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Bundling and economies of scope.

The digital convergence that occurs in telecommunications and Media industries and its effects are now increasing. Telecom incumbents, cable operators, mobile operators and internet providers are more and more induced to undertake bundling strategies (double, triple and quadruple play). Bundling refers to the practice of selling two or more differentiated products within a package. Pure bundling means that the goods are available only as a package form. Mixed bundling means that the goods are available separately as well as in a package. Tying refers to the behaviour of selling one product conditional on the purchase of another product (1). Double play is a strategy that consists of bundling either fixed telephony and internet or internet and digital television or mobile telephony and internet. With triple play, operators bundle fixed telephony, internet and digital television. Adding mobile telephony to the package yields to quadruple play.

In the ultrabroadband (2) world, telecom incumbents, internet providers, cable operators and mobile operators will compete through bundling. Bundling undertakings pushes those players into head-on competition. As a result of the increasing competitive pressure, market players will likely differentiate their products through quality. The adoption of Next Networks Generation will offer a higher bandwidth delivery and a better quality of services. However, the delivery of ultrabroadband to the residential market requires huge infrastructure investments. Market players will have to differentiate their offerings through contents in order to cover networks investments and to lessen the competitive pressure. The objective of this paper is to show how bundling impacts competition that holds both in telecommunications and Media industries.

Part of the literature on bundling claims that it can be used for anticompetitive ends. The leveraging market power theory argues that a vertically integrated firm, which is a monopolist in one market (good 1), can restrain competitors' sales in a competitive market (good 2) through tying. The validity of this theory has been criticized by the school of Chicago (see POSNER, 1976). WHINSTON (1990) reconsiders the leverage theory's hypothesis. He shows that when the goods 1 and 2 are independent tying is profitable for the monopolist because of its potential of excluding his rival from the market 2. By contrast, when the goods 1 and 2 are complementary, the monopolist never finds it worthwhile to tie in order to reduce competition in the market 2. The reason lies in the fact that when the good 1 is essential for all uses of the two goods the monopolist can always benefit from more competition in the market 2 because it boosts demand for good 1. NALEBUFF (2004) and PEITZ (2005) show that in a situation where a company that has market power in two goods and that is facing the incursion of an entrant in one of those markets can use bundling in order to deter entry. Using a dynamic model, CARLTON & WALDMAN (2002) show how a monopolist in one market can enjoy bundling to extend its monopoly into a newly emerging market. Choi (1996) examines the effect of bundling on R&D incentives. He finds that bundling provides a channel through which monopoly slack in one market can be shifted to another. Finally REY & TIROLE (2005) show that bundling serves as a means to foreclose entry. This literature has clearly influenced antirust authorities to regulate bundling by firms with market power (3).

Another part of the literature suggests that firms use bundling to enhance their efficiency. ADAMS & YELLEN (1976) MACAFEE, Mac MILLAN & WHINSTON (1989) and SHAPIRO & VARIAN (1998) show that bundling allows a monopolist to perform an implicit price discrimination. When the willingness to pay differs a lot across consumers (in other worlds when willingness to pay is negatively correlated) bundling helps the monopolist to extract consumer surplus and to increase its profits. When the willingness to pay becomes positively correlated the price discrimination effect disappears. Furthermore bundling allows firms to achieve economies of scope in supply. Bundling together services such as telephony internet and television reduces managing advertising and marketing cost because all the services can be advertised and distributed together. To that purpose France Telecom has recently rebranded its MaLigneTV and Wanadoo divisions into the single brand Orange. CRAMPES & HOLLANDER (2006) argue that bundling creates economies of scope in the digital economic because it has made sounds, pictures and data perfect substitute that can be injected into the "electronic pipes".

Finally, several contributions (including papers of ARMSTRONG & VICKERS, 2006; ECONOMIDES, 1993; MATUTES & REGIBEAU, 1992) study bundling in duopolies. These authors find that mixed bundling puts firms in a prisoner's dilemma situation because firms are better off when they both commit not to use mixed bundling than when they both use such strategy. THANASSOULIS (2007) finds that when consumers have firm-specific preferences mixed bundling raises firms' profits. However, when firm-specific preferences disappear mixed bundling pushes firms in a prisoner's dilemma situation.

