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The pricing of international telecommunications services by monopoly operators
INFORMATION ECONOMICS AND POLICY
ELSEVIER
Information Economics and Policy 8 (1996) 107-123
The pricing of international telecommunications services by monopoly operators a~
Martin Cave " , Mark P. Donnelly b ~Departmem of Economics, Brunel, the University of West London. Uxbridge. Middlesex UB8 3PH, UK hCoopers & Lybrand, London, UK Received 12 August 1994: accepted 30 November 1995
Abstract International telecommunications operators usually set their own tariffs, but traditionally reimburse one another at a uniform settlement rate. We identify profit maximising tariffs where settlement rates are initially allowed to differ. We then explore Nash bargaining over settlement rates. We show that only under circumstances which are unlikely to occur in practice will two monopoly operators agree on a system of common settlement rates. However, we show that one operator in collusion with its regulatory authority always has an incentive to insist on uniform settlement rates as a precondition for negotiation.
Key words: Accounting rate system; Bilateral bargaining; International telecommunications JEL Classification: L96; FI3
1. Introduction
The cost of an intercontinental telephone call has fallen dramatically over the past 35 years. For example, the per minute cost of using trans-Atlantic cable was $2.53 in 1956, $0.04 in 1988, $0.02 in 1992 and is still coming down. The costs of originating and terminating the call in the countries concerned have also fallen, but by a smaller proportion. However, although intercontinental call charges or collection rates have fallen, Cave and Michie (1991) argue that in many cases they * Corresponding author. Department of Economics, Brunel, Uxbridge, United Kir~gaom. Tel: +44 1895 203320 Fax: +44 1895 274697. 0167-6245/96/515.00 Copyright © 1996 Elsevier Science B.V. All fights reserved Pll SO 167-6245 ( 9 6 ) 0 0 0 0 4 - 2
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M. Cave. M.P. Dmmellv I h~fonnation Economics and Policy 8 (1996) 107-123
have not fallen by anything like the margin necessary to account for the reduction in cost. One explanation is that Ramsey-type pricing is being practised to cover non-traffic-sensitive costs. This implies that a greater mark-up should be charged on market segments with a lower elasticity of demand. However, in empirical work the elasticity of demand is higher on international calls than on national calls. Thus if Ramsey-type pricing were being followed the divergence in mark-up would be in the opposite direction. A more plausible explanation lies in the accounting arrangements by which telecoms operators reimburse each other through a system of settlement rates paid for delivering an intercontinental ca!!~ This system of settlement rates partly explains why international charges have not fallen to match the reductions in cost resulting from advances in technology. ~ Cave and Michie (1991) show that the settlement rate is a component of marginal cost, and thus feeds into collection rates charged by telecoms operators in the usual manner. This leads to a form of 'double marginalisation' (see Milgrom and Roberts, 1992, pp. 550-551 ). The first margin is the excess of the settlement rate over the cost of completing an incoming call. This is then fed into setting of the collection rate, establishing a second margin. As a consequence, prices are higher when set by monopolists at each end than would be charged by joint profit-maximising monopolists at each end, or by an operator which owned or part-owned the facilities in the other country. Moreover, the settlement rate system also creates an incentive for the operator receiving more calls than it makes to keep the settlement rate high. This paper examines the incentives faced by monopoly operators in fixing settlement rate~ and call charges in an environment of double marginalisation. We do not explicitly consider the role of the rcgulator in the model, even though regulators in many instances have to approve settlement and collection rates. The reason for this is that we regard the interests of the regulator and of its monopoly operator as being broadly congruent. Typically, profits from international calls are used to cross-subsidise domestic services, often at the regulators' behest. Regulators thus have an interest in maximising profits. This approach is supported by the casual observation that the regulatory body working most publicly to reduce accounting and settlement rates is at present the FCC, and - given the general predominance of outgoing over incoming calls in the US - both regulator and operators have an interest in reducing the settlement rates on US routes. The organisation of the paper is as follows. Section 2 describes accounting arrangements whereby telecoms operators reimburse each other for incoming calls and presents a survey of the literature. Section 3 analyses Bertrand-Nash noncooperative pricing policy of international telecoms operators with given settlement rates. Section 4 investigates bargaining over settlement rates. Since intercontinental telecoms operators have traditionally agreed on a system of This is due to advances in technology such as the introduction of seabed cables using fibre optics.
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common settlement rates, Section 5 explores the circumstances in which such an agreement will occur. Section 6 considers how the results are effected by a more complex sp':cification of demand conditions. The main conclusion of the paper is that a Nash-bargained (Nash, 1950) system of common settlement rates emerges only in exceptional circumstances; but that one operator acting in collusion with its regulatory authority always has an incentive to insist on equal settlement rates as a precondition for negotiation. Finally, Section 7 draws some conclusions.
2. Accounting arrangements Between any two countries o and i the price Po set for interna6onal telephone calls Xo and charged to the customer in country o is referred to as the tariff or collection rate; similarly for country i. Since an outgoing call from country o is an incoming call for country i, the two operators must enter into a cooperative arrangement. The 'operating agreement' negotiated by the carriers describes the technical details of interconnection and the terms of reimbursement. The two operators agree a rate known as the accounting rate A R Payme~t~ fnr delive~ of a call is then made in proportion to AR and is known as the settlement rate SR. The proportion of the accounting rate paid by the operator originating the call to the operator terminating the call is called the 'accounting rate share' ARS. Hence the settlement rate is given by SR = ARS*AR. Generally the accounting rate is split 50:50 between the two operators.-" The principle of a 50:50 division of the accounting rate was established in the 1930s. "Up to the early 1930s the bulk of intercontinental telecommunications traffic was accounted for by the British Empire telecommunications system, dominated by Cable & Wireless. A key element of the company's strategy was the routing through London of most traffic originating in the Empire, regardless of whether this was the most direct route available" (Ergas and Paterson (1991, p. 30)). This had the effect of minimising net payments to non-UK operators. At the same time, European Post, Telegraph and Telephone operators (FITs) were entering into their own arrangements. Unlike C&W these operators did not have end-to-end control of international exchanges, and were obliged to "...negotiate joint service provision arrangements with other carriers on a relatively equal footing" (Ergas and Paterson (1991, p. 31 ). Initially these arrangements were developed for the handling of international telegrams. The development of international telephony led to important changes in z For a fuller account of the historic financial arrangements between international telecoms operators see Eward (1985), Johnson (1989/91), Cave and Michie (1991), and Ergas and Paterson (1991). The settlement rate applied to intematic, nal calls is not the only model for establishing call charges. Within Europe and the Mediterranean basin (TEUREM) settlement rates are determined per 100 Km of distance plus an amount added for the cost of completing an incoming call. Settlement rates for termination and/or transit are thus cost based and related to distance. Yet a different systen~ operates between the US and Canada. See OECD (1995) for further details.
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these agreements. In particular, "...attempts were made to objectively determine the costs involved in providing...linternational telephone calls]...and to use these costs as a basis for jointly setting rates and dividing revenues" (Ergas and Paterson ( 1991, p. 31 ). However, a more relevant challenge to the British system came not from continental Europe but from the US. The procedure of internal routing imposed severe penalties on US operators. In response AT&T became increasingly concerned over this loss in revenue, and set out to reform the system. In particular, AT&T set out to negotiate direct routing arrangements with major operators within the British system. These arrangements provided for both short-distance transit and, more importantly, a 50:50 split of the accounting rate. For example, in 1938 AT&T rea~:hed an agreement with the Australian operator AWA. That agreement set out established settlement rates for US-Australia calls, and provided that the rates 'shall be the same in both directions'. AT&T's efforts to reform the existing system were assisted by the US regulatory authorities. In marked contrast to other countries, international telephony in the US was provided by a number of operators. After !936 the US Federal Communications Commission (FCC) was concerned that monopoly operators overseas would 'whipsaw' US carriers. As a result, the principle of a 50:50 division of a preagreed accounting rate became "entrenched in FCC oversight procedures and acquired the status of a precondition for joint service with the US" (Ergas and Paterson (1991, p. 33). It is this feature of common settlement rates on which we focus.~ Young (1993) develops an evolutionary model of bargaining between two classes of homogenous individuals. The essential idea is that each bargainer's expectations are shaped by precedent. In each period one agent is drawn at random from each class. These agents take an incomplete sample from past settlements. Each then chooses a best reply assuming that these past settlements are a reasonable predictor of the other's response. "It may happen...that a succession of bargainers coordinate by chance on the same rule over a period of time. This establishes a set of common precedents.,.This feedback loop eventually drives society towards a fixed division" (Young, 1993, p. 146). However, this division will be 50:50 only if each class of bargainers is heterogeneous and there is some mixing between classes. Young's model is inappropriate in explaining a 50:50 division in the context of bilateral monopoly intercontinental telecoms operators: clearly each class consists of only one operator, and is therefore homogeneous; there is no mixing between operators;
One possibilitythat accounts for the almost universal practice of dividing the accounting rate into equal parts is that operators are not maximisingprofits on international routes and choose an equal division of the accountingrate on the basis of equity. Yet in practice, whereas domestic tariffsplausibly reflect equity considerations, most operators seem prepared to earn high rates of return on international calls, and are probably reluctant to make transfers to overseas operators.
