered. In terms of the heterogeneity of industry characteristics and firm scale, zombie firms have a stronger crowding out effect on the employment growth of non-labor-intensive industries and small and medium-scale firms. The robustness of the basic conclusions was tested by replacing the instrumental variables and the measure indicators. This paper provides theoretical basis and empirical evidence for the local government to firmly promote the clean-up of zombie firms.

[12] Pay-What-You-Want Pricing under Competition: Breaking the Bertrand Trap, with Jose Fernandez and Babu Nahata, Journal of Behavioral and Experimental Economics (2019) 

This paper investigates the viability of Pay-What-You-Want (PWYW) pricing when firms compete without restrictions of a minimum payment requirement or of consumer knowledge about firms' costs. We show that the equilibrium outcomes are different when underpayers, consumers who pay less than marginal cost, are present as opposed to when they are absent. In particular, when PWYW pricing is practiced without restricting the presence of underpayers and without any minimum payment requirement, then the only two equilibrium structures are: either both firms use the posted price and earn zero profits, or one firm adopts PWYW pricing and the other uses the posted price. The asymmetric pricing equilibrium leads to a softening of price competition where both firms earn positive profits and the Bertrand Trap is broken.

[13] Neutrality of Third-Degree Price Discrimination, with Babu Nahata, International Review of Economics Education (2021) 

This note shows that compared to uniform pricing, third-degree price discrimination can be neutral. For linear demands, having all price intercepts of submarkets’ inverse demands to be the same is the necessary and sufficient condition for third-degree price discrimination to be neutral. For general demands, when all submarkets’ demands are proportional to each other, not only will all the submarkets be served under uniform pricing, but all prices before and after price discrimination will be the same.

[14] A Combination of Loyalty Discounts and Resale Price Maintenance under Differential Retail Service Investments, with Zili Wang, Shiyu Tan, and Xiaogang He, Economic Research Journal （《经济研究》） (2021) (First-prize Winner, Jiangxi Provincial Outstanding Achievement Award in Social Science, China)

How to distinguish a pro-competitive resale price maintenance (RPM) from an anticompetitive one is a difficult question faced by economists and antitrust enforcement． Although impacts of various vertical contracts together with RPM have been examined in the literature, the implications of a combination of loyalty discounts with RPM on efficiency are understudied. In this paper, we find that under imperfect information, the combination of loyalty discounts with RPM will improve efficiency over the combination of a two-part tariff ( 2PT) with RPM. In particular, we consider different combinations of a 2PT or loyalty discounts with RPM under different information environments and study their impacts on differential retail service investments. We show that, when there is information asymmetry between a manufacturer and two retailers as well as imperfect information between the two retailers, the combination of loyalty discounts and RPM can implement the industry optimal, differential retailer service investments whereas the combination of 2PT and RPM cannot. This is because RPM imposes retail price uniformity ex post, the differential 2PTs ex ante will induce opportunistic behavior in investment which prevents the differential retail service investments from being chosen. In contrast, the loyalty discounts can compensate differential retail service investments based on different sales ex post. Thus, the combination of loyalty discounts and RPM can implement the industry optimal outcome. This not only maximizes the manufacturer's profits, but also improves consumer welfare over the combination of 2PT and RPM. Our findings provide a new rationale for the loyalty discounts and RPM combination, and a solution to the dilemma of supplying differential services under  RPM posed by Telser ( 1960).

[15]   With Linear Pricing, Can Profit-Maximizing Monopoly Output be Socially Efficient? with Babu Nahata, Bulletin of Economic Research (2022)

We revisit the prevailing wisdom that a profit-maximizing monopolist using linear pricing cannot produce socially efficient output. We show that when market demand function exhibits a flat portion, the prevailing wisdom may not be true. Such a “midway landing” in demand is consistent with weakly convex preferences, and many general demand functions such as any polynomials of degree three and higher. Thus, our analysis demonstrates that the output distortion resulting from linear pricing by a profit-maximizing monopolist is demand specific. In general, neither monopoly per se nor linear pricing is the main reason for social inefficiency.

[16]   Optimal Nonlinear Pricing by a Dominant Firm under Competition,  Guofu Tan and Adam Chi Leung Wong, American Economic Journal: Microeconomics (2022)

We consider a nonlinear pricing problem faced by a dominant firm competing with a minor firm. The dominant firm offers a general tariff first, and then the minor firm responds with a per-unit price, followed by a buyer choosing her purchases. By developing a mechanism-design approach to solve the subgame perfect equilibrium, we characterize the dominant firm's optimal nonlinear tariff, which exhibits convexity and yet can display quantity discounts. In equilibrium the dominant firm uses a continuum of unchosen offers to constrain its rival's potential deviations and extract more surplus from the buyer. Antitrust implications are also discussed. 

Working Papers

Tying, Vertical Integration and Pareto-improving Foreclosure, with Babu Nahata

This paper examines the relationship between tying and vertical integration when an input monopolist can require its downstream buyer to purchase a competitively supplied input from it, or integrate forward in the downstream market. Both practices would result in foreclosure of independent suppliers of the other input. We show tying is an imperfect substitute for vertical integration and provide the necessary and sufficient condition when the two practices are equivalent. When they are not equivalent, the total welfare under tying is higher than that under vertical integration. This raises the question of whether a harsher treatment of tying than vertical integration in our current antitrust enforcement is economically sound. More interestingly, compared with the no tying case, tying can be Pareto improving, despite it does exclude rivals. Both the input monopolist and consumers are strictly better off when no other firms are worse off. Further, we offer the necessary and sufficient condition for Pareto improvement.

The Limit of Market-Share Contracts, with Mingjun Xiao

Market-share contracts are a pricing scheme that conditions not only on a buyer's purchase quantity from a seller but also on the seller’s share in the buyer's total purchase, which is a contentious issue in antitrust. This paper studies the optimal market-share contract a dominant firm can offer when competing with a minor firm, where the minor firm can only respond to the dominant firm’s market-share contract with a per-unit price. We construct pseudo additively separable tariffs to implement any subgame equilibrium following the dominant firm's market-share contract. This implementation yields a tight lower bound of buyer’s surplus under any subgame equilibrium. With such a tight lower bound, we transform the optimal contracting problem into an optimization/selection of the class of subgames. We then characterize the profit limit the dominant firm can achieve through its market-share contract. In the limit, the dominant firm can extract full surplus as if it were the monopoly supplier to the buyer and squeeze both the minor firm's profit and the buyer's surplus to zero. Such a limit of market-share contracts always dominates exclusive dealing from the dominant firm's perspective, resulting in a profit level beyond its marginal contribution to the efficient outcome. Moreover, our analysis reveals that the optimal market-share contract we have characterized cannot be further enhanced even if the dominant firm is granted the freedom to offer contracts more intricate than the market-share contracts.

 Neutral or Not? The Role of Uncertainty-Induced Feelings in Vertical Competition, with Lin Liu and Dongyuan Zhan, NET Institute Working Paper No. 16-14

A Simple Framework for Assessing Partial Foreclosure Effects of All-Units Discountsiency, with Guofu Tan