Price Competition with Reduced Consumer Switching Costs: The Case of “Wireless Number Portability” in the Cellular Phone Industry
Mengze Shi∗ Jeongwen Chiang** Byong-Duk Rhee***
First draft: May 2001 Revised: September 2002
∗
Assistant Professor of Marketing, Rotman School of Management, University of Toronto, Canada. Professor of Marketing, Department of Marketing, National University of Singapore, Singapore. *** Associate Professor of Marketing, Department of Marketing, Syracuse University. **
Corresponding Address: Jeongwen Chiang, Professor of Marketing, Department of Marketing, National University of Singapore, Singapore 117591.
[email protected]
Abstract In this paper we study how a reduction of consumer switching costs may affect market competition in the wireless telecommunication industry. The reduction of switching costs can be achieved through the implementation of a regulatory policy called Wireless Number Portability (WNP) that allows consumers to retain the same phone numbers when they switch service providers. By reducing consumers’ switching costs, WNP was intended to intensify price competition and facilitate the growth of new service providers. However, our analysis shows that, when networks incur interconnection costs, a reduction of switching costs may accelerate the process of market concentration. With positive interconnection costs, the networks charge lower usage fees for the calls within the same networks than for calls between the networks. Such network-based price discounts provide the large network with a competitive advantage because its subscribers are more likely to enjoy price discounts than the subscribers to a small network. Consequently, subscription to the large network can become more attractive even though the large network charges higher fees to exploit the consumers’ switching costs. We relate our analytical results to the empirical evidence from the Hong Kong market where WNP was adopted in March of 1999.
2
1. Introduction Consumers often have to incur costs when they switch from one supplier to another. Klemperer (1995) defines switching costs as a result of “a consumer’s desire for compatibility between his current purchase and a previous investment.” The previous investment might be the purchase of physical equipment, consumers’ learning of product functions, or the accumulated mileage in a frequent flier program. 1 As switching costs reduce the consumers’ incentives to change their suppliers, firms tend to charge higher prices to their current customers. This implies that the firms’ current market shares can be important determinants for their future market shares and profits. In general, the existing research concludes that consumer switching-costs tend to increase the firms’ abilities to exploit their existing customers and to reduce the firms’ incentives to attract new customers (e.g. Klemperer 1987a, Klemperer 1987b, Farrell and Shapiro 1988, Beggs and Klemperer 1992, Klemperer 1995.). In line with this stream of research on consumer switching costs, our paper investigates the effect of switching costs on market competition. More specifically, we study how a reduction of switching costs may affect price competition and the firms’ market shares in the wireless communication industry. The reduction of switching costs can be achieved through the implementation of a policy called “Wireless Number Portability” (WNP). The Federal Communications Commission (FCC) issued the ruling on WNP in 1996 to foster more competition and facilitate the entry of digital communication service providers. This policy requires all wireless service providers to comply with the mandate that consumers can retain their phone numbers when they switch service providers. 2 Regulators and consumer advocates believed that this new policy would significantly ease the burden of network switching. As a result, WNP should induce more competition, help the new market entrants, and benefit consumers (Armstrong 1997). The beliefs about these anticipated consequences were further reinforced by the incumbent service operators’ negative reactions towards WNP. The industry argued that the market was already very competitive and, more importantly, they believed WNP was not essential to foster more competition (CTIA report 1998). Upon a successful forbearance petition from the industry, the mandate of WNP was postponed from June of 1999 to Nove mber of 2002.
1
Readers may refer to Klemperer (1995) for an overview of the types of switching costs and related literature. Unlike the fixed line case, before the implementation of WNP, a cellular phone user who switches his service provider has to forgo his original phone number and obtain a different number from the new provider. 2
3
While WNP was postponed in the U.S., it has already been implemented in a number of foreign markets. 3 For example, Singapore mandated the policy in April 1997, the UK in January 1999, Hong Kong in March 1999, The Netherlands in May 1999, while Ireland, Australia, and Germany imposed WNP in 2000. Since the implementation of WNP in these markets can be viewed as natural experiments, their outcomes could serve as useful evidence to support any theoretical results. From the data gathered both before and after the WNP implementation in Hong Kong, we find that, first, consistent with the expectations, the unit prices dropped significantly after WNP. However, after WNP was implemented, the large operator gradually gained market share, while small firms were struggling to hold their market positions. The latter observation is interesting because when large operators in Hong Kong first learned about WNP from the government, they vigorously objected to the idea for they believed they would lose their market shares to their smaller rivals. Moreover, the result is inconsistent with the existing view that the incumbent would lose market share by exploiting the loyal customers (Klemperer 1988, Klemperer 1995). To help understand these observations, we extend the existing studies on the competition with consumer switching costs to the telecommunication industry. In an oligopoly telecommunications market, the networks have to incur interconnection costs in order to connect the callers from the different networks. 4 As a result, the firms’ variable service costs are higher when the callers are located with the different networks. Following the pricing practices in the wireless industry, we allow the firms to price the communications within the networks (called onnet calls) differently from the communications between the networks (called off-net calls) (Laffont, Ray, and Tirole 1998b). Such a network-based discriminatory pricing scheme consists of a fixed access fee, a usage-based variable fee for the on- net calls, and another usage-based variable fee for the off- net calls. Consistent with the existing literature, we find that the large network charges a higher fixed access fee to exploit their customers’ switching costs. We also find that networks provide price discounts for communications within the networks. Since a large network has more subscribers, subscription to the large network provides greater opportunity for a consumer to enjoy on- net price discounts. Following a reduction of switching costs through WNP, both networks’ fixed fees decrease as expected, leading to a smaller difference between 3
In Hong Kong, Singapore, Europe, and some other regions, WNP is called Mobile Number Portability (MNP).
4
the networks’ fixed fees. When the difference is sufficiently small, the value of on- net price discounts may dominate consumers’ network choice decisions, making a subscription to the large network the more attractive option. In this scenario, the large network can gain market share from the small network after the implementation of WNP. We organize the rest of this paper as follows. In Section 2 we provide a case study on WNP in the Hong Kong market. In Section 3 we propose a model for the competition with consumer switching costs. We analyze the equilibrium pricing strategies and market shares as well as the impact of WNP in Section 4. In Section 5 we discuss the sensitivity of our results to model assumptions. Finally we state our conclusions in Section 6 and suggest several directions in which to extend our model.
2. WNP and the Hong Kong Wireless Phone Market In this section we provide a case study of the Hong Kong wireless phone market. The case study not only sheds insights onto the likely consequences of WNP, but also offers empirical support for the formal discussions given in the next section.
2.1. Hong Kong Wireless Phone Market In February 2001, Hong Kong had a population of 6.7 million and approximately 4.23 million wireless phone service subscribers. This made Hong Kong one of the most penetrated ma rkets in the world. There were six wireless network operators with a combined total of ten digital networks. Among them, four GSM licences (Orange, CSL 1010, and Smartone) and one CDMA licence (XGX) were awarded from 1992 to 1993. Six PCS licences (1+1, Extra, One2Free, New World, Peoples, and Sunday) were awarded in September 1996. Some companies owned multiple networks. For example, Hutchison operated Orange network (both GSM and PCS) and XGX, while SmarTone owned both Smartone (GSM) and Extra. The Office of the Telecommunication Authority (OFTA) required all of the networks to be interconnected and provided guidelines for how networks should charge for interconnection. The availability of number portability was considered by OFTA as essential for the development of wireless telecommunications in Hong Kong and for the delivery of enhanced
4
We assume the interconnection charge is exogenously determined (for studies on alternative methods to determine interconnection cost, see Armstrong, Doyle, and Vickers, 1996 and Laffont, Ray, and Tirole, 1998a and 1998b).
