An economic analysis of the receiver pays principleweb.khu.ac.kr/~jyookim/paper/rpp.pdf · An economic analysis of the receiver pays principle ... 800-number services are other examples

Information Economics and Policy 13 (2001) 231–260www.elsevier.nl / locate /econbase

An economic analysis of the receiver pays principlea , bJeong-Yoo Kim *, Yoonsung Lim

aDepartment of Economics, Dongguk University, 3-26, Pildong, Chungku, Seoul 100-715,South Korea

bDepartment of Economics, Dongguk Women’s University, Seoul, South Korea

Received 29 August 2000; received in revised form 3 January 2001; accepted 3 January 2001

Abstract

This paper examines the effect of the receiver pays principle (RPP) on the calling price,social welfare and interconnection charge. A significant difficulty with introducing thissystem in telecommunications pricing is the possibility that the receiving party may refuseto receive a call if the charge he has to bear is very high. We find the condition under whichno calls are refused and show that the profit maximizing prices charged to the calling partyand the receiving party must satisfy this condition. We demonstrate that the calling priceunder RPP must be lower than the price under the caller pays principle (CPP), that the profitof a firm will be increased under RPP, but that the consumer surplus will not necessarily beincreased under RPP despite the lowered calling price. Also, we show that, if the demandfunction is linear, the reciprocal interconnection charge under RPP is higher than that underCPP. 2001 Elsevier Science B.V. All rights reserved.

Keywords: Caller pays principle; Receiver pays principle; Interconnection charge

JEL Classification: D11

1. Introduction

The most striking characteristics of the telecommunications industry might bethe presence of two kinds of externalities, network externalities and call exter-nalities. Network externalities result from the fact that a subscriber to a network ismade better off by being able to communicate with more people if more people

*Corresponding author. Tel.: 182-2-2260-3716; fax: 182-2-2260-3716.E-mail address: [email protected] (J.-Y. Kim).

0167-6245/01/$ – see front matter 2001 Elsevier Science B.V. All rights reserved.PI I : S0167-6245( 01 )00036-1

232 J.-Y. Kim, Y. Lim / Information Economics and Policy 13 (2001) 231 –260

subscribe to the network. Call externalities occur since both the calling party andthe receiving party may benefit from a phone call, even though the cost usuallyfalls entirely on the caller. Therefore, call externalities are the product of aparticular usage fee payment system, the so-called the caller pays principle (CPP)under which the caller only is charged for a call, while network externalites are acharacteristic inherent in the telecommunications industry.

Then, a natural question arises: why is CPP is being used instead of the receiverpays principle (RPP) under which the receiving party is charged in part for a call

1as well, given the obvious free-riding of the receiving parties? The traditionalrationale for this apparent unfairness is that, even if the receiver is bound to bear apart of the calling charge, the reduced amount of fees for a person in calling andthe additional amount of fees to bear in receiving are almost averaged out, if thecalling ratio and the receiving ratio are similar, so that CPP is equivalent to RPP.Furthermore, if we take into account technical difficulties and administration costsinvolved with collecting charges from the receivers as well, it seems that there is

2no reason to use RPP instead of CPP. However, in fact, this is true only in arestricted sense. First of all, there currently coexist several networks inter-connected to each other, say the Public Switched Telephone Network (PSTN) and

3mobile networks, whose call traffic patterns are asymmetric. In most countries, alarge proportion of calls originating from a mobile network terminate on the PSTNand only a small proportion of calls made on the PSTN terminate on mobilenetworks. This implies that subscribers to mobile networks subsidize subscribersto the PSTN. This observation weakens the strong rationale that has justified CPPand favours an alternative fee system whereby the receiver pays for part of aphone call. Moreover, even in a situation where there is no mobile network, andasymmetry in calling patterns is not significant, internalization of call externalitiesby dividing a calling charge between the caller and the receiver would lower thecalling price, thereby increasing calling, which would obviously affect socialwelfare.

1 Recently, the use of RPP is observed in some restricted situations. In particular, the US and someother countries (e.g., Hong Kong) have adopted RPP in mobile call pricing. However, it is well-knownthat this is for a technological reason, rather than for an economic reason. Since mobile serviceproviders do not have distinct network access codes, a consumer cannot tell whether the call he ismaking terminates on the fixed network or on the mobile network. Therefore, it may be consideredunfair to charge the high price of the mobile phone call to a consumer who does not realize whichnetwork he is calling. Collect call services and toll-free, 800-number services are other examples ofRPP.

2 CPP may be a historically established convention. In the past when only the manual or themechanical switching system was feasible, it would have been technically impossible to implementRPP, and so resulting CPP became a long-standing payment system.

3 According to the Ovum report by Joseph and Nourouz (1996), only 33% of all mobile calls in USare incoming. Doyle and Smith (1998) also observe this asymmetric call patterns in the UK market.These observations imply that the balanced calling pattern assumption often used in literature isviolated in reality.

J.-Y. Kim, Y. Lim / Information Economics and Policy 13 (2001) 231 –260 233

Of course, RPP is not the only way to internalize call externalities. Manyinformal mechanisms seem to have a similar effect. For instance, voluntarynegotiations between calling parties may help internalize some call externalities(Coase, 1960). However, Acton and Vogelsang (1990) suspects that suchvoluntary negotiations are highly unlikely (especially for international calls)because negotiations that would lead to internalization themselves require phonecalls. On the other hand, Littlechild (1977) points out that ‘‘friends who talk longdistance regularly can agree to take turns.’’ In other words, he regards callexternalities as not substantial relative to network externalites since they can be

4easily internalized by cooperation between calling parties. However, this argu-ment is based on a repeated relation between the parties. Since a large proportionof telephone communications are accidental, it is hard to expect enough internali-

5zation of call externalites by cooperation.In this paper, we examine the effect of RPP on the calling price, social welfare

and the interconnection charge. A significant difficulty in introducing this systemin telecommunications pricing is the possibility of nuisance calls that give negativeutility to the receivers. However, this may not be a serious problem in a practicalsense. Usually, a receiver can tell whether the call he is receiving is a nuisance ornot within a very short time interval, such as 5–10 s. So, if the receiver is chargedonly after the lapse of 5–10 s from the instant he received the call, this problemwill disappear (even if a small amount of losses to the firm are inevitable).Recently developed services such as selective call blocking, caller line identifica-tion or a voice mail system will also serve to alleviate this problem. Anotherproblem is the possibility that the receiving party may refuse to receive a call if the

6charge he has to bear is unreasonably high. We find the condition under which nocalls are refused and show that the profit maximizing prices charged to the callingparty and the receiving party must satisfy this condition.

Two models are provided in this paper. First, in a simple model with a singlenetwork, we demonstrate that the calling price under RPP must be lower than theprice under CPP. Also, we find some interesting results that the profit of a firm willbe increased under RPP but that consumer surplus will not be necessarilyincreased under RPP despite the lowered calling price. However, it will also beshown that, if the demand for calls has a constant price elasticity, the consumer

4 There may be other reasons why the literature has paid little attention to call externalities. First, itis hard to estimate the value of receiving a call. Also, most of the literature has been concentrated onthe analysis of local calling where the (marginal) price is close to zero (Acton and Vogelsang, 1990).

5 Also, Squire (1973) points out that marginal cost pricing is not efficient in the presence of callexternalities and asserts that the price of calls should be below their marginal costs. This is correct, ofcourse, but it would not be economically feasible to implement such pricing, since the service providerwould lose money unless someone else, say, the government makes up for the losses.