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and each operator has access to the entire history of past settlements, not an incomplete sample. Hakim and Lu (1993), on the other hand, examine settlement rates in the context of a one period Nash strategic form game. In particular, they assume that intercontinental telephone calls in each direction are perfect substitutes. Each operator therefore faces a Bertrand-type demand schedule determined by the lower price prevailing in either continent. In addition, they constrain settlement rates a priori to be equal. One of their main results is that under symmetric costs, the 50:50 division is 'incentive compatible for collusion', in which each operator willingly maintains a collection rate that maximises j o i n t profits while at the same time pursuing individual profit maximising strategies. Our paper differs from Hakim and Lu's in three respects. First, we assume there is no substitution between intercontinental calls. We discuss this further in Section 7. Second, we explicitly examine bargaining over settlement rates. Finally, we do not constrain settlement rates a priori to be equal.
3. Noncooperative pricing policies For simplicity we assume only two countries o (outgoing) and i (incoming) 4 Let demand for outgoing calls in o and i be given by X o = X o ( P o) and Xi--xi(ei) respectively. We assume Xo(.) and X~(.) are continuously differentiable up to any degree desired and impose OXklOP k < 0 for k=i,o. Initially we allow the settlement rates to differ, though both countries take them as fixed. Profit for operator o is given by rr,,(P,,) = I P , , - SRj - OCIX,,(Po) + ISRo - IClX~(P~)
(la)
where SR i is the settlement rate paid on outgoing calls from country o to country i, SR o is the settlement rate received on incoming calls from country i to country o, O C is the per unit cost of an outgoing call, assumed to be positive, and I C the per unit cost of an incoming call, also assumed to be positive.5 We assume [ P o - S R , OCIXo(P o) is strictly concave in Po- Similarly for country i profit is given by ~(P~) = [P~ - SR o - OC]Xi(P,) + [SR~ - ICIXo(P o)
Again we assume [ P i - S R o - O C I X i ( P i )
(lb)
is strictly concave in P~. In Eq. (la) and
4 For simplicity we assume the market for international calls is independent o f Uae market . . domestic or national calls. ~ Let P,~,~ solve X,,(P,M,)=O and P~,~ solve PM'r'~I , ~ , ) = O. ":¢e as:;ume p~t and P,,~1 are finite. Moreover, we assume p M > I c + O C for k = i , o (for an end-to-end m o n o p o l i s t the true marginal cost o f an Jt intercontinental call is I C +
OC).
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M. Cave, M.P. Donneily I b#mnation Economics and Policy 8 (1996) 107-123
Eq. (Ib) we have assumed the cost of processing an outgoing call is the same in both countries; the same is true for incoming calls. While these are obviously strong assumptions, we believe them to be true in advanced western countries where the vertical separation of equipment suppliers from operators ensures that technology is fully transferable and relative factor input prices are broadly comparable. 6 In order to model equilibrium collection rates between two separate international telecoms operators, each operator assumes the collection rate in the other country will remain constant. Concentrating on operator o, the programme is Max -n'o(Po) s.t. {e,,)
Po->0.
(2)
Let P* be the argmax of i:,;q. (la). The fact that "fro is additively separable in (Po, SR, OC) and (P~, SR~) rc:@ectively implies P* is independent of Pi and SR o. In this case Po* is optimal wl:~wver level (Pi, SR o) is set. Hence Po* is of the form p, = P o• (SRi, OC). Similarly for operator i P*,=P*,(SR o, OC). The functions Po*(-) and P~*(.) are quasi reac'tion functions. The pair (P~*,Po*) constitutes the unique Rational Conjectures Equilibrium. It is easy to show that OP* o IOSR~> 0 and
OP*o/OOC>O.
4. Bargaining In Eq. (la) and Eq. (lb) the pair of settlement rates (SR o, SR i) is common to both operators. In bargaining over settlement rates 7 operator o will form a i conjecture of the form P i = P , , ( S R , , , S R i ) and operator i of the form Po = P~o(SR,,,SRi). We assume operators are smart and impose Pi=P°(SRo, SRi) = , i (SR,,,.) and P,,= P,,&,:~,,, SR~)-- P , ,* (SR~,.); that is, each operator is sufficiently • intelligent to be able to compute the equilibrium solution (P*, P*). This seems not unreasonable since (i) there are only two operators, (ii) from Eq. (la) and Eq. (lb) each operator is assumed to know the other operator's demand function for outgoing calls, and (iii) costs are the same. We consider three cases.8 In case one each operator is assumed to treat the partner's settlement rate as exogenous. This is equivalent to modelling a noncooperative game; the outcome of this game then serves to determine the threat We are currently researching the case where the per unit costs of the two operators differ. 7 Following the discussion in Section 2, SR, = ARS~AR and SR,, = ARS~,AR. Since ARS~ + ARS,, = ! (or equivalently SR, + SR,, = AR), in bargaining over settlement rates our model allows for bargaining over both the accounting rate SR, + SR, and accounting rate shares SR~ I(SR, + SR,). We are grateful to an anonymous referee for this point. Each operator is assumed to have von Neumann-Morgenstern utility U,,, U, defined over aL, and r L respectively. Normalise utility so that U , ( 0 ) = U,(0)= 0, and assume each operator is risk neutral. Together these imply U = ~r, and U, ='r L.
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point in cases two and three. In case two we allow SR o and SR i to differ. Finally, in case three we impose the restriction SRo =SR,.
4.1. Case one: Non-cooperative determination of settlement rates In this case we model the determination of settlement rates as a noncooperative strategic form game. In particular, each operator can set its own settlement rate at any level it desires but treats the partner's settlement rate as given. Let SR~ solve Xo(P*o(SRw))=O and SR~o~ solve X~(P*,(SRo,.))=O. That SR~ for k = i , o is not infinity follows from the fact that Xk is dispensable (cf. fn. 5). We define strategy spaces for o and i as So={O<-SRo<--SRMo} and S~={O<--SR~<--SR~} respectively. Concentrating on operator o the profit maximisation programme is Max rro(SR o)
{SR,,ES,,i
=
[Po(SRi,.)
-
SR~
-
OCIXo(Po(SR~))
-t-, [SR,, - ICIX,(P, (SRo,.)).
(3)
First-order necessary conditions are dTro
dX i dP~
dSRo-[SRo - 1Cl de~ dSR----~o+ X, <-0
(4)
and [ d~ro 1
Let SR,*° equal the argmax of Eq. (3). Similarly, let SR *~ equal the argmax of operator i's profit maximisation programme.
Proposition 1. The pair (SR o , SR *~) is a Nash noncooperative equilibrium. Proof.
We have to show that ~ro(SR o ,SR~*i)>-~ro(SRo, SR~*~) V SRo~S o and i. Since (4) is independent of SR~ the solution SIC*° is valid for any value of SR~ including SR~ ~. Hence xro(SR o~o , SR*, ~)>--aro(SRo, SR*, ) V SR o E S o. Similarly for operator i. l--1
$o ~ i ( S R o ,SR*,i)>_~ro(SR*o°,SR~)VSRiES
l~,go
Corollary 1. ~rk(SR o , SRi*i)>0 for k = i , o . Proof.
This follows from the fact that IC
i-1
Like all Nash noncooperative equilibria, the pair (SR o ,SR~ i) is inefficient. However, since profits are positive, the profits pair (-tro(SRo,o , S g , i ), Ir~(SR o$o , SR*i)) will serve as a threat point in cases two and three.
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4.2. Case two: Different settlement rates
Let SR* = { S R = ( S R o, SR~) • 0<-SR,, <-SR*'o and O<-SRi<-SR*,~}. Each operator is assumed to maximise profits defined over SR*. In order to simplify matters we shall concentrate on operator o. In this case the programme is * ¢ro(SRo,SR~) = [,r j *o(SRi,.) - SR~ - OC]Xo(Po(SR~,.))
Max {(SR,,SRi)ESR }
+ [SR o - ICIX~(P~(SRo,.)).
First-order necessary conditions are bE,
(6)
9
dX i dP~
- ° + X~ < O, c3SR° - [SR o - ICl d p ~ -dSR
(7)
O'rr,, OSR i
-
-
Xo_
(8)
[ 07r° ]
OSRo SR,, = O,
(9)
afro 1 -~i_]SRi
=0.