5
benefits to consumers. In Consultation Paper on Number Portability for Mobile Phone Services in Hong Kong (1997), OFTA stated that, “the introduction of mobile number portability would remove the hindrance for mobile customers to move to their preferred operators and would further promote and encourage competition in the mobile industry.” In response to OFTA’s consultation, the new PCS entrants voiced their supports. “We (PCS operators) believe that the presence and implementation of WNP would remove one of the major barriers to full competition in mobile services in Hong Kong given the high percentage of mobile customers who are reluctant or unwilling to change operators if it would mean changing their mobile telephone numbers.” However, the established operators were more skeptical about the need for WNP. It seemed that the PCS operators welcomed WNP for the reduction of switching costs, making it easier for them to attract those users who were locked in with incumbent networks. In contrast, the existing networks were not supportive of WNP because they expected to lose the chance to exploit the switching costs of their current customers. Despite objections from incumbent networks, OFTA moved to implement WNP in Hong Kong on March 1, 1999. Before the launch of WNP, some mobile phone networks (Sunday in particular) advertised extensively the upcoming availability of WNP. The advertising campaigns and media coverage raised public awareness about WNP to a very high level in Hong Kong. According to a survey conducted by the authors prior to the implementation, 471 out of 488 respondents reported they were aware of WNP. Consumers were also very responsive to this new policy. According to OFTA’s statistics, in March 1999 alone, there were more than 102,000 applications for switching networks with number portability.
2.2. Impact of WNP in the Hong Kong Wireless Phone Market We collected data on the networks’ prices and market shares for the period from November 1998 to September 1999. Thus we have a period of approximately six months both before and after the implementation of WNP, respectively. We next discuss the observed pattern of unit price (charge per minute) and market shares.
6
Figure 1: Charge Per Minute (Total Free Airtime/Monthly Fee, Basic Service Package)
Market Share (%)
3.5 3 2.5 2 1.5 1 0.5 0 11/98 12/98 01/99 02/99 03/99 04/99 05/99 06/99 07/99 08/99 09/99 Time (Month/Year)
1010
One2Free
1+1
Orange
XGX
Smartone
Extra
People
Sunday
New World
Unit Price Figure 1 shows the average price per minute charged by networks from November 1998 to September 1999. We compute the average price of the basic package (the package with the lowest tariff and smallest amount of free air time) offered by each network. For example, in November 1998, CSL charged HK$360 (approximately US$45) for 120 minutes of free airtime. We then calculate the average price as HK$3 per minute. Figure 1 clearly indicates that most networks decreased their prices significantly around the time of WNP implementation. For instance, in February 1999, CSL 1010 dropped its price from HK$3/minute to HK$1.733/minute and One2Free reduced its price from HK$3.18 to HK$1.68 per minute. Thus, consistent with OFTA’s goal, overall market prices were significantly reduced with the implementation of WNP.5 Since each mobile phone network’s positioning strategy and market position had been relatively stable over time, comparing prices of the same networks over a period of time provides a good indication of the impact caused by WNP.
5
The only exception was with Peoples network, a new entrant with a PCS network with a very small market share. We noticed that Peoples network charged the lowest price in late 1998 to attract consumers in order to build a user base. We thus speculate that Peoples increased its price later as an adjustment when its market share was stabilized, which happened to coincide with WNP.
7
Figure 2: Market Shares by Networks
Market Share (%)
25 20 15 10 5 0 11/98
12/98
01/99
02/99
03/99
04/99
05/99
06/99
07/99
08/99
09/99
Time (Month/Year) 1010
One2 Free
1+1
Orange
XGX
Smartone
Extra
People
Sunday
New World
Market Structure We show in Figure 2 the networks’ market shares approximately six months before and six months after the implementation of WNP. A surprising observation was that Orange, the largest network, steadily gained market share following the implementation of WNP. Meantime, the smaller players such as Peoples and Sunday did not see any improvement in their shares. Peoples, the smallest network in the market, actually lost part of its market share towards the end of observation period. Sunday launched a huge advertising campaign through TV commercials and newspaper advertisement during the period to attract switchers. However, despite the heavy promotional campaigns, Sunday hardly gained any market share. In summary, the market structure became more divergent after the implementation of WNP: the largest network became even larger, while the small ones were struggling even harder to keep their market shares. The above observation implies that under some conditions the implementation of WNP would provide larger networks with advantages in competing against small networks for market share. Since WNP decreased the consumer switching costs, we conjecture that a reduction of switching costs may accelerate the market concentration. In the years following the implementation of WNP, talks on merger and acquisition between the large and small operators in Hong Kong have been reported regularly. For instance, it was widely speculated that Sunday was in talk s with
8
New World Mobility (Chan 2001, Ling 2001) and more recently with CSL (Kwok 2002). To the best of our knowledge, such an effect of the reduced switching costs has never been discussed in any of the published reports or consultation papers of the telecommunication authorities. In order to identify and understand the reasons behind this outcome, we next propose a game theoretical model to formally examine how the change of switching costs may affect the dynamics of market structure in the wireless communication industry.
3. A Model In this section we develop a model of price competition between wireless phone networks. We consider a market of size N where two wireless phone networks (denoted as i = a or b) provide basic wireless communication service. The two networks are interconnected so that a subscriber to one network can communicate with a subscriber to the other network. In our model, the two networks compete in a single-period game where the networks set their prices first and then the consumers make network subscription decisions. Prior to the game, the consumers subscribed to either one of the two networks. We let firm a and b’s current network sizes be N θ a and N θ b respectively where θ a + θ b = 1 . Without loss of generality, we further assume that θ a ≥ θ b . Thus, network a had a larger number of subscribers than network b. In an extreme case where θ b =0, firm b becomes a new entrant to the market that was monopolized by network a. Next we provide more details of the wireless phone services in Section 3.1. We describe the consumers’ service valuations in Section 3.2. We model the consumers’ network choice decisions in Section 3.3. Finally, we formulate the networks’ pricing problems in Section 3.4.
3.1. Wireless Phone Service: Cost and Price We distinguish between wireless communications within the same network and communications between the networks. Following Laffont, Ray, and Tirole (1998b), we refer to such communications that are originated and terminated within the same networks as “on-net” calls, and the communications that are initiated at one network but terminated at the other network as “off- net” calls. Networks have to incur interconnection costs when connecting two consumers located on different networks. As a result, each network has higher marginal costs for the off- net calls than the on-net calls. We assume that the interconnection costs are exogenously determined by government regulations. (For an example of government guidelines on the charges for
9
interconnection between networks, readers may see Statement of HKTA May 1998.) We further assume that competing networks have the same constant marginal costs and let c and ηc be each network’s marginal cost for on-net and off-net calls respectively, with η being the ratio of the cost between off- and on- net calls for both networks. Based on the above discussions, it is necessary that η>1 and η increases with the interconnection costs. Wireless phone operators, bearing in mind the costs of interconnection, set their service prices differently based on the location of callers. Following the pricing practices in the wireless phone markets of the U.S., Canada, U.K., Australia, Hong Kong, and Singapore, we assume that the networks employ a network-based discriminatory pricing scheme, { Fi , p ii , p ij } for network i, where Fi is the fixed access fee, p ii is the unit variable fee for on- net calls, and p ij is the unit variable fee for off- net calls. 6 The first subscript of the variable fees represents the originating network and second subscript represents the terminating network. Similarly, we let q ii and q ij be the amount of on-net and off- net communications respectively. At the end of a billing period, network i charges a customer the total amount (denoted by Ti ) as follows: Ti = Fi + pia q ia + pib qib , (i = a or b).
(1)
3.2. Consumer Valuation of Communication Service The value of a consumer’s communications with another consumer depends on the strength of their social tie. We assume that the social tie between each pair of consumers can be at either one of two levels: no tie or a positive tie. If two consumers have no tie, then they derive zero utility from the communications. Consequently, these two consumers will not pay for any communications between them. If two consumers have a positive tie, then each of them derives positive utility u (q ) from an amount of communications q. As standard in the literature, we assume that the utility function u (q ) is monotonically increasing and concave with respect to the quantit y of communication q. We further assume that in equilibrium the utility u (q ) is large enough for the consumers to join either network. Since the pairs of consumer having no ties do 6
Most wireless service operators in Hong Kong adopt network-based discriminatory pricing schemes. For example, New World PCS offered a basic service package in March 1999 in which, for HK$138, a consumer could receive a total of 160 minutes, among them 60 minutes must be spent on within-network communications. Given that New World PCS’s market share was below 15% at that time, the pricing scheme adopted by New World PCS clearly favoured communications within networks (60/160 = 37.5% which is much larger than 15%).