6 Many US mobile subscribers are not willing to give their mobile phone numbers to anyone butclose friends and family because they pay for all the incoming calls they receive. The fact that all callshave to be paid for by the receiving party is viewed as a major barrier to high penetration of mobilephones into the US market.


surplus will be unambiguously increased under RPP. Second, we show that theresults obtained in the model with a single network are all carried over to a generalmodel with two networks in which each network operator charges both the calling

7price and the receiving price for a call originating from the network. Also, wederive some implications of the RPP system on the access pricing. In particular, itis shown that introducing RPP has a negative effect on the interconnection chargein the sense that the reciprocal access charge is higher under RPP than under CPP.

Recently, Laffont and Tirole (2000) independently made an analysis of thereceiver pays principle in an alternative model where the receiving price of a callcan be determined by the operator of the network on which the call terminates.Although this may be a more realistic model, one faces a serious non-convexityproblem in analyzing it. If price discrimination between on-net calls and off-netcalls is allowed, a firm tends to make the receiving price for an off-net call as highas possible. A similar problem can occur even in the case of no price discrimina-

8tion as long as the receiver can refuse to receive calls. Based on this argument,they suggest that the receiving prices be either subject to regulate or determinedcooperatively. Our setup provides another way how to overcome the nonconvexityproblem by alleviating firms’ incentive to increase receiving prices.

To the best of our knowledge, the first paper that deals with the receiver paysprinciple in telecommunications pricing is Doyle and Smith (1998). Their main

9interest, however, lies in the effect of RPP on prices of calls to mobiles. In theirmodel, a mobile service provider sets a total posted price of a fixed to a mobilecall and a mobile subscriber receiving a call from a fixed phone pays the amount

10equal to the total posted price minus the charge paid by the call originator. After

7 To make it possible for a telecommunications service provider to charge the receiving price directlyto the customer of the other network, all carriers are required to release freely information for theircustomers upon request by another carrier, which is ensured by the US Telecommunications Act, 1996.It provides ‘‘each . . . local exchange carrier has the duty to provide, to any requesting telecommunica-tions carrier for the provision of a telecommunications service, nondiscriminatory access to networkelements on an unbundled basis . . . . A local exchange carrier shall provide such unbundled networkelements in a manner that allows requesting carriers to combine such elements in order to provide suchtelecommunications service.’’ (US Telecommunications Act, 1996, section 251, c3) In addition, ‘‘Atelecommunications carrier that receives or obtains proprietary information from another carrier forpurposes of providing any telecommunications service shall use such information only for suchpurpose, and shall not use such information for its own marketing efforts.’’ (the US Telecommunica-tions Act, 1996, section 702, b) Gans and King (2000a) suggests an easier way to implement directcharging with the actual billing being done by the customer’s carrier in return for a billing fee.

8 For detailed analysis, see Laffont and Tirole (2000).9 There had been a great concern expressed by UK customers who felt that the prices of calling to a

mobile phone were unduly high before OFTEL’s investigation into the prices in June 1996 (OFTEL,1998).

10 This mechanism also enables callers to be free from concerns about whether the calls they aremaking terminate on a fixed or mobile network.


all, the price for receiving a call is determined by the mobile service provider towhich the receiver subscribe, which is the main feature that is distinguished fromour model. Also, in order to avoid complexities involved with price discriminationbetween on-net and off-net calls, they assume that all calls made by mobilesubscribers terminate on the fixed network. Moreover, the option of using RPP isavailable only to one firm (mobile service provider) in their model. Our paperimproves their analysis in this respect.

2. A simple model with a single network

There are one firm (or network) supplying telephony services and two11representative subscribers, indexed by i 5 1, 2, calling to each other. We assume

12each call generates positive utility both for the caller and for the receiver. If onlythe caller pays for a call, neither consumer has any reason to refuse to receive anycall made to him as long as it yields positive utility.

Thus, if consumer 1 makes q calls to consumer 2 and consumer 2 makes q1 2

calls to consumer 1, the number of calls consumer 1 (consumer 2) is willing toreceive is the same as q (q , respectively). Both consumers have the same2 1

ipreferences satisfying some regular properties. Denoting by U (q , q ) the utilityi jifunction of consumer i for j ± i, we make the following assumptions on U (q , q ).i j

i iAssumption 1. U (q , q )is additively separable, i.e., U (q , q ) 5 u(q ) 1 v(q ),i j i j i j

j ± i, i 5 1, 2.

Assumption 2. v( ? ) 5uu( ? ), for some u [ (0,1].

Assumption 3. u(0) 5 0, u9( ? ) . 0 and u0( ? ) , 0.

Assumption 1 makes the decision of each consumer independent of each other.Assumption 2 reflects the fact that willingness to pay for calling and for beingcalled are usually not the same and that the person with the higher willingness to

11 We are assuming implicitly that both consumers have joined the network. This is not a restrictiveassumption because consumers who have joined the network have the option of making no calls andreceiving no calls, so that they have no reason to hesitate to join the network unless they have to paythe subscription fee or the fixed fee per period. Also, even if they have to pay some fee irrespective oftheir usage, this assumption can be justified by the observation that the term of subscription contracts isoften 1 year or longer. A similar view can be found in Economides et al. (1998).

12 In reality, some calls may give negative utility to the receiver. These can be called nuisance calls.We ignore the possibility of nuisance calls in this article on the ground that the receiver can distinguishnuisance calls from calls yielding positive utility and discontinue the conversation himself in seconds.


pay usually initiates a call. Assumption 3 implies that the call made and the call13received are not perfect substitutes.

The firm is assumed to incur a variable cost c( . 0) per call. We assume that afixed cost per subscriber is negligible and that the costs of building facilities aresunk.

Decisions by the firm and the consumers are made sequentially; first, the firmsets its price schedule, and then, consumers choose the quantity of callings, q , q1 2

14simultaneously. The firm may practice various pricing strategies, for example,two-part tariffs, price discrimination between two consumers, etc. However, forexpositional simplicity, we assume throughout that the firm uses uniform linearpricing under both the caller pays principle and the receiver pays principle.

2.1. Caller pays principle

If the firm charges p per call to the caller, the consumer i’s net surplus fromC ijoining the network and consuming q , q , denoted by V , is U (q , q ) 2 pq . The1 2 i i j i

first-order condition implies that consumer i chooses q * satisfyingi

C≠V i]] *5 u9(q ) 2 p 5 0, i 5 1, 2 (1)i≠qi

*By the implicit function theorem, we can write consumer i’s demand q fori

*making calls as a function of p, i.e., q 5 D( p) where D9( p) , 0.i

Then, the firm chooses p* solving

Cmax p ( p) 5 ( p 2 c)Q 5 2( p 2 c)D( p), (2)p

where Q is the total quantity of callings. Assuming that the second-order conditionis satisfied, the profit-maximizing price, p*, must satisfy

D9( p*) 1 ( p* 2 c)D9( p*) 5 0, (3)

or in terms of elasticities,

h( p*)]]]p* 5 c( . c), (4)h( p*) 2 1

where h is the price elasticity of demand, and h /h 2 1 is a markup factor.

13 Imperfect substitutability comes from u0( ? ) , 0. As a matter of fact, making calls incursadditional costs of looking for the numbers and dialing them both of which the receiving party avoid,while receiving calls incurs the extra costs of being abruptly interrupted, etc.

14 In this model, the firm’s pricing decision has no effect on consumers’ subscription decision. Thisfeature of the model will be modified in Section 3.