(10)
Note that the additively separable nature of "tro(SRo, SRi) implies Eq. (7) and Eq. (8) are independent. This in turn implies that for any SR i o's isoprofit contours are strictly concave at SR*o° (see Fig. 1)) ° Let S R * * ° = ( S R * o * ° , S R * , * ° ) E S R * solve Eq. (6). Similarly let SR **i= (.gR** ~--o i, S R * * i ) E SR* solve operator i's profit maximisation programme. Note that Eq. (7) and Eq. (9) are identical to Eq. (4) and Eq. (5). Moreover, since Eq. (7) and Eq. (8) are independent, the solution SR*o *° is the same. That is, SRo* * ° = SR*o °. The same reasoning applies to i. Clearly each operator wants to pay a zero termination charge but receive as large as one as possible): This obvious conflict is expressed as Proposition 2.
,....oC~R**°,SR**O) # ( S R o**i, SRi**i).
We justify our 'two-stage' approach as follows. Instead of maximising with respect to P. (the first stage) and then with respect to (SR,,. SR,) (the second stage) operator o could have simultaneously maximised with respect to (P,, SR,,, SR,). In this case, however, if the bargained settlement rates differed from o's preferred rates, then o's preferred collection rate is no longer optimal. With our two-stage approach, o's collection rate is always optimal. "' In Fig. ! lower isoprofit curves represent higher levels of profit. ~mThat SR." and SR~' are not infinity follows from the fact that X,, and X are dispensable goods (cf. fn. 5).
M. Cave, M.P. Donneily 1 hlformation Econonzics and Policy 8 (1996) 107-123
!15
SR i
(SRo'O ,SRi*i )=(SRo'*0 ,SRi"i )
SR**N
,SR'*N )
(SRo "N ,SRi°N ) SRi *N
'
!
'
I
I
I I I
I
SR'*N
SRo*N
k
SRo'o
SRo
Fig. I.
Proof. The proof is obvious and is omitted. Corollary 2. Proof.
SR**°~SR**°; i.e. neither operator wants equal settlement rates.
Again the proof is obvious and is omitted.
Since by Proposition 2 optimal settlement rates for o and i differ, some form of bargaining mechanism will have to be. established. We assume bargaining takes place within a Nash fixed threat bargaining model. The Nash model is not the only model of bargaining available. However, it does have the nice property of satisfying Edgeworth's reqmrements; " ~2 and as argued above, Young's model is J2 Edgeworth's requirements are: first that any agreement must make both parties at least as well off as no agreement (called individual rationality); and second that any agreement must be Parete optimal.
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inappropriate. The set of feasible settlement rates is SR*. Let ax-SR*---)R 2 be defined by ~r=~r(SR)=(~ro(SR),~ri(SR)) where SR~SR*. The set H * = {~r(SR)'SRESR*} parametrically defines the profit possibilities set. We take the ,o threat point to be d=~r(SR o ,SR.*,~) given by d in Fig. 1 In Fig. 1 the locus of tangencies between isoprofit contours is the contract curve. Given the above F * = ( H * , d) constitutes a two-agent fixed threat bargaining game. The game is one without side payments since these are currently impracticable. Let SR*oN and SR.*,N represent the Nash bargaining solution to F*. Since a Nash solution satisfies individual rationality, it is clear that SRo*N>0 and SR~ N>0. Complementary slackness then requires O'trlOSRo=O and O'rrlOSR~=0.
Proposition 3. SR *N = SR *N (= SR *N) if and only if ~ro(IC, IC)= 7ri(IC, IC). In this case SR *N = IC. Proof. -? Fi:st-order necessary conditions evaluated at SR *N are o-S-~o(SR , SR *N) = ~ [SR *N - IC]-d~~ d-fiR-° + X~ - rroX~= 0,
(ll)
OSR---~(SR"N, SR *N) = ~, [SR *N _ ICI dXo dPo dP o dSR~ + X° - ~X° = 0.
(12)
Rearranging slightly yields dXi d P ? ]
~ [SR*N _ 1Cl dP~ dSR o = X~[E, - N], dX° d P o ]
71"0 [SR *N -
IC] dp ° dSR~ = Xo[zr~ - Cro].
(13)
(14)
The right-hand sides of Eq. (13) and Eq. (14) have opposite signs. However, the left-hand sides have the same sign. Hence equality can be preserved only if both sides are equal to zero. If rro(SR *N, SR*N)~ri(SR *N, SR*N), then from Eq. (13) and Eq. (14) Xo(P*o(sR*N))=X~(P~*(SR*N))=O and SR*N=IC. But then aXo(SR*N, SR*N)=xri(SR *N, sR*N)=0, a contradiction. Hence "tro(SR*N, SR*N) = 7ri(SR*N, SR*N). Suppose 7ro(SR*N, SR*N)=~ri(SR*N, SR*N)=O. By corollary ,o one ~rk(SRo ,SRi*i)>o for k=i,o. Hence ~ro(SR*N, SR*N)=rri(SR*N, SR*N)=O violates individual rationality. This leaves "rro(SR*N, SR*N)= "ffi(SR *N, SR*N)>0. In this case SR*N=IC is the only solution. ~ B y the Intermediate Value Theorem H* is convex. This implies that a unique interior solution exists. By footnote 5 ~o(IC, IC)=~ri(IC, I C ) > 0 and Eq. ( 11 ) and Eq. (12) are only satisfied at SR*oN=SRi*N=IC. [-] It follows from Proposition 3 mat 7ro(IC, I C ) ~ ( I C ,
IC) is necessary and
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sufficient to establish SR,*N 5~SR~ N. T h e two operators will bargain on a common settlement rate if and only if the profits maxima evaluated at an incoming cost-based settlement rate are the same. If demand were the same in both countries, this would be the case. It might also arise from other combinations of circumstances, but generally the operators would find it in their interests to agree different settlement rates as illustrated in Fig. 1.
4.3. Case three: A common settlement rate In this case each operator is constrained to face a common settlement rate SR. Define the restricted domain SR**={SR~_SR* :SRo=SR~}. Concentrating on operator o the programme is Max
{SR~SR "*}
~o(SR) =[P*o(SR,.) - SR - OC]Xo(P~,(SR,.)) +[SR - IC]X,(Pi(SR,.)). (15)
Let SR ***° be the argmax of Eq. (15). Similarly, let SR ***~ solve i's profit maximisation problem. As before, the likely emergence of conflicts of interest between the operators over the settlement rate is expressed as
Proposition 4.
SR***°=SR ***i if and only if Xo(P*(IC, .))=Xi(P*, (IC, .)).
Proof.
The proof proceeds by way of two lemmas and is relegated to the appendix.
If Xo(P*o(IC, .))~X~(P*(1C, .)) a bargaining mechanism will have to be established. Again we assume bargaining takes place within a Nash fixed threat bargaining model. In this case we define the restricted profit possibilities set H * * ={'tr(SR) : SRESR**}. We assume the threat point remains d = ,o r(SRo, SR*').
Given the above F * * = ( H * * , d) constitutes a two-agent fixed threat bargaining game. The Nash solution to F * * is denoted SR **N (see Fig. 1).
5. Why a c o m m o n settlement rate
The two operators have traditionally agreed to an equal division of the accounting rate into common settlement rates. By Proposition 3 if rro(IC, IC)= 7ri(IC, IC) then SR*oN=SR*, N. On the other hand, if aro(IC, IC)¢:xri(IC, IC) then SR*oN¢:SR~*~ and the model fails to account for a system of common settlement rates. However, under the assumptions we have made, a solution to the restricted
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Nash bargaining problem in case three (Section 4.3 is guaranteed to exist. 13 Moreover 'trk(SR **N, SR **N )>'rrk(SR o.o , SR *i) for k = i , o by individual rationality. In this case there is at least one point on the 45 ° degree line in Fig. l that affords greater profits than the threat point d. Since the outcome of a Nash bargaining game is Pareto efficient, one operator, say o, must experience a loss in profit while the other operator i experiences a gain in a move away from a negotiated system in which settlement rates are allowed to differ to a negotiated system in which they are not. Thus one of the operators i has an incentive to collude with its regulatory authority and insist on a system of common settlement rates as a precondition for negotiation) 4 The question then becomes 'is such a threat credible?' Recall from ~ection 2 that after 1936 the principle of a 50:50 division of a preagreed accounting rate became "entrenched in FCC oversight procedures and acquired the status of a precondition for joint service with the US". In this case the threat is credible since the choice is between the point on the 45 ° line or point d. The other operator o accepts this precondition because individual rationality dictates that ,.rro(SR**N, SR**N)~ "tro(SR o.o , SR *~) and informational asymmetries preclude its regulator from imposing particular settlement rates.