More precisely, in the paper of MATUTES & REGIBEAU (1992) it is shown that the nature of the Nash equilibrium depends on consumers' price reservation (denoted [eta]) for a system composed of two goods. When [eta] is not very high the bundling sub-game has the structure of a prisoner's dilemma. The present paper is an extension of Matutes and Regibeau's important work with two key differences. Firstly by contrast to Matutes and Regibeau who normalise the costs of production to zero, production is costly in our model. Moreover, we suppose that mixed bundling creates economies of scope on the supply side. Secondly the timing of the game differs from Matutes and Regibeau's one. We start from a situation where both firms sell the goods separately and we suppose each firm can chose to use a mixed bundling pricing strategy. With mixed bundling firms provide a discount to consumers who buy the goods close to the same firm (the one stop-shoppers). In others words, the price of the bundle must be slightly lower than the sum of the products sold separately.

We show that firms always have a unilateral incentive to target a discount to consumers who buy the two goods close to the same firm. The Nash equilibrium is one of mixed bundling. Moreover, the economies of scope (created by mixed bundling) act to reduce (increase) firms' profits when the consumers' price reservation is high (low). With high consumers' prices reservation firms are in a prisoner's dilemma. However with low consumers' prices reservation and high economies of scope mixed bundling acts to increase firms' profits. Finally, we find that economies of scope tend to reduce (increase) consumer surplus and social welfare when the consumers' price reservation is high (low).

The rest of the paper comes as follows. The model is presented in the following section. In the 3rd section we give the sub-game outcomes where both firms sell the goods separately. In the 4th section we analyse firms' incentive to use mixed bundling and the mixed bundling outcomes. Then we analyse the impact of bundling and economies of scope on profits, consumer surplus and welfare. The paper's results are related to a short industry analysis in the section after. The last section draws the main conclusions.

* The model

We model a duopoly where two firms, denoted i (i = A, B), are competing and produce the two components, denoted j (j = 1,2), of a system. Each component produced by firm A is differentiated, a la Hotelling, from the equivalent component produced by firm B. Consumers differ in their ideal specification of the components and are represented in a unit square. Firm A is located at the origin of the square while firm B is located at the point (1,1). Consumers can mix and match the two goods and thus can chose between four different systems. Consumers located at the South-West corner buy the two goods close to firm A (system AA ). Consumers located at the North-West corner buy the good 1 close to firm A and the good 2 close to firm B (system AB). Consumers located at the South-East corner buy the good 1 close to firm B and the good 2 close to firm A (system BA). Consumers located at the North-East corner buy the two goods close to firm B (system BB). A consumer who purchases one unit of a system made of good 1 of firm i and good 2 of firm i obtains a utility of

u = [eta]-[lambda][[theta].sub.1] -[lambda][[theta].sub.2]-[p.sub.i1] -[p.sub.i2]

where ([[theta].sub.1], [[theta].sub.2]) [member of] [[0,1].sup.2]. [[theta].sub.i] represents consumer's location for good i between firm A and firm B x [lambda] represents the parameter of differentiation. [p.sub.ij] is the price of good j produced by firm i. The unit cost of production when the goods are sold separately is denoted c. It is assume to be the same for the goods 1 and 2. The cost of producing the bundle is denoted [c.sub.b]. As bundling creates economies of scope we have c [less than or equal to] [c.sub.b] < c. The game is a two-stage game. At the first stage firms set the prices that maximize their profits when the goods are sold separately. In the second stage firms can decide to adopt a mixed bundling strategy. We solve the game by backward induction.

