Do Exclusivity Arrangements Harm Consumers? Jihui Cheny

Qiang Fuz

August 2013

Abstract This paper explores the rami…cations of exclusivity arrangements, e.g., iPhone’s partnership with wireless carriers, for market competition and consumer welfare. Two …rms compete in a primary good market, and a monopolistic …rm o¤ers a value-adding good. The primary good can be consumed alone, while the value-adding good must be consumed with the primary good. The monopolistic …rm forms an exclusivity partnership with one of the primary good providers. Buyers are able to consume the value-adding good only if they patronize the monopolistic …rm’s exclusive partner. This practice allows the monopolistic …rm to extract surplus from the primary good market. Surprisingly, consumers bene…t from the exclusivity arrangement. However, overall social welfare declines, despite improvements to consumer welfare. JEL Nos: L1, L2, L4, L5 Keywords: Exclusivity, Consumer Welfare, Market E¢ ciency, Hotelling, Two-Part Pricing

1

Introduction

Firms are increasingly using exclusivity arrangements to exploit their market power. For instance, public interest was aroused by Apple’s initial marketing strategy for the iPhone, in which Apple has granted only a few wireless carriers the exclusive right to carry the product. In the U.S., Apple locked its iPhone exclusively into AT&T’s network for nearly four years before awarding “pseudo-exclusivity”to Verizon in early 2011.1;2 Prior to March We are grateful to two anonymous referees, Michael R. Baye, Andrei Hagiu, David Loomis, Sue H. Mialon, Chunhui Miao, James E. Prieger, Rati Ram, Christian Roessler, Ralph Winter, Julian Wright, and Lan Zhang for their very helpful comments and suggestions. We would also like to thank seminar participants at University of Illinois and session participants at the 9th International Conference of Industrial Organization and the Chinese Economist Society 2011 Meeting for their helpful comments. All errors remain ours. y Department of Economics, Illinois State University, Campus Box 4200, Normal, IL61790 U.S.A.; Tel: (309) 438-3616; Fax: (309) 438-5228; Email: [email protected]. z Department of Strategy and Policy, National University of Singapore, 15 Kent Ridge Drive, Singapore, 117592; Tel: (65) 6516-3775; Fax (65) 6779-5059; Email: [email protected]. 1 The other two major wireless carriers, Sprint and T-Mobile, have been allowed to include the iPhone in their device lineups since October 2011 and April 2013, respectively. 2 Source: “Verizon may pay Apple for iPhone semi-exclusive” by Marguerite Reardon, CNET news (http://news.cnet.com/8301-30686_3-20024767-266.html).

2012, China Unicom had been the exclusive carrier in China, Apple’s second-largest market. The suspension of iPhone’s exclusivity practice in the European and Singaporean markets is mainly due to an “unfavorable”legal environment, which Apple had not foreseen.3 In this paper, we provide a stylized analysis of exclusivity arrangements in a context that resembles Apple’s iPhone case. The model includes an assembly between an “upstream”…rm (e.g., Apple) that occupies a substantially wide market niche and duopolistic “downstream” …rms (e.g., wireless carriers). Each of the downstream …rms produces a primary (essential) good, which provides a platform for consumers to use a value-adding (nonessential) complementary good o¤ered by the upstream …rm. An exclusivity partnership between the monopolistic …rm and one of the duopolistic …rms limits the availability of the value-adding good on the other platform. As a result, its buyers will be forced to patronize the exclusive partner of the monopolistic …rm. We provide an equilibrium analysis of …rms’behavior under such an exclusivity arrangement. This allows us to formally evaluate the rami…cations of exclusivity practice for consumer welfare and market e¢ ciency. Exclusivity arrangements exist in many other contexts. For example, Electronic Arts, a major game developer, has launched games that can only be played on Sony’s PlayStation 3. Many publishers sell electronic versions of their works exclusively on selected platforms, e.g., Amazon’s Kindle. Similar arrangements are also observed in digital media distribution networks, e.g., News Corp’s exclusive tablet newspaper, The Daily, on the iPad.4 However, the exclusivity arrangement between Apple and its partner wireless carriers has unique characteristics that fundamentally distinguish it from the usual practice, in which the primary good provider (e.g., the Kindle and the iPad), rather than the value-adding good provider (e.g., e-books and video games), typically predominates in an exclusivity partnership. The bargaining power of upstream …rms is often largely limited by the nonessential nature, functional dependence, and/or ample supply of close substitutes of the value-adding goods they produce. Their sales largely rely on the extensive consumer base and distribution networks of the primary good (i.e., platform) providers. It is the platform’s strategies, as a market intermediary between consumers and value-adding or complementary good providers, that contribute more to the ultimate market structure (see Rysman, 2009). The opposite, however, is observed in the iPhone case: Its marketing strategy has been widely regarded as an attempt to “change the existing relationship radically between mobile handset manufacturers and mobile operators.”5 Apple’s continuing marketing success and unique product image, along with its independently integrated product lines, allow its prod3

Source: “German Court Ruling Triggers Major Review for iPhone Sales across Europe,”Global Insight, November 2007. 4 The Daily discontinued operations on December 15, 2012. 5 Source: “German Court Ruling Triggers Major Review for iPhone Sales across Europe,”Global Insight, November 2007.

2

ucts (e.g., the iPhone) to substantially di¤erentiate themselves from rival devices and acquire a unique and wide market niche. Its leadership in the smartphone-handset market has given Apple the upper hand in its negotiations with wireless carriers.6 Its exclusivity arrangement has substantially a¤ected the balance of power in the downstream wireless market, and has been viewed by carriers as an e¤ective means of preempting their rivals. For instance, the CEO of China Mobile, the leading wireless provider in the massive Chinese telecommunication market, acknowledged in public that the …rm had been under strong pressure to include the iPhone in its lineup in order to please its unhappy customers.7 Verizon explicitly demanded, in its negotiations with Apple, that Sprint and T-Mobile be excluded from iPhone’s distribution channels.8 Apple’s distinctive exclusivity practice has caused substantial controversy and aroused strong regulatory concerns. In 2009, four U.S. senators led a petition to persuade the Federal Communications Commission (FCC) to investigate the exclusivity arrangement between Apple and AT&T.9 The FCC and the Department of Justice (DOJ) then launched an investigation into exclusionary handset arrangements. In Paris, a court rejected Apple’s exclusivity agreement with France Telecom and ordered Apple to unlock the mobile device, a ruling that was widely regarded as a victory for French consumers. Despite the high-pro…le debates caused by iPhone’s exclusivity, its implications for market e¢ ciency and consumer welfare have yet to be formally analyzed. This paper attempts to …ll in the gap. We o¤er a stylized but potentially useful analysis of an economic relationship that resembles the iPhone context, with a particular focus on the strategy of the upstream …rm (value-adding good provider) and its impact on competition in the downstream (platform) market and consumer welfare. In our model, consumers are uniformly distributed on a “square city” (Gans and King, 2006). Two duopolistic downstream …rms, which produce a primary good, are located at opposite ends of a horizontal line across the middle of the square, while a monopolistic upstream …rm, which produces a value-adding good, is located at the center of the square. The primary good can be consumed alone, while the value-adding good must be used together with the primary good in a …xed (one-to-one) proportion. In the benchmark case, where exclusivity is absent, the monopolistic …rm and the duopolistic …rms set their prices independently. When the monopolistic …rm is allowed to practice exclusivity, 6

Apple’s success is undoubtedly due in large part to then-CEO Steve Jobs’reputation of being uncompromising in the tech world. 7 Source: “Updated: China Mobile wants iPhone and iPad,” iPhonAsia.com, March 2010. 8 Source: “Verizon may pay Apple for iPhone semi-exclusive,” by Marguerite Reardon, CNET news (http://news.cnet.com/8301-30686_3-20024767-266.html). 9 They argued that “for many consumers, the end result of these exclusionary arrangements is being channeled to purchase wireless service from a carrier that has monopolistic control over the desired handset and having to pay a premium price for the handset because the market is void of any competition for the particular handset” (Source: “Department of Justice launches review of handset arrangements,” by Tom Braithwaite and Richard Waters, Financial Times, July 7, 2009).