6. A more complex demand specification Like other telephone calls, international calls are unusual economic goods in that the cooperation of at least two parties is required for the good to be made available. Since only one party is normally billed for the call, there is an externality associated with any call, which - since the call can be refused - is normally positive. When calls between two parties are made frequently, this externality can be internalised by agreed rotation. Decisions to make calls may also be influenced by altruism, or the presence of inter-dependent utilities. Finally, where tariffs for outgoing and incoming calls differ, the parties can agree that the call should be made where rates are lower, possibly with a side payment. ~n operational terms, some of these effects can be captured by introducing into the demand equations variables cupturing reciprocation (outgoing calls eliciting incoming calls) and reversion (calling from the cheaper country) effects. The demand functions in Section 3 are augmented by the tariff charged and the volume
~3The set SR* is a k-cell and is therefore compact. The set SR** is a closed subset of SR* and is therefore also compact. Since "trk(SR) is continuous on SR**, a solution to the restricted Nash bargaining problem exists. ~4Due to information asymmetries the regulator is hardly in a position to insist ,an particular settlement rates, but it is in a position to insist on a settlement rate rule. The 50:50 division is one such rule.
M. Cave, M.P. Donnelly I h~formation Economics and Policy 8 (1996) 107-123
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of calls made in the other country, becoming Xo=X,,(Po, Pi, X~) and Xi-X,(P,,, P,, Xo) respectively. The effect of this change is to eliminate the additively separable nature of ax, and "rri, thus complicating the analysis significantly. The problem throughout is that operator o has to take into account the indirect effect of its preferred settlement rate, which feeds into operator i's collection rate. This both influences call reversion and (by affecting the level of calls from i to o) elicits a new level of call reciprocation. It can easily be shown that the presence of reciprocation does not allow the own-price effect and the cross-price effect to be signed; that is, with reciprocation the total derivatives OXo I OP, and/gXo/0P~ are ambiguous. Acton and Vogelsang (1992) investigate the presence of reciprocation and reversion effects on the basis of annual data for call minutes between the US and 17 Western European countries over the period 1979-86. They find that the total own-price effect is negative and statistically significant at the 5% level while the total cross-price effect is ambiguous and statistically insignificant at the 5% level) s However, this last result must be interpreted with care. Reciprocation alone is likely to produce negative cross-price elasticity, while reversion alone will generate a positive cross-price elasticity. As Acton and Vogelsang (1992, p. 318) point out: "coefficients that are not statistically significant from zero could be consistent with the absence of either motivations or with both motivations cancelling one another out". On the other hand, Cheong and Muilins (1991) construct an econometric model to investigate whether telephone traffic deficits on individual routes out of the US are the result of tariff differences between outgoing and incoming calls or lower income levels in destination countries. Cheong and Mullins find that while relative income levels are important in explaining traffic imbalances, the impact of tariff differentials is statistically insignificant. Even though for the period of the study tariff rates in countries such as Italy, Greece and the Federal Republic of Germany were up to twice as high as corresponding US rates, call reversion was still not a significant feature compared to relative income levels. Adopting a different approach, Sandbach (1995) empirically develops an argument previously proposed by Acton and Vogelsang (1992). The latter argue that there are transaction costs involved in call reversion. Therefore, call reversion occurs only after the tariff differential between the outgoing and incoming route exceeds the transaction cost. Sandbach includes his econometric model both the
i.s Appelbe et al. (1988) and Larson et al. (1990) investigate the presence of reciprocation only and not reversion. Both studies find that reciprocation is strongly present and statistically significant at the 1% level. Hence reversion cannot be eliminated from the demand functions (eliminating reversion allows the own-price effect to be unambiguously signed). However, both of these studies consider the presence of reciprocation only. These studies then suffer from a potential "omitted variables" problem which the authors do not address.
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M. Cave, M.P. Donnelly / blformation Economics and Policy 8 (1996) 107-123
tariff differential and a nonlinear term in the tariff differential which only takes effect when the differential between outgoing and incoming calls exceeds $0.90 a minute. This last term is included to test the hypothesis that call reversion only occurs when the price differential exceeds a threshold. Data were collected on 154 international routes. Both the ordinary tariff differential and the nonlinear tariff differential are statistically insignificant at the 5% confidence level. Sandbach (1995, p. 11) notes: "[The]...data set included 6 pairs of routes in which the premium for an incoming call (compared to an outgoing call) exceeded 50 cents a minute. If call reversal were a significant phenomena at these levels of price differential, the model should have identified it. The most extreme case was the UK to Japan route where, despite a premium of 130 cents a minute, traffic is still 10% heavier into than out of the UK. From this analysis, we concluded that, for a very large range of price differentials between incoming and outgoing traffic, call reversal is not a significant phenomenon." While call reversion is interesting from a theoretical point of view and although there is much recent discussion of the phenomenon, the empirical evidence suggests that its effects are still statistically insignificant. Evidence in favour of reciprocation appears to be stronger in terms of its statistical significance (see footnote 15). At the same time, the Acton and Vogelsang study finds no statistical significance in the combined effect of the two phenomena. We believe that our simplified demand specification is thus empirically justifiable) 6
7. Discussion This paper has shown how profit maximising monopoly intercontinental telephone operators will set accounting and settlement rates. We have shown how the two rates are jointly determined in both a cooperative and a non-cooperative context: both are higher in the latter case. The paper has also shown that common settlement rates will only emerge in unlikely circumstances. A necessary and sufficient condition is that the profits maxima evaluated at an incoming cost-based settlement rate are the same. If demand were the same in both countries, this would be the case. It might also arise from other combinations of circumstances, but generally the operators would find it in their interests to agree different settlement rates. ~" From a modelling point of view, the incorporation of both reciprocation and reversion effects influences the reaction functions and may thus lead to a situation in which no equilibrium exi~,,ts. When only one of the effects is present, however, it can be shown that an equilibrium exists. (Proofs of these propositions are available from the authors.)
M. Cave, M.P. Donneily I Information Economics and Policy 8 (1996) 107-123
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However, although there is nothing intrinsic in a 50:50 division of the accounting rate, one of the operators in collusion with its regulator always has an incentive to insist on a system of common settlement rates as a precondition for negotiation in preference to a system which allows settlement rates to differ. The other operator will accept this precondition since the threat is credible and the profit it earns under a system of common settlement rates is greater than under a system of unilaterally imposed settlement rates.
Acknowledgments We would like to thank Jonathan Michie for help with an earlier version of this paper, and Cheryl Mourisseav for helpful comments and suggestions.
Appendix 1 Differentiating Eq. (15) and the corresponding profit function for i, first-order necessary conditions are dzro dSR
dXi dP~ X o + X~ + [ S R - I C l d p ~ d S e -< 0,
(A.1)
dR dSR
dXo dPo X i + Xo + [ S R - I C l d p ° dSR <- 0,
(A.2)
[ d~o-I d-ff~JSR = 0,
(A.3)
[d~] ~--R-JSR = 0.
(k.4)
Lemma 1. IC.
SR * * * ° = SR ***i (= SR**) if and only if SR ***° = 1C and SR ***i=
Proof. ~ S u p p o s e SR ***°= SIC***~ ( = SR***). There are two cases to consider. (i) S R * * * - 0 . In this case Eq. (A.l) and Eq. (A.2) imply
dXo d e o dX i dP~ - IC-dp i dSR <- 1 C dP - - o dSR"
(A.5)
This is a contradiction. Therefore S R * * = O is not possible. (ii) SR***>0. In this case complementary slackness implies
M. Cave, M.P. Donnelly / h~formation Economics and Policy 8 (1996) 107-123
122
[SR*** - 1Cl-d ,
dP; -
dX,, dP,: [SR*** - IC]dp ° dSR
(A.6)
Since the two sides of this equation are of opposite sign, they can be equal only if SR*** = IC. ~ I f SR***°= IC and SR***i= IC, then SR***°= SR ***~. [-1
Lemma 2. SR ***° (SR***i)=IC if and only if Xo(P*o(IC,.))=Xi(P*(IC,.)). Proof.
=,Suppose SR*o** =IC>O. First-order necessary conditions reduce to d~-o(IC)
dSR
Xo(P*,,(IC,.)) + X~(P~ (IC,.)) <- 0
(A.7)
However, since S R * * * - I C > 0 , complementary slackness requires daro/dSR=O. ~ L i k e the proof of Proposition 3 a unique solution exists; and SR ***° =IC satisfies the first-order condition. I-I Proposition 4 is then an immediate consequence of Lemmas 1 and 2.
References Acton, J.E and I. Vogelsang 1992, Telephone demand over the Atlantic: Evidence from co,retry-pair data, Journal of Industrial Economics XL, 1-19. Appelbe, T.W., N.A. Snihur, C. Dineen, D. Fames and R. Giorano, 1988, Point-to-point modelling: An application to Canada-Canada and Canada-United States long distance calling, Information Economics and Policy 3, 311-331. Cave, M. and J. Michie, 1991, Developing competition in international telephone service, In: F. Klaver and E Slaa, eds., Telecommunication: New signposts to old roads (IOS Press, Amsterdam). Cheong, K. and M. Mullins, 1991, International telephone service imbalances, Telecommunications Policy, April, 107-118. Ergas, H. and E Paterson, 1991, International telecommunications settlement arrangements, Telecommunications Policy, Feb., 29-48. Eward, R., 1985, The deregulation of international telecommunications (RAND, Santa Monica, CA). Hakim, S.R. and D. Lu, 1993, Monopolistic settlement agreements in international telecommunications, Information Economics and Policy 5, 145-157. Johnson, L.L., 1989/91, Dealing with monopoly in international telephone service: A U.S. perspective, Information Economics and Policy, 225-234. Larson, A.C., D.E. Lehman and D.L. Weisman, 1990, A general theory of point-to-point long distance demand, In: A. deFontenay, M.H. Shugard and D.S. Sibley, eds., Telecommunications demand modelling (North-Holland, Amsterdam). Milgrom, E and J. Roberts, 1992, Economics organisation and management (Prentice Hall, New York). Nash, J., 1950, The bargaining problem, Econometrica 18, 155-62.