2.2. Receiver pays principle

Suppose that the firm charges p ( $ 0) per call to the caller and p ( $ 0) per callC R

to the receiver. Then, one of the serious problems that one could expect toencounter would be the possibility that the receiver might refuse to receive a call ifp were very high. In the following, we will first find the condition for the priceR

vector ( p , p ) to prevent any call from being refused, solve for the profit-C R

maximizing price vector under the constraint that the condition is satisfied, andshow that any price vector violating the condition cannot be profit-maximizing.

Let q (q ) denote the number of calls consumer i intends to make (receive,i,C i,R

respectively). He will solve

Rmax V 5 u(q ) 1 v(q ) 2 p q 2 p qi i,C i,R C i,C R i,Rq ,C, q ,Ri i

* *Let q , q , i 5 1,2 be the optimal solutions for this program. Then, first-orderi,C i,R

conditions imply thatR

≠V i]] *5 u9(q ) 2 p 5 0 (5)i,C C≠qi,C

R≠V i]] *5 v9(q ) 2 p 5 0 (6)i,R R≠qi,R

*Meanwhile, in order for no call to be refused, it must be the case that q # q*i,C j,R

* *and q # q , j ± i. The first inequality implies that no call from consumer i isi,R j,R

refused and the second inequality implies that no call is refused by consumer i.From these inequalities, we can get a simple condition of no call refusal given bythe following lemma.

Lemma 1. No call is refused if and only if p #up .R C

* * * *Proof. q # q and q # q together with (5) and (6) are equivalent toi,C j,R i,R j,R21* 9 *p #up , since p # v9(q ) 5 v9(u ( p )) 5up and up $uu9(q ) 5R C R j,R C C C j,R

21 219 9uu9(v ( p )) 5uu9(u ( p /u )) 5 p from Assumptions 2 and 3.R R R

If p #up , all intended calls are actually realized. Thus, in that case, q andR C i,C

q can be used to denote the number of calls made and received, respectively.i.R

The firm’s optimization problem with the constraint that no call be refused isthen

Rmax p ( p , p ) 5 2( p 1 c)D( p )C R C Cp , pC R

subject to P #upR C

We can see that the profit goes up unambiguously as p is increased up to up .R C


* *Thus, the optimal prices, p , p must make the constraint binding, yieldingC R

* *p 5up . This observation enables us to transform the constrained optimizationR C

program into

R˜max p ( p ) 5 2h(1 1u )p 2 cjD( p ) (7)C C CPC

Assuming that the second-order condition is satisfied, we have

c]]* *D( p ) 1Sp 2 DD9( p ) 5 0, (8)C C C1 1u

or in terms of elasticities,

*h( p )1 C]]]]]*p 5 c. (9)C 1 1u *h( p ) 2 1C

At this point, some may wonder if the firm could do better by freeing itself fromthe constraint. However, the following lemma tells us that is not possible, so wecan confine ourselves to the constrained optimization problem to search for theprice vector maximizing its profit. Proposition 1 summarizes this.

Lemma 2. The price vector violating the condition for no call refusal cannot beprofit-maximizing.

Proof. See Appendix A.

* *Proposition 1. The profit-maximizing price vector under RPP is ( p , p ) whereC R

* * *p satisfies (8) and p 5up .C R C

2.3. Comparison

We are in position to compare the outcome under RPP with that under CPP.Several comparison results are in order.

* *Proposition 2. p* . p ( $ p ).C R

Proof. It follows directly from Eqs. (3) and (8) and the second-order conditions ofthe optimization programs (2) and (7) (see Fig. 1).

The intuition for Proposition 2 is clear. Charging a price p to the receiver inR

addition to the caller is equivalent to lowering the unit cost by p . If the unit costR

is lowered, a profit-maximizing firm would charge a lower price.If we let the total quantity of calls to be supplied under CPP (under RPP,

C R C R* * *respectively) be Q (Q ), we have Q 5 q 1 q and Q 5 o minhq ,1 2 i51,2, j±i i,C


Fig. 1. Calling prices under CPP and RPP.

* * *q j 5 q 1 q . Then, the following corollary is a direct consequence ofj,R 1,C 2,C

Proposition 2.

R CCorollary 1. Q . Q .

The intuition behind Corollary 1 is that, under RPP, consumers do not take p 1 pC R

into account in choosing the quantity of call-makings, but p only. p affects onlyC R

the quantity of call-receivings, but the actual quantity of calls is totally determinedby the quantity of call-makings, since, in equilibrium, p is so set that no callsR

may be refused.Also, we have the following proposition.

* *Proposition 3. p 1 p $ p* if h9( p) $ 0 for all p.C R

* * * * *Proof. P 1 P 5 (1 1u )p 5 (h( p ) /h( p ) 2 1)c $ (h( p*) /h( p*) 2 1)c 5 p*C R C C C

*if h9( p) $ 0, ; p, since p* . p from Proposition 2.C

*The intuitive reason why the ratio of p to p* is related to the derivative of theC

elasticity of demand is as follows. Introducing RPP lowers the price the callermust pay per call. If the demand becomes less elastic as the price falls (h9( p) islarge), the profit-maximizing firm must charge a high p relative to the case thatC


adopting RPP makes the demand more sensitive to price. In the meantime, it is not* *difficult to imagine a situation where p 1 p , p* For example, if we have aC R

15kinky demand curve, so that it is very steep above some particular price level andbecomes very flat below it, the firm will find it to its advantage to charge a verylow calling price, since it can greatly increase the total quantity of callings.

C Rˆ ˆLet p , p be optimal values of the programs (2), (7), respectively. Then, wehave

R Cˆ ˆProposition 4. p . p .

R C ˜ˆ ˆProof. This is obvious from the definitions of p and p , since p( p) . p( p) forall p.

The intuition for Proposition 4 is that RPP shifts the demand curve outwards,˜ ˜ ˜ ˜ ˜which can be seen from p(p ) 5 (p 2 c)D(p /1 1u ) where p ; p 1 p is the totalC R

unit price under RPP. This result is, in fact, not surprising, considering that, underRPP, the firm could be at least as profitable as under CPP, since it always has theoption of charging exactly the same price as it charges under CPP.

On the other hand, consumer surplus under two alternative fee systems can becomputed as

C * *CS 5 O hu(q ) 1 v(q* ) 2 p*q ji j ii51,2, j±i

q*i (10)221 *5Oh(1 1u )E D (q ) dq 2 p*q ji i i

i510

2R * * * * * *CS 5Ohu(q ) 2 p q 1 v(q ) 2 p q ji,C C i,C i,R R i,R

i51q*i,C (11)

221 * *5 (1 1u ) O h E D (q ) dq 2 p q j.i i C i,C

i510

In words, the difference in consumer surplus between RPP and CPP is equal tothe unambiguous increase in surplus due to the increased quantities of callings plusthe change in surplus due to the total price consumers pay. Therefore, it is clearthat RPP increases consumer surplus if it does not increase the total price, i.e.,

* *p 1 p # p*. Moreover, if it increases the total price but not very much, i.e.,C R

15 A kinky demand curve, of course, involves non-differentiability at the kinked point. However, wecan slightly modify it into a differentiable function by smoothing around the point.


16* * *p 1 p ¯ p*, which is implied by h( p ) ¯h( p*), the effect of the increase inC R C

consumer surplus due to the increase in the volume of callings dominates theeffect of the increase in surplus due to the higher total price, so that consumersurplus would be increased.

C RFig. 2 illustrates the case of u 5 1. CS can be measured as 2A 1 B 1 Dand CSas the area of 2(A 1 B 1 C). Thus, the relative magnitude of consumer surplusunder two systems depends on the relative size of D and B 1 2C and, in general,

*we cannot conclude that one is larger than the other. In particular, if p is quiteC

close to p* so that B and C are very small, consumer surplus under RPP may besmaller than under CPP.