10
not communicate with each other, in the rest of the paper we focus our attention only on the pairs with positive ties. We assume that each consumer has a positive tie with a number, n, of people in the market. A consumer decides the optimal amount of communications with another consumer by comparing the marginal utility of communications with the variable fees charged by the firms. For a consumer who subscribes to network i, the consumer decides q ( pij ) ,7 the optimal amount of communication with a subscribes to network j, by solving problem (P1): (P1)
v( pij ) = max{u( q ij ) − pij q ij }. q ij
(2)
Since the utility from the communications is identical among all pairs of consumers with positive ties, each pair of consumers has the same demand function for the service. As networks may price discriminate the calls based on the callers’ network locations, a consumer’s valuation, and hence the optimal amount of communications, varies with the network location of the other person with whom the consumer intends to communicate. For example, if network i provides a discount to the on- net calls, then the consumers at network i will talk more with their friends on the same network and talk less with their friends on other networks. In other words, v( p ii ) can be different from v( p ij ) where i≠j. To simplify the notation, we let v ii = v( pii ) and v ij = v( pij ) . So far we have discussed the value of communications between a pair of consumers. A consumer’s total value of communications is the aggregation of service valuations over all n pairs connected with the (focal) consumer. Since the firms may price the service differently according to the location of callers, it is necessary to identify the network locations of the consumer’s personal communication network. Following Ray, Laffont, and Tirole (1998b), we assume a uniform calling pattern where each wireless phone user has the same chance to communicate with any other wireless phone users. In other words, the n people with whom a consumer has positive ties are uniformly distributed in the market. The assumption implies that, if firm i’s market share is σ i (i=a,b), then a subscriber to network i should communicate with
7
The demand elasticity of q* ( pij ) captures the competition between wireless phone operators and other industries
such as fixed line networks and the Internet that satisfy similar communication needs. When fixed line networks and/or Internet service providers offer cheaper and more convenient service, the demand for wireless phone communications will become more elastic. Given our focus on the wireless phone industry and WNP, we take the strategies of fixed line networks and other related competitors as given.
11
n σ a number of subscribers at network a and n σ b number of subscribers at network b. We let wi denote the total value of communications for a consumer that subscribes to network i. Then, wi = nσ a via + nσ b v ib − Fi , (i=a, b).
(3)
In equation (3), the value of on- net communications ( v ii ) and value of off- net communications ( v ij ) are weighted by the distribution of the personal communication networks. Both values of on-net and off- net communications are determined by equation (2).
3.3. Consumers’ Network Choices Each consumer chooses a network to subscribe based on her network preference and value of the service packages that the networks provide. We let the networks’ service quality be exogenously given and focus on price competition. We assume that the services provided by the competing networks are not differentiated. However, a consumer has to incur a cost if switching away from the current network to the other network. Klemperer (1995) identifies five sources of switching costs. One is the need for compatibility with existing equipment. For example, the wireless phone handsets used for one network may not be compatible with another network. In switching the networks, the consumers may have to buy new handsets. The second source is the transaction costs of switching suppliers. For example, a consumer may need to register and apply for the access to the other network’s service. Sometimes the networks may charge a start up fee for the new accounts. In the markets where WNP is not implemented, consumers have to inform all of their contacts the change of pho ne numbers. Such inconvenience can be particularly costly for the business users who have to change all the stationary and risk losing customers. In a survey conducted by authors in February 1999, the change of telephone numbers was cited as the number one reason for not switching the networks. 8 The third source is the costs of learning to use new brands. Since the networks may have different ways to serve their customers, the new customers will have to learn how to navigate through the service providers’ websites to look for information. The fourth source is the discount coupons and similar promotional devices. For example, most networks hand out new handsets at discount prices or even free. In exchange for
8
In the survey, when 488 respondents were asked about the sources of switching costs, 253 respondents mentioned the change of telephone numbers, 180 mentioned handset change, 186 mentioned termination of contracts, 77 mentioned loss of service, 137 mentioned poorer coverage, 109 mentioned poorer sound quality, and 12 of them mentioned higher prices.
12
the new handsets, consumers are required to stay with the networks for a given period of time. The penalty for leaving these contracts prematurely is typically much larger than the price differences between the competing networks. The wireless phone networks in Hong Kong asked consumers to pay the prices of handsets up front and then deduct the monthly rebates from their bills. The typical value of rebates ranges from US$6.5~$13, which was much greater than the price difference between networks. Finally, consumers may have psychological cost of switching. We denote a consumer’s cost of switching from network i to j by ψ ij . Due to the network switching costs, a consumer’s current network choice affects the consumer’s future network choice decisions. For a consumer that subscribed to network i, the consumer’s value of service subscription will be wi if the consumer stays with the same network, but w j -ψ ij if the consumer switches to the other network (j). Note that a consumer incurs the switching cost if and only if the consumer switches from one network to the other. The size of switching costs varies among the consumers. To model such heterogeneity, we assume that the switching cost of each firm’s customers is uniformly distributed in the interval [0, Ψ]. Klemperer (1987b) also adopts a uniform distribution for the heterogeneous switching costs, but the analysis was limited to a symmetric case where two firms had the same market share. Klemperer (1995) suggests more work to model the heterogeneous switching costs. 10 We illustrate the market structure by Figure 3 where distance AO=BO=Ψ. The rectangles AFGO and BRLO represent network a and b’s customers respectively. Since network a’s size is equal to N θ a , OG is equal to N θ a /Ψ. Similarly, OL is equal to N θ b /Ψ. Since network a is larger than network b, OG is larger than OL. Figure 3 also shows that, given the networks’ prices, the networks’ demand functions are quasi- linear. With the implementation of WNP, there is a sudden reduction in the consumer switching costs. We model such a change by reducing Ψ to 10
In the survey that authors conducted in February 1999, when asked whether to stay or switch once WNP was implemented, 309 respondents claimed to stay even with WNP. These 309 respondents were further asked to indicate the amount of rates that the current networks could raise (in percentage) before the respondents would consider switching to other networks. The result (“switching cost”) was distributed in a fairly wide range from 5% to 100% of current rates. Among them, 12% of respondents would not switch even if current service networks increased price by 50%.
13
Ψ’. Correspondingly, the distribution of customers become MDEO and NKHO for network a and b respectively. Clearly, a reduction of consumer switching costs brings the consumers closer to each other and each network’s market share becomes more sensitive to the prices. The networks’ equilibrium market shares are determined by the location of the marginal consumers who are indifferent between staying with the existing network and switching to the other network. Suppose that in the equilibrium firm k does not gain market share. Then the marginal (indifferent) consumer switches from network k to the other network i (i≠k) and incurs a switching cost ψ *k ,i . Since the marginal consumer is indifferent between subscribing to the either network, the marginal consumer’s switching costs is determined by the following equation: ψ *k ,i = wi − wk , where k≠i.
(4)
Figure 3. Consumer Switching Costs Network a’s customers N θ a
Network b’s customers Nθb
D
E
F
G H
K
L
A (Ψ)
M (Ψ’)
O
R
N (Ψ’)
B (Ψ)
In equilibrium, all of the network k’s current customers whose switching costs are lower than ψ *k ,i switch to network i. But the rest of network k’s current customers whose switching costs are
higher tha n ψ *k ,i will be retained. Meantime, all of the other network (i)’s current customers repeatedly purchase from the same network. Since the switching cost ψ k ,i is uniformly distributed in the interval [0, Ψ], network k’s new market share becomes σ k = θ k − θ kψ *k ,i / Ψ . It
14
is important to note that a consumer’s expected value of subscription depends on the consumer’s belief about each network’s market share. We assume that the consumers unilaterally (not coordinated in cohorts) choose one of the networks to subscribe to. The consumers are fully informed about the market characteristics and the other players’ decisions rules. We also assume that consumers can form rational expectations about the networks’ equilibrium market shares. In other words, consumers know the market shares σ a and σ b when evaluating the networks by Equation (3). Given these assumptions, we substitute Equations (3) and (4) into σ k = θ k − θ kψ *k / Ψ and obtain the following market share equations.