3

the game proceeds as follows. First, the monopolistic …rm announces its exclusivity contract, which speci…es the price of its value-adding good. Second, it runs an auction to sell its exclusive partnership, and invites the duopolistic primary good providers to bid for the partnership. Under the exclusive arrangement, the monopolistic …rm “locks” its product to the primary good o¤ered by its exclusive partner. Finally, the duopolistic …rms simultaneously set their prices, and consumer purchases take place subsequently. We show that the monopolistic …rm bene…ts from exclusivity in spite of its loss of market share due to exclusion. This practice allows it to leverage its market power in the (nonessential) value-adding good market so as to extract surplus from the primary good market. Paradoxically, consumers as a whole also bene…t from the exclusivity practice. The reasons are as follows. Exclusivity fundamentally alters all three …rms’pricing behaviors, leading to an overall gain in consumer welfare. First, exclusivity enhances price competition: The excluded …rm is forced to undercut its rival to avoid losing its market share even further, which intensi…es price competition and, in turn, bene…ts consumers in the primary good market. This is a “competition-enhancing” e¤ect. Second, under exclusivity, the monopolistic …rm strategically “underprices” its value-adding good through a two-part pricing strategy. The lower price boosts demand for the good and increases the appeal of the primary good o¤ered by its partner. This e¤ect ampli…es the rent that accrues to its exclusive partner, which allows the monopolistic …rm to recoup the foregone sales revenue (from its value-adding good) through the higher revenue from the bidding contest, and consumers of the value-adding product bene…t from the low price. This rationale largely resembles the conventional wisdom of Cournot (1838), which evaluates a merger between two monopolistic complementary good providers. Similar to the merger, the exclusive partnership in our model compels the monopolistic …rm to internalize the externality between the two complementary goods. Furthermore, the twopart pricing strategy strengthens the competition-enhancing e¤ect: A lower price for the value-adding good would further handicap the excluded …rm in the primary good market, thereby compelling it to undercut its rival even more. This analysis yields interesting implications. In contrast to the popular view that exclusivity arrangements jeopardize consumer welfare, our analysis demonstrates otherwise. Our results cast doubt, for instance, on the court ruling against Apple in France on the grounds that it threatened consumers’interests. Even so, the results of welfare analysis should be interpreted with caution. First, the practice redistributes surplus among di¤erent consumers, and leads some to gain at the expense of others. Second, social welfare declines despite the gains in consumer welfare. These observations highlight the complexity of evaluating the rami…cations of exclusivity arrangements. Details are provided in our formal analysis. The rest of the paper is organized as follows. A brief review of relevant literature is

4

provided below. The model is set up in Section 2 and analyzed in Section 3. Section 4 describes welfare implications and Section 5 concludes the paper.

Relevant Literature Our analysis is related to the extensive literature on tying and bundling. The conventional framework for tying usually involves a multi-product …rm that monopolizes at least one good, and focuses on the …rm’s incentive to bundle its own products. A tie-in sale has been interpreted as a price-discriminating device (see Adams and Yellen, 1976; McAfee et al., 1989; Bakos and Brynjolfsson, 1999; and Armstrong, 2006a), or as a foreclosure or entry-deterrence strategy (Whinston, 1990; Choi and Stefanadis, 2001; Carlton and Waldman, 2002; and Nalebu¤, 2004). In a recent paper, Mialon (2011) demonstrates the anti-competitive e¤ect of a bundling strategy when it motivates merger. A handful of papers have identi…ed tying sales as an e¤ective means of altering price competition between …rms. These studies typically involve one …rm monopolizing one good and competing against others in the market for another good. Carbajo et al. (1990) and Chen (1997) demonstrate that a …rm may prefer to sell its multiple independent goods in bundles, as that creates product di¤erentiation. In contrast, Carlton et al. (2010) assume that consumers only value a system that consists of two goods, with one (primary good) monopolistically supplied and the other (complementary good) competitively supplied. They show that a …rm that monopolizes the primary good may prefer to tie its complementary good. Tying allows the monopolist to alter price competition in the complementary good market, thereby shifting rent from that market to its own.10 Gans (2011) extends Carlton et al. (2010) to a more general framework in which the primary good o¤ered by the monopolistic …rm can be consumed alone. Furthermore, consumers value the complementary good o¤ered by di¤erent …rms asymmetrically. Both Carlton et al. (2010) and Gans (2011) demonstrate the social cost associated with tying and its ambiguous e¤ects on consumer welfare. More recently, Miao (2010) studies a monopolistic system maker’s (e.g., Microsoft’s) decision to introduce a separate application or an upgraded system that integrates the application (bundle) when the application can be supplied by other …rms. Miao (2010) focuses on the intertemporal and compatibility concerns of the monopolist in introducing systems of di¤erent generations. Our paper is related to this set of studies because we also focus on a mechanism that leverages the monopolistic power of one market to alter pricing competition in the other and “squeeze” its rent. However, there are a few fundamental di¤erences. First, unlike these studies, we do not consider multi-product …rms. In our context, a monopolistic …rm 10

In contrast to most existing studies, Carlton et al. (2010) allow for reverse tying, such that consumers can add a second complementary good to the bundle “system.”

5

arti…cially locks its own (nonessential complementary) product to its exclusive partner’s primary good, and rent is shifted through a side payment. Second, the monopolistic …rm in our model o¤ers a nonessential good whose consumption relies on a competitively supplied essential good that can be consumed alone. This ‡avor has rarely been included in the literature. Most existing studies assume either (1) that only the monopolist produces the essential good, or (2) that consumers must consume two goods together in a system.11 Our paper is also related to the literature on exclusivity arrangements, which has conventionally focused on exclusivity arrangements in vertical distribution channels (e.g., Hart and Tirole, 1990; O’Brien and Sha¤er, 1992; McAfee and Schwartz, 1994; Fumagalli and Motta, 2006; and Jing and Winter, 2011).12 Our study mainly di¤ers from these works in two respects. First, this literature typically studies strategic wholesale contracting between an upstream manufacturer and downstream retailers, with the former selling its product to one of the latter and relinquishing control over retail prices. Our choice of an “a¢ liated”market over a standard vertical market structure is driven by the iPhone’s unique sales strategy. The contractual arrangement we consider corresponds to the “a¢ liation”mode (e.g., Hagiu and Lee, 2011),13 under which an upstream …rm (e.g., Apple) retains control over the price of its own product and sells the product directly to consumers, while “locking”its product to that of its downstream exclusive partner. As revealed by our analysis, the ability of the monopolistic …rm to price its good triggers profound strategic interactions. It also signi…cantly a¤ects downstream market structure and welfare distribution. Second, following Gans and King (2006), we adopt a “square city”framework to model demand structure, which re‡ects consumers’multidimensional preferences and also distinguishes our paper from the majority of the literature on exclusivity. Hagiu and Lee (2011) bridge the two strands of literature on vertical relation and twosided markets, and are the …rst to di¤erentiate explicitly between upright sale and a¢ liation. They analyze how “multihoming” or exclusivity may endogenously arise when content is matched to platforms, in either contractual mode. In contrast, we focus on the welfare implications of exclusivity arrangements under “exclusive a¢ liation.” Our modeling approach also di¤ers subtly from that of Hagiu and Lee (2011). First, we assume that the monopolistic …rm …rst commits to an exclusivity plan and the two duopolistic …rms then bid to become 11

One notable exception is provided by Gans and King (2006), who consider the bundling of goods between di¤erent …rms. In this context, two independent and unrelated goods are each produced by two sellers. They show that two coalitions would endogenously arise in equilibrium, each comprising two …rms that produce the two goods. Consumers can purchase a bundle of the two goods at discount from either coalition. 12 There is a small amount of research on exclusivity in the context of two-sided markets. In a recent working paper, Chowdhury and Martin (2010) investigate the relevant conditions under which a platform (e.g., newspapers) may bundle a critical product (e.g., columns and comic strips). 13 The “a¢ liation”mode is more typically featured in the literature on two-sided markets, which focuses on the central role played by market intermediaries. See, for example, the theoretical contributions of Caillaud and Jullien (2003) and Armstrong and Wright (2007), and the empirical study of Prieger and Hu (2010).