Proposition 5. Consumer surplus under RPP is larger than consumer surplus* *under CPP, if p* $ p 1 p . However, it is not necessarily larger in general.C R


Example 1. Suppose u(q) 5 2 bq(q 2 2l) where b . 0,l . 0 and q , 1. Thisutility function satisfies assumption 3, since u9(q) 5 2b(1 2 q) . 0 and u9(q) 5

Fig. 2. Consumer surpluses under CPP and RPP.

16 This may occur when h( p) is decreasing or increasing very slowly in p around p*, or morefundamentally, if D0( p) is very large at p*.


2 2b , 0. From the consumers’ problem, we have q* 5 D( p) 5 l 2 ( p /2b),2yielding h9( p) 5 (2bl /(2bl 2 p) ) . 0. First-order conditions of the firm’s problem

*give p* 5 bl 1 c /2 and p 5 bl 1 (c /2(1 1u )). Then, consumer surplus underC

CPP and under RPP can be computed as

2 21 c cC 2 2] ] ]H JCS 5 2b(1 1u ) l 2 Sl 1 D 2 bHl 2S D J,4 2b 2b

21 cR 2 ] ]]]CS 5 2b(1 1u ) l 2 l 1F GH J4 2b(1 1u )2c2 ]]]2 b(1 1u ) l 2 ,F H J G2b(1 1u )

so that

22b(1 1u ) c 2C R ]]] ]]] ]S DW ; CS 2 CS 5 l 1 2 l 1F GH J2 2b2b(1 1u )2 2c c2 2]]] ]1 b(1 1u ) l 2 2 bHl 2S D J.F H J G 2b2(1 1u )

C RSince lim W 5 ` and lim W 5 2 `, we can conclude that CS . CS if ab→` b→0R Clinear demand curve has a very flat slope (b is very large), while CS . CS if the

slope gets very steep.

Example 2. Suppose u(q) 5 L ln(q 1 1) where L( . 0) is a constant. This utilityfunction also satisfies Assumption 3, since

L L]] ]]]u9(q) 5 . 0, u9(q) 5 2 , 02q 1 1 (q 1 1)

]Œ *for all q $ 0. We have q* 5 D( p) 5 L /p 2 1 if p , L, p* 5 cL and p 5C]]]ŒcL /1 1u if c , L , 4c from optimization problems of consumers and the firm.2Also, we can see that h( p) 5 L /(L 2 p) . 0 and thus h9( p) 5 1/(L 2 p) . 0 so

]]]* * *long as L . p. The observation that p 1 p 5 (1 1u )p 5 (1 1u )cL . p*œC R C

confirms Proposition 3. Consumer surplus under two systems, respectively, is]S RŒcomputed as CS 5 (1 1u )L ln L /c 2 2L 1 2 cL, CS 5 (1 1u )hL ln(1 1u )L /

]]] ]]C R ]Œ ŒŒc 2 2L 1 2 cL /1 1u j. Then, f(u, L) ; CS 2 CS 5 Lh2 c(1 2 1/ 1 1u ) 2] 23 / 2Œ(1 1u ) L ln(1 1u )j , f(u, c). Since f(0, c) 5 0 and (f(u,c) /u ) 5 (1 1u ) 2

1 2 ln(1 1u ) , 0 for all u . 0, we have f(u, L) , 0 for all u [ (0,1] andR Cc , L , 4c, so that CS . CS in this case.

12(1 /h)Example 3. Suppose u(q) 5 (q /1 2 (1 /h)), where h . 1. This utility yieldsa constant price elasticity of demand. Straightforward algebra leads us to q* 5

2h * *D( p) 5 p , p* 5h /(h 2 1)cand p 5 1/(1 1u ) h /(h 2 1)c. Notice that p 1C C

*p 5 p*. Also, we haveR


hC 12h]]CS 5 (1 1u ) 2 1 ( p*)H Jh 2 1

andh(1 1u )R 12h]]]CS 5 ( p*) .

h 2 1

R C h 12hTherefore, CS 2 CS 5 [2 /(h 2 1)]h(1 1u ) 2 (uh 1 1)j( p*) . 0, since (1 1h

u ) .uh 1 1 for all h . 1.

The result that consumers can be better off under RPP would be far fromsurprising. Under CPP, each consumer chooses the amount of callings equating his

*marginal utility of call-makings to the price (u9(q ) 5 p). However, since eachi

call-making generates positive call externalities on the other party, calls areunderconsumed under this regime. Notice that, given the price, consumers could

17be both better off by making more calls. On the other hand, under RPP, callexternalites are internalized; the calling party equates his marginal utility of

*call-makings to the calling price (u9(q ) 5 p ) and the receiving party equates hisi,C C

*marginal utility of call-receivings to the receiving price (v9(q ) 5 p ), and as ai,R R18result, the externalities created by the caller are paid for by the receiving party.

2.4. Discussion on the assumption of the additive separability

We have assumed that the utility function of each consumer is additivelyseparable. Due to this assumption, the marginal utility of making (receiving,respectively) a call does not depend on the amount of calls received (made), sothat the quantity of calls that a consumer intends to make (receive) will bedetermined independently of the quantity of calls that he intends to receive (make)unless the budget constraint is binding.

17 This cooperation may be possible in a noncooperative way if the consumers are intimate friends orfamily, so that they interact with each other. In that case, according to the conventional supergameliterature, consumers can internalize externalities and achieve efficiency by agreeing to make thenumber of calls per unit period that maximizes their total indirect utility (from making and receivingcalls) and reverting to the one-period equilibrium outcome forever thereafter if either party breaks theagreement.

18 The possibility that consumer welfare may be decreased under RPP is caused by the monopolypower of the firm. However, if prices of the firm are regulated in a way that the regulated prices areequal to the marginal cost under the constraint that no call is refused, i.e.,

c ≠]] ]]¯ ¯ ¯p 5 c, p 5 , p 5 c,C R1 1u 2 1u

consumer surplus would always be larger under RPP.


Although this assumption simplifies the analysis significantly, it is also true that19the independence property implied by this assumption is a restrictive feature of

the model. It may be more plausible that the optimal amounts of calls that aconsumer intends to make and receive are interrelated with each other. Morespecifically, it is highly likely that an increase in the amount of calls receiveddecreases the marginal utility of calls made, thereby leading him to make fewercalls. Below, we will see how the results obtained so far can be affected if theutility function is not additively separable.

Suppose consumers have the CES utility function given byi r r 1 /rU (q , q ) 5 A(a q 1 a q ) ,i,C i,R 1 i,C 2 i,R

where r , 1. The optimization problem of each consumer under RPP yields thefollowing first-order conditions.

R≠V i r 21 (1 /r )21]] *5 Aa (q ) K 2 p 5 0 (12)1 i,C C≠qi,C

R≠V i r 21 (1 /r )21]] *5 Aa (q ) K 2 p 5 0, (13)2 i,R R≠qi,R

r r* *where K ; a (q ) 1 a (q ) . These equations give us1 i,C 2 i,R

ß*q a pi,C 1 R] ]]5 , (14)S D*q a pi,R 2 C

where ß ; 1/1 2 r. ß is usually called the elasticity of substitution. Therefore, ascalls made and calls received are considered as more substitutable, i.e., ß becomes

* *larger, the difference between q and q gets bigger. Also, since each consumeri,C i,R

* * * *has the identical utility function, we have q 5 q and q 5 q for all i 5 1, 2.i,C C i,R R

* *Thus, the condition for no call to be refused, q # q , is reduced to p # (a /C R R 1

a )p . Since this condition must be binding for profit maximization of the firm, it2 C

* * * *is implied that p 5 (a /a )p , i.e., a p 5 a p . The rest of the analysis givenR 1 2 C 1 C 2 R

in Section 2.2 will remain unaffected qualitatively.