σk =
Ψ − n( vii − v ki ) − ( Fk − Fi ) θ ; Ψ − θ k n( vaa + v bb − v ab − vba ) k
σi =
θ i Ψ − θ k n( v kk − vik ) + θ k ( Fk − Fi ) . Ψ − θ k n( vaa + v bb − v ab − v ba )
(5.1)
(5.2)
where i=a or b and i≠k. From the above equations, we can also derive the loss of market share for firm k,
θk − σ k =
θ i n( v ii − v ki ) − θ k n( v kk − v ik ) + ( Fk − Fi ) θk . Ψ − θ k n( v aa + vbb − vab − vba )
(6)
According to equation (6), the number of network k’s customers switching to network i depends on on- net variable fees, off- net variable fees, the fixed fees, and current network sizes. First, more people will switch from network k to network i when network k charges higher prices (hence smaller value of communications v kk and v ki ). More people will switch away from network k when network i charges lower prices (hence higher value of communications v ik and vii ). Second, since a consumer has to pay a fixed fee for the subscription, a network’s market share decreases with the amount of fixed fee the network charges and increases with the fixed fee charged by its competitor. Third, network k’s loss of market share decreases with switching cost, measured by Ψ, because a larger switching cost implies that current customers are more loyal and less likely to be lured away by the other networks. Finally, equation (6) indicates that the current network size matters. By subscribing to a larger network, a consumer is more likely to find “friends” within the same network and hence enjoy the on-net price discounts. However, its impact on the equilibrium market share is unclear so far.
15
3.4. Networks Pricing Strategies Now we formulate networks’ price decisions. In the beginning of game, the networks simultaneously decide and post their prices to the public. The competing networks’ objectives are to maximize their own profits.
(P2)
[
Max π i = Nσ i nσ i ( p ii − c )q( pii ) + nσ j ( p ij − ηc )q( p ij ) + Fi
(Fi , pii , pij )
]
where i,j=a,b, i≠j, σ i and σ j are given by Equations (5.1) and (5.2) .
In problem (P2), network i earns profits from N σ i number of consumers. After the networks post their prices, the consumers decide the ir optimal amount of communications through problem (P1). Every subscriber to network i expects to communicate q( p ii ) amount of time with each of the nσ i people within the same network, and q( p ij ) amount of time with each of the nσ j people at the other network j. In subscribing to network i, a consumer expects to pay a fixed fee Fi, nσ i pii q ( pii ) amount of variable fees for on- net communications, and nσ j pij q ( p ij ) amount of variable fees for off- net communications. The consumers make the ir network choice decisions by considering both the value of communications, wi , given by Equation (3), and potential switching costs. We assume that the networks have a rational anticipation of the consumers’ network choice behaviour when making their price decisions in the beginning of the game. In next section we derive the equilibrium pricing strategies and the networks’ equilibrium market shares. We suppose that the maximum switching cost Ψ is sufficiently high that, in equilibrium, both networks have positive market shares. In other words, networks find it optimal not to price so aggressively as to reach the competitor’s most loyal customers. To ensure the existence of such a pure-strategy equilibrium, we assume that the first-order conditions of (P2) will yield a unique equilibrium. We include the analysis and discuss the specific conditions in Appendix 1.
4. Model Analysis 4.1. Equilibrium Pricing Strategies
16
We start our analysis by characterizing the equilibrium results. For a specific level of market share that a network intends to achieve, we study the optimal pricing plan that the network should offer to maximize its profit. According to equations (5.1 and 5.2), given network j’s pricing strategies {F j , p jj , p ji } , network i’s market share function depends on its fixed fee ( Fi ), on-net price ( p ii ), and off- net price ( p ij ). To achieve a specific level of market share, σ i , network i can employ one of the many feasible pricing strategies, {Fi , pii , p ij } that lead to the same desired level of consumer valuation, ( wi ). Take network j’s pricing strategy as given and have network i’s equilibrium market share fixed at σ i , we reformulate (P2) as (P3)
[
Max π i = Nσ i nσ i ( pii − c )q ( pii ) + nσ j ( pij − ηc )q ( p ij ) + Fi
(Fi , pii , pij )
s.t. nσ i vii + nσ j v ij − Fi = wi , (i≠j, i,j = a or b).
] (7)
Equation (7) requires that network i’s pricing plan should provide a given level of consumer valuation of communications wi . This is a necessary constraint in order to ensure that network i achieves market share σ i . In Appendix 1 we show that the first-order conditions lead to the following results: p ii = c ; p ij = ηc . (i≠j, i,j = a or b).
(8)
Thus, in equilibrium, both networks charge the variable fees equal to the marginal costs. Ray, Laffont, and Tirole (1998b) obtained the same results in a model where the two competing networks are identical and consumers have constant demand elasticity. We extend their results to a case with asymmetric market shares, positive consumer switching costs, and general demand functions. The interpretation of for the above result is as follows. To achieve a given level of market share ( σ i ), a network must offer a specific amount of value for the users’ wireless communications ( wi ). Suppose that {pii , p ij , Fi } is one of the feasible packages that satisfy (7). Keep p ij the same and consider a unit increase of p ii , then the value of on- net communications will decrease by the amount n σ i vii′ . In order to maintain the overall value, wi , the network has to reduce the fixed fee from Fi to Fi + nσ i v ′ii . Such a move affects the network’s profits in three
17
( ) − Nn(σ ) v′
ways. First, the network’s profit increases by Nn σ i q ( pii ) due to the increased on-net margin. 2
Second, the network’s profit decreases by
2
i
ii
due to the lowered fixed fee. By Roy’s
Identity, v 'ii = - q( p ii ) resulting from the consumer’s optimal quantity decisions. Therefore these two effects cancel out. Finally, the move also decreases the amount of on- net communications, leading to a change in profit by Nn( σ i ) 2 ( pii − c )q ′( pii ) , which is ne gative if p ii > c , zero if p ii = c , and positive if p ii < c . Clearly the equilibrium on- net price has to be equal
to the marginal cost of on-net calls ( p ii = c ). Otherwise, the network can increase its profit by moving its on-net price towards the marginal cost. Following exactly same reasoning, the equilibrium off- net price should be equal to the marginal cost of off- net calls. The above discussions have direct implications on the amount and value of communications. Since the on- net price is lower than the off- net price, the amount of communications between each pair of consumers is larger if two consumers are located on the same network, and smaller if they subscribe to different networks. Similarly the value of communications between a pair of users will be higher if they subscribe to the same network. In other words, q ( pii ) > q ( pij ) and vii > v ij . In the rest of paper, we let ∆v = v (c ) − v(η c) . We next simplify problem (P2) to (P4) by substituting in the results of equation (8). (P4)
Max π i = Nσ i Fi ; Fi
where σ i =
θ i Ψ − θ k n∆v − θ k ( Fi − F j ) Ψ − 2θ k n∆v
, (i,j=a,b, i≠j).
(9)
We solve the equilibrium fixed fees from the first-order conditions in Appendix 1.
Fi* =
1 + θi Ψ − n∆v , (i=a,b). 3θ k
(10)
We summarize the equilibrium results in the following proposition.
Proposition 1: Networks’ equilibrium variable fees are equal to the marginal costs. The fixed fees are given by Equation (10).
We now discuss the results for the equilibrium fixed fees. First, the network that has a larger current user base tends to charge a higher fixed fee. By lowering the fixed fee, on the one hand, a 18
network is able to attract more users (by retaining some customers with small switching costs or attracting the competitor’s customers). On the other hand, the network extracts lower profits from its loyal users (those with high switching costs). Since network a has more loyal customers than network b, it costs more for network a than for network b to lower the fixed fee. Consequently the larger network is more interested in exploiting loyal consumers’ switching costs, but has less incentive to attract non-loyal users. From Equation (10) we can obtain the difference between the competing networks’ fixed fees.
Fa* − Fb* =
θ a −θ b Ψ 3θ k
(11)
Equation (11) shows that the difference between the two networks’ fixed fees is smaller if network a loses its market share at equilibrium than if network b loses market share. This is because network a is larger and hence the demand is more elastic to the price change. As illustrated in Figure 3, OG is higher than OL. Second, equation (10) shows that the equilibrium fixed fees increase with the switching cost. With larger switching costs, consumers (hence the demand functions) are less price sensitive. Thus, networks are able to charge higher fixed fees without losing much market share. As both networks’ fixed fees increase with the switching costs, as shown by equation (11), the difference between two networks’ fixed fees also increases with the switching costs. Finally, the equilibrium fixed fees will be lower if the value of the on-net discounts, n∆v , is higher. When the on-net price discounts provide a higher value, having additional subscribers to a network can enhance the value of their subscription significantly. The effect of a network’s fixed fee on its market share is two- fold. A lower fixed fee reduces a subscriber’s payment. In addition, as the lowered fixed fee attracts more subscribers, it increases the ir opportunities to enjoy on-net price discounts. The latter (indirect) effect becomes more significant in consumers’ network choice decisions when n∆v is higher. Therefore, with larger n∆v , the networks’ market shares become more sensitive to their fixed fees. Consequently, the equilibrium fixed fees will be lower.
