Switching costs in vertically related markets
*
Tommaso M. Valletti** London School of Economics and Centre for Economic Policy Research This version: September 1999 Abstract In the presence of switching costs, firms are often interested in expanding current market shares to exploit their customer base in the future. However, if the product is sold by retailers, manufacturers may face the problem of extracting too much surplus from the retailer. If this happens, then the latter has not an incentive to build a subscriber base. This paper would like to connect two unrelated streams in the literature, respectively on switching costs and vertical restraints. An upstream-downstream duopoly model is presented to analyse the mutual incentive for firms to enter into particular trading relationships when consumers are repeat-purchasers. When switching costs are high, then integrated structures are predicted. On the other hand, when lock in effects are not too relevant, mixed structures with independent and integrated firms emerge as an equilibrium in growing industries. The results are discussed with reference to the UK mobile telecommunications industry. Keywords: switching costs, vertical restraints, integration, foreclosure
* I am grateful to Pedro Pita Barros, David Salant, John Sutton and seminar participants at LSE, Lisbon, Madrid, Stockholm, and various conferences for useful discussions and comments. I also acknowledge the very constructive comments provided by General Editor William Shepherd and by an anonymous referee. ** Address for correspondence: Department of Economics, LSE, Houghton Street, London WC2A 2AE, UK. E-mail:
[email protected]
1.
Introduction
Consumer switching costs make changing suppliers expensive and tend to lock consumers into the firms they were previously patronising. If those who buy from a firm now have a desire to buy from the same firm next period, then it is natural that increasing market share is in the firm's interest. In a stylised two-period model of switching costs, a firm is usually willing to serve a larger set of customers in the first period than in traditional models because this enlarges its 'captive' segment of the market in the following period. This theory of heightened competition for market shares in the initial phase justifies strategies like giving cheap introductory offers to new customers, even if such behaviour involves some sacrifice of short-run profit. Switching costs lead to rents, but in turn these rents induce greater competition in the early stages of the market's development. Thus firms face a trade-off between future profits and present losses caused by the aggressive first-period behaviour. The net effect is often ambiguous and switching costs can actually make firms worse off (Klemperer, 1987).1 The literature on switching costs has found important implications for many questions of industrial economics (see Klemperer, 1995, for a survey of recent work). However, all models assume that the product is sold by the manufacturer himself. This is a good first approximation from a theoretical standpoint, and in many cases it is also reflected in reality. Banks - with high transaction costs in closing an account with one firm and opening another with a competitor - are a good example. In other cases, especially for many consumer purchases, it is possible to draw a clear distinction between manufacturers' brands and retailers' services associated with its characteristics or location and it becomes more questionable whether it is satisfactory to model manufacturing and retailing operations carried by the same firm. Products with high 'brand loyalty' can be sold in supermarkets, or alternatively the producer may decide to retail the good directly or using exclusive dealers. Computers and software compatible with them, are products that involve substantial 'learning' costs: What is the best strategy to sell the combined product? Cars, it is said, are also associated with strong brand loyalty ('psychological' costs) and, in virtually all cases, car manufacturers decide to sell using a single retailer in a given territory or similar forms of franchise systems. Even airlines with 'frequent-flyer' programmes - perhaps the most cited example of a product involving switching costs may sell their tickets using independent travel agents. 1
Switching costs can also explain why prices can be higher with identical firms than with differentiated ones. If firms differentiate their products, some consumers may decide to switch firm despite they incur in some costs. On the other hand, if firms offer functionally identical products, then product characteristics cannot be a reason to patronise the other firm. In this sense, switching costs represent an artificial way of product differentiation rather than a real one (Klemperer, 1995).