6

the exclusive partner. Hagiu and Lee (2011) allow competing platforms to o¤er contracts that specify payments contingent on ultimate a¢ liation choices (exclusivity or multihoming). Second, Hagiu and Lee (2011) assume that platform providers set their prices …rst, while we assume that the nonessential, value-adding good provider, as a forward-looking …rst mover, leads in pricing its goods, which manipulates behavior in the primary good market.14 These modeling nuances …t di¤erent contexts of interests. In particular, our model is intended to re‡ect the basic premise that the monopolistic …rm dominates in the exclusivity partnership, i.e., with a superior ability to choose and commit to business modes and contractual terms. The two papers thus complement each other. We also demonstrate later in the paper that (1) the monopolistic …rm bene…ts from such practice in the current context, and (2) these modeling features are consistent with stylized facts. Finally, our analysis relates to the licensing literature as well. To provide an analogy, the monopolist in our model represents a licensor who invites downstream …rms to bid for the right to sell its value-adding product. The monopolist in our model directly sells the product to consumers. In contrast, the licensor in the literature typically sells (intangible) property rights or assets to licensees, which are then used as a valuable input to produce a …nal product. Early studies on licensing consider three selling strategies, including …xed-fee, royalties, and auctions (e.g., Kamien and Tauman, 1984, on …xed-fee plus royalties; Kamien and Tauman, 1986, on …xed-fee vs. royalties; Katz and Shapiro, 1985b, 1986, both on licensing auctions) and …nd that compared to …xed-fee and royalties, the most pro…table method is for the inventor to auction licenses (Kamien, 1992). For example, Katz and Shapiro (1986) examine the impact of the licensor’s ownership to downstream …rms, both as an independent entity and a joint venture, on market outcome, and consider optimal licensing strategies under di¤erent scenarios. More recently, Sen and Tauman (2007) consider a selling strategy that consists of an entry fee and royalties. This is similar to the two-part tari¤ the monopolist adopts in our context, in which the monopolist receives its rents through a …xed fee and earns zero pro…t from the sales of its product. The di¤erence is that two di¤erent groups – the winning …rm and consumers, respectively – pay for each part of the tari¤ in our model, while the same party pays for both parts under a typical two-part tari¤ scheme such as that in Sen and Tauman (2007). Several studies in the licensing literature incorporate spatial competition similar to our model. For example, Poddar and Sinha (2004) compare di¤erent selling strategies between an outside and inside innovators and show welfare improvements in all cases in the spatial framework. They focus on optimal licensing strategies, while our focus is exclusivity and its welfare implications. In addition, Poddar and Sinha consider a single product, while 14

In a sense, both papers assume that dominant …rms move …rst in pricing their goods.

7

Figure 1: The Market of a “Square City” our model includes two complementary goods. In a related study, Kabiraj and Lee (2011) introduce product di¤erentiation from both the horizontal and vertical dimensions and argue that …xed-fee licensing is pro…table provided the quality di¤erential is su¢ ciently large. They show that the technology transfer is welfare-enhancing given both improved consumer and producer surplus. Aside from exclusivity, another di¤erence is that Kabiraj and Lee (2011) consider a single product with multi-dimensional characteristics, while our model includes two products each with one characteristic.

2

Setup

Following Gans and King (2006), we consider a two-good market as a square city. The structure of the market is illustrated in Figure 1. A unit mass of consumers is uniformly distributed within the square. Two competing …rms (i = 1; 2) provide a primary good X, while a monopolistic …rm sells a value-adding good Y . The primary good X can be consumed alone. The value-adding good Y , however, must be consumed along with X in a one-to-one proportion. To provide an analogy, suppose that X represents voice and data services in the wireless market,15 while Y represents a premium smartphone handset (e.g., an iPhone). Furthermore, the marginal costs of producing these products are normalized to zero. As depicted in Figure 1, the two competing …rms are located at the end points of the horizontal axis, 0 and 1. The monopolistic …rm is located at the center of the square, i.e., the point with the coordinate ( 21 ; 12 ). Each consumer’s preference is characterized by his position 15

It is reasonable to assume that each consumer possesses a basic phone that allows him/her to enjoy non-premium voice services.

8

(x; y). If a consumer purchases primary good X from …rm 1, he incurs a travel cost of dX x, while he incurs a travel cost of dX (1 x) if he purchases the good from …rm 2. Similarly, if a consumer purchases product Y from the monopolistic …rm, he bears a travel cost of dY jyj, where jyj measures his vertical distance between his location and the center point. Each consumer has inelastic demand of up to one unit for each good. He receives a utility u if he consumes product X and v if he consumes product Y . Further, the utility u is assumed to be su¢ ciently large to sustain full market coverage of X. If a consumer purchases dX x in the primary good market and both X and Y from …rm 1, he receives U1 = u pX 1 Y U1Y = v p dY jyj in the value-adding good market, respectively. If he purchases both dX (1 x) and U2Y = v pY dY jyj, from …rm 2, the consumer receives U2 = u pX 2 respectively. When a consumer chooses not to purchase Y , he receives zero in the valueadding good market. A unit mass of consumers is uniformly distributed on the square city. A consumer’s preference between …rms 1 and 2 for the primary good is independent of the travel cost he has to bear when consuming Y . To provide an analogy, a consumer’s valuation of a smartphone is ex ante independent of preference between wireless networks. A few remarks are in order for the model.16 First, this model can be viewed as a variant of Hotelling’s linear-city framework, in which consumers have mutli-dimensional preferences. However, the current model di¤ers from most existing models in a multi-characteristic Hotelling game. For example, Irman and Thisse (1998) allow a good to have n characteristics such that …rms can di¤erentiate their products in n dimensions. In contrast, both goods in the current model have only one characteristic. Second, for simplicity, we let the monopolistic …rm be positioned at the center of the city, or ( 12 ; 12 ), and the two primary good providers at (0; 21 ) and (1; 21 ), respectively. However, our main predictions remain qualitatively the same when these simplifying assumptions are relaxed. Holding other things equal (i.e., without an exclusivity arrangement), only horizontal locations matter for …rms 1 and 2, while only the vertical location matters for the monopolistic …rm. Hence, a more general setting would allow the two duopolistic …rms to be located at (0; y) and (1; y), respectively, for 8y 2 [ 12 ; 12 ], and the monopolistic …rm at (x; 12 ), with x deviating from 21 . To focus our attention on the most relevant case, it is further assumed that (marginal) travel costs are su¢ ciently large, and that the value of Y to consumers is in an intermediate range. These assumptions are stated as follows. Assumption 1 v

dX .