4.2. Equilibrium Market Share To obtain the networks’ equilibrium market shares, we substitute the equilibrium fixed fees (10) into the market share function (9).
19
1 +θ i σi =
3 Ψ − θ k n∆v , (i=a,b). Ψ − 2θ k n∆v
(12)
Equation (12) indicates how the size of a network’s current customer base affects the network’s future market share. Specifically, we can infer from equation (12) that, σ a −σ b =
θ a − θb Ψ . 3 Ψ − 2θ k n∆v
(13)
Clearly, the assumption of θ a > θ b leads to σ a ≥ σ b . As a special case where the interconnection cost is equal to zero (η=1), equation (12) shows that network a’s market share decreases from θ a to (2θ a + θ b ) 3 and network b’s market share increases from θ b to (θ a + 2θ b ) 3 . Network a becomes smaller because it charges a higher fixed fee to exploit the switching costs of its current customers. If we project the dynamics of the the networks’ market shares by repeating such a single-period game, we would anticipate that eventually the two networks’ market shares converge and become equal. The same market dynamics were obtained in Beggs and Klemperer (1992). However, with a positive interconnection cost, equation (13) shows that σ a − σ b exceeds (θ a - θ b ) 3 and increases with n∆v . As discussed earlier, if a consumer subscribes to the large network, the consumer will have a bigger proportion of his social network within the same network and therefore enjoy a greater amount of on- net price discounts. The difference in the amount of discounts offered by competing networks is proportional to n∆v . Therefore, as shown in equation (13), the large network (a) enjoys greater competitive advantage when consumers have larger communication networks (n) or when the interconnection cost (η) is high. When the benefit of on- net price discounts is sufficiently large, σ a − σ b can be even larger than θ a - θ b . In that case, the large network actually gains market share from the small network even though the large network charges a higher fixed fee. This result can lead to a change of market shares completely different from that projected in the current literature (e.g. Farrell and Shapiro 1988, Beggs and Klemperer 1992, Nilssen 1992, To 1996). We now investigate whether the outcomes discussed above can be found in the pure strategy equilibrium. Recall that we designate network k as the network whose market share declines, i.e. θ k ≥ σ *k . In Appendix 1, we substitute the equilibrium market shares given by
20
equation (12) into the condition σ i ≤ θ i
and identify the following conditions. If
2 θ b < Ψ n∆v < 3θ b , there exists a pure strategy equilibrium where σ a > θ a . If Ψ n∆v > 3θ a , *
there exists a pure strategy equilibrium where σ a ≤ θ a . Note that the ratio Ψ n∆v measures the *
relative size of the switching costs compared with the consumer valuation of on- net price discounts. The ratio decreases with the value of the network-based price discounts but increases with the consumer switching costs. When Ψ n∆v < 3θ b , the value of on- net discounts is sufficiently high that there exists a pure strategy equilibrium where the large network gains market share. On the other hand, when Ψ n∆v > 3θ a , the value of on-net discounts is small enough that the large network loses market share. In this case, the two networks’ market shares are expected to converge to become equal. We summarize the above results in Proposition 2.
Proposition 2: When Ψ n∆v < 3θ b , there exists a pure strategy equilibrium where σ a > θ a . When *
Ψ n∆v > 3θ a , there exists a pure strategy equilibrium where σ a ≤ θ a . *
Proposition 2 reiterates the two contrasting effects of the networks’ current market shares on their future market shares. On the one hand, the large network charges a high fixed fee to exploit their current customers’ switching costs. On the other hand, the large network offers greater opportunities to enjoy network-based price discounts. The consumers have to compare the benefits from network-based price discounts with the cost due to high fixed fees. When the cost of high fixed fees dominates in the consumers’ network choice decisions, some consumers switch from the large network to the small network, narrowing the gap between two networks’ market shares. When the value of on- net discounts is sufficiently large, some consumers switch from the small to the large network, even though they have to pay high fixed fees. In this case, the difference between the two networks’ market shares will grow. Relatively speaking, when the on- net price discounts become more valuable, the ratio Ψ n∆v is smaller. Thus, the large network obtains a larger market share when consumers have bigger personal communicatio n networks or smaller switching costs.
21
4.3. A Reduction of Switching Costs We now study how the equilibrium results would change with a reduction of the consumer switching costs achieved through the implementation of WNP. We first discuss the changes of the equilibrium prices and market shares. Second, we analyze the changes in the consumers’ service valuations. Finally, we discuss the implications on the total fixed fees that consumers pay to the networks and the networks’ profits.
Implications on Equilibrium Prices and Market Shares According to equation (10), both networks’ equilibrium fixed fees increase with the switching costs. Therefore, a reduction of switching costs due to number portability should lower the fixed fees charged by the competing networks. Moreover, from equation (11) we can further infer that the difference between the fixed fees charged by the two competing networks will also be reduced. These results are consistent with the observations we obtained from the Hong Kong market. With a reduction of consumers’ switching costs, WNP decreases the ratio Ψ n∆v and thus increases the weight of on-net price discounts in the consumers’ network choice decisions. Since the consumers are more likely to enjoy on-net price discounts within the large network, subscription to the large network becomes more attractive. Therefore, the implementation of WNP should increase large network’s market share. Following Proposition 2, with a sudden reduction of switching costs, the ratio Ψ n∆v may become so small that the benefit of larger onnet price discounts dominates the cost of paying a higher fixed fee to the large network. In that case, some consumers will switch from the small network to the large network and the market shares exhibit a divergent pattern such as we observed in the Hong Kong market. Imagine a scenario where Ψ > 3θ a n∆v before WNP, but Ψ < 3θ b n∆v after the WNP, then the implementation of WNP can dramatically change the dynamics of market structure from a convergent trend to a divergent trend. We summarize the above results in Proposition 3.
Proposition 3 By reducing consumers’ switching costs, WNP can decrease both networks’ equilibrium fixed fees, and increase the large network’s market share. If WNP reduces switching costs to
22
Ψ < 3θ b n∆v , then WNP will further widen the gap between the competing networks’ market shares.
Implications on Total Service Valuations Since WNP affects the equilibrium prices and market shares, WNP should affect consumers’ service valuations too. Recall that, following a uniform calling pattern, a subscriber to network i expects the value of communications to be nσ iv( c ) + nσ j v( ηc ) . To obtain the total value of communications, we aggregate this amount over the entire market and substitute in the equilibrium market shares. N ∑ σ i [nσ iv( c ) + n( 1 − σ i )v( ηc )] = Nn[v( c ) − 2 ∆vσ aσ b ] .
(14)
i = a ,b
Equation (14) shows that the total value of communications decreases with σ aσ b . Since σ a ≥ σ b and σ a + σ b =1, we can conclude that σ aσ b decreases with σ a . According to Proposition 3, a reduction of switching costs due to WNP would increase network a’s market share and hence decrease the value of σ aσ b . Therefore, a reduction of switching costs through WNP can increase total consumer valuations for the communications. Essentially, with a bigger difference between two networks’ market shares, overall, consumers are more likely to enjoy the network-based price discounts and therefore hold higher valuations for the communication service.
Proposition 4. By reducing consumers’ switching costs, WNP can increase consumers’ total service valuations.
Implications on Total Fixed Fees and Networks’ Profits Proposition 3 shows two contrasting effects that WNP has on the total fixed fees consumers pay. On the one hand, a reduction of switching costs decreases both networks’ fixed fees. On the other hand, the large network increases its market share. Since the large network charges a higher fixed fee than the small network, an increased market share for the large network means that more consumers will subscribe to the large network and pay the high fixed fees. To examine
23
the overall effect of WNP on total fixed fees, we aggregate the fixed fees over all the subscribers to the two networks.