The main business cases that motivate this paper can be found in the telecommunications industry: network operators can sell services to the final users or recur to service providers: this is true for Internet services, value-added services, mobile telecoms, etc., all situations including consumer switching costs (additional software or hardware needed, change of number, etc.). The following table, borrowed from Shapiro and Varian (1999) shows how, at a more general level, switching costs and lock-in effects are ubiquitous in information systems. Type of lock-in Contractual commitments Durable purchase Brand-specific training Information and databases Specialized suppliers Search costs Loyalty programs
Switching costs Compensatory or liquidated damages Replacement of equipment; tends to decline as the durable ages Learning a new system, both direct cost and lost productivity; tends to rise over time Converting data to new format; tends to rise over time as collection grows Funding of new supplier; may rise over time if capabilities are hard to find Combined buyer and seller search costs; includes learning about quality of alternatives Any lost benefits from incumbent supplier, plus possible need to rebuild cumulative use
Table 1: Types of lock-in and associated switching costs (source: Shapiro and Varian, 1999, p. 117) Once the distinction between manufacturers and retailers is introduced, it is not clear whether the manufacturer can easily delegate the task of acquiring market shares to the retailer. Vertical arrangements take a variety of forms, and they have been studied by a very rich literature on vertical integration, vertical restraints and market foreclosure (surveys can be found in Katz, 1989, Waterson, 1993, Irmen, 1998, and Rey and Tirole, 1999). The literature has focused on several issues, including the elimination of successive mark-ups, or the attempt to raise rivals' costs. However, no reference is made to the fact that market power may arise from the existence of consumer switching costs. In such a case, a model of an upstream/downstream industry would have to include additional features such as a time dimension and a mechanism to allocate future rents among the vertically-related firms. This paper would like to connect these two streams in the literature by exploring the implication of switching costs on the firm's internal organisation and on its supply relationships. In this paper I consider a framework where two upstream firms can supply two downstream firms and firms compete in quantities at both stages of production, after having made their decisions about integration. My interest is not to consider very
complicated contractual arrangements; rather I will concentrate on two 'natural' forms, namely vertical integration and complete independence. I address the question of the contractual choice by considering a game in which pairs of firms decide which contract to sign based on anticipated profits that would occur in subsequent stages. This of course requires the solution of situations where integrated and non-integrated pairs coexist, whether such situations will actually occur in equilibrium or not. The contract games that I study do not assume that integrated firms do not trade with non-integrated firms, rather I analyse if foreclosure may arise in equilibrium. I show that the presence of switching costs has a strong influence on market foreclosure. Since customers are eventually locked in with a retailer, by foreclosing a retailer, an upstream firm may renounce to part of the rent extractable from the captured customer in later stages of the game. At the same time, foreclosure in the initial phases may limit expensive battles for market shares. I will show that the incentive to invest in market share can be so high that an independent retailer is completely pre-empted in the initial phase of the game, while it turns to an independent manufacturer in later stages. The remainder is organised as follows. Section 2 describes the mobile telecommunications industry in the UK and it addresses the role of network operators and of service providers. Section 3 presents a simple upstream-downstream duopoly model to analyse the mutual incentive for firms to enter into particular trading relationships in the presence of switching costs. The model is solved in section 4, where the focus is on foreclosure and pre-emption. Section 5 concludes.
2.
The UK mobile telecommunications industry
The UK mobile telecommunications industry is relevant to this paper for two reasons. Firstly, switching costs are important and there is a practice to subsidise terminals in order to secure customers that will produce cash-flow in the future. Secondly, a regulatory decision was initially made to have vertical separation between network operations and service provision. A later switch in the regulatory regime allowed for integration. Prices of handsets have declined steadily over the past fifteen years. According to various surveys reported by the newsletter FinTech-Mobile Communications, hand portables costed to the subscriber an average of £2000 in 1985, £900 in 1988, £300 in 1990. Now mobile phones in different versions are sold in the range £0-70. Technological progress is a reason for this and it is documented that manufacturers have lowered equipment prices, but there must be also a different motive in operation when portable phones are given away below cost or even for free (see Valletti and Cave, 1998).
The persistence of the pattern of discounts suggests that handset prices are used to create a market and prices of air time to exploit it. Such strategic behaviour can arise if consumers incur costs when they switch suppliers. An incumbent firm may then find it profitable to expand sales, tying customers to its brand and leaving fewer customers available for potential entrants. Switching costs are usually defined as resources, in addition to the purchase price, spent to consume the product when such resources cannot be recovered if the consumer changes supplier. In cellular telecommunications, the customer must be connected to one operator for at least 12 months. In addition, if she breaches a contract, she has often to pay a release fee. If she switches operator, she obviously has to repay the connection fee. The phone itself may not work if used on a different network (hardware lock).2 Some further switching costs relevant to mobile users can be the subscriber number (stationery costs), and special links with other services.3 The importance of switching costs is reflected in the churn rate (percentage of the subscriber base that disconnects in a given period). There are huge seasonal fluctuations in churn rates and it is not easy to distinguish exit from migration, but a reasonable figure is between 20% and 30% in a year. In launching cellular telephony in the early 1980s, the UK Government decided to license two network operators - Cellnet and Vodafone, but to prevent the networks from producing or selling communications apparatus, and retailing air time directly to the public. As a result, a substantial service provider industry came into being. When PCN networks - Mercury One-2-One and Orange - started operations in 1993, a decision was made to allow them to sell to customers through direct sales organisations, for which only separate accounts, rather than separate companies were required. Subsequently, the licences of Cellnet and Vodafone were amended to permit them to operate in the same way. All operators could then choose between being integrated and selling through independent service providers. PCN operators sold their services in ways which hitherto have wholly bypassed service providers. Incumbents first continued to sell using the same retailing structure as before, then, after a transition phase, they changed their policy and decided to set up special service operators to sell directly to the consumer market. In recent times, the diffusion of mobile phones and the much higher level of competition at the network level are changing the nature of the market. Competition in the industry has heated up, with a range of new tariffs differentiated in complex ways. In
2
Digital phones were introduced in 1993 and they were not compatible with analogue ones. At present, digital phones are compatible with any operator, but they contain proprietary software information. The user can switch operator only after buying such software lock. 3 Barclaycard, UK's largest card provider has a link with Cellnet to provide free access to credit card services. The deal involves smart cards able to display a menu on the phone screen, so that the user can check balances, transactions, etc. A similar deal has been signed between Vodafone and TSB Trustcard.