Assumption 2 2v < dY < 4v: The …rst assumption rules out the possibility of full foreclosure in equilibrium. That is, when the monopolistic …rm locks Y to the primary good o¤ered by one …rm, the other 16

We thank an anonymous reviewer for these valuable points.

9

…rm will not lose its most loyal consumers (i.e., those who are located in the vicinity of the position of that …rm). In the second assumption, the condition 2v < dY implies that the market for Y is never fully covered. Exclusivity does not pay o¤ otherwise, and welfare analysis would be less interesting when the monopolistic …rm does not implement the strategy in the …rst place. However, dY is also assumed to not be prohibitively high, i.e., dY < 4v.17 Under this condition, the monopolistic …rm still retains su¢ cient market coverage. This assumption thus allows our analysis to focus on the most relevant case, in which the monopolistic …rm serves a nontrivial market niche.

3

Analysis

A benchmark case without an exclusivity agreement is …rst considered. The equilibrium when the monopolistic …rm is allowed to practice exclusivity is then derived.

3.1

Benchmark: Mandatory Unlocking

We consider a case in which the monopolistic …rm is prohibited from locking its product to the primary good o¤ered by either of the duopolistic …rms (e.g., the iPhone in France). In the benchmark case, all …rms price and sell their products independently. Consumers who purchase Y can purchase X from either duopolistic …rm. The timing of the game is as follows: 1. The monopolistic …rm announces its price pY . 2. The duopolistic …rms simultaneously announce their prices for X, pX i (i = 1; 2). 3. Consumers observe pY and (pX i ) and make their purchases. The competition in the primary good market is analogous to that in a conventional Hotelling model. The demand for …rm 1 is then determined by the equation u pX dX x = 1 X u p2 dX (1 x). We then have Di =

(pX j

pX i ) + dX . 2dX (pX pX )+dX

(1)

j i Hence, a …rm i’s pro…t function i (p) = pX . A unique equilibrium exists, in i 2dX X X X which …rms each charge p1 = p2 = dX and earn 1 = 2X = d2X .

17

Or, equivalently, the complementary good is assumed to substantially add to consumers’utility.

10

In the market for product Y , the type of marginal consumer is determined by setting Y v pY dY y = 0. The monopolistic …rm thus faces a demand of 2(vdYp ) , and its pro…t is given by (pY ) =

3.2

2pY (v pY ) . dY

In equilibrium, it charges

v 2

and earns a pro…t of

v2 2dY

.

Exclusivity

We now allow the monopolistic …rm to form an exclusivity partnership with one of the duopolistic …rms.18 We consider a three-stage game. The timing of moves is stated as follows. 1. The monopolistic …rm announces its exclusivity plan and runs an auction to sell its exclusive partnership. The exclusivity contract commits to locking the monopolistic …rm’s product to the primary good o¤ered by the winning …rm. It stipulates a price pY 0 for the value-adding good,19 and demands that only consumers of the partner …rm be eligible to purchase Y (at the contractually stipulated price pY ). 2. Upon observing the exclusivity plan, the two competing …rms bid for the partnership. We assume that the bidding contest takes the form of a sealed-bid, …rst-price auction. Firms simultaneously submit their bids bi 2 R+ . The higher bidder wins and enters the exclusive partnership. A tie would be broken randomly. Further, the contest has free entry. 3. The duopolistic …rms simultaneously announce their prices for X, pX i (i = 1; 2). 4. Consumers observe pY and (pX i ) and make their purchases. A few remarks are in order before we proceed to solve for the equilibrium. First, the bargaining between the monopolistic …rm and the two downstream …rms is modeled as a bidding contest, in which the duopolistic …rms submit their bids of lump-sum “subsidies” for the exclusivity partnership. Second, we assume that the monopolistic …rm commits to its price pY as part of the terms that it demands for the exclusivity deal prior to the bidding contest. Hence, the duopolistic …rms price their products after the exclusivity partnership is formed, which leads to a sequential-pricing game. This modeling nuance closely mirrors Apple’s marketing practice for the iPhone and is consistent with casual observations from the U.S. wireless market.20 For instance, Apple announced (e.g., in preorder) the price of the 18

For the purpose of this paper, we do not consider the option of “outright sale”by the monopolistic …rm in the model. An outright sale refers to a vertical relation case in which the monopolistic …rm does not control the pricing and/or sales of its value-adding good and relays all these decisions to its downstream …rm(s). 19 For the sake of analytical convenience and expositional e¢ ciency, it is assumed that the monopolistic …rm is unable to price Y below its marginal cost, i.e., pY 2 [0; 1). This assumption allows for tractability. It can also be interpreted as a regulatory restriction. 20 Source: “Verizon Deal May Expose iPhone Flaws,” by Joe Nocera, New York Times, January 14, 2011.

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iPhone and its network technology long before the associated wireless plan was revealed.21 Wireless carriers, however, continue to update the details of their service plans for the iPhone and other wireless devices.22 This setting re‡ects the superior bargaining power of the monopolistic …rm and its ability to manipulate the behavior of downstream …rms (i.e., their pricing). Indeed, stylized facts evidence that wireless carriers have been “more willing to give in to Apple’s terms.”23 Furthermore, we demonstrate below (see Proposition 2) that when practicing the exclusivity strategy, it is in the monopolistic …rm’s best interest to bundle the price of the value-adding good pY into the contract. 3.2.1

Price Competition in the Primary Good Market

Without loss of generality, let …rm 1 be the winner. Each consumer faces one of three purchase options: (1) purchasing X from …rm 2; (2) purchasing X only from …rm 1; or (3) purchasing the “bundle” of both X (from …rm 1) and Y (from the monopolist). Figure 2 illustrates the market segmentation with an exclusivity arrangement. In this scenario, …rm 1 secures a larger market share. As Figure 2 shows, some consumers who would otherwise patronize …rm 2 (i.e., those who are located in the right half of the square city) may switch to …rm 1 if they highly value product Y , i.e., when they are located su¢ ciently close to the center of the square city in the vertical dimension.24 21

For example, when Verizon announced its iPhone launch in January 2011, it only discussed the price (which started at $199) for the phone, but “wouldn’t discuss service plans” (Source: “Verizon Unwraps iPhone,” by Shayndi Raice and Yukari Iwatani Kane, Wall Street Journal, January 12, 2011). 22 Note that wireless carriers independently design their service plans, which are typically uniform within their own wireless networks and independent of the handset a subscriber uses. 23 Source: “Analyst: Verizon Wants Pseudo-Exclusive on iPhone,” by John Paczkowski, Digital Daily, December 6, 2010. 24 For the sake of brevity, we do not consider the case in which a foreclosure (i.e., one …rm drives the other out of the market by undercutting price) can arise in the equilibrium. This possibility is precluded by the two regularity assumptions stated in Section 2.

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Let Di denote a …rm i’s market share. The consumers of …rm 1 can be split into two groups. One group purchases X only, which we denote by D1X , while the other group purchases both X and Y , which we denote by D1XY . The following lemma depicts the equilibrium in the primary good market under an exclusivity plan (pY ). Lemma 1 (i) The partner …rm (…rm 1 by default) charges pX 1 = dX + primary good and secures a market share of D1 = 12 + (v

pY

)

dY

dX +

pY )3

2(v 3dX d2Y (v pY )2 3dY

+ 1 2

pY )2

(v 2dX dY

+

(v pY )2 . 6dX dY

(v pY )2 3dY

for the

A share of consumers D1XY =

purchases both X and Y . Firm 1 earns a total pro…t of

pY )2

(v 6dX dY

1

=

from the primary good market.