3. A general model with two networks

In this section, we relax some assumptions made in Section 2 and extend ourdiscussion to a more general model. The main changes in assumptions are asfollows. First, we consider a situation in which there are two substitutablenetworks rather than only one network. Second, we posit a continuum ofconsumers who may differ in their tastes instead of two representative consumers.

19 This does not imply that there is no substitutability between calls made and calls received.


Finally, we abandon the assumption that consumers’ network affiliation is fixedand consider their subscription decision as well.

We adapt Hotelling’s linear city model to analyze competition between twodifferentiated networks. Consumers are uniformly distributed over [0,1]. Twofirms are supplying differentiated networks, and one of them (‘firm 1’) is locatedat x 5 0 and the other (‘firm 2’) is at x 5 1. For parsimony of notation, we will1 2

use an index i to indicate a firm.Each firm has the following cost structure. It incurs a variable cost c per (either

inbound or outbound) call. c is assumed to be equal to 2c . We may think of c as0 0

the equal costs of transmitting voice signals from originating ends to a switcherand from a switcher to terminating ends. The rest of the assumptions on costsmade in the previous section are preserved.

Let q denote the number of calls a consumer located at x makes to a consumerxyxat y and U (q , q ;y [ [0,1]) denote the utility function of a consumer at x whenxy yx

he makes q calls to a consumer at y and receives q calls from him for y [ [0,1].xy yxxBy abusing notation u( ? ),v( ? ), we make assumptions on U ( ? , ? ) which are

essentially the same as those in the previous section.

x x 1 1Assumption 4. U ( ? , ? ) is additively separable, i.e., U 5 e u(q )dy 1 e v(q )0 xy 0 yx

dy.

Assumption 5. v( ? ) 5uu( ? ) for some u [ (0, 1].

Assumption 6. u(0) 5 0, u9( ? ) . 0 and u0( ? ) , 0

We model the interaction among firms and the consumers as a four-stage game.In the first stage, firms agree upon the reciprocal access charge a for interconnec-

20tion between networks, and in the second stage, they choose their pricing21schedules simultaneously. In the third stage, consumers pick a network that they

will subscribe to, and in the final stage, the subscribers choose their quantities ofcallings simultaneously. We assume that consumers are not allowed to subscribe to

20 US imposes reciprocity by law. (See the US Telecommunications Act, 1996, section 251, b5.)While some other countries (e.g., Korea, Japan, New Zealand, Mexico) do not. (See the Ovum reportby Ladbrook and Jeffery, 1999.) Theoretically, imposing reciprocity eliminates the problem of doublemarginalization that appears under non-reciprocal access pricing.

21 Some may wonder if we need the interconnection charge in addition to receiving charges underRPP. We consider a model in which each firm collects charges for a call from the caller and the receiverunlike the model of Laffont and Tirole where the firm originating a call collects charges only for theoriginating service and the other firm collects terminating charges. So, the interconnection charge isnecessary in our model. Even though the other firm is able to bill the receiving charges to the receiverand keep the fee for the terminating service, this system is not optimal to firms since they can increaseprofits by determining the interconnection charge cooperatively which is in general not equal to thereceiving price.


more than one network. Also, we assume that any given consumer is equally likelyto call any other consumer, regardless of the network he joins, i.e., for any x,

22q ; q for all y.xy x

The valuation of a consumer at x joining network i and consuming (q , q ) isx y

assumed to bexV (x) 5 r 2 t x 2 x 1 U (q , q ) 2 T (q , q ), (15)u ui i x y i x y

23where r is the direct benefit from joining a network, t x 2 x is the disutility fromu uideparture from the favorite service characteristics of a consumer at x and T (q ,i x

q ) is the amount of money that should be paid for (q , q ). t can be interpreted asy x y

a measure of product differentiation between two telecommunication servicesprovided by network 1 and network 2.

We assume throughout that the market is covered, so that N < N 5 [0,1] where1 224N is the set of subscribers to firm i.i

Before we begin the analysis, we make some simplifying assumptions.

Assumption 7. D9( p) 5 0 for all p where u9(D( p)) 5 p.

mm mÃssumption 8. 0 , P , P , 2(1 1u )t where P ; max P( p) 5 ( p 2pm˜ ˜c)D( p),P 5 max P( p) ; h(1 1u )p 2 cjD( p).

Assumption 7 implying that u9( ? ) is a constant simplifies the analysis a greatdeal. Assumption 8 is a technical assumption which ensures that the degree ofproduct differentiation, t, is sufficiently high.

3.1. Caller pays principle

We solve this by backward induction. Suppose the reciprocal access charge a isagreed upon, prices of two firms p , p , are set, and the resulting market share of1 2

firm 1 is given by s. Then, the optimization problem of a consumer located at xwho joins network i is

x xmax U (q , q ) 2 T (q , q ) 5 U (q , q ) 2 p qx y i x y x y i xqx

1

5 u(q ) 1E v(q )dy 2 p q (16)x y i x

0

22 Many authors (Rohlfs, 1974; Laffont et al., 1998a,b; Armstrong, 1998; Economides et al., 1998)used this so-called ‘balanced (or uniform) calling pattern assumption’, even though they admit that it isobviously not true in reality. Doyle and Smith (1998) is an exception.

23 We are assuming that the direct benefits from joining network 1 and network 2 are the same.24 This may be justified by the assumption that r is very large.


The first-order condition of this problem implies

i*u9(q ) 5 p , (17)x i

i*where q is the optimal amount of callings of a consumer located at x whox

subscribes to network i. As in Section 2, we can write the demand function of ai*consumer at x joining network i as q 5 D( p ) for all x.x i

In determining his network affiliation, a consumer at x correctly anticipates whatC Ci ˆ ˆ* *q and q for all y and for all i, j 5 1, 2 will be, and compare V (x) and V (x)x y, j 1 2

Cˆwhere V (x) is the equilibrium valuation of a consumer located at x joiningi

network i under CPP. In this case, we have

C 1 1 2 1ˆ * * * *V (x; p , p ) 5 r 2 tx 1 u(q ) 1 E v(q )dy 1 E v(q ) dy 2 p q1 1 2 x y y 1 x

y[N y[N1 2

5 r 2 tx 1 u(D( p )) 1 n v(D( p )) 1 n v(D( p )) 2 p D( p ),1 1 1 2 2 1 1

(18)

CV̂ (x; p , p ) 5 r 2 t(1 2 x) 1 u(D( p )) 1 n v(D( p )) 1 n v(D( p ))2 1 2 2 1 1 2 2

2 p D( p ), (19)2 2

where n is the measure of N , i 5 1, 2. Then, the equilibrium market share s*i iC Cˆ ˆmust satisfy V (s*; p , p ) 5 V (s*; p , p ), and thus, by using n 5 s*, we1 1 2 2 1 2 1

obtain

1 1] ]s*( p , p ) 5 n* ( p , p ) 5 1 hn( p ) 2 n( p )j, (20)1 2 1 1 2 1 22 2t

where n( p ) 5 u(D( p )) 2 p D( p ).i i i i

We will solve the price setting stage, taking the reciprocal access charge asgiven, and then look at the determination of the access charge. For a given accesscharge a, firm i’s profit is