particular, pre-paid cards have become very popular. Switching costs are decreasing in their importance: for instance number portability is available from January 1999, pre-paid tariffs do not require the subscriber to be connected for at least 12 months, analogue networks are being phased out so technological lock-ins are less relevant. All of these changes have generated a profile for the sector quite different from the situation in the past. In particular, household buyers are increasingly acquiring handsets through independent high-street retailers and multiple outlets, that represent new entrants at the retailing level. To summarise, the UK mobile telecoms industry represents a nice experiment where high consumer switching costs generated integrated structures, while lower switching costs are now associated with both integrated and independent firms. In the sections below I propose a simple model that tries to rationalize these changes.
3. The model Costs and vertical structure. The market comprises two upstream manufacturers (I will also refer to them as 'network operators') indexed by h, k = A, B and two downstream retailers ('service providers'), indexed by i, j = 1, 2. In absence of switching costs, products are homogeneous and can be produced and sold by any pair once a link is established. In principle, each firm can establish two potential links, one with each firm at the superior/inferior layer, but it will be determined endogenously which potential links are established by contractual configurations. One unit of the upstream good is needed to produce one unit of the final good. Production exhibits constant return to scale. For the sake of simplicity, marginal costs are normalised to zero. Demand. There are two periods of time. Downstream firms (or divisions) 1 and 2 get respectively n1 and n2 customers at t = 1 in the following manner. Firms decide how many customers to supply. When firm i connects ni customers, then the resulting price is p = a - (n1 + n2). This can be rationalised by considering myopic consumers who buy at most one unit of either good (they connect to a network). Each consumer's utility is z - p if a unit is bought at a price p, where z is uniformly distributed on a support with upper limit a. At t = 2, there is consumption according to a linear demand function. Individual demand of each customer is: x = b - p. Positive parameters a and b define the relative importance of the markets in the two periods. Some customers are completely locked in after the initial purchase (they have infinite switching costs) and some of them are free to
change supplier in the second period. Let 0 < µ < 1 denote the fraction of customers of the latter type.4 Time structure. The game starts with a contract decision, followed by market competition in each period t = 1, 2. Contract decision. Upstream firm h and downstream firm i, together, make a contract decision. Their strategy set is {F, VI} where F = freedom, VI = vertical integration. In order to ensure that all four firms are active in the market, I will assume that each upstream firm can integrate at most with one downstream firm. Each pair simultaneously decides which contract to sign. This set presents us with three basic contractual configurations for the following stages (see also figure 1): (F, F), (VI, VI), (F, VI). These are long-term contracts that specify the input supply relationship for both periods. On the other hand, payments are determined only for the current period. [Figure 1 about here] Market competition. In each period, an input price has to be specified as well as intermediate and final outputs. All firms are Cournot competitors. Upstream producers/ divisions decide on the quantities of the intermediate good to supply. In doing so they face the derived demand anticipated from the downstream decisions of downstream firms/divisions. In the downstream stage, firms compete in the quantity produced of the final good, taking as given the price of the intermediate good used as an input.5 In order to clarify the differences in terms of the substages of the production stage and of the determination of the input price, I repeat the main features of the various contractual configurations signed by firm i and firm h (see also the table below, where xh and qi are the quantities supplied upstream and downstream):
4
The same analytical structure can capture a situation in which some customers die between periods and are replaced by a market of size n3 of uncommitted ones while surviving customers are locked in. Under this interpretation µ represents the exit rate ('churn' rate in the telecoms industry). In particular, the two interpretations coincide in the steady-state case that I will consider in the remainder with n3 = µ(n1 + n2). 5 It could be argued that the sequential Cournot specification is somewhat arbitrary, although frequently encountered in the literature. I believe however that this is an attractive and tractable way of focusing on the double marginalisation problem that is typical of vertical structures under oligopoly. In Valletti (1999), I extended the basic model, allowing for exclusivity contracts and for a more general bargaining process with side payments and I show that the qualitative results of this paper do not change. See also Kühn (1997), for a full analysis of non-linear pricing in vertically related markets.
• When a pair is VI, the upstream division supplies its downstream division at a zero transfer price and may also eventually supply other retailers (there are no commitment problems as in Hart and Tirole, 1990). When integrated and non integrated firms coexist, I restrict the trade of the VI firm to non-negative sales of input (Gaudet and Long, 1996, consider the case of an integrated firm that may make net purchases of the input from non integrated producers in order to raise rivals' costs via higher input prices). • When one retailer is free, its input price is determined in the open market (market clearing). Contractual relationship VI F
Input price
Upstream decision
transfer = marg. cost market clearing
Downstream decision
max (π i + π h )
max π h
x h ≥q i , q i
xh
max π i qi
The model is solved backwards. In the following sections, I will first consider the equilibrium outcomes of the market competition game under various contractual configurations, first at t = 2, then at t = 1. The results will then be used to solve for the contract game, obtaining the subgame perfect equilibrium of the whole game.