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OECD, 1995, International telecommunications practices and principles: A progress review tOECD, Paris). Sandbach, I., 1995, International telephone traffic, callback and policy implications, Mimeo. (NERA, London). Young, H.E, 1993, An evolutionary model of bargaining, Journal of Economic Theory 59, 145-168.
ELSEVIER
Information Economics and Policy 8 (1996) 107-123
The pricing of international telecommunications services by monopoly operators a~
Martin Cave " , Mark P. Donnelly b ~Departmem of Economics, Brunel, the University of West London. Uxbridge. Middlesex UB8 3PH, UK hCoopers & Lybrand, London, UK Received 12 August 1994: accepted 30 November 1995
Abstract International telecommunications operators usually set their own tariffs, but traditionally reimburse one another at a uniform settlement rate. We identify profit maximising tariffs where settlement rates are initially allowed to differ. We then explore Nash bargaining over settlement rates. We show that only under circumstances which are unlikely to occur in practice will two monopoly operators agree on a system of common settlement rates. However, we show that one operator in collusion with its regulatory authority always has an incentive to insist on uniform settlement rates as a precondition for negotiation.
Key words: Accounting rate system; Bilateral bargaining; International telecommunications JEL Classification: L96; FI3
1. Introduction
The cost of an intercontinental telephone call has fallen dramatically over the past 35 years. For example, the per minute cost of using trans-Atlantic cable was $2.53 in 1956, $0.04 in 1988, $0.02 in 1992 and is still coming down. The costs of originating and terminating the call in the countries concerned have also fallen, but by a smaller proportion. However, although intercontinental call charges or collection rates have fallen, Cave and Michie (1991) argue that in many cases they * Corresponding author. Department of Economics, Brunel, Uxbridge, United Kir~gaom. Tel: +44 1895 203320 Fax: +44 1895 274697. 0167-6245/96/515.00 Copyright © 1996 Elsevier Science B.V. All fights reserved Pll SO 167-6245 ( 9 6 ) 0 0 0 0 4 - 2
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M. Cave. M.P. Dmmellv I h~fonnation Economics and Policy 8 (1996) 107-123
have not fallen by anything like the margin necessary to account for the reduction in cost. One explanation is that Ramsey-type pricing is being practised to cover non-traffic-sensitive costs. This implies that a greater mark-up should be charged on market segments with a lower elasticity of demand. However, in empirical work the elasticity of demand is higher on international calls than on national calls. Thus if Ramsey-type pricing were being followed the divergence in mark-up would be in the opposite direction. A more plausible explanation lies in the accounting arrangements by which telecoms operators reimburse each other through a system of settlement rates paid for delivering an intercontinental ca!!~ This system of settlement rates partly explains why international charges have not fallen to match the reductions in cost resulting from advances in technology. ~ Cave and Michie (1991) show that the settlement rate is a component of marginal cost, and thus feeds into collection rates charged by telecoms operators in the usual manner. This leads to a form of 'double marginalisation' (see Milgrom and Roberts, 1992, pp. 550-551 ). The first margin is the excess of the settlement rate over the cost of completing an incoming call. This is then fed into setting of the collection rate, establishing a second margin. As a consequence, prices are higher when set by monopolists at each end than would be charged by joint profit-maximising monopolists at each end, or by an operator which owned or part-owned the facilities in the other country. Moreover, the settlement rate system also creates an incentive for the operator receiving more calls than it makes to keep the settlement rate high. This paper examines the incentives faced by monopoly operators in fixing settlement rate~ and call charges in an environment of double marginalisation. We do not explicitly consider the role of the rcgulator in the model, even though regulators in many instances have to approve settlement and collection rates. The reason for this is that we regard the interests of the regulator and of its monopoly operator as being broadly congruent. Typically, profits from international calls are used to cross-subsidise domestic services, often at the regulators' behest. Regulators thus have an interest in maximising profits. This approach is supported by the casual observation that the regulatory body working most publicly to reduce accounting and settlement rates is at present the FCC, and - given the general predominance of outgoing over incoming calls in the US - both regulator and operators have an interest in reducing the settlement rates on US routes. The organisation of the paper is as follows. Section 2 describes accounting arrangements whereby telecoms operators reimburse each other for incoming calls and presents a survey of the literature. Section 3 analyses Bertrand-Nash noncooperative pricing policy of international telecoms operators with given settlement rates. Section 4 investigates bargaining over settlement rates. Since intercontinental telecoms operators have traditionally agreed on a system of This is due to advances in technology such as the introduction of seabed cables using fibre optics.
M. Cave. M.P. Dmmelly I hlformation Economics and Policy g (1996) 107-123
109
common settlement rates, Section 5 explores the circumstances in which such an agreement will occur. Section 6 considers how the results are effected by a more complex sp':cification of demand conditions. The main conclusion of the paper is that a Nash-bargained (Nash, 1950) system of common settlement rates emerges only in exceptional circumstances; but that one operator acting in collusion with its regulatory authority always has an incentive to insist on equal settlement rates as a precondition for negotiation. Finally, Section 7 draws some conclusions.
2. Accounting arrangements Between any two countries o and i the price Po set for interna6onal telephone calls Xo and charged to the customer in country o is referred to as the tariff or collection rate; similarly for country i. Since an outgoing call from country o is an incoming call for country i, the two operators must enter into a cooperative arrangement. The 'operating agreement' negotiated by the carriers describes the technical details of interconnection and the terms of reimbursement. The two operators agree a rate known as the accounting rate A R Payme~t~ fnr delive~ of a call is then made in proportion to AR and is known as the settlement rate SR. The proportion of the accounting rate paid by the operator originating the call to the operator terminating the call is called the 'accounting rate share' ARS. Hence the settlement rate is given by SR = ARS*AR. Generally the accounting rate is split 50:50 between the two operators.-" The principle of a 50:50 division of the accounting rate was established in the 1930s. "Up to the early 1930s the bulk of intercontinental telecommunications traffic was accounted for by the British Empire telecommunications system, dominated by Cable & Wireless. A key element of the company's strategy was the routing through London of most traffic originating in the Empire, regardless of whether this was the most direct route available" (Ergas and Paterson (1991, p. 30)). This had the effect of minimising net payments to non-UK operators. At the same time, European Post, Telegraph and Telephone operators (FITs) were entering into their own arrangements. Unlike C&W these operators did not have end-to-end control of international exchanges, and were obliged to "...negotiate joint service provision arrangements with other carriers on a relatively equal footing" (Ergas and Paterson (1991, p. 31 ). Initially these arrangements were developed for the handling of international telegrams. The development of international telephony led to important changes in z For a fuller account of the historic financial arrangements between international telecoms operators see Eward (1985), Johnson (1989/91), Cave and Michie (1991), and Ergas and Paterson (1991). The settlement rate applied to intematic, nal calls is not the only model for establishing call charges. Within Europe and the Mediterranean basin (TEUREM) settlement rates are determined per 100 Km of distance plus an amount added for the cost of completing an incoming call. Settlement rates for termination and/or transit are thus cost based and related to distance. Yet a different systen~ operates between the US and Canada. See OECD (1995) for further details.