* *p ( p , p ; a) 5 n ( p 2 c)D( p ) 1 n n* (a 2 c )(D( p ) 2 D( p )),i 1 2 i i i i j 0 j i

j ± i (21)

This means that the profit of a firm is the sum of the profit from inbound calls andthe net monetary inflow from interconnection. The first-order conditions of theprofit maximization problems imply that the symmetric Nash price p* must satisfy

t2 ]( p* 2 c)hD( p*) 2 tD9( p*)j 2 tD( p*) 1 (a 2 c )D9( p*) 5 0 (22)02

or


1]p* 2 c 2 (a 2 c )01 2

] ]]]]]]P( p*) 5 1 2 h( p*) (23)t p*

Unfortunately, neither the existence of the symmetric Nash equilibrium nor theuniqueness of the equilibrium is guaranteed for all a. In particular, if the accesscharge is very high, a firm will find it profitable to make its own subscriber choosea small number of callings by increasing its price, in order to enjoy a high accesssurplus, and this incentive may make no price in a relevant range be anequilibrium one. However, it is quite plausible to have a symmetric equilibrium, ifa is very close to c . To see that, denote the right hand side of (23) by C( p). We0

¯ ¯have C(c) . 0,C(p ) , 0 where D(p ) 5 0. Since C( p) is continuous in p, there¯exists a symmetric equilibrium p*(a) satisfying (23) in a relevant range of p, [c, p ]

(see Fig. 3).Assuming that there exists an equilibrium, we have the following proposition.

25Proposition 6. Under Assumptions 7 and 8, p* is increasing in a (see Fig. 4).

Fig. 3. Symmetric equilibrium under CPP.

25 mIn fact, without Assumption 8, we can show that, if a # c , p*(a) , p and p*(m) is increasing in0

a, if p*(a) ever exists, since

D9 1 D9] ] ]C 9( p) 5 F1 2Hp* 2 c 2 (a 2 c )J , 0,0D 2 D

mD9( p )1m ] ]]C( p ) 5 2 (a 2 c ) # 0m02 D( p )mand P( p ) ± 0.


Fig. 4. Monotonicity of the equilibrium price in a.


The intuition behind Proposition 6 is that, if a is increased, it will be optimal fora firm to charge a higher price in order to decrease the demand for calls originating

26from it, thereby increasing an access surplus.Now, let us look for the collusive reciprocal access charge. To maximize joint

Cprofits, the colluding firms will set their reciprocal access charge a satisfying

C≠P( p*(a ))]]]] 5 0.

≠a

C m mTherefore, it must be that p*(a ) 5 p where p maximizes P( p). The followingCproposition displays some properties of a .

26 It t, is very small, however, an increase in p may result in losing a large number of subscribers. Ifthis effect exceeds the effect of increasing an access revenue, the equilibrium price p* may bedecreasing in a.


CProposition 7. (i) The access charge under CPP, a , is strictly higher than the27 Cmarginal cost of access, c . (ii) a is decreasing in t.0


CThe last part of this proposition implies that a ¯ c if t is so large that028consumers’ subscription decision is very insensitive to a change in the prices,

which is consistent with the results of Armstrong (1998) and Laffont et al.29(1998a).

3.2. Receiver pays principle

We now consider the case where both firms operate under the receiver paysprinciple. Let p (P , respectively) denote the price that firm i charges for callsi,C i,R

made (received). Also, let q (q , respectively) be the quantity that axy,C xy,R

consumer at x makes to (received from) a consumer at y. Then, the assumption ofthe balanced calling pattern implies that q ; q for all y and that q 5 qxy,C x,C xy,R x, i,R

if y [ N where q is the quantity of calls that a consumer at x receives fromi x, i,R30another consumer belonging to network i. Notice that a caller does not need to be

concerned about which network he is calling to, while a receiver must beconcerned about from which network he is receiving a call.

Given the prices p , p , i 5 1, 2 and the market share s, a consumer at x whoi,C i,R

joins network i faces the following optimization problem

xmax U (q , q ) 2 T (q , q ) 5 u(q )xy,C xy,R i xy,C xy,R x,Chq , q jxy,C xy,R y[[0,1]

2 2

1O E v(q )dy 2 p q 2O E p q dy (24)xy,R i,C x,C i.R xy,Ri51 i51

y[N y[Ni i

First-order conditions imply that

27 This result, consistent with that of Armstrong (1998) and Laffont et al. (1998a), may not be thecase if networks compete with price discrimination and two-part tariffs. Firms would collude on aninterconnection charge lower than the marginal cost of access in that case. See Gans and King (2000b).

28 This can be seen from

*≠N*≠N D( p*)ji] ] ]]5 2 5 2 , j ± i.≠p ≠p 2ti i

29 This corresponds to the case that s9(0) 5 0 in Armstrong (1998) and s 5 0 in Laffont et al.(1998a).

30 Here, we are implicitly assuming that a receiver can tell which network a particular call originatesfrom. In practice, this may be possible by various mechanisms for distinguishing between wanted andunwanted calls that were mentioned in Section 1.


i*u9(q ) 5 p , x [ N (25)x,C i,C i

i*v9(q ) 5 p , y [ N , j 5 1,2 (26)xy,R j,R j

i i* *where q (q , respectively) is the optimal number of calls that a consumer at xx,C xy,R

who joins network i intends to make (to receive from another consumer at y)under RPP.

Again, if we impose the condition for no call refusal, we must have

i j i j* * * *q # q , q $ q , y [ N , i, j 5 1, 2 (27)x,C yx,R xy,R y,C j

Then, it can be shown that the condition for no call refusal given by (27) isreduced to p #up in a similar way as in Section 2.j,R j,C

As seen in the case of CPP, the equilibrium market share under RPP, s**, isdetermined as a result of the subscription decision of consumers who compare

R Rˆ ˆV (x) and V (x) where1 2

R x i i i i i iˆ * * * * * *V (x) 5 r 2 tux 2 x u 1 U (q , q , q ) 2 T (q , q , q )i i x,C x,1.R x,2,R i x,C x,1,R x,2,R

R Rˆ ˆThus, s** can be found by V (s**) 5 V (s**), so that s**( p , p ) 5 1/1 2 1,C 2,C

2 1 1/2t(n( p ) 2 n( p )). Notice that the market share is not affected by the1,C 2,C

prices for receiving calls. A consumer receives the same number of calls from eachnetwork no matter which network he joins, thereby he pays the same for receivingcalls in either case regardless of the receiving prices, which implies that hissubscription decision can never be affected by the receiving prices charged byfirms.

Given the access charge a, firm i solvesR *max p 5 n *( p 1 p 2 c)D( p )i i i,C i,R i,Cp , pi,C i,R

* *1 n *n *(a 2 c )(D( p ) 2 D( p )), j ± ii j 0 j,C i,C

subject to up $ p , (28)i,C i,R

*where n * is the equilibrium number of subscribers to network i under RPP whichi

is equal to s**( p , p ). In this general case, too, p ( ±up ) cannot be1,C 2,C i,R i,C

optimal for firm i, since a slight increase in p could leave the number ofi,R

subscribers to firm i and their callings unaffected, thereby increasing the profit.Thus, the optimization problem given by (28) can be simplified into

Rˆ *max p ( p ) 5 n *h(1 1u )p 2 cjD( p )i i,C i i,C i,Cpi,C

* *1 n *n *(a 2 c )hD( p ) 2 D( p )j (29)i j 0 j,C i,C

*The first-order conditions imply that the symmetric equilibrium calling price pC

must satisfy


t2 ]* * * * *h(1 1u )p 2 cjhD( p ) 2 tD9( p )j 2 t(1 1u )D( p ) 1 (a 2 c )D9( p )C C C C 0 C2

5 0 (30)

or

1]*(1 1u )p 2 c 2 (a 2 c )C 01 2˜] ]]]]]]]]* *P( p ) 5 1 1u 2 h( p ) (31)C C*t pC

Assuming that a symmetric equilibrium exists, we can establish the followingcounterparts of Propositions 6 and 7 under RPP. We will omit the proofs, since theproofs of Propositions 6 and 7 can be adapted in a straightforward way.