4.
Solution
4.1
Market competition
(VI, VI) •t=2 Denote by 1 and 2 the integrated pairs (A + 1) and (B + 2). At t = 2 firms can either exploit their existing base or deliver a total quantity qi to the new market. The profit of an integrated firm (manufacturer + retailer) is: b2 (1 if q i = 0 4 − µ)ni πi = qi + qj qi + qj (b − )[q i + (1− µ )n i ] o.w. max n3 n3 qi Defining K = b/(2 + µ), equilibrium price and profit of firm 1 are the following (expressions for firm 2 are symmetric):6
6
Full proofs and the Appendix are available from the author on request.
p= (1)
b =K 2+µ
π i = (n i + µn j )K 2 It is easy to show that it never happens that no quantity is sold to the new market, asking the monopoly price to captive customers. The firm is always better off by selling to the newly opened market even if this leads to a lower price. The 'expansion' effect dominates and this feature will be true under all configurations studied in this paper. The previous expressions also tell that the price is higher than the Cournot price. Looking at extreme cases, it becomes the monopoly price when µ = 0, i.e. when everybody is locked in - equivalently no new customer enters - so that monopoly power is fully exercised. On the other hand when µ = 1 we get the Cournot solution (all old customers are lost, so there simply remains quantity competition over the newly opened market). These results are exactly along Klemperer's lines (Klemperer, 1987), although they are derived using a different model. •t=1 The subgame perfect equilibrium of the market game is found by maximising each firm's total profit from the two periods: V i (n 1 , n 2 ) = n i [a − (n 1 + n 2 )] + δπ i (n 1,n 2 ) where δ is the discount factor (common to both manufacturers and retailers once the distinction is introduced) and πi is the equilibrium second-period profit given by eq. (1). The equilibrium is: n i = (a + δK 2 ) / 3 = (a + W ) / 3 (2)
p = (a − 2W ) / 3 V i + h (VI, VI) = (a + W )[a + W(1+ 3µ)] / 9
It is instructive to compare the expressions with the standard Cournot outcome in each period, which is the reference point in the absence of switching costs (µ = 1) and when firms are myopic (δ = 0). Prices are lower in the first period because firms compete for market share that is valuable later. This effect depends on W = δK 2 and it becomes more important as b and δ increase and as µ decreases, i.e. as the second-period profits become more relevant per se (high b), they are not discounted much (high δ), or derive from customers being locked-in (low µ).
(F, F) •t=2 Each downstream firm is free to buy from any upstream firm. Denote by w the input price faced by both retailers. Retailers maximise their profits with respect to own quantities, taking such input price as given. The retailers' first-order conditions determine the final output rates (qi). Demand for the final good (q) has to be equal to demand for the intermediate good (x), and after substitution one finds the inverse demand function w(x A ,x B ) for upstream firms. Upstream firms then maximise their profits with respect to their supply of inputs: max π h = w(x A ,x B )x h . The solution turns out to be: xh
w = b/3 p = K(4 + µ ) / 3 (3)
π h = (1 + µ)(2 + µ)(n1 + n2 )K 2 / 9 π i = (n i + µ n j )4K 2 / 9
Expressions show standard effects deriving from double marginalisation. Prices under freedom are higher than under vertical integration. Remember that integrated firms are closer to the monopoly outcome the more customers are locked-in (low µ). This suggests that freedom in period 2 has adverse effects if switching costs are important, but there may be an interest to have separate firms with successive mark-ups if customers are uncommitted, so that separation allows the manufacturers to avoid costly competition in the final market. •t=1 The analysis is conducted as at t = 2. Retailers i = 1, 2 attract the number of customer that maximise their profit over the two periods, taking the input price w in the first period as given. Market clearing for the intermediate good gives the inverse demand for inputs w(x A ,x B ) , which is then used to maximise the manufacturers' profits (h = A, B): V h (x A ,x B ) = w(x A ,x B )x h + δπ h (n1 (w(x A ,x B )), n2 (w(x A , x B ))) . Calculations give: x h = n i = 2[9a + W (6 + 3µ + µ 2 )] / 81 w = [9a − 2W µ(3 + µ )] / 27 (4)
p = [45a − 4W (6 + 3µ + µ 2 )] / 81 V i (F, F) = 4[9a + W (6 + 3µ + µ 2 )][9a + W (6 + 21µ + µ 2 )] / 6561 V h (F, F) = 2[9a + W (6 + 3µ + µ 2 )][9a + 4W (3 + 3µ + µ 2 )] / 2187