* Independent selling

Let us consider the sub-game where the firms sell the components separately. We assume first that the whole market is served. A consumer located at ([[theta].sub.1], [[theta].sub.2]) will purchase the system AA rather than the system AB if [p.sub.A1] + [p.sub.A2] + [lambda] [[theta].sub.1] + [lambda] [[theta].sub.2] [greater than or equal to] [p.sub.B1] + [p.sub.A2] + [lambda](1-[[theta].sub.1]) + [lambda] [[theta].sub.2]. She will purchase the system AA rather than the system BA if [p.sub.A1] + [p.sub.A2] + [lambda][[theta].sub.1] + [lambda][[theta].sub.2] [greater than or equal to] [p.sub.A1] + [p.sub.B2] + [lambda][[theta].sub.1] + [lambda] (1-[[theta].sub.2]). Equilibrium prices and profits of the sub-game are given by

[p.sup.*.sub.ij] = [lambda] + c,

[[pi].sup.*.sub.ij] = [lambda]. [1]

This is a valid solution as long as the whole market is indeed served at the equilibrium prices of the sub-game (i.e. as long as

[eta]-[p.sub.A1] -[p.sub.A2] -[lambda]( [[theta].sub.1] + [[theta].sub.2]) [greater than or equal to] 0 or [eta] [greater than or equal to] 3[lambda] + 2c. When [eta] [greater than or equal to] 3[lambda] + 2c, the whole market is not served at the equilibrium prices derived in equation [1] (4). There are three different cases. For low reservation prices firms behave as local monopolists. The different systems' market shares do not touch. The consumer located at ([[theta].sub.1], [[theta].sub.1]) will purchase the two components close to the firm A if [p.sub.A1] + [p.sub.A2] + [lambda] [[theta].sub.1] + [lambda] [[theta].sub.2] [greater than or equal to] [eta]. The consumer located at ([[theta].sub.1], [[theta].sub.2]) will purchase the system AB if [p.aub.A1] + [p.sub.B2] +[lambda] [[theta].sub.1] + [lambda] (1-[[theta].sub.2]) [greater than or equal to] [eta]. The consumer located at ([[theta].sub.1], [[theta].sub.2]) will purchase the system BA if [p.sub.B1] + [p.sub.A2] +[lambda] (1-[[theta].sub.1]) + [lambda] [[theta].sub.1] [greater than or equal to] [eta]. This is a valid solution as long as [eta] < 1/6(5[lambda], + 12c). For higher prices of reservation, there is direct competition between the systems but the market is not completely covered. The consumer located at ([[theta].sub.1], [[theta].sub.2]) indifferent between consuming system AA, consuming system AB and consuming nothing satisfies both [p.sub.A1] + [p.sub.A2] + [lambda] [[theta].sub.1] + [lambda] [[theta].sub.2] [greater than or equal to] [eta] and [p.sub.A1] + [p.sub.B2] + [lambda] [[theta].sub.1] + [lambda](1-[[theta].sub.2]) [greater than or equal to] [eta]. This is a valid solution as long as the whole market is not completely served, i.e. as long as 3[lambda] + 2c > [eta] [greater than or equal to] 1/6 (5[lambda] + 12c). Finally, when 3[lambda] + 2c >[eta] [greater than or equal to] [lambda]-2[bar.p] firms engage in a limit in the sense that each firm sets its prices such that its markets just touch the other markets (i.e. consumer surplus is zero on the markets boundaries). Figure 2 represents the different systems' market shares according to consumers' reservation prices when firms sell the goods separately.

[FIGURE 1 OMITTED]

* Mixed bundling

Suppose next that firms can target a discount to the consumers who purchase the two goods close to the same firm. It turns out that a firm always has a unilateral incentive to do so. Figure 3 represents firm A's unilateral incentive to target a bundling price to consumers who one stop-shop. The dotted line describes the impact of such deviation on firms' market shares.

[FIGURE 2 OMITTED]

Proposition 1: Suppose the two firms initially sell the goods separately. Then a firm's profit always increases if it unilaterally targets a bundling price to consumers who one-stop shop such that [p.sub.ib] < [p.sub.i1] + [p.sub.i2].