*Proposition 8. Under Assumptions 7 and 8, p is increasing in a.C

RProposition 9. (i) The collusive access charge under RPP, a , exceeds theRmarginal cost of access, c . (ii) a is decreasing in t.0

Again, the following lemma suggests that we can content ourselves with thesolution with the constraint that no call is refused.

Lemma 3. A pair of symmetric prices ( p , p ) such that p .up cannot be profitC R R C

maximizing.


9Intuitively, if a firm charges a slightly higher calling price p than p , itC C

increases the number of its subscribers but decreases the number of the rival’ssubscribers in the same proportion, while it does not affect the number of callingsper subscriber at all, since it is determined solely by the receiving price. Thisleaves the total demand for callings originating from it the same as before;however, it obviously increases the revenues from each subscriber. Therefore, itwould be always profitable to charge a higher calling price than p , implying thatC

the ongoing price pair ( p , p ) cannot be part of an equilibrium. We nowC R

summarize with

* *Proposition 10. The profit-maximizing price vector under RPP is ( p , p ) whereC R

* * *p satisfies (31) and p 5up .C R C


3.3. Comparison

We are now ready to compare the outcomes under two regimes. For ourpurpose, it will be convenient to introduce a parameter to integrate two Eqs. (22)and (30) into one equation as follows;

12 ]F H J G(lp 2 c)D( p) 5 t lD( p) 1 lp 2 c 2 (a 2 c ) D9( p) , (32)02

where l 5 1 under a caller pays regime and l 5 1 1u under a receiver paysregime. Let us allow an imaginary change in l continuously from 1 to 1 1u.

ˆ ˆ ˆDenoting p satisfying (32) by p(a, l), we have p(a, 1) 5 p*(a) and p(a, 1 1u ) 5

*p . Then, the following propositions can be established.C

* *Proposition 11. p*(a) . p (a) for all a such that both p*(a) and p (a) exist.C C


This proposition says that, given a, firms charge higher calling prices under CPPthan under RPP. The intuition is that positive receiving prices under RPP havevirtually the same effect as reducing the marginal costs, and as a result, profit-maximizing calling prices are lowered under RPP.

C R*Proposition 12. p*(a ) . p (a ).C

m C R m*Proof. This is immediate, since p 5 p*(a ) . p (a ) 5 p .C C

Proposition 12 implies that the calling price under CPP is higher than underRPP in an equilibrium where the reciprocal access charge is optimally set.

C RHowever, in general, we cannot tell which of the two, a , a , is higher.Now, a natural question that arises is which of the agreed-upon access charge

under two regimes is higher. The following proposition provides the answer.

R CProposition 13. a . a .


Introducing RPP lowers the equilibrium calling price given the access charge,and the higher access charge yields higher calling prices under both regimes. Thus,firms must set a higher access charge under RPP than under CPP to induce the

mcollusive calling price p so long as it does not differ from the collusive callingCmprice under CPP p very much (Fig. 5).

Finally, we will see the implication of RPP on profits of firms and consumerR R C C r Rˆ ˆ ˆ* * *surplus. First, it is easy to see that p ( p (a )) . p ( p (a )) since p ( p (a )) 5i C i C i C


Fig. 5. Access charges under CPP and RPP.

C C1 1 ˆ] ] *maxh(1 1u )p 2 cjD( p) . max( p 2 c)D( p) 5 p ( p (a )). Also, when firmsi C2 2

pick the collusive access charge and charge equilibrium prices, consumer surplusC C1 / 2 m m 0 m mˆ ûnder CPP is computed as e V (x; p , p )dx 1 e V (x; p , p )dx 5 r 10 1 1 / 2 2

m m m(1 1u )u(D( p )) 2 p D( p ) 2 t /4, and, similarly, consumer surplus under RPP isR R1 / 2 m m 1 m m mˆ âs e V (x; p , p )dx 1 e V (x; p , p )dx 5 r 1 (1 1u )u(D( p )) 2 (1 10 1 C C 1 / 2 2 C C C

m mu )p D( p ) 2 t /4. Therefore, the effect of RPP on consumer surplus is exactlyC c

identical to the case of a single network described in Section 2, as long as the formof the utility function is the same in the two cases. Proposition 14 summarizes this.

Proposition 14. The collusive joint profits are larger under RPP than under CPP,but the effect of RPP on consumer surplus is ambiguous.

4. Concluding remarks and caveats

In this paper we have explored the effect of the receiver pays principle (RPP)both in a model with one PSTN and in a model with one PSTN and one mobilenetwork. Our main findings are that, under mild conditions, RPP can increase notonly the consumer surplus but also the firm’s profit and that RPP makes firms set ahigher reciprocal access charge than CPP does.

In practice, it will be a controversial issue whether replacing CPP by RPP willimprove social welfare or not. The regulatory authority who concerns itself withmaximizing consumer surplus may hesitate to adopt RPP on the ground that it may


reduce consumer surplus since the inelastic demand for telecommunication*services will keep p high enough. However, we strongly believe that it is notC

very likely to occur because consumer surplus will be increased under RPP unlessthe price elasticity of demand gets smaller very rapidly as the price falls.

We may consider various alternative models. First, firms may use more generaltariffs than the simple linear pricing used throughout in this paper. If firms offertwo-part tariffs instead of linear tariffs, for example, incorporating RPP will affectthe usage fee while it will leave the fixed fee unaffected. RPP functions as

31lowering the usage fee for the caller but it does not affect the fixed fee. Also,firms can price discriminate between on-net calls an off-net calls. This kind ofprice discrimination under CPP is analyzed in details in Laffont et al. (1998b) andit would be possible to extend their arguments to the regime where the receiverpays some. Second, it is common that two networks have different cost structures.In particular, the marginal cost of mobile termination is much higher than that offixed termination in practice. In this case, the desired access charges of eachnetwork will certainly be different and it seems unfair to the mobile serviceprovider to require the reciprocal access charge. However, if we do not imposereciprocity of access charge, the consequence that each firm sets a separate accesscharge would be high access charges due to double marginalization (Laffont et al.,1998a). In this respect, it will deserve to see how the effect of introducing RPP onthe access charges can be affected in this nonreciprocal environment. Third, firmsmay adopt an alternative payment system whereby the called party pays all as inthe US mobile service. Or, firms may collect charges from their respectivesubscribers themselves as interconnection charges whenever they receive callsfrom the other network rather than allow the other network to collect the chargesand then make settlements afterwards. However, such schemes will be generallysuboptimal since they are just special cases of the general scheme considered inSection 3. Fourth, we may endogenize the firms’ decisions about whether they willchoose CPP or RPP. If one firm adopts RPP and the other does CPP, a consumerwho subscribes to the service provider adopting CPP will pay the whole price forhis making calls and be charged for calls received from the other network as welland thus it is expected that the network size of the firm adopting RPP will belarger. Therefore, we conjecture that both firms will adopt RPP in equilibrium.Finally, in reality, several mobile telephony companies are operating together withone PSTN provider or two PSTN providers. In particular, if there are severalPSTN’s and several mobile networks involved, we may address the issue ofstrategic alliances between a PSTN and a mobile network which are exclusive toeach other.