! 10
M. Cave. M.P. Donneliv I h!fonnation Economics and Policy 8 (1996) 107-123
these agreements. In particular, "...attempts were made to objectively determine the costs involved in providing...linternational telephone calls]...and to use these costs as a basis for jointly setting rates and dividing revenues" (Ergas and Paterson ( 1991, p. 31 ). However, a more relevant challenge to the British system came not from continental Europe but from the US. The procedure of internal routing imposed severe penalties on US operators. In response AT&T became increasingly concerned over this loss in revenue, and set out to reform the system. In particular, AT&T set out to negotiate direct routing arrangements with major operators within the British system. These arrangements provided for both short-distance transit and, more importantly, a 50:50 split of the accounting rate. For example, in 1938 AT&T rea~:hed an agreement with the Australian operator AWA. That agreement set out established settlement rates for US-Australia calls, and provided that the rates 'shall be the same in both directions'. AT&T's efforts to reform the existing system were assisted by the US regulatory authorities. In marked contrast to other countries, international telephony in the US was provided by a number of operators. After !936 the US Federal Communications Commission (FCC) was concerned that monopoly operators overseas would 'whipsaw' US carriers. As a result, the principle of a 50:50 division of a preagreed accounting rate became "entrenched in FCC oversight procedures and acquired the status of a precondition for joint service with the US" (Ergas and Paterson (1991, p. 33). It is this feature of common settlement rates on which we focus.~ Young (1993) develops an evolutionary model of bargaining between two classes of homogenous individuals. The essential idea is that each bargainer's expectations are shaped by precedent. In each period one agent is drawn at random from each class. These agents take an incomplete sample from past settlements. Each then chooses a best reply assuming that these past settlements are a reasonable predictor of the other's response. "It may happen...that a succession of bargainers coordinate by chance on the same rule over a period of time. This establishes a set of common precedents.,.This feedback loop eventually drives society towards a fixed division" (Young, 1993, p. 146). However, this division will be 50:50 only if each class of bargainers is heterogeneous and there is some mixing between classes. Young's model is inappropriate in explaining a 50:50 division in the context of bilateral monopoly intercontinental telecoms operators: clearly each class consists of only one operator, and is therefore homogeneous; there is no mixing between operators;
One possibilitythat accounts for the almost universal practice of dividing the accounting rate into equal parts is that operators are not maximisingprofits on international routes and choose an equal division of the accountingrate on the basis of equity. Yet in practice, whereas domestic tariffsplausibly reflect equity considerations, most operators seem prepared to earn high rates of return on international calls, and are probably reluctant to make transfers to overseas operators.
M. Cave, M.P. Dmmelly I h~formation Economics and Policy 8 (1996) 107-123
ii1
and each operator has access to the entire history of past settlements, not an incomplete sample. Hakim and Lu (1993), on the other hand, examine settlement rates in the context of a one period Nash strategic form game. In particular, they assume that intercontinental telephone calls in each direction are perfect substitutes. Each operator therefore faces a Bertrand-type demand schedule determined by the lower price prevailing in either continent. In addition, they constrain settlement rates a priori to be equal. One of their main results is that under symmetric costs, the 50:50 division is 'incentive compatible for collusion', in which each operator willingly maintains a collection rate that maximises j o i n t profits while at the same time pursuing individual profit maximising strategies. Our paper differs from Hakim and Lu's in three respects. First, we assume there is no substitution between intercontinental calls. We discuss this further in Section 7. Second, we explicitly examine bargaining over settlement rates. Finally, we do not constrain settlement rates a priori to be equal.
3. Noncooperative pricing policies For simplicity we assume only two countries o (outgoing) and i (incoming) 4 Let demand for outgoing calls in o and i be given by X o = X o ( P o) and Xi--xi(ei) respectively. We assume Xo(.) and X~(.) are continuously differentiable up to any degree desired and impose OXklOP k < 0 for k=i,o. Initially we allow the settlement rates to differ, though both countries take them as fixed. Profit for operator o is given by rr,,(P,,) = I P , , - SRj - OCIX,,(Po) + ISRo - IClX~(P~)
(la)
where SR i is the settlement rate paid on outgoing calls from country o to country i, SR o is the settlement rate received on incoming calls from country i to country o, O C is the per unit cost of an outgoing call, assumed to be positive, and I C the per unit cost of an incoming call, also assumed to be positive.5 We assume [ P o - S R , OCIXo(P o) is strictly concave in Po- Similarly for country i profit is given by ~(P~) = [P~ - SR o - OC]Xi(P,) + [SR~ - ICIXo(P o)
Again we assume [ P i - S R o - O C I X i ( P i )
(lb)
is strictly concave in P~. In Eq. (la) and
4 For simplicity we assume the market for international calls is independent o f Uae market . . domestic or national calls. ~ Let P,~,~ solve X,,(P,M,)=O and P~,~ solve PM'r'~I , ~ , ) = O. ":¢e as:;ume p~t and P,,~1 are finite. Moreover, we assume p M > I c + O C for k = i , o (for an end-to-end m o n o p o l i s t the true marginal cost o f an Jt intercontinental call is I C +
OC).
I12
M. Cave, M.P. Donneily I b#mnation Economics and Policy 8 (1996) 107-123
Eq. (Ib) we have assumed the cost of processing an outgoing call is the same in both countries; the same is true for incoming calls. While these are obviously strong assumptions, we believe them to be true in advanced western countries where the vertical separation of equipment suppliers from operators ensures that technology is fully transferable and relative factor input prices are broadly comparable. 6 In order to model equilibrium collection rates between two separate international telecoms operators, each operator assumes the collection rate in the other country will remain constant. Concentrating on operator o, the programme is Max -n'o(Po) s.t. {e,,)
Po->0.
(2)
Let P* be the argmax of i:,;q. (la). The fact that "fro is additively separable in (Po, SR, OC) and (P~, SR~) rc:@ectively implies P* is independent of Pi and SR o. In this case Po* is optimal wl:~wver level (Pi, SR o) is set. Hence Po* is of the form p, = P o• (SRi, OC). Similarly for operator i P*,=P*,(SR o, OC). The functions Po*(-) and P~*(.) are quasi reac'tion functions. The pair (P~*,Po*) constitutes the unique Rational Conjectures Equilibrium. It is easy to show that OP* o IOSR~> 0 and
OP*o/OOC>O.
4. Bargaining In Eq. (la) and Eq. (lb) the pair of settlement rates (SR o, SR i) is common to both operators. In bargaining over settlement rates 7 operator o will form a i conjecture of the form P i = P , , ( S R , , , S R i ) and operator i of the form Po = P~o(SR,,,SRi). We assume operators are smart and impose Pi=P°(SRo, SRi) = , i (SR,,,.) and P,,= P,,&,:~,,, SR~)-- P , ,* (SR~,.); that is, each operator is sufficiently • intelligent to be able to compute the equilibrium solution (P*, P*). This seems not unreasonable since (i) there are only two operators, (ii) from Eq. (la) and Eq. (lb) each operator is assumed to know the other operator's demand function for outgoing calls, and (iii) costs are the same. We consider three cases.8 In case one each operator is assumed to treat the partner's settlement rate as exogenous. This is equivalent to modelling a noncooperative game; the outcome of this game then serves to determine the threat We are currently researching the case where the per unit costs of the two operators differ. 7 Following the discussion in Section 2, SR, = ARS~AR and SR,, = ARS~,AR. Since ARS~ + ARS,, = ! (or equivalently SR, + SR,, = AR), in bargaining over settlement rates our model allows for bargaining over both the accounting rate SR, + SR, and accounting rate shares SR~ I(SR, + SR,). We are grateful to an anonymous referee for this point. Each operator is assumed to have von Neumann-Morgenstern utility U,,, U, defined over aL, and r L respectively. Normalise utility so that U , ( 0 ) = U,(0)= 0, and assume each operator is risk neutral. Together these imply U = ~r, and U, ='r L.
M. Cave. M.P. Donneily I h~fonnation Economics and Policy 8 (1996) 107-123
113
point in cases two and three. In case two we allow SR o and SR i to differ. Finally, in case three we impose the restriction SRo =SR,.
4.1. Case one: Non-cooperative determination of settlement rates In this case we model the determination of settlement rates as a noncooperative strategic form game. In particular, each operator can set its own settlement rate at any level it desires but treats the partner's settlement rate as given. Let SR~ solve Xo(P*o(SRw))=O and SR~o~ solve X~(P*,(SRo,.))=O. That SR~ for k = i , o is not infinity follows from the fact that Xk is dispensable (cf. fn. 5). We define strategy spaces for o and i as So={O<-SRo<--SRMo} and S~={O<--SR~<--SR~} respectively. Concentrating on operator o the profit maximisation programme is Max rro(SR o)
{SR,,ES,,i
=
[Po(SRi,.)
-
SR~
-
OCIXo(Po(SR~))
-t-, [SR,, - ICIX,(P, (SRo,.)).
(3)
First-order necessary conditions are dTro
dX i dP~
dSRo-[SRo - 1Cl de~ dSR----~o+ X, <-0
(4)
and [ d~ro 1
Let SR,*° equal the argmax of Eq. (3). Similarly, let SR *~ equal the argmax of operator i's profit maximisation programme.
Proposition 1. The pair (SR o , SR *~) is a Nash noncooperative equilibrium. Proof.
We have to show that ~ro(SR o ,SR~*i)>-~ro(SRo, SR~*~) V SRo~S o and i. Since (4) is independent of SR~ the solution SIC*° is valid for any value of SR~ including SR~ ~. Hence xro(SR o~o , SR*, ~)>--aro(SRo, SR*, ) V SR o E S o. Similarly for operator i. l--1
$o ~ i ( S R o ,SR*,i)>_~ro(SR*o°,SR~)VSRiES
l~,go
Corollary 1. ~rk(SR o , SRi*i)>0 for k = i , o . Proof.