Proof. Suppose that the two firms sell the goods separately and that firm i decides to target a bundling price to consumers who one stop shop such that [p.sub.ib] < [p.sub.i1] + [p.sub.i2] where [p.sub.ib] = [p.sub.i1] + [p.sub.i2]--[epsilon] is the price of the bundle and [epsilon] (> 0) is small. When the whole market is served firm i gains, on the

one hand, (p -[epsilon]-c) ([epsilon]/2[lambda]) + ([[epsilon].sup.2]/8 [[lambda].sup.2]) (2p-[epsilon]-2c). On the other hand, firm i loses [epsilon] (1/2 + [epsilon]/2[lambda])--[epsilon]/4. Such deviation is profitable if [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Using

sub-game equilibrium prices of (1), it turns out that this condition is satisfied for ([epsilon]/8[[lambda].sup.2]) (2[lambda]--[epsilon]) + 1/4 > 0, which is true for [epsilon] small (5).

The argument is in the same spirit as that used by MacAFEE, PRESTON, McMILLAN & WHINSTON (1989), ARMSTRONG & VICKERS (2006), and THANASSOULIS (2007). Proposition 1 thus stipulates that the only Nash equilibrium is the one of mixed bundling. Our result differs from the one of Matutes and Regibeau because in our model mixed bundling is a pricing decision rather than a commitment.

We now turn to the mixed bundling sub-game outcomes. Suppose first that the whole market is served, the consumer located at ([[theta].sub.1] [[theta].sub.2]) purchases firm A's bundle rather than the system BA if [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] She purchases firm A's bundle rather than the system AB if [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. She purchases firm B's bundle rather than the system BA if [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Last, she purchases firm B's bundle rather than the system AB if [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. This is a valid solution as long as the market is completely covered.

When the market is not completely covered, three cases are possible. In the first case firms behave as local monopolists. A consumer located at ([[theta].sub.1], [[theta].sub.2]) purchases firm A's bundle if [p.sub.Ab] + [lambda] [[theta].sub.1] + [lambda] [[theta].sub.2] [greater than or equal to] [eta]. She purchases firm B's bundle if [p.sub.Bb] + [lambda](1-[[theta].sub.1]) + [lambda](1-[[theta].sub.2]) [greater than or equal to] [eta]. For higher reservation prices, the whole market is not served and firms are direct competitors. The consumer located at ([[theta].sub.1], [[theta].sub.2]) is indifferent between purchasing either firm A's bundle or the system AB or nothing satisfies both [p.sub.Ab] + [lambda][[theta].sub.1] + [lambda] [[theta].sub.2] [greater than or equal to] [eta] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. The consumer is indifferent between purchasing either firm A's bundle or the system BA or nothing satisfies both [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. The consumer is indifferent between purchasing either firm B's bundle or the system AB or nothing satisfies both [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. The consumer is indifferent between purchasing either firm B's bundle or the system BA or nothing satisfies both [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Finally for higher reservation prices firms engage in a limit price.

Figure 3 represents the different systems' market shares according to consumers' reservation prices when firms use mixed bundling.

[FIGURE 3 OMITTED]

* Impact of bundling and economies of scope

Proposition 2 highlights the impact of economies of scope (created by bundling) on firms' profits according to market coverage.

Proposition 2: Economies of scope act to reduce (increase) firms' profits when the market is completely (partially) covered.

We now seek to understand the intuition underlying proposition 2. When the whole market is served mixed bundling acts to create more head-on competition. Systems AA and BB become direct competitors. This pushes the equilibrium prices charged for the bundles down. As firms' bundles become more attractive, one-stop shoppers increase at the expense of two-stop shoppers. Moreover, the discount targeted to the one-stop shoppers is increasing with the economies of scope. Thus, the effect created by mixed bundling increase with the economies of scope. The economies of scope make the bundles more attractive and acts to increase the number of one-stop shoppers. Clearly the economies of scope act to reduce firms' profits when the whole market is served. In other words, the efficiency enhancement created by economies of scope is absorbed by the increasing competition. When the market is completely served firms are in a prisoner's dilemma situation because [[pi].sup.Ind.sub.A] > [[pi].sup.Bund.sub.A].