(ii) Firm 2 charges a price pX 2 = dX Y 2

(v pY )2 , secures 3dY (v pY )2 1 2 6dX dY

a market share of D2 =

1 2

(v pY )2 , 6dX dY

and earns a pro…t of 2 = dX (v 3dpY ) . (iii) Firm 1 secures a greater market share than …rm 2, i.e., D1 > D2 . Proof. See Appendix. Recall that in the benchmark case with mandatory unlocking, the two …rms charge a price dX in symmetric equilibrium. Comparing the equilibrium prices for X with that in X the benchmark equilibrium, it is straightforward to see that pX 1 rises but p2 falls. That is, to obtain the privilege of purchasing Y , …rm 1’s consumers have to pay a higher price for X than in the benchmark case. However, those who remain with …rm 2 and forgo the opportunity of buying Y now enjoy a discount in the primary good market: Firm 2 must undercut to retain its clientele. 3.2.2

Equilibrium at the Bidding Stage

As Lemma 1 indicates, exclusivity allows the winning …rm to obtain a competitive edge in 2(v pY )2 the primary good market. For a given pY , it earns an extra pro…t of = 1 . 2 = 3dY The bidding subgame boils down to a two-player symmetric complete-information auction. Each …rm i always has an incentive to marginally outbid the rival for any bid bj 2 [0; ). As a standard result, each …rm bids in the unique pure-strategy Nash equilibrium, and one …rm (…rm 1 by default) is chosen as the exclusive partner.25 3.2.3

Equilibrium Exclusivity Plan

Now we turn our attention to the equilibrium strategy of the monopolistic …rm. The …rm collects a pro…t of Y (pY ) from selling Y . It also receives revenue through the partner …rm’s bid . Hence, the overall pro…t of the monopolistic …rm is given by m = Y (pY ) + . 25

One would obtain the same equilibrium outcome if the contest takes the form of an English auction with alternate bidding rules.

13

At the beginning of the game, the monopolistic …rm chooses pY 2 [0; 1) to maximize m , internalizing its e¤ect on primary good market competition. Standard technique yields the solution to the subgame perfect equilibrium of the game. Proposition 1 (a) In the unique subgame perfect equilibrium of the game, the monopolistic …rm charges pY = 0 for the value-adding good and receives a pro…t (from the winning bid) 2 2v 2 , which is higher than it would receive in the benchmark case ( = 2dv Y ). of m = 3d Y 2 (b) The partner …rm (…rm 1 by default) secures a market share D1 = 12 + 6dXv dY and earns 1

= dX +

v2 3dY

1 2

+

v2 6dX dY

from the primary good market, while the losing …rm (…rm 2 by

default) secures a market share D2 =

1 2

v2 6dX dY

, and earns

2

= dX

v2 3dY

1 2

v2 6dX dY

:

Proof. See Appendix. As Proposition 1(a) indicates, the monopolistic …rm gets better o¤ when it is allowed to exercise exclusivity. In equilibrium, the monopolistic …rm simply charges the marginal cost (pY = 0) to consumers and earns zero pro…t from retailing the product. The foregone revenue from selling Y is compensated for by a higher bid at the auction. The logic for this observation will be further explained in Section 4.1. Under this two-part pricing strategy, the monopolistic …rm charges the value-adding product at its marginal cost and does not pro…t from retailing its own product. The low price, however, allows its exclusive partner to acquire a greater advantage in the downstream primary good market. The extra pro…ts that the exclusive partner receives under the contract eventually …nd their way back to the monopolistic …rm through a higher bid, which compensates for the sales revenue that the monopolistic …rm has sacri…ced. Note that under the benchmark case, linear pricing (without a fee) is imposed. Thus, the di¤erence in pricing modes between the two cases may contribute to the pro…tability of the exclusivity deal. This prediction of the monopolistic …rm’s underpricing is largely consistent with the stylized facts in the iPhone case. For instance, the price of an iPhone 4 ranges from $199 to $299, depending on model speci…cations. Apple pays manufacturers an average of $244 for each iPhone, according to Apple’s …nancial …lings.26;27 Although the details of Apple’s exclusivity contracts have not been disclosed, it was estimated that AT&T paid Apple an 26

Source: “Does Apple Enjoy a Licensing Loophole on iPhone?” by Don Clark, Wall Street Journal, November 20, 2009 (http://blogs.wsj.com/digits/2009/11/20/does-apple-enjoy-a-licensing-loophole-on-iphone). 27 When the iPhone was …rst introduced to the market, it had a price tag of $499. The high price, as a typical marketing tool to sell “hot” new products, contained a premium that early adopters were willing to pay. The price of an iPhone quickly declined and stabilized. The current price schedules should be considered as a more appropriate benchmark, as they are set to target mainstream consumers instead of a small group of early adopters. The price dynamics of the iPhone are consistent with those of many other popular electronics products when newer models are released and technology advances. Our model, however, is not designed to capture the dynamic features of Apple’s pricing strategy.

14

average of approximately $550 for each iPhone under its exclusivity contract.28 3.2.4

Discussion

In setting up the model, we have assumed that the monopolistic …rm moves …rst in pricing its product and that it bundles its price in the exclusivity contract. This assumption arguably re‡ects the monopolistic …rm’s superior ability to dominate its negotiations with the downstream duopolistic …rms. We now relax this assumption and allow the monopolistic …rm to not commit to pY during the bargaining process, but to announce it after the bidding. The underlying question is whether it pays for the monopolistic …rm to include pY in the exclusivity contract. Next, we consider a case in which the three …rms are allowed to set their prices after an exclusivity contract has been awarded to the winning bidder. The following result is obtained. Proposition 2 The monopolistic …rm strictly prefers to bundle its price pY into the exclusivity contract. Proof. See Appendix. If the monopolistic …rm sets the price after settling the amount of transfer in exchange for the exclusivity partnership, it would then be tempted to charge a higher price for its valueadding good. The higher price leads to a loss of market share for the monopolistic …rm, which reduces the rent its exclusive partner could collect ex post from the primary good market. Anticipating that, the duopolistic …rms would bid less for the partnership, which jeopardizes the overall pro…t of the monopolistic …rm. We conclude that the monopolistic …rm prefers to commit to its price and include it in the exclusivity contract. In the current setting, we consider Apple as a monopolistic …rm in the value-adding good market (i.e., the iPhone market). However, in the more broadly de…ned smartphone market, multiple producers, including Samsung and Nokia, coexist. In the presence of competition, depending on whether or not Apple practices exclusivity, rivals would certainly react di¤erently. The exclusivity deal increases …rm asymmetry/product di¤erentiation in the primary good market, which would in turn soften competition. Formal modeling of this situation, however, is beyond the scope of this paper.

4

Who Bene…ts from an Exclusivity Arrangement?

The above equilibrium result allows us to explore the welfare implications of exclusivity arrangements. 28

Source: “Is There a Method in Cellphone Madness?” by Saul Hansell, New York Times, November 15, 2009.