This follows from the fact that IC
i-1
Like all Nash noncooperative equilibria, the pair (SR o ,SR~ i) is inefficient. However, since profits are positive, the profits pair (-tro(SRo,o , S g , i ), Ir~(SR o$o , SR*i)) will serve as a threat point in cases two and three.
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M. Cave. M.P. Donnelly I Information Economics and Policy 8 (1996) 107-123
4.2. Case two: Different settlement rates
Let SR* = { S R = ( S R o, SR~) • 0<-SR,, <-SR*'o and O<-SRi<-SR*,~}. Each operator is assumed to maximise profits defined over SR*. In order to simplify matters we shall concentrate on operator o. In this case the programme is * ¢ro(SRo,SR~) = [,r j *o(SRi,.) - SR~ - OC]Xo(Po(SR~,.))
Max {(SR,,SRi)ESR }
+ [SR o - ICIX~(P~(SRo,.)).
First-order necessary conditions are bE,
(6)
9
dX i dP~
- ° + X~ < O, c3SR° - [SR o - ICl d p ~ -dSR
(7)
O'rr,, OSR i
-
-
Xo_
(8)
[ 07r° ]
OSRo SR,, = O,
(9)
afro 1 -~i_]SRi
=0.
(10)
Note that the additively separable nature of "tro(SRo, SRi) implies Eq. (7) and Eq. (8) are independent. This in turn implies that for any SR i o's isoprofit contours are strictly concave at SR*o° (see Fig. 1)) ° Let S R * * ° = ( S R * o * ° , S R * , * ° ) E S R * solve Eq. (6). Similarly let SR **i= (.gR** ~--o i, S R * * i ) E SR* solve operator i's profit maximisation programme. Note that Eq. (7) and Eq. (9) are identical to Eq. (4) and Eq. (5). Moreover, since Eq. (7) and Eq. (8) are independent, the solution SR*o *° is the same. That is, SRo* * ° = SR*o °. The same reasoning applies to i. Clearly each operator wants to pay a zero termination charge but receive as large as one as possible): This obvious conflict is expressed as Proposition 2.
,....oC~R**°,SR**O) # ( S R o**i, SRi**i).
We justify our 'two-stage' approach as follows. Instead of maximising with respect to P. (the first stage) and then with respect to (SR,,. SR,) (the second stage) operator o could have simultaneously maximised with respect to (P,, SR,,, SR,). In this case, however, if the bargained settlement rates differed from o's preferred rates, then o's preferred collection rate is no longer optimal. With our two-stage approach, o's collection rate is always optimal. "' In Fig. ! lower isoprofit curves represent higher levels of profit. ~mThat SR." and SR~' are not infinity follows from the fact that X,, and X are dispensable goods (cf. fn. 5).
M. Cave, M.P. Donneily 1 hlformation Econonzics and Policy 8 (1996) 107-123
!15
SR i
(SRo'O ,SRi*i )=(SRo'*0 ,SRi"i )
SR**N
,SR'*N )
(SRo "N ,SRi°N ) SRi *N
'
!
'
I
I
I I I
I
SR'*N
SRo*N
k
SRo'o
SRo
Fig. I.
Proof. The proof is obvious and is omitted. Corollary 2. Proof.
SR**°~SR**°; i.e. neither operator wants equal settlement rates.
Again the proof is obvious and is omitted.
Since by Proposition 2 optimal settlement rates for o and i differ, some form of bargaining mechanism will have to be. established. We assume bargaining takes place within a Nash fixed threat bargaining model. The Nash model is not the only model of bargaining available. However, it does have the nice property of satisfying Edgeworth's reqmrements; " ~2 and as argued above, Young's model is J2 Edgeworth's requirements are: first that any agreement must make both parties at least as well off as no agreement (called individual rationality); and second that any agreement must be Parete optimal.
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inappropriate. The set of feasible settlement rates is SR*. Let ax-SR*---)R 2 be defined by ~r=~r(SR)=(~ro(SR),~ri(SR)) where SR~SR*. The set H * = {~r(SR)'SRESR*} parametrically defines the profit possibilities set. We take the ,o threat point to be d=~r(SR o ,SR.*,~) given by d in Fig. 1 In Fig. 1 the locus of tangencies between isoprofit contours is the contract curve. Given the above F * = ( H * , d) constitutes a two-agent fixed threat bargaining game. The game is one without side payments since these are currently impracticable. Let SR*oN and SR.*,N represent the Nash bargaining solution to F*. Since a Nash solution satisfies individual rationality, it is clear that SRo*N>0 and SR~ N>0. Complementary slackness then requires O'trlOSRo=O and O'rrlOSR~=0.
Proposition 3. SR *N = SR *N (= SR *N) if and only if ~ro(IC, IC)= 7ri(IC, IC). In this case SR *N = IC. Proof. -? Fi:st-order necessary conditions evaluated at SR *N are o-S-~o(SR , SR *N) = ~ [SR *N - IC]-d~~ d-fiR-° + X~ - rroX~= 0,
(ll)
OSR---~(SR"N, SR *N) = ~, [SR *N _ ICI dXo dPo dP o dSR~ + X° - ~X° = 0.
(12)
Rearranging slightly yields dXi d P ? ]
~ [SR*N _ 1Cl dP~ dSR o = X~[E, - N], dX° d P o ]
71"0 [SR *N -
IC] dp ° dSR~ = Xo[zr~ - Cro].
(13)
(14)
The right-hand sides of Eq. (13) and Eq. (14) have opposite signs. However, the left-hand sides have the same sign. Hence equality can be preserved only if both sides are equal to zero. If rro(SR *N, SR*N)~ri(SR *N, SR*N), then from Eq. (13) and Eq. (14) Xo(P*o(sR*N))=X~(P~*(SR*N))=O and SR*N=IC. But then aXo(SR*N, SR*N)=xri(SR *N, sR*N)=0, a contradiction. Hence "tro(SR*N, SR*N) = 7ri(SR*N, SR*N). Suppose 7ro(SR*N, SR*N)=~ri(SR*N, SR*N)=O. By corollary ,o one ~rk(SRo ,SRi*i)>o for k=i,o. Hence ~ro(SR*N, SR*N)=rri(SR*N, SR*N)=O violates individual rationality. This leaves "rro(SR*N, SR*N)= "ffi(SR *N, SR*N)>0. In this case SR*N=IC is the only solution. ~ B y the Intermediate Value Theorem H* is convex. This implies that a unique interior solution exists. By footnote 5 ~o(IC, IC)=~ri(IC, I C ) > 0 and Eq. ( 11 ) and Eq. (12) are only satisfied at SR*oN=SRi*N=IC. [-] It follows from Proposition 3 mat 7ro(IC, I C ) ~ ( I C ,
IC) is necessary and
M. Cave, M.P. Donnelly I hlforn~ation Econmnics and Polh,v 8 (1996) 107-123
!!7
sufficient to establish SR,*N 5~SR~ N. T h e two operators will bargain on a common settlement rate if and only if the profits maxima evaluated at an incoming cost-based settlement rate are the same. If demand were the same in both countries, this would be the case. It might also arise from other combinations of circumstances, but generally the operators would find it in their interests to agree different settlement rates as illustrated in Fig. 1.
4.3. Case three: A common settlement rate In this case each operator is constrained to face a common settlement rate SR. Define the restricted domain SR**={SR~_SR* :SRo=SR~}. Concentrating on operator o the programme is Max
{SR~SR "*}
~o(SR) =[P*o(SR,.) - SR - OC]Xo(P~,(SR,.)) +[SR - IC]X,(Pi(SR,.)). (15)
Let SR ***° be the argmax of Eq. (15). Similarly, let SR ***~ solve i's profit maximisation problem. As before, the likely emergence of conflicts of interest between the operators over the settlement rate is expressed as
Proposition 4.
SR***°=SR ***i if and only if Xo(P*(IC, .))=Xi(P*, (IC, .)).
Proof.
The proof proceeds by way of two lemmas and is relegated to the appendix.
If Xo(P*o(IC, .))~X~(P*(1C, .)) a bargaining mechanism will have to be established. Again we assume bargaining takes place within a Nash fixed threat bargaining model. In this case we define the restricted profit possibilities set H * * ={'tr(SR) : SRESR**}. We assume the threat point remains d = ,o r(SRo, SR*').
Given the above F * * = ( H * * , d) constitutes a two-agent fixed threat bargaining game. The Nash solution to F * * is denoted SR **N (see Fig. 1).