31 C R C RFirst-order conditions of the profit maximization problem imply that F 5 F 5 t where F (F ) isi l i l

the fixed fee charged by firm i under CPP (RPP, respectively).


Acknowledgements

We are grateful to Hyung Bae, Chang-Ho Yoon, editorial advice, an anonymousreferee, seminar participants at Korea Telecommunications (KT), SK Telecom,audiences at the 8th World Congress held at Seattle, Washington, the conference ofKorean Industrial Organization Association, the Applied Microeconomics Work-shop held at the Korea Foundation for Advanced Studies, the TelecommunicationsPolicy Workshop sponsored by the Korea Association for TelecommunicationsPolicies for helpful comments. We especially benefited from conversation with J-J.Laffont.

Appendix A

Proof of Lemma 2ˆ ˆ ˆ ˆ ˆ ˆConsider a price vector (p , p ) such that p , p /u. This implies q (p ) 5C R C R i,R R

ˆ ˆ ˆ ˆ ˆ ˆD(p /u ) , D(p ) 5 q (p ), i ± j where q ( p ) and q ( p ) are defined asR C j,C C i,R R i,C C

ˆ ˆsatisfying u9(q ( p )) 5 p ,v9(q ( p )) 5 p , respectively. Then, we can choosei,C C C i,R R R

ˆ ˆ ˆ ˆ ˆ9 9´ . 0 such that p 5 p 1 ´ , p /u and still q (p ) , q ( p ). It is obvious thatC C R i,R R j,C CR Rˆ ˆ ˆ9p ( p ,p ) . p (p ,p ).C R C R

Proof of Proposition 5*If p* 5 (1 1u )p 1 ´ for some ´ $ 0, we haveC

q*i,C2

R C * *CS 2 CS 5 (1 1u ) O E u9(q)dq 2 p qC i,C5 6i510

q*i2

* *2O (1 1u ) Eu9(q)dq 2 h(1 1u )p 1 ´jqC i3 4i510

q*i,C2 2

* * * *5 (1 1u ) O E u9(q)dq 2 p (q 2 q ) 1 ´ O qC i,C i i3 6i51 i51q*i

2 2

* * * * * * *. (1 1u )O hu9(q )(q 2 q ) 2 p (q 2 q )j 1 ´ O qi,C i,C i C i,C i ii51 i51

2

*5 ´ O q $ 0ii51

Proof of Proposition 6mTotal differentiation of (23) gives us dp (a) /da 5C /P 2C . In equilibrium,a p p

we have


D9 1 D9 D9 P( p*(a))] ] ] ] ]]]F H J G H JC 5 1 2 p*(a) 2 c 2 (a 2 c ) 5 2 2 , 0p 0D 2 D D t

mby Eq. (23) and Assumption 8. If p*(a) # p implying P ( p*(a)) $ 0, we havep1]dp*(a) /da . 0, since C 5 2 D9 /D . 0.a 2

On the other hand, a bit more of calculus shows that dp*(a) /da 5 2 (t /2)D9 /D2where D 5 D 2 2tD9 1 2( p* 2 c)DD9. Also, the second-order condition requires

2that 2D 1 D9h3( p* 2 c)D 2 2tj . 0. Using this, we have

2 2D . D 2 2D 2 ( p* 2 c)DD9 5 2 Dh( p* 2 c)D9 1 Dj . 0,

msince ( p* 2 c)D9 1 D , 0 if p* . p . Therefore, the conclusion follows thatdp*(a) /da . 0.

Proof of Proposition 7Substituting a 5 c into (23) and multiplying both sides by D( p*(c )), one has0 0

D( p*(c ))0]]]( p*(c ) 2 c)D9( p*(c )) 1 D( p*(c )) 5 P( p*(c )) (A1)0 0 0 0t

mAssumption 8 implies that p*(c ) ± p . Also, the nonnegativity of symmetric0

equilibrium profits implies that P( p*(a)) . 0 for all a. Thus, it follows thatm C Cp ; p*(a ) . p*(c ), so that a . c by Proposition 6 (see Fig. A1). The proof of0 0

the second part is obvious.

Fig. A1. Access charge under CPP in excess of access cost.


Proof of Lemma 3If p .up , we haveR C

-

1p1,RRˆ ]S S DDV (x) 5 r 2 tux 2 x u 1E u D dy 1 n v(D( p )) 1 n v(D( p ))i i 1 1,R 2 2,Ru

0

p p1,R 2,R] ]H S D S DJ2 p n D 1 n D 2 n p D( p ) 2 n p D( p )i,C 1 2 1 1,R 1,R 2 2,R 2,Ru u

ˆ ˆ ˆ ˆSuppose (p , p ) such that p .up is a symmetric equilibrium price vector.C R R C

Simple algebra leads to

1 1 ˜] ] ˆ ˆ ˆ*s** 5 n * 5 1 (p 2 p )Q(p , p ; s**)1 C 1,C R R2 2t

where

p p1,R 2,R˜ ] ]S D S DQ( p , p ; s) 5 sD 1 (1 2 s)D .1,R 2,R u u

R ˜ * *Also, we have p 5 ( p 1 p 2 c)Q 1 n *n *(a 2 c )hD( p ) 2 D( p )j.i,C i,R 1 2 0 i,R j,R

ˆ ˆ9If firm i charges p 5 p 1 ´ such that p .up , we havei,C C R i,C

≠s** 1 ˜]] ] ˆ ˆ5 2 Q(p , p ; s**)R R≠p 2t1,C

in a symmetric equilibrium, so that

R *≠n **≠p ≠n * ji i˜]] ˆ ˆ ˆ ]] ˆ ]] ˆ5 Q(p , p ; s**) 1 (p 1 p 2 c) D(p ) 1 D(p )H JR R C R R R≠p ≠p ≠pi,C i,C i,C

˜ ˆ ˆ5 Q(p , p ; s**) . 0,R R

implying that firm i always has an incentive to increase p .C

Proof of Proposition 11Ît is sufficient to show that ≠p(a, l) /≠l , 0. Total differentiation of (32) gives

2ˆ≠p(a,l) t(D 1 pD9) 2 pD t(1 2h) 2 pD]]] ]]]]] ]]]]5 5 ,

≠l S DS

2 ˆwhere S 5 lD 1 2(lp 2 c)DD9 2 2tlD9. Since ≠p(a, l) /≠a . 0 implies thatˆS . 0, we have ≠p(a, l) /≠l , 0.


Proof of Proposition 13C Ra and a satisfy

m C1]p 2 c 2 (a 2 c )1 02m m] ]]]]]]P( p ) 5 1 2 h( p )mt p

m R1](1 1u )p 2 c 2 (a 2 c )1 C 02m m˜] ]]]]]]]]P( p ) 5 1 1u 2 h( p )mC Ct pC

Straightforward computation leads us

3 32 a b aR C ] ] ]] ]H S D Ja 2 a 5 (1 1u ) 2 c 2S 2 bc D . 0,2 0 02 1 1u 2tb

where D( p) 5 a 2 bp.

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Economics 29, 38–56.Laffont, J.-J., Tirole, J., 2000. On the receiver pays principle, MimeoLittlechild, S., 1977. The role of consumption externalites in the pricing of telephone service. In:

Wenders, J.T. (Ed.), Pricing in Regulated Industries: Theory and Application. Regulatory MattersDivision, Mountain States Telephone and Telegraph Co, Denver.

OFTEL (Office of Telecommunications UK), 1998, Prices of calls to mobile phones — Statement,London.


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