1 + θ aσ a + θ bσ b (1 + θ b ) + (θ a − θ b )σ a N ∑ σ i Fi = N Ψ − n∆v = N Ψ − n∆v 3θ k 3θ k i = a ,b
(15)
Our analysis in Appendix 1 shows that, with a reduction of switching costs, the total fixed access fees will be lower. Therefore, the first effect that WNP would reduce both networks’ fixed fees dominates the second effect that more consumers subscribe to the larger network and hence pay the (relatively) higher access fee. The implication of this result is that, overall, the consumers pay a smaller amount of fixed access fees for their network subscriptions.
Proposition 5. By reducing consumers’ switching costs, WNP can decrease the total fixed fees that consumers pay to the networks.
Proposition 5 also implies that industry- level profits should decrease with the reduction of consumer switching costs through the implementation of WNP. Since the equilibrium variable fees are equal to the marginal costs, the networks earn their profits only from the fixed access fees. Therefore, the networks’ total profits from the service are the total fixed access fees that consumers pay. With the reduction of switching costs through WNP, on the one hand, both networks reduce their fixed access fees. On the other hand, the large network, which charges a higher fixed fee than the small network, attracts more customers to its network. The results of Proposition 5 shows that the first effect dominates the second. One of the stated objectives for WNP was to facilitate the growth of small networks. Therefore, it is useful to examine the impact of WNP on the small network (b)’s profit. π b = Nσ b Fb =N
( 1 + θ b )Ψ 3 − θ k n∆v 1 + θ b Ψ − n∆v , Ψ − 2θ k n∆v 3θ k
(16)
where k=a if Ψ / n∆v > 3θ a ; k=b if 2θ b < Ψ n∆v < 3θ b . In equation (16), with a reduction of consumer switching cost, both the small network’s fixed access fee and its market share decrease. Thus, a reduction of switching costs through WNP
24
should always lower the profits of the small network. 11 Summarizing the above analysis, we can conclude that, with a sudden reduction in switching costs, the small network not only lowers its fixed access fee but also suffers a reduction of its market share, leading to a sharp decrease in the small network’s profits. Again, the reason behind this result is that WNP increases the importance of the network-based price discounts and decreases the importance of switching costs in consumers’ network choice decisions. This result clearly indicates that WNP will reduce a small network’s profits and weaken the small firm’s chance of survival. Since the operation of business requires a substantial amount of expenses in maintaining communication facilities and service employees, a reduced switching cost can make it more difficult for the small networks to breakeven. A special case of interest is the impact of WNP on the ease of entry to the market by the new operators. In this case, we have θ a = 1 and θ b = 0 . We can solve the fixed access fee and market share according to equation (10) and (12). Fb* =
1 Ψ − n∆ v ; 3
(17)
σb =
1 Ψ − 3n∆v . 3 Ψ − 2n∆ v
(18)
In order for the entry to be profitable, both the fixed fee of equation (17) and market share of equation (18) need to be positive and large enough to cover the initial entry costs. The conditions indicate that the switching cost needs to be sufficiently large that at least the fixed fee, Fb* =
1 Ψ − n∆v , is positive. When the switching cost is reduced below this level, the new 3
operator will not find the entry profitable. Clearly, a reduction of switching costs through WNP makes market entry less likely to be profitable.
Proposition 6. By reducing consumers’ switching costs, WNP will decrease the total industry profits and makes it more difficult for the small network to survive.
11
The result holds true when the switching cost decreases from Ψ > 3θ a n∆v to a switching cost of Ψ’< 3θ b n∆v . In
this case, the small network (b)’s equilibrium market share decreases from a value above θ b to a value below θ b .
25
5. Discussions In this section, we discuss the sensitivity of our results to the two modelling assumptions. First, we assumed that both networks implement the network-based discriminatory pricing schemes. We show in Section 5.1 that our results still hold even if the firms cannot price discriminate according to the callers’ network locations. Second, we did not consider the arrival of new users who do not have switching costs. In Section 5.2 we discuss the implications to our results of including a segment of new users.
5.1. Absence of Netwo rk-based Price Discounts According to Proposition 1, it is optimal for both networks to adopt the network-based discriminatory pricing schemes. In equilibrium, both networks charge variable fees equal to their marginal costs. By allowing the firms to adopt such a pricing mechanism, we are able to achieve a closed- form solution that explicitly demonstrates the network size benefit. However, since implementing such a pricing scheme requires additional information management, networks may need to incur extra costs in the implementation. These extra costs could be sufficiently large to prevent the firm from implementing the network-based price discrimination. As a result, the networks have to charge identical variable fees for the communications both within and across the networks. To examine the implications, we analyze, in Appendix 2, the network price competition without network-based price discrimination. We find that, with the absence of network-based price discrimination, the large network (a) can still gain market share from the small network when the switching cost is sufficiently small, specifically, Ψ < θ n(η c − c)[ q ( p* ) + q ( p* ) + q ( ~ p )] , b
a
b
(19)
where p a and p b are firm a and b’s equilibrium variable prices, respectively. Price ~ p is a price defined in Appendix 2 and its value is between p a and p b . The properties of condition (19) appears similar to the condition Ψ n∆v < 3θ b given in Proposition 2. Specifically, the large firm’s equilibrium market share increases with the interconnection costs and the size of an individual’s social communication network, but decreases with the consumer switching costs. In conclusion, with or without network-based price discrimination, the reduction of switching costs In addition, since θ a Ψ < θ b Ψ ′ , the small network’s fixed access fee will be lower with the reduction of switching costs, both directions reducing the small network (b)’s profits.
26
would increase the large network’s market share. The large network can even gain market share from the small network if the switching costs are reduced to a sufficiently low level.
Proposition 7. Without network -based price discrimination, by reducing consumer switching costs, WNP can still increase the large network’s market share. The large network gains market share from the small network if Ψ < θ b n(ηc − c )[ q( p*a ) + q ( p*b ) + q( ~ p )] .
Proposition 7 indicates that, with the absence of network-based price discounts, the large network still enjoys a size benefit in competition. However, the large firm benefits from the consumer switching costs in a very different way. Without the network-based price discounts, each firm charges one variable fee for all the communications regardless of the callers’ locations. The large network’s average variable cost is lower than that of the small network. Specifically, the average variable cost is n (σ ac + σ bηc ) for network a and n (σ aηc + σ b c ) for network b. Interestingly, with positive interconnection costs and without network-based price discounts, the network size benefit is transformed into the large network’s cost advantage.
5.2. New Users without Switching Costs In our model, we assume that all consumers were users of the existing networks. As a result, they incur switching costs when changing their suppliers. In many markets, especially those markets with significant growth, there is a segment of new users who do not have switching costs. Studies on such a market with switching costs show that the firm with more existing customers tends to charge a higher price to exploit the customers’ switching costs and consequently attracts less new users (e.g. Klemperer 1987a and 1987b, Farrell and Shapiro 1988, Beggs and Klemperer 1992.). To extend our model, we can adopt an approach similar to that of Klemperer (1987b) by adding a mass of consumers with zero switching costs to the current uniform distribution. We can interpret the mass with zero switching costs as the size of the new segment. We next discuss the expected results from such an extension. (We do not explicitly solve the problem. In fact, such a model may not have a pure strategy equilibrium.) First, since the average consumer switching cost is lower with more new users, the equilibrium prices should decrease with the size of the new segment. Second, as long as the new segment is not too big, we expect the same 27
qualitative implications of our propositions 1 – 7 to hold. With positive interconnection costs, the networks are still expected to practice network-based discriminatory pricing and hence subscription to the large network means more opportunity to enjoy the on- net price discounts. With a reduction of switching costs, the difference between networks’ fixed fees becomes smaller and then the new users will find the subscription to the large network more attractive. If the switching costs are sufficiently small relative to the value of on-net price discounts, the new users will join the large network and make the large network even larger. Finally, as the new segment becomes larger, the network size effect diminishes. With a larger new segment, firms pay more attention to the new customers and less attention to the existing users. In addition, the value of on- net price discounts becomes closer as the relative difference between networks’ sizes and the consumer switching costs (weighted by the segment size) decreases. In an extreme case, if all the consumers are new arrivals, there are no switching costs and the market price will be drive n to the marginal costs.