15

4.1

Consumer Welfare

Primarily, we investigate the e¤ect of exclusivity on consumer welfare. Consumers derive utility from consuming X and Y . They make payments to these …rms in exchange for the products, and also bear the travel costs. Let W0 and W1 denote consumer welfare in the benchmark case (without exclusivity) and in the exclusivity case, respectively. Our analysis allows us to conclude the following. Proposition 3 Consumers as a whole bene…t from exclusivity arrangements, i.e., W1 > W0 . Proof. See Appendix. Overall, consumer surplus increases when exclusivity is in place. In contrast to the prevailing view, our analysis suggests that banning exclusivity arrangements may, paradoxically, hurt consumers as a whole. A number of e¤ects loom large in the presence of exclusivity arrangements. On the one hand, exclusivity generates two positive e¤ects on consumer welfare. First, the monopolistic …rm strategically underprices Y , which e¤ectively internalizes the externality between Y and …rm 1’s X as a pair of complements. Under exclusivity, customers who patronize the exclusive partner (…rm 1) receive not only the primary good, but also the privilege of enjoying the value-adding good Y (at an additional price pY ). Hence, a lower pY makes …rm 1’s X more appealing than its rival’s, which ampli…es the rent from the exclusivity arrangement, thereby in‡ating …rms’bids. By underpricing Y , the monopolistic …rm sacri…ces its retailing revenue but is “subsidized” by …rm 1 through its bid. This practice allows a subset of consumers (D1XY ) to enjoy the value-adding good Y at a lower price. The mechanism is referred to as a two-part pricing strategy. Second, this practice intensi…es price competition in the primary good market. In equilibrium, …rm 2 charges a lower price than it does in the benchmark case. Handicapped by …rm 1’s exclusivity partnership, …rm 2 undercuts its rival to protect its clientele. Firm 1, as the exclusive partner, demands a premium price for its X. However, its product also entitles a consumer to buy Y at a low price, which could also improve consumer welfare. In the benchmark case, consumers pay a total of dX + v2 if they buy both X and Y , while they pay 2 only dX + 3dv Y in the exclusivity arrangement case.29 In summary, exclusivity intensi…es price competition in the primary good market, thereby allowing (a subset of) consumers to pay less for their consumption of X. This mechanism is referred to as a “competition-enhancing” e¤ect. Furthermore, the competition-enhancing e¤ect has a positive interaction with the twoY part pricing strategy. Note by Lemma 1 that pX are strategic complements, i.e., 2 and p 29

By Assumption 1, we must have

v 2

>

v2 3dY

.

16

@pX 2 @pY

> 0. The competition-enhancing e¤ect is magni…ed when the price of Y is lower. A lower pY exacerbates …rm 2’s disadvantage, which adds downward pressure to its pricing of X. On the other hand, this practice distorts market competition and consumer behavior, thereby resulting in disutility to consumers as well. Exclusivity in‡icts welfare loss on four subsets of consumers. First, a subset of …rm 1’s “loyal customers” (those who are located su¢ ciently close to zero along the x axis) would purchase X only (if they are located far away from the center in the vertical dimension). They end up paying more for X, because …rm 1 charges a premium price. Second, a subset of …rm 2’s initial customers in the benchmark case, who highly value Y , would switch to …rm 1. The bene…t these consumers receive from a lower pY can be o¤set by the higher travel costs required for consuming X. Third, a subset of …rm 1’s initial customers, who purchase X only, would switch to …rm 2 because of its lower price for X. These consumers bear a higher travel cost to take advantage of paying less for X. Finally, a subset of …rm 2’s “loyal customers” are excluded from consuming Y . Taken together, the positive e¤ects unambiguously dominate the negative ones. Consumers, as a whole, bene…t from the practice.30 This result adds new insight into the iPhone’s widely debated exclusivity practices. However, the result must be interpreted with caution, as exclusivity triggers welfare redistribution among consumers: Some gain at the expense of others. Furthermore, our welfare analysis is based on assumptions of inelastic demand and a covered market for the primary good.

4.2

Primary Good Producers

We now explore the e¤ects of exclusivity on the pro…tability of the primary good industry and obtain the following. Proposition 4 In the primary good market, both …rms are worse o¤ when the monopolistic …rm is allowed to practice exclusivity. Proof. See Appendix. With a higher product price and an expanded market share, …rm 1 receives higher pro…ts from its sales in the primary good market under an exclusivity arrangement. However, the two duopolistic …rms are left in a prisoner’s dilemma in the …erce bidding war. By practicing exclusivity, the monopolistic …rm is able to leverage its market power to extract surplus from 30

Additional analysis reveals the intricate redistribution of consumer surplus. More speci…cally, consumers (as a whole) realize a gain from the market of Y , but su¤er a loss in the market of X due to the distortion. However, the gain dominates the loss, leading to an overall rise in welfare. We do not include the details to economize on the presentation.

17

the primary good market, as the winning …rm surrenders its rent in the primary good market through its bid. Meanwhile, the losing …rm responds by aggressively undercutting the price, which in turn worsens the outside option for the winning …rm and allows the monopolistic …rm to charge an even higher fee. The monopolistic …rm’s ability to practice exclusivity jeopardizes both …rms’pro…tability in the primary good market. Another interesting observation arises from Proposition 4: Overall pro…t declines under 2v 2 , while after exclusivity. Recall from Proposition 1 that the monopolistic …rm receives 3d Y 2 2 surrendering the bidding fee, both …rms 1 and 2 earn the same pro…t, (dx 3dv Y )( 12 6dXv dY ). 2 2 2v 2 Hence, the overall pro…t under exclusivity amounts to 2(dx 3dv Y )( 21 6dXv dY )+ 3d , while pro…t Y 2 v2 in the benchmark case is dX + 2dY . It is then straightforward to show that (dX + 2dv Y ) > 4 2v 2 2v 2 31 + 9dXv d2 ) + 3d ]. That is, overall pro…t shrinks under exclusivity. This fact [(dX 3dX Y Y underlines the fact that the monopolistic …rm bene…ts from the exclusivity arrangement at the expense of the competing duopolistic …rms. In theory, exclusivity may be pro…table for the monopolistic …rm – even if both duopolistic …rms (before submitting the bidding fee) earn less than in the benchmark case – as long as the loss to the losing …rm su¢ ciently exceeds that to the winning …rm. Our results are consistent with the stylized facts: It has been reported that AT&T su¤ered a loss from its exclusive iPhone deal with Apple. Even though it had successfully lured subscribers away from its competitors, AT&T ended up with a dip in its pro…ts: In the second quarter of 2009, pro…ts fell by $0.27 billion compared to the same quarter a year earlier.32 AT&T’s loss was mainly due to the heavy subsidy it paid for the iPhone. As previously mentioned, on average, AT&T was estimated to have subsidized $550 of the price of each iPhone, which is $200 - $300 more than the estimated cost of other smartphones.33 AT&T’s major competitors’pro…ts also declined during the same period.

4.3

Social Welfare

In sum, both the monopolistic …rm and consumers (as a whole) bene…t from exclusivity arrangements, while the duopolistic …rms in the primary good market lose. Despite the gain in consumer surplus, the overall social surplus declines under exclusivity, which is stated as follows. Proposition 5 Social welfare declines as the result of an exclusivity arrangement. 31

Recall that by Assumption 1 v v2 2dY

dX , we have 2v 2 3dX

v2 dX dY

v4 9dX d2Y

v dY

. Further, by Assumption 2 (2v < dY ), we 2

2

4

2

2

2v v v v 2v < It follows that (dX + ) [(dX + ) + 3d ] = 2d = 18d [9 dX have dY ] > 0: 9dX d2Y Y Y Y 32 Source: “iPhone Buoys AT&T Subscriptions –but Hurts Pro…t,”by Marguerite Reardon, CNET News, July 23, 2009. 33 Source: “IPhone May Cost Verizon $5 Billion in First Year,”by Amy Thomson, Bloomberg Businessweek, Feburary 16, 2011. v dY

1 2.

18

Proof. See Appendix. The cost of this practice in the primary good market (for the two duopolistic …rms) more than o¤sets the gains that accrue to consumers and the monopolistic …rm. Our analysis thus indicates the complexity of evaluating the rami…cations of exclusivity arrangements: Social welfare falls in our model under exclusivity when the two competing …rms’ pro…ts in the primary good market are taken into consideration.