5. Why a c o m m o n settlement rate
The two operators have traditionally agreed to an equal division of the accounting rate into common settlement rates. By Proposition 3 if rro(IC, IC)= 7ri(IC, IC) then SR*oN=SR*, N. On the other hand, if aro(IC, IC)¢:xri(IC, IC) then SR*oN¢:SR~*~ and the model fails to account for a system of common settlement rates. However, under the assumptions we have made, a solution to the restricted
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Nash bargaining problem in case three (Section 4.3 is guaranteed to exist. 13 Moreover 'trk(SR **N, SR **N )>'rrk(SR o.o , SR *i) for k = i , o by individual rationality. In this case there is at least one point on the 45 ° degree line in Fig. l that affords greater profits than the threat point d. Since the outcome of a Nash bargaining game is Pareto efficient, one operator, say o, must experience a loss in profit while the other operator i experiences a gain in a move away from a negotiated system in which settlement rates are allowed to differ to a negotiated system in which they are not. Thus one of the operators i has an incentive to collude with its regulatory authority and insist on a system of common settlement rates as a precondition for negotiation) 4 The question then becomes 'is such a threat credible?' Recall from ~ection 2 that after 1936 the principle of a 50:50 division of a preagreed accounting rate became "entrenched in FCC oversight procedures and acquired the status of a precondition for joint service with the US". In this case the threat is credible since the choice is between the point on the 45 ° line or point d. The other operator o accepts this precondition because individual rationality dictates that ,.rro(SR**N, SR**N)~ "tro(SR o.o , SR *~) and informational asymmetries preclude its regulator from imposing particular settlement rates.
6. A more complex demand specification Like other telephone calls, international calls are unusual economic goods in that the cooperation of at least two parties is required for the good to be made available. Since only one party is normally billed for the call, there is an externality associated with any call, which - since the call can be refused - is normally positive. When calls between two parties are made frequently, this externality can be internalised by agreed rotation. Decisions to make calls may also be influenced by altruism, or the presence of inter-dependent utilities. Finally, where tariffs for outgoing and incoming calls differ, the parties can agree that the call should be made where rates are lower, possibly with a side payment. ~n operational terms, some of these effects can be captured by introducing into the demand equations variables cupturing reciprocation (outgoing calls eliciting incoming calls) and reversion (calling from the cheaper country) effects. The demand functions in Section 3 are augmented by the tariff charged and the volume
~3The set SR* is a k-cell and is therefore compact. The set SR** is a closed subset of SR* and is therefore also compact. Since "trk(SR) is continuous on SR**, a solution to the restricted Nash bargaining problem exists. ~4Due to information asymmetries the regulator is hardly in a position to insist ,an particular settlement rates, but it is in a position to insist on a settlement rate rule. The 50:50 division is one such rule.
M. Cave, M.P. Donnelly I h~formation Economics and Policy 8 (1996) 107-123
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of calls made in the other country, becoming Xo=X,,(Po, Pi, X~) and Xi-X,(P,,, P,, Xo) respectively. The effect of this change is to eliminate the additively separable nature of ax, and "rri, thus complicating the analysis significantly. The problem throughout is that operator o has to take into account the indirect effect of its preferred settlement rate, which feeds into operator i's collection rate. This both influences call reversion and (by affecting the level of calls from i to o) elicits a new level of call reciprocation. It can easily be shown that the presence of reciprocation does not allow the own-price effect and the cross-price effect to be signed; that is, with reciprocation the total derivatives OXo I OP, and/gXo/0P~ are ambiguous. Acton and Vogelsang (1992) investigate the presence of reciprocation and reversion effects on the basis of annual data for call minutes between the US and 17 Western European countries over the period 1979-86. They find that the total own-price effect is negative and statistically significant at the 5% level while the total cross-price effect is ambiguous and statistically insignificant at the 5% level) s However, this last result must be interpreted with care. Reciprocation alone is likely to produce negative cross-price elasticity, while reversion alone will generate a positive cross-price elasticity. As Acton and Vogelsang (1992, p. 318) point out: "coefficients that are not statistically significant from zero could be consistent with the absence of either motivations or with both motivations cancelling one another out". On the other hand, Cheong and Muilins (1991) construct an econometric model to investigate whether telephone traffic deficits on individual routes out of the US are the result of tariff differences between outgoing and incoming calls or lower income levels in destination countries. Cheong and Mullins find that while relative income levels are important in explaining traffic imbalances, the impact of tariff differentials is statistically insignificant. Even though for the period of the study tariff rates in countries such as Italy, Greece and the Federal Republic of Germany were up to twice as high as corresponding US rates, call reversion was still not a significant feature compared to relative income levels. Adopting a different approach, Sandbach (1995) empirically develops an argument previously proposed by Acton and Vogelsang (1992). The latter argue that there are transaction costs involved in call reversion. Therefore, call reversion occurs only after the tariff differential between the outgoing and incoming route exceeds the transaction cost. Sandbach includes his econometric model both the
i.s Appelbe et al. (1988) and Larson et al. (1990) investigate the presence of reciprocation only and not reversion. Both studies find that reciprocation is strongly present and statistically significant at the 1% level. Hence reversion cannot be eliminated from the demand functions (eliminating reversion allows the own-price effect to be unambiguously signed). However, both of these studies consider the presence of reciprocation only. These studies then suffer from a potential "omitted variables" problem which the authors do not address.
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tariff differential and a nonlinear term in the tariff differential which only takes effect when the differential between outgoing and incoming calls exceeds $0.90 a minute. This last term is included to test the hypothesis that call reversion only occurs when the price differential exceeds a threshold. Data were collected on 154 international routes. Both the ordinary tariff differential and the nonlinear tariff differential are statistically insignificant at the 5% confidence level. Sandbach (1995, p. 11) notes: "[The]...data set included 6 pairs of routes in which the premium for an incoming call (compared to an outgoing call) exceeded 50 cents a minute. If call reversal were a significant phenomena at these levels of price differential, the model should have identified it. The most extreme case was the UK to Japan route where, despite a premium of 130 cents a minute, traffic is still 10% heavier into than out of the UK. From this analysis, we concluded that, for a very large range of price differentials between incoming and outgoing traffic, call reversal is not a significant phenomenon." While call reversion is interesting from a theoretical point of view and although there is much recent discussion of the phenomenon, the empirical evidence suggests that its effects are still statistically insignificant. Evidence in favour of reciprocation appears to be stronger in terms of its statistical significance (see footnote 15). At the same time, the Acton and Vogelsang study finds no statistical significance in the combined effect of the two phenomena. We believe that our simplified demand specification is thus empirically justifiable) 6
7. Discussion This paper has shown how profit maximising monopoly intercontinental telephone operators will set accounting and settlement rates. We have shown how the two rates are jointly determined in both a cooperative and a non-cooperative context: both are higher in the latter case. The paper has also shown that common settlement rates will only emerge in unlikely circumstances. A necessary and sufficient condition is that the profits maxima evaluated at an incoming cost-based settlement rate are the same. If demand were the same in both countries, this would be the case. It might also arise from other combinations of circumstances, but generally the operators would find it in their interests to agree different settlement rates. ~" From a modelling point of view, the incorporation of both reciprocation and reversion effects influences the reaction functions and may thus lead to a situation in which no equilibrium exi~,,ts. When only one of the effects is present, however, it can be shown that an equilibrium exists. (Proofs of these propositions are available from the authors.)
M. Cave, M.P. Donneily I Information Economics and Policy 8 (1996) 107-123
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However, although there is nothing intrinsic in a 50:50 division of the accounting rate, one of the operators in collusion with its regulator always has an incentive to insist on a system of common settlement rates as a precondition for negotiation in preference to a system which allows settlement rates to differ. The other operator will accept this precondition since the threat is credible and the profit it earns under a system of common settlement rates is greater than under a system of unilaterally imposed settlement rates.
Acknowledgments We would like to thank Jonathan Michie for help with an earlier version of this paper, and Cheryl Mourisseav for helpful comments and suggestions.
Appendix 1 Differentiating Eq. (15) and the corresponding profit function for i, first-order necessary conditions are dzro dSR
dXi dP~ X o + X~ + [ S R - I C l d p ~ d S e -< 0,
(A.1)
dR dSR
dXo dPo X i + Xo + [ S R - I C l d p ° dSR <- 0,
(A.2)
[ d~o-I d-ff~JSR = 0,
(A.3)
[d~] ~--R-JSR = 0.
(k.4)
Lemma 1. IC.
SR * * * ° = SR ***i (= SR**) if and only if SR ***° = 1C and SR ***i=
Proof. ~ S u p p o s e SR ***°= SIC***~ ( = SR***). There are two cases to consider. (i) S R * * * - 0 . In this case Eq. (A.l) and Eq. (A.2) imply
dXo d e o dX i dP~ - IC-dp i dSR <- 1 C dP - - o dSR"
(A.5)
This is a contradiction. Therefore S R * * = O is not possible. (ii) SR***>0. In this case complementary slackness implies
M. Cave, M.P. Donnelly / h~formation Economics and Policy 8 (1996) 107-123
122
[SR*** - 1Cl-d ,
dP; -
dX,, dP,: [SR*** - IC]dp ° dSR
(A.6)
Since the two sides of this equation are of opposite sign, they can be equal only if SR*** = IC. ~