6. Conclusion Wireless Number Portability (WNP) is a policy that has been implemented, or is under consideration, in many countries in order to reduce consumer switching costs. Since the existence of switching costs locks in the consumers to their current suppliers, the incumbent firms can charge higher prices to exploit consumer loyalty, but the new entrants may find it difficult to attract consumers away from their current suppliers. It is then believed that, by reducing consumers’ switching costs, WNP will intensify price competition and facilitate the growth of small or new networks. In this paper we present the observations of the Hong Kong market where WNP was implemented in March 1999. We find sharp price decreases as expected, but a divergent trend between networks in their market shares. The observations raise questions as to why a sudden reduction in switching costs through WNP should lead to such unexpected trends. Our analysis shows that the outcome s observed in the Hong Kong market can be a result of the network interconnection costs. When networks have positive interconnection costs, the marginal cost is lower for on-net calls than off- net calls. If the firms can price discriminately according to the callers’ network locations, then the equilibrium variable fees for the on-net calls will be lower than the variable fees for the off- net calls. As a result, by subscribing to the large
28
network, a consumer can enjoy more on-net price discounts. Comparing the value of the subscription to the firms, we see that on the one hand, the large network charges a higher fixed access fee to exploit its customers’ switching costs. On the other hand, the large network provides its customers with more opportunity to enjoy on- net price discounts and hence a higher value of communication service. Given the size of interconnection costs, when the switching costs are high, the large network charges a very high fixed fee and loses some market share to the small network. When the switching costs are low, the large network charges a fixed fee closer to its competitor and gains market share from the small network. Therefore, a reduction of switching costs through WNP can make the large network compete more fiercely on price and attract more consumers with its advantage of offering more on-net price discounts. In this scenario, a sudden reduction of switching costs could accelerate the process for the large network to overtake the small network. We have also examined the implications of the reduction of switching costs due to WNP on consumers’ service valuations and firms’ profits. Since the reduction of switching costs increases the large network’s market share, overall, more consumers subscribe to the same network and can therefore enjoy more on- net price discounts. As a result, the consumers obtain higher values from the communication services. We also find that the reduction of switching costs decreases total fixed fees paid by the consumers. Therefore, overall consumer surplus increases with the reduction of switching costs through WNP. However, one should treat such a positive impact with caution because it may not be sustained in the long run. With reduced switching costs, we find that the small networks lose market share and their operations become much less profitable. If the market share gap continues to expand in a highly penetrated market like Hong Kong, smaller firms may eventually have to exit the market. If the market consolidates and only large operators prevail, then the prices may go up again as a consequence of the more concentrated market structure. In such a scenario, the resulting increase of market concentration may defeat the original purpose of implementing WNP. It thus suggests that regulators in those highly penetrated markets should take extra caution in implementing such policies as WNP to induce additional competition. In a recent response to the widely speculated merger talks between Sunday and New World Mobility, the director of Hong Kong OFTA anticipated the emergence of more merger proposals. Interestingly, while stressing the need to maintain the level
29
of competition, the director mentioned the low tariffs in Hong Kong and showed a rather positive attitude towards such merger proposals (Chan 2001). This paper can be extended in a number of directions. One direction is to expand the firms’ strategy space in response to the reduction of switching costs. For example, in this paper we focus on the networks’ competition in basic mobile phone service. One extension is to examine the firms’ strategies in the development and pricing of value added service. In this extension, one also can study the impact of reduced switching costs through WNP on related equilibrium marketing strategies. Another extension is to study bundling pricing for the handsets and phone service. Research has shown that price decisions for communication service and handsets should be integrated (Jain, Muller and Vilcassim 1999). A study of the price bundles should provide a more complete picture for the impact of WNP on the networks’ pricing strategies. Another direction is to study other implications of WNP besides reducing switching costs. For example, while WNP is intended to reduce consumers’ switching costs, the implementation may also have implications for the interconnection costs. Bernardi and Nuijten (2000) state that the implementation can increase the interconnection costs for individual calls. The additional cost includes incremental operating costs of additional switching processes, switching paths and transmission links associated with WNP.12 For example, WNP could be implemented by a “call forwarding” method that forwards all the calls first to a central database to search for the identity of callers before connecting to the other end. The additional conveyance cost leads to extra interconnection costs. Since the equilibrium variable fees are equal to the marginal costs, the extra interconnection charges due to WNP may increase the network-based price discounts. Therefore, like a reduction of switching costs, an increased interconnection cost also leads to a smaller value for the ratio Ψ n∆v . Consequently, if the implementation of WNP increases the interconnection cost, we can infer such implications on the equilibrium results as the lowering of the fixed fees, and the increasing of the large network’s market share. The results stated in our propositions about the impact of reduced switching costs due to NP will all be strengthened.
12
Technical details on the implementation of WNP are available in the consultation reports of the telecommunication authorities, e.g., NERA (1999) report for Hong Kong Telecommunication Authority and the Bernardi and Nuijten (2000) report for the European Telecommunication Office.
30
Appendix 1. Equilibrium Results with Network-based Discounts Variable Fees (P3)
[
Max π i = Nσ i nσ i ( pii − c )q ( pii ) + nσ j ( pij − ηc )q ( p ij ) + Fi
(Fi , pii , pij )
such that nσ i vii + nσ j v ij − Fi = wi , (i≠j, i,j = a or b).
] (7)
Rewrite equation (7) as Fi = nσ i v ii + nσ j vij − wi . Substituting the fixed fee into network i’s objective function and taking the first-order conditions with respect to the on- and off- net prices. ∂π ( σ i ) = 0 , then q( p ii ) + ( pii − c )q ′( pii ) + v ′( pii ) = 0 . ∂p ii
(A1)
∂π i ( σ i ) = 0 , then q( p ij ) + ( p ij − ηc )q′( p ij ) + v ′( pij ) = 0 . ∂p ij
(A2)
i
By Roy’s identity, q( p ii ) + v ′( pii ) = 0 and q( p ij ) + v ′( pij ) = 0 are the solutions to problem (P1). Then the equations (A1) and (A2) become: p ii = c ,
(A3)
p ij = η c .
(A4)
Fixed Fee Max π i = Nσ i Fi ;
(P4)
Fi
where σ i =
θ i Ψ − θ k n∆v − θ k ( Fi − F j ) Ψ − 2θ k n∆v
, i,j=a,b,and i≠j.
(9)
Taking the first-order conditions with respect to the fixed fees, θ i Ψ − θ k n∆v − θ k ( 2 Fi − F j ) ∂π i =N = 0 , where i,j=a,b, and i≠j. ∂Fi Ψ − 2θ k n∆v
(A5)
Solving the above first-order conditions, we have
Fi* =
1 + θi Ψ − n∆v , where i=a,b. 3θ k
(A6)
Market Shares
31
Substituting the fixed fees at (A6) into equation (9), we obtain the equilibrium market shares:
1 +θ i
3 Ψ − θ k n∆v , where i=a,b. Ψ − 2θ k n∆v
σi =
(A7)
The above market share equations need to satisfy 1≥ σ a ≥0.5≥ σ b ≥0. Given 1≥ θ a ≥0.5≥ θ b ≥0, we find that condition (A7) is equivalent to Ψ>
3 θ a n∆ v . 1+ θ b
(A8)
We assume that (A8) holds for analytical convenience. This condition requires that the maximum switching cost is large enough that each network will have a positive market share at equilibrium. To ensure that the first-order conditions (A5) define the networks’ optimal strategies, it is necessary and sufficient that
2 Nθ k ∂ 2π i =− 0 . 3
Since 1≥ θ a ≥0.5≥ θ b ≥0, if k=a, 2θ a ≥1 then Ψ > 3θ a n∆v ;and if k=b, 2 θ b 3θ a n∆v , there exists an equilibrium that k=a (σ a < θ a ); *
(II). If 3θ b n∆v > Ψ >
3 * θ a n∆v , there exists an equilibrium that k=b ( σ b < θ b ). 1 + θb
Appendix 2. Equilibrium Results without Network-based Discounts
32
Without network-based price discounts, network i’s price is a two-part tariff { Fi , p i }. The network’s problem can be formulated as follows: (Supposing that network k loses market share at equilibrium.)