4.4

An Extension

For simplicity and tractability, the current model abstracts network e¤ects that often loom large in the telecommunication market (Katz and Shapiro, 1985a). Users of a larger wireless carrier bene…t from positive externalities such as unlimited mobile-to-mobile calling within the same network. With a growing subscriber base, wireless providers also have more incentive and …nancial capability to improve network-speci…c plans/features, such as network upgrades and post-purchase services. Our model can readily be extended to embrace this consideration. Following the literature on network e¤ects that use Hotelling models, we assume that when using the primary good provided by …rm i, the utility function of a consumer includes an extra component, f (Di ), where Di denotes …rm i’s market share or network size. As in previous studies (e.g., Armstrong, 2006b; Miao, 2010; Doganoglu and Wright, 2010; Doganoglu and Grzybowski, 2013), we assume f (Di ) = kDi where k > 0 is the additional utility associated with network size. This network externality does not alter the equilibrium fundamentally in the benchmark case. Because of symmetry, the extra component kDi is cancelled out between the two …rms when solving for the marginal consumer’s utility-maximization problem. Hence, the same equilibrium results as in the original setting. By contrast, the network e¤ects, kD1 and kD2 , amplify the asymmetry between the two …rms caused by exclusivity. Consumers who derive nontrivial utility from consuming Y would be more inclined to purchase X from …rm 1, which allows them to bene…t from a larger network. Speci…cally, a consumer faces three choices: purchasing X only from …rm 1; purchasing X from …rm 2; and purchasing both X (from …rm 1) and Y (from the monopolist). The market is split into three segments, which are de…ned by the following conditions: (dX + k)x = u pX (dX + k)(1 x) u pX 1 2 and u

pX 1 +v

pY

(dX + k)x = u

pX 2

(dX + k)(1

x):

These conditions are analogous to those in our original analysis, and qualitatively similar 19

equilibrium results would hold. In fact, adding the network e¤ect further strengthens the previous results. Additional asymmetry is generated through the network e¤ect coe¢ cient k, which leads to further distorted market division between the two duopolistic …rms and additional welfare implications. In this case, …rm 1’s consumers bene…t from a larger network, while those of …rm 2 are disadvantaged because of its shrinking network. Furthermore, the gain in the former group more than o¤sets the loss in the latter because …rm 1 must secure a larger market share under exclusivity, given the linearity.34 The extra utility from the expanded network also mitigates the loss of those who only purchase X from …rm 1 (at a higher price due to exclusivity). Therefore, we expect that the overall consumer-welfare comparison would be tilted more favorably toward exclusivity. The presence of network e¤ect allows …rm 1 to outperform …rm 2 even further under exclusivity, which in turn increases the amount of rent the monopolistic …rm is able to extract through its bidding revenue.

5

Conclusion

In this paper, we construct a stylized model to investigate the welfare implications of exclusivity arrangements, using the iPhone as a motivating example, given the wide in‡uence and unique characteristics of its marketing practice. We demonstrate that this practice distorts competition and leads to market ine¢ ciency. Consumers as a whole, however, bene…t from it. The practice leads to redistribution among consumers, as some gain at the expense of others. Meanwhile, the monopolistic …rm extracts additional surplus from the primary good market, which renders the two …rms in that market strictly worse o¤. Overall, social welfare declines. Our analysis o¤ers one perspective on the controversial practice of exclusivity arrangements and yields useful implications. Caution must be exercised, however, when interpreting the …ndings, as the analysis is built on a stylized model that glosses over many nuances, such as strategic interactions among …rms that practice exclusivity arrangements across multiple markets. Our study takes an early step in understanding the rami…cations of this popular practice and related welfare implications. Hence, we would caution readers to view our study as a positive exploration that attempts to uncover various underlying concerns, rather than a normative judgment. A thorough and more conclusive appraisal of an exclusivity arrangement’s e¤ects on welfare and competition, which would more constructively addresses antitrust concerns, demands a more comprehensive model to formally include many other relevant factors. Much room for extensions is left open. First, our model assumes inelastic demand and a fully 34

This e¤ect would be more signi…cant if the network e¤ect is convex in the size of market demand.

20

covered market for the primary good; additional quali…cations would result if we do not allow full coverage. In that case, competition in the primary good market would be less intense, which attenuates the “competition-enhancing” e¤ect that contributes to the gain in consumer welfare – namely, intensi…ed competition brought about by exclusivity. More importantly, this would also reduce the monopolistic …rm’s ability to extract rent from the primary good market, which would cast doubt on the pro…tability of an exclusivity practice in the …rst place. Second, we do not explicitly consider the monopolistic …rm’s incentive to develop innovative products. Our analysis shows that exclusivity allows the monopolistic …rm to reap higher returns, and implies that banning exclusivity adversely a¤ects the …rm’s incentive to innovate. The overall e¤ect on social welfare needs to be re-evaluated to address this concern, which deserves a formal analysis in a more general setup. Third, we focus on the niche market of a given product, but abstract away the potential entry of competing substitutes. How exclusivity initiated by market leadership a¤ects subsequent market entry remains an intriguing question. Alternatively, the monopolistic …rm’s opportunistic concerns could also be included in the model. Another reasonable setting would be one in which the duopolistic …rms collude in bidding for the exclusivity partnership. In that case, substantially more extensive strategic interactions could be expected, although modeling subtle interactions would be technically di¢ cult. Finally, while the current model investigates a very simple benchmark case, there are alternative considerations. One could include a sequential-move game in which the monopolistic …rm …rst announces its price for the value-adding good and a …xed fee (i.e., the value-adding good is only available to buyers of the primary good whose producer agrees to pay the fee). Upon observing the price and the fee, the two competing …rms simultaneously decide …rst whether or not to pay the …xed fee and then their prices for the primary good. These extensions are beyond the scope of the current study, but will remain a priority for the authors in future research.

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Appendix Proof of Lemma 1 Proof. The mass of consumers who purchase X alone from …rm 1 is D1X = 2( 21 1

pY

2(v dY

)

(pX 2

pX 1 )+dX

2dX

D1XY = 2xy + y x =

(pX 2

y)x =

, and the mass of consumers who purchase both X and Y is pX 1 )+dX dX

(v pY ) dY

+

1 2

(v pY ) (v pY ) . Adding dX dY Y 2 (pX pX 2 1 )+dX + (v2dXpdY) : 2dX

these together, the

entire market share for Firm 1 is given by D1 = A …rm i, i = 1; 2, earns from the primary good market a pro…t i = Di pX i . We now derive the equilibrium in this market. The …rst-order condition for …rm 2’s pro…t function is (pX pX pX (v pY )2 d 2 X dD2 2 1 )+dX ] 2d2X . It follows in the equilibrium given by dp X = D2 + p2 dpX = [1 2dX 2dX dY 2

2

pX 2 =1 2dX 24

D1 :

(2)

Firm 1 maximizes 1 by choosing an optimal price pX 1 . The …rst-order condition is then X Y 2 p (pX pX )+d d 1 X dD1 1 given by dp = D1 = 2 2d1X X + (v2dXpdY) : X = D1 + p1 dpX = 0, which yields 2d X 1 1 X X X Hence, we must have in equilibrium pX 1 +p2 = 2dX , which is equivalent to p2 = 2dX p1 . X X Y 2 p (2d 2p )+d Insert it into (2), and we obtain 2d1X = X 2dX1 X + (v2dXpdY) , which leads to pX 1 = dX +

(v pY )2 (v pY )2 , and pX . Thus, it follows that pX 2 = dX 2 3dY 3dY (pX pX (v pY )2 (v pY )2 1 2 1 )+dX D1 = + 2dX dY = 2 + 6dX dY , and D2 = 1 21 2dX