A preliminary comparison of (2) and (4) shows that under vertical integration, price in the first period is lower than under freedom. This is due to two effects: double mark-ups, and the reduced weight put by retailers on future profits from their customer base. Independent firms 'invest' less in market share. I will check later if joint profits of independent firms can be greater than the profit of an integrated pair when period-1 profits dominate. (F, VI) •t=2 Imagine firms (B + 2) are integrated. The other two firms are not bound by any contract. In principle the two divisions of the integrated firm can still supply the other retailer or be supplied by the other manufacturer. If firm A wants to sell to the retailing division of firm (B + 2), then the wholesale price has to be equal or less than the internal transfer price. For any w > 0, then A can only hope to sell through retailer 1. It remains to be seen whether the manufacturing division of the integrated firm decides to participate in the intermediate good market by supplying retailer 1. This is considered in the next lemma (the proof is in the Appendix). Lemma 1. If n 12 (2 − 3µ − 3µ 2 ) − µn 1n 2 (7 + µ ) − 4n2 2 < 0 , then the integrated firm forecloses the independent retailer. If n 12 (2 − 3µ − 3µ 2 ) − µn 1n 2 (7 + µ ) − 4n2 2 > 0 then the integrated firm sells also via the other retailer. A sufficient condition to have an equilibrium with foreclosure is to have sufficiently low switching costs: µ ≥ (−3 + 33) / 6 ≅ 0.457 . If switching costs are high (µ < 0.457), the integrated firm would then prefer to sell to the independent retailer only if its market share is sufficiently small compared to the rival: 2 n 1 / n 2 ≥ µ (7+ µ ) +(4−1−6µµ )−632µ2+16 µ + µ . The last expression is increasing in µ, then we have found a lower bound at µ = 0 that has to be satisfied in order to have equilibrium without foreclosure: n 1 / n 2 > 2 . A symmetric solution (equal market shares) will always exhibit foreclosure (see figure 2). To summarize, Corollary 1. Foreclosure always arises when given market shares are relatively similar and when switching costs are not too important. Conversely, foreclosure does not arise if given market shares are asymmetric and switching costs are important. This finding is a generalisation of some results obtained in the literature on vertical mergers and market foreclosure (Salinger, 1988; Ordover et al., 1990): in the
absence of switching costs (µ = 1) a VI firm always finds foreclosure a profit-maximising strategy. Suppose, on the other hand, that a VI firm sells a certain amount on the open market. If it pulls these intermediate goods off the market and uses them to produce additional units of the final product, total final output and therefore price are unchanged. But the firm earns a greater profit per unit by selling the output at the final good level than it would by selling the inputs to the product at the intermediate level. This is true so long as switching costs are not too important. When previous customers are locked in with a retailer, then foreclosure may not be optimal anymore since the upstream manufacturer loses access to such customers that can be contacted only via the independent retailer. In particular, when the independent retailer has many customers that patronised him before and are likely to continue to buy from him, then the integrated firm participates in the intermediate goods open market in order to obtain a share of the profits that could not be secured by its retailing division. The complete foreclosure which is imposed by Salinger (1988) when integrated and non integrated firms coexist, turns out not to be an innocuous assumption when switching costs are brought into the picture.7 Foreclosure may not arise when exogenous market shares are sufficiently asymmetric and switching costs are relevant. I consider next what happens when market shares are endogenized. [Figure 2 about here] •t=1 Let us analyse now the market competition phase at t = 1. In the Appendix I demonstrate the following lemma. Lemma 2. An equilibrium without foreclosure at t = 2 cannot emerge. When the inequality given by eq. (5) is satisfied, then the independent retailer completely shuts down in the first period and the equilibrium is given by eq. (6). (5)
a / W < (8 + 8µ + µ 2 ) / 16
7 Schrader and Martin (1998) have shown that the results of Salinger (1988) also depend on the assumption of Cournot reaction to input sales and Bertrand reaction to input purchases. With symmetric Cournot beliefs at the intermediate good level, an integrated firm would accept incrementally higher input costs because this would drive up the costs of non-integrated final good producers.
n 1 = 0, n2 = a / 2 + W (4 + µ 2 ) / 32 p = a / 2 − W(4 + µ 2 ) / 32 (6)
V B+ 2 (F, VI) = [16a + W (4 + µ)2 ]2 / 1024 V1 (F, VI) = µW[16a + W (4 + µ )2 ] / 128 V A (F, VI) = µ(2 + µ)W[16a + W (4 + µ)2 ] / 256
When the first-period profits are sufficiently small compared to the second period, the integrated pair has a very strong incentive to invest in market share. When the inequality expressed by eq. (5) is satisfied, the incentive is so strong that the independent retailer prefers not to get any customer in the first period. As a result, also the independent manufacturer remains idle at first, and the independent pair just waits for the following period when it can supply those consumers without switching costs. I study next whether this asymmetric equilibrium emerges in the whole game or the independent retailer and manufacturer want to avoid the first period pre-emption by integrating.
4.2
Contract game
In section 4.1, I derived equilibrium profits for manufacturers and retailers under various contractual configurations. These equilibrium outcomes are recalled in the table below and are used to solve the contract game. Each contracting pair selects the strategy that maximises joint profits, taking as given the strategy of the other contracting pair. The matrix is symmetric and the dashed numbers refer to equations in the text where the firms' identities are reversed.
V A + V1 VI F
V B + V2
VI
F
(2), (2) (6), (6)
(6'), (6') (4), (4)
Calculations show that when the rival pair is made of independent firms, then integration is always profitable: V i + h (VI, F) > V i (F, F) + V h (F, F) . On the other hand the best reply to an integrated rival depends on the following inequality: V i + j (VI, VI) > V i (F, VI ) + V j (F, VI) ⇔ W / a ≤ max[0,1 / h(µ )], where 2 2 h(µ ) = (9µ − 12 µ − 32 + 3µ 144 + 24 µ + 13µ ) / 32
Since h has to be positive, a necessary condition to have asymmetric equilibria is that µ should be high enough (in particular the RHS is positive when µ > 0.89). The equilibria of the game are summarised in figure 3. The dotted line represents condition (5), the points above it have a negative FOC for the non integrated firm in the first period. In summary, pre-emption and foreclosure can emerge in equilibrium. In that case, losses are made in period 1 by the pre-empting integrated firm (i.e. customers are subsidised). The non-integrated pair prefers to be idle in the first period for two reasons: first period profits are not particularly big and µ is high. It is then left to the integrated firm to make the first period harvest of customers since they will not be locked in the future. If, on the other hand, switching costs are relevant, the best response to an integrated pair is to integrate as well. It should also be noted that firms are never caught in a prisoner's dilemma when a symmetric equilibrium emerges: calculations show that joints profits for couple (i + h) under (F, F) are lower than under (VI, VI) when condition (5) is satisfied.8 The findings of the paper are summarised in the following proposition. Proposition 1. A symmetric equilibrium emerges with integrated pairs when profits in the second period are not too big and/or switching costs are relevant. Otherwise one pair integrates and the other remains free. In the latter case there is complete pre-emption in the first period and foreclosure in the second period. Off the equilibrium path, at t = 2 foreclosure of an independent dealer by an integrated firm would not arise if the market share of the integrated firm in the final market is small and switching costs are high, so that participation in the intermediate market is needed to have access to the customers captured by the independent retailer. However, foreclosure always arises in equilibrium once future profits are taken into account so that market shares are endogenised. [Figure 3 about here]
8
This result can be also contrasted with static models that have considered the foreclosure problem and the incentives to integrate. With a symmetric number of upstream and downstream firms, Gaudet and Van Long (1996) have shown that there always exists an equilibrium where all firms are vertically integrated. In particular such an equilibrium is unique when the number of upstream firms in sufficiently small (less or equal than 4). Using numerical results, they also conjecture that vertical integration is a dominant strategy when complete foreclosure is imposed exogenously. Moreover, they show that firms would face a prisoner's dilemma. Here, even in the simple 2 x 2 case, the coexistence of integrated and non-integrated firm can arise as an equilibrium outcome.
5.
Discussion and concluding remarks
This paper presented an upstream-downstream duopoly model to analyse the mutual incentive for firms to enter into particular trading relationships in a market with consumer switching costs. I have shown how the presence of switching costs points towards integration as a way of investing sufficiently in a base of repeat purchasers. However, I have also found a region where integrated and non-integrated firms coexist. In the latter case, non-integrated firms are idle in the first period and sell to the customers only in the second period. Hence there is a wave of entry in the second period which occurs only when the market is growing and switching costs are not too important. This not due to any uncertainty or first-mover advantage; rather entry does not occur at first because otherwise it would expand the subscriber base too much: it is better to leave it to the integrated rival to make the initial costly investment, and then benefit in part from the harvest in later stages since customers will be either newcomers or they will not be seriously locked in. I have neglected all welfare implications since the aim of the paper was to provide some insights into what determines the private profitability of particular contractual solutions in the presence of switching costs and double marginalisation.9 I also provided results on market foreclosure: the mere possibility of adopting such strategies out of equilibrium is important in determining the type and characteristics of the equilibria that may arise out of the contract game. In particular, foreclosure of an independent retailer by an integrated rival always arises as an equilibrium of the whole game (i.e. when market shares are endogenous). With exogenous market shares, foreclosure would not arise if switching costs are relevant and market shares are asymmetric. The empirical predictions of the paper are clear. If we can partition industries into two groups according to the relevance of switching costs, those with high switching costs and those with low switching costs, we would expect integrated structures in the former case and mixed structures in the latter. Mixed structures would be particularly likely in growing industries, where independent firms are made of latecomers not entering in the initial stages of competition. These theoretical findings can be contrasted with the empirical evidence in the UK mobile telecommunications industry, described in Section 2. I recall here that, when the incumbents were allowed to integrate downstream, they first continued to sell using the
9
The welfare analysis is very simple. Integration has two effects: it removes double mark ups in the second period and it makes firms more aggressive in the first period, attracting more subscribers. As a result, customers are strictly better off under vertical integration than with independent firms. Recalling that firms are never caught in a prisoner's dilemma, vertical integration yields a Pareto improvement.
same retailing structure as before, then, after a transition phase, they changed their policy and decided to sell directly to consumers. On the other hand, the new entrants immediately decided to be integrated. All this happened when consumer switching costs were particularly high. Hence we have two facts in line with the prediction of the model. At the time an institutional change occurred, incumbents with similar market shares continued to sell through their existing system of service providers, including independent ones. This can be compared with the prediction of the model: at t = 2, for given market shares, it is optimal to sell a rival product if the latter has a substantial market share (this was the case for incumbents) while this would not be true if the market share is small (as in the case of new entrants, who could then only sell in house). Once market shares are endogenized, then the model predicts integration in the presence of relevant switching costs, which is what happened after the initial transition phase. On the other hand, a different retailing structure has emerged in more recent times. Switching costs have considerably decreased, and contracts can be signed also with independent high-street retailers and multiple outlets. This finding is again consistent with the prediction of the model: in later stages of a growing market with mild switching costs, we would expect the coexistence of integrated incumbents and independent entrants. It is interesting to note that the regulator is now considering the possibility of additional entry upstream, after having received applications for the so-called "indirect access" to incumbents that would give service providers and their customers the chance to select, on a call-by-call basis, which operator carry their calls for them. In the mobile telecommunications industry, it is the service provider that bills the customer. The operator has no means of direct access to its users (lack of customer details, less control over credit checking, difficulty of establishing a standard level of customer services). This is in line with the model proposed: once a customer is connected to a network, she is locked in with the retailer. An interesting question that is left for future research is related to the differences arising once customers are 'owned' by manufacturers rather than retailers.
References Gaudet, Gérard and Ngo Van Long, 1996, "Vertical Integration, Foreclosure, and Profits in the Presence of Double Marginalization," Journal of Economics & Management Strategy 5(3): 409-32 Hart, Oliver and Jean Tirole, 1990, "Vertical Integration and Market Foreclosure," Brookings Papers on Economic Activity, Microeconomics: 205-76 Irmen, Andreas, 1998, "Precommitment in Vertical Chains," Journal of Economic Surveys 12(4): 333-359
Katz, Michael L., 1989, "Vertical Contractual Relations," in R. Schmalensee and R.D. Willig (eds.), Handbook of Industrial Organization, vol. 1: 655-721, North-Holland, Amsterdam Klemperer, Paul, 1987, "Markets with Consumer Switching Costs," Quarterly Journal of Economics 102: 375-94 Klemperer, Paul, 1995, "Competition when Consumers have Switching Costs: An Overview with Applications to Industrial Organization, Macroeconomics, and International Trade," Review of Economic Studies 62(4): 515-39 Kühn, Kai-Uwe, 1997, "Nonlinear Pricing in Vertically Related Duopolies," RAND Journal of Economics 28(1): 37-62 Ordover J.A., G. Saloner and S.C. Salop, 1990, "Equilibrium Vertical Foreclosure," American Economic Review 86: 127-42 Rey, Patrick and Jean Tirole, 1999, "A Primer on Foreclosure," Handbook of Industrial Organization, Vol. 3, North-Holland, Amsterdam (forthcoming) Salinger, Michael A., 1988, "Vertical Mergers and Market Foreclosure," Quarterly Journal of Economics 77: 345-56 Schrader, Alexander and Stephen Martin, 1998, "Vertical Market Participation," Review of Industrial Organization, 13: 321-31 Shapiro, Carl and Hal Varian, 1999, Information Rules: A Strategic Guide to the Network Economy, Harvard Business School Press, Boston (MA) Valletti, Tommaso M., 1999, "Market Foreclosure and Exclusivity Contracts when Consumers Have Switching Costs," presented at the 27th Telecommunications Policy Research Conference, Alexandria (VA) Valletti, Tommaso M. and Martin Cave, 1996, "Competition in UK Mobile Communications," Telecommunications Policy 22(2): 109-31 Waterson, Michael, 1993, "Vertical Integration and Vertical Restraints," Oxford Review of Economic Policy 9(2): 41-56
A
B
A xB1 • 0
2
1
B+2
A+ 1
1 (F, VI) Figure 1: Basic contractual configurations
(F, F)
B+2
(VI, VI)
nj /ni no foreclosure
foreclosure 21/2
µ 0 0.457 1 Figure 2: Foreclosure of independent retailer j by integrated firm i at t = 2
W/a 1/h
VI, VI
F, VI
µ 0
1 Figure 3: Equilibrium contractual configurations
Appendix (not for publication) Proof of Lemma 1. The algebra of market competition at t = 2 in the (F, VI) case leads to: q1 =
µn 1 + n2 bµ (n1 + n 2 ) − 2w(n1 + µn 2 ) 2+µ n1 + n2
q2 =
µ n2 + n1 bµ(n1 + n 2 ) + w(µn1 + 2n 2 − µn 2 ) n1 + n 2 2+ µ
Denoting by xB1 and xA1 the quantities supplied to the independent retailer respectively by the manufacturing division of the integrated firm and by the upstream operator A, then the equilibrium condition in the intermediate market gives w(x A1 ,x B1 ) = (n 1 + n2 )[b(n1 + µn 2 ) − (2 + µ )(x A 1 + x B 1 )] .The analysis of the FOCs of manufacturers (n1 + µn 2 )[2n 2 + n1 (1 + µ )] shows that two cases may arise according to the importance of switching costs. • If n 12 (2 − 3µ − 3µ 2 ) − µn 1n 2 (7 + µ ) − 4n2 2 < 0, then the integrated firm forecloses the independent retailer (xB1 = 0) and the equilibrium profits are: π B + π2 =
K 2 (µn 1 + n2 )[(3 + 2µ)n1 + (4 + µ)n 2 ]2 4[2n2 + n1 (1+ µ )]2
K 2 (n 1 + n2 )(µn2 + n1 )(2 + µ ) πA = 4[2n 2 + n 1 (1 + µ )] (A1)
π 1 = (µn 2 + n 1 )K 2 / 4
• If n 1 (2 − 3µ − 3µ ) − µn 1n 2 (7 + µ ) − 4n2 > 0 then the integrated firm sells also via 2
2
2
the other retailer and the equilibrium profits are:
π B + π 2 = [n14 (4 + 32µ + 49µ 2 + 33µ 3 + 9µ 4 ) + 2n 13 n 2 (20 + 86µ + 102µ 2 + 43µ 3 + 3µ 4 ) + n1 2 n2 2 (120 + 336µ + 259µ 2 + 46µ 3 + µ 4 ) + 2n1 n2 3 (76 + 128µ + (A2)
45µ 2 + 5µ 3 ) + n 2 4 (72 + 44µ + 10µ 2 + µ 3 )]b2 (n1 + n 2 ) / [D 2 (2 + µ )] π A = b2 (n1 + n 2 )[n1 (2 + 3µ) + n 2 (4 + µ )]2 [n 1(1 + µ) + 2n 2 ](n 1 + µn2 ) / [D2 (2 + µ )] π 1 = 4b2 (n 1 + n2 ) 4 (n1 + µn 2 ) / D 2 D = n12 (6 + 7µ + 3µ 2 ) + n1 n 2 (16 + 15µ + µ 2 ) + n 2 2 (12 + 4µ)
Proof of Lemma 2. Imagine there is foreclosure at t = 2. Using expressions (A1) it is possible to analyse the market competition phase at t = 1. The independent retailer faces a wholesale price w while the retailing division of the integrated firm does not; their FOCs are respectively: (A3) (A4)
a − 2n1 − n 2 − w + A (x) ≤ 0, n1[a − 2n 1 − n 2 − w + A (x )] = 0 a − n1 − 2n 2 + B(x) = 0 A (x) = W / 4 B(x ) =
W[4 + µ + (3 + 2µ )x][8 + 2µ + (6 + 11µ + 3µ 2 )x + (3 + µ + 4µ 2 + 2µ 3 )x 2 ] 4(2 + x + µx) 3
where x = n1 / n2 . Assume first that there is an interior solution (i.e. n 1 > 0 in (A3)). Solving the system of FOCs gives: (A5)
n 1 / n 2 = [a + 2A (x ) − B(x ) − 2w] / [a + 2B(x) − A (x ) + w]
B(x) is increasing in x, hence the RHS reaches a maximum when x = 0. Since 2 B(0) = W (4 + µ) / 16 ≥ W > A (x ), it is thus demonstrated that n 1 ≤ n 2 , confirming the foreclosure assumption at t = 2 (recall figure 2 or Corollary 1). A fortiori foreclosure at t = 2 happens when n1 = 0: in particular, when a / W < (8 + 8µ + µ 2 ) / 16 , then (A3) always holds with the inequality sign for any w, hence the independent retailer completely shuts down in the first period and the equilibrium is given by eq. (6) in the main text.10 When a / W > (8 + 8µ + µ 2 ) / 16 , there would not be a corner solution any more. In this case it is not possible to obtain a closed form solution, and the equilibrium has to be found numerically. However, I can show, by contradiction, that an equilibrium without foreclosure cannot exist. Imagine, on the contrary, that such equilibrium exists at t = 2, so that eq. (A2) are relevant. Market competition at t = 1 gives the same FOCs as eq. (A3) and (A4) where A(x) and B(x) would take different expressions (omitted here for the sake of brevity), and an interior solution would be the same form as eq. (A5). Since it can be shown that also in this case A(x) < B(x) for every x, it would turn out that the integrated firm has always at least as many customers as the independent retailer, violating the region of validity of eq. (A2). Hence the region without foreclosure at t = 2 cannot emerge in equilibrium once market shares are endogenous.
10
It can also be easily checked that a corner solution with n2 = 0 can never arise. In fact, by solving eq. (A3) with respect to n1 and substituting the result into eq. (A4), would always give a positive FOC for the integrated firm, hence providing an incentive to supply some customers.