[
Max π i = Nσ i nσ i ( pi − c )q( pi ) + nσ j ( p i − ηc )q( pi ) + Fi
(P5)
pi ,Fi
]
where σ i = θ i + ( wi − w j )θ k / Ψ = θ i + [nv( p i ) − nv( p j ) − Fi + F j ]θ k / Ψ
Variable Fees (P6)
(A10)
[
Max π i = N σ i nσ i ( p i − c )q( pi ) + nσ j ( pi − ηc )q( pi ) + Fi p i ,Fi
]
such that nv( p i ) − Fi = wi , (i≠j, i,j = a or b).
(A11)
Rewriting equation (A11) as Fi = nv( pi ) − wi , and substituting the fixed fee into network i’s objective function and taking the first-order conditions with respect to the variable fee.
[
]
∂π i ( σ i ) = 0 , then nq( p i ) + nσ i ( p i − c ) + nσ j ( pi − ηc ) q ′( pi ) + nv ′( pi ) = 0 . (A12) ∂p i
By Roy’s identity, nq( p i ) + nv ′( pi ) = 0 . Then equation (A11) becomes: p i = σ i c + σ jηc .
(A13)
Fixed Fee Using equation (A13), problem (P5) can be reformulated as follows. (P7)
Max π i = Nσ i Fi ; Fi
where σ i = θ i + [ nv( p i ) − nv( p j ) − Fi + F j ]θ k / Ψ .
(A10)
Taking the first-order derivative with respect to the fixed fee against (A10). ∂σ i θ k = nv ′( pi ∂Fi Ψ
∂σ ∂σ ) c i − ηc i ∂Fi ∂Fi
− nv ′( p j
∂σ ∂σ ) − c i + ηc i ∂Fi ∂Fi
− 1 .
From above equation and using Roy’s Identity, we can derive the first-order derivative as follows.
33
∂σ i θ nθ = − k Γ , where Γ = 1 − k (ηc − c )(q ( p a ) + q ( p b ) ) and i=a,b. ∂Fi Ψ Ψ Since
(A14)
∂σ i < 0 , it is necessary that ∂Fi
Γ =1−
nθ k (ηc − c )(q ( p a ) + q ( p b ) ) >0. Ψ
(A15)
To obtain the fixed fees, we take the first-order condition with respect to the fixed fees.
∂π i ∂σ i = N σ i + F = 0 , where i=a, b. ∂Fi ∂Fi i
(A16)
Substituting equations (A10) and (A14) into equation (A16), and then taking the difference between two firms’ first order conditions, we obtain the difference between the two networks’ fixed fees.
Fa − Fb =
Ψ( θ a − θ b ) / θ k + 2 n[ v( p a ) − v( pb )] . 2 +1 Γ
(A17)
Market Shares Substituting the difference between the fixed fees of (A17) into equation (A10), we obtain the market shares:
σ i − θi =
nθ k [ v( pi ) − v( p j )] 1 − (θ i − θ j ) + Γ , where i,j=a,b. 2 +1 Γ Ψ
(A18)
Taking the difference between two networks’ market shares as given by (A18), we have: 2nθ k [v ( p a ) − v( pb )] 1 − 2(θ a − θ b ) + Γ 2 +1 Γ Ψ Using the mean value theorem and Roy’s Identity, there exists ~ p ∈ ( p a , p b ) such that σ a − σ b = θ a − θb +
(A19)
v ( p a ) − v( pb ) = v′( ~p )( p a − pb ) = − q( ~p )[(σ a c + σ bηc) − (σ b c + σ aηc )] = (σ a - σ b )(ηc − c )q ( ~p) Substituting (A20) into (A19), we can obtain the following: σa −σb 2θ n (ηc − c)[ v( p a ) + v ( pb ) + v( ~p )] =1 3+ k θ a −θ b Ψ
(A20)
(A21)
From (A21), we conclude that network a increases its share ( σ a − σ b > θ a − θ b ) if Ψ < θ k n(ηc − c )[ q( p a ) + q( pb ) + q ( ~ p )] .
(A22)
34
References Armstrong, Mark (1997), “Competition in Telecommunications,” Oxford Review of Economic Policy, Vol. 13, No. 1, 64-82. Armstrong, Mark, Doyle, Chris, and John Vickers (1996), “The Access Pricing Problem: A Synthesis,” Journal of Industrial Economics, Volume XLIV, No. 2, pp. 131-150. Australian Communications Authority (ACA) report, Implementation Date for Mobile Number Portability in Australia: A Preliminary View, March 2000. Beggs, Alan and Paul Klemperer (1992), “Multi-period Competition with Switching Costs,” Econometrica, Vol. 60, No. 3, 651-666. Bernardi, Marco and Jack Nuijten (2000), “Number Portability for Mobile Network,” report prepared for the European Telecommunication Office. Cellular Telecommunications Industry Association (CTIA), In the Matter of Telephone Number Portability, August 1998. Chan, Karen (2001), “Operators Deny Moves to Merge,” Hong Kong iMail, Dec. 12, P 1. Dolan, Robert J. (1987), “Quantity Discounts: Managerial Issues and Research Opportunities,” Marketing Science, Vol. 6, No. 1, pp. 1-22. Farrell, Joseph and Carl Shapiro (1988), “Dynamic Competition with Switching Costs,” Rand Journal of Economics, Volume 19, No. 1, pp. 123-137. Federal Communications Commission Report No. WT99-1, FCC Grants Forbearance of Local Number Portability For Wireless Carrier, February 8, 1999. Hong Kong Telecommunication Authority (HKTA) report, “Feasibility Study & Cost Benefit Analysis of Number Portability for Mobile Services in Hong Kong,” Consultation conducted by NERA and Smith System Engineering, May 1999. Hong Kong Telecommunication Authority (HKTA) statement, Charges for Interconnection between Public Mobile Radiotelephone Service (PMRS), Personal Communication Services (PCS) and Value Added Services (VAS) and the Public Switched Telephone Network (PSTN), May 15, 1998. Hong Kong Telecommunication Authority (HKTA) report, Implementation of Number Portability in Hong Kong SAR, September 1999. Jain, D., Muller, E. and N. J. Vilcassim (1999), “Pricing Patterns of Cellular Phones and Phones and Phonecalls: A Segment-level Analysis,” Management Science, 45, 2, 131-141. Klemperer, Paul (1987a), “The Competitiveness of Markets with Switching Costs,” Rand Journal of Economics, 18, 138-150. Klemperer, Paul (1987b), “Markets with Consumer Switching Costs,” Quarterly Journal of Economics, 102, 375-394. Klemperer, Paul (1987c), “Entry Deterrence in Markets with Consumer Switching Costs,” Economic Journal, 97, 99-117. Klemperer, Paul (1988), “Welfare Effects of Entry into Markets with Switching Costs,” Journal of Industrial Economics, 37, 159-165. Klemperer, Paul (1995), “Competition When Consumers Have Switching Costs: An Overview with Applications to Industrial Organization, Macroeconomics, and International Trade,” Review of Economics Studies, 62, 515-539. Kwok, Ben (2002), “Sunday Backs Consolidation But Denies Talks on Merger,” South China Morning Post, Hong Kong, July 9, P 4. Laffont, Jean-Jacques, Rey, Patrick, and Jean Tirole (1998a), “Network Competition I: Overview and Nondiscriminatory Pricing,” Rand Journal of Economics, Vol. 29, No.1, pp.1-37.
35
Laffont, Jean-Jacques, Rey, Patrick, and Jean Tirole (1998b), “Network Competition II: Price Discrimination,” Rand Journal of Economics, Vol. 29, No.1, pp.38-56. Ling, Connie (2001), “Imminent Wave of Consolidation Appears Headed for Teeming Asian Telecom Market,” Wall Street Journal, East Edition, Oct 30, B11. Mason, Charles (1999), “The Burden of Number Portability,” America’s Network, August 1, Vol. 13, Issue 12, pp. 58-60. Nilssen, Tore (1992), “Two Kinds of Consumer Switching Cost,” Rand Journal of Economics, Vol. 23, No. 4, 579-589. Tirole, Jean (1988), The Theory of Industrial Organization, MIT Press. To, Theodore (1996), “Multi-period Competition with Switching Costs: An Overlapping Generations Formulation,” The Journal of Industrial Economics, Vol. XLIV, No. 1, 81-87.
36