We also need to …nd out the demand for the add-on 2(v pY )2 +dX 3dY

Y

Y 2

Y

2(v pY )2 . Hence, we have 3dY Y 2 Y 2 (v p ) = 12 (v6dXpdY) . 6dX dY product Y , or D1XY , which is given

pX 1 =

Y 3

Y 2

(v p ) p ) + (v2dXpdY) = (v dYp ) 2(v + (v2dXpdY) : = dX dY 3dX d2Y To see whether …rm 1 ends up with a higher demand for X under exclusivity, we Y 2 Y Y x: We have y x = v dYp v2dpX = (v2dXpdY) , and 12 x = simply compare y x and 12

by

1 2

D1XY

2(v pY )2 +dX 3dY

2dX

= 2

(v pY )2 . 3dX dY

It is straightforward to show that

1 2

x < y x since

(v pY )2 2dX dY

(v pY ) = 6dX dY : Thus, …rm 1 gains more demand for X under exclusivity arrangement than in the benchmark case, at the expense of …rm 2. The computation of equilibrium pro…ts is straightforward by simple algebra. (v pY )2 3dX dY

Proof of Proposition 1 Proof. In the add-on product Y market, we …rst search for the optimal price pY of the monopolistic …rm. We have XY d d m XY Y dD1 = + D + p 1 dpY dpY dpY 4 (v pY ) + v 2pY = 3 dY

2(v pY )2 (v pY ) + 3dX d2Y 2dX dY

1 dY

+

4(v pY ) 3dY

1 2

(v

pY )pY dX dY (3)

When pY = 0, the last equation becomes d m = dpY

v[

1 2v 2 + 3dY 3dX d2Y

v 2dX dY

We now establish the following: Whenever the condition

25

1 3dY

(4)

] +

2v 2 3dX d2Y

v 2dX dY

> 0 is met,

d m dpY

must be negative for all pY 2 [0; v]. We rewrite (3) as

d m = dpY

2(v pY )2 (v pY ) 4 pY 1 + ] + 3dY 3dX d2Y 2dX dY 3 dY Y 2 Y 2(v p ) (v p ) 4(v pY ) 1 (v pY )pY 1 Y + + 2p dY 3dX d2Y 2dX dY 3dY 2 dX dY Y 2 Y Y 2 1 2 2(v p ) (v p ) 8(v p ) 3(v pY ) Y = v[ + ] + p + 3dY 3dX d2Y 2dX dY 3dY 3dX d2Y 2dX dY v[

: (5)

(v pY ) 2(v pY )2 2v 2 < 2dXv dY for all pY 2 2dX dY 3dX d2Y 3dX d2Y (v pY ) pY )2 [0; v). Hence, we must have 3d1Y + 2(v > 0. We now claim that 3d2Y + 2dX dY 3dX d2Y 3(v pY ) pY )2 (v pY ) pY ) 8(v pY )2 8(v pY )2 < 3d1Y + 2(v . We establish it by verifying 3(v > 2dX dY 2dX dY 2dX dY 3dX d2Y 3dX d2Y 3dX d2Y Y Y 2 Y Y 2 (v p ) 2(v p ) , which is equivalent to (vdX pdY ) > 2(vdX pd2 ) . The last inequality obviously 2dX dY 3dX d2Y Y Y holds i¤ 2(vdYp ) < 1 (by Assumption 1). Hence, we must have the expression in equation (v pY ) pY )2 (5) < (v pY )[ 3d1Y + 2(v ] < 0. 2dX dY 3dX d2Y 2 v > 0. It boils down to 13 We then need to verify the condition 3d1Y + 3d2v 2 2dX dY X dY v 1 2v ( ). Because dX v and dY < 4v, 31 dvX ( 12 3d2vY ) > 31 ( 12 61 ) = 0: dX 2 3dY

The assumption v
dX . 2 Next, the overall travel cost for the consumption of product X is given by TX = [ x2 + Z x Z y y (x x) x (1 x)2 0 0 0 ]d + T T , where T T is given by T T = 2d 1dydx = (2x 1) X t t t X t t t 2 x 0 Z x 2dX (2x 1)[y yx (x x)]dx = 2dX y[( x + x + 12 )(x + x) 23 (x2 + xx + x2 ) ( x + x)] = x dX y [2x2 3

4x2 + 2xx

3 x].

Hence, TX = dX [(x2 We can rewrite equation (6) as 2 ( 12 + 3d v d X Y

2

)2

]+

v 3dY

(2

1 2

+

v 2dX

v3

T dX

1 y x + ) + (2x2 2 3 =

2 [ x2

+

4x2 + 2xx

(1 x)2 ] + y3 [2x2 2

2 v2 + 4 21 3dXv dY 3dX dY 2v 4 > d4X given dY > 34 v: 9dX d2Y

(6)

3 x)]:

2

4x + 2xx 3) 2dvX =

1 4

3 x] = [ +

v3 6d2X dY

( 12

v2 3dX dY

)2

2 2v 4 9d2X d2Y

+

:

Clearly, TX = d4X + 6dX dY Thus, compared to the benchmark case, consumers incur higher transportation costs in the base product market. Overall, consumers in the X market are worse o¤. To purchase the value-adding good Y , consumers incur travel cost TY = xy 2 dY + Z y Z x xy y 2 2dY 1dxdy = xy 2 dY + dY 3xy : y 0

x

Finally, we examine the consumer surplus for consuming Y , which is given by WY = 2 2 2 3 2v 3 v4 + 2dXv dY ]v [xy 2 dY + dY 3xy ] = 2dv Y + 3dXv dY : D1XY v TY = [ dvY 3dX d2Y 3dX d2Y Compared to the benchmark case, consumer surplus from consuming the add-on product 2 3 Y is higher under an exclusivity arrangement. It can be easily shown that 2dv Y + 3dXv dY 2 v4 > 4dv Y , since dY > v3 : 3dX d2Y Now we are at the position to compare the overall consumer welfare under both cases. 2 Now we can rewrite equations for W0 and W1 as W0 = u 5d4X + 4dv Y , and W1 = u MX ! 4 3 2v 4 dX + 9dXv d2 + d4X + 6dXv dY 2 4 9d 5dX v3 v2 X dY Y TX +WY = u =u : + 9d2v 2 2 3 4 4 6dX dY 2dY v v v X dY + 3dX d2 2dY 3dX dY Y

Comparing them yields W1 2v 4 9dX d2Y

W0 =

3 2 2v 4 + 6dXv dY + 2dv Y 9dX d2Y dY > 43 v, which follows

5dX 4

> 0. The last inequality holds if

27

+ 5d4X

v2 4dY

=

Assumption 1.

v3 6dX dY

2

+ 4dv Y

Proof of Proposition 4 Proof. Recall that in equilibrium, both …rms bid . The duopolistic …rms end up with the same overall pro…t, although …rm 1 earns more from the primary good market. Compare dX 2 with the equilibrium pro…t of 2 in the benchmark case. The claim is straightforward.

Proof of Proposition 5 Proof. We now consider the overall change in social welfare. We have 2v 4 9dX d2Y

that

+ 4v 2 dY

v2 6dY

+

2v 2 3dY

2

( 6dXv dY

6v + 9dX >

4v 2 dY

1) =

v2 4dY

6v + 9 23 v =

+

v3 6dX dY

4v 2 dY

v4 9dX d2Y

=

v2 36dX dY

4v 2 dY

W =

v3 6dX dY

6v + 9dX . Note

> 0 given Assumption 2: Thus, we have

28

2

+ 4dv Y W < 0.