When the market is partially covered, mixed bundling continues inducing firms to reduce the price of their bundle. Beside this effect mixed bundling allows firms to get part of the demand that was not covered when the goods were sold separately. The discount targeted to the one-stop shoppers continues to increase with the economies of scope. Economies of scope act to increase the demand effect and thus contribute to increase firms' profits. When the unit cost is high and the economies of scope are strong mixed bundling acts to increase firms' profits [[pi].sup.Bund.sub.A] > [[pi].sup.Ind.sub.A]. However when the economies of scope are weak and/or when the cost of production is low, mixed bundling puts firms in a prisoner's dilemma situation.

Proposition 3 highlights the impact of economies of scope on firms' consumer surplus and welfare.

Proposition 3: Economies of scope tend to increase consumer surplus and tend to decrease (increase) welfare when the market is completely (partially) covered.

The intuition of this result is the following. Economies of scope tend to increase consumer surplus because it make prices to go down. Indeed when systems are local monopolies economies of scopes push the price charged for the bundle down. When the markets overlap the systems are directly competing. Thus, economies of scope push all the prices down. When the market is not completely served, economies of scope clearly act to increase industry welfare. When the market is completely covered, the reduction in profits outweights the rise in consumer surplus. Thus economies of scope tend to reduce industry welfare.

* Industry insights

The factors that induce players to undertake bundling differs depending on the type of player. Cable operators and internet providers are moving toward bundling with aggressive intents. Because of technological and regulatory reasons cable operators offered triple play in Europe and US markets before telecom incumbents and internet providers did (6). Internet providers use bundling as a way to access market and in order to gain market share from its competitors. The most representing example is Fastweb (an Italian internet provider) or Free (a French Internet Provider). On the other hand, telecom incumbents and mobile operators use bundling as a defensive way (because they want to protect their core market). The undertakings of bundling strategy push the four types of players in a head on competition in several markets with for immediate result an additional increase in the competitive pressure. This was not the players' first purpose. This result seems consistent with the pricing mechanism and the prisoner's dilemma situation highlighted in our model.

* Conclusion

With the increasing convergence that occurs in telecommunications and Media industries market players are more and more induced to undertake bundling strategies. We develop a duopoly model where firms can adopt a mixed bundling pricing and where mixed bundling creates economies of scope on the supply side. We draw a distinction between full market coverage and partial market coverage and show that firms always have an unilateral incentive to target a discount to the consumers who one-stop shop. Thus the Nash equilibrium is the one of mixed bundling. The economies of scope created by mixed bundling act to reduce (increase) firms' profits when the market is completely (partially) covered. Indeed when the market is completely covered, the economies contribute to increase the competitive pressure because they increase the one-stop shoppers area. However, when the market is not completely covered the economies of scope act to increase firms' demands and thus firms' profits. Finally, we show that economies of scope always tend to increase consumer surplus and to lower (increase) welfare when the market is completely (partially) covered.

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(1) See TIROLE (2005) for a more complete distinction between bundling and tying.

(2) Ultrabroadband refers to the transmission rates above 1Gbps on the residential market.

(3) Telecoms incumbents bundling strategies are regulated by national regulatory authorities. The French regulator (ARCEP) allows incumbent bundling offerings if they can be replicated by competitors. The Italian regulator (AGCOM) has forbidden Telecom Italia to sell television, telephony and broadband services within a bundle. In the United States, Regional Bell Operating Companies could not offer bundles of wireline and wireless services until recently ...

(4) Note that consumers get a positive utility if c [less than or equal to] 1/2[eta]. Thorough the model firms produce if the condition is satisfied.

(5) We give the detailed proof for the full market coverage case. Concerning the partial market coverage case, the proof is available in an appendix that is ours.

(6) Note that in the USA the Telecommunications Act of 1996 has helped cable operators' initiation of telecommunications business. In the United Kingdon, the Oftel allowed cable TV companies to offer telephony in 1991.

Antonin ARLANDIS

Orange Labs and University of Montpellier, France
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Title Annotation:Ultrabroadband: the next stage in communications
Author:Arlandis, Antonin
Publication:Communications & Strategies
Date:Nov 1, 2008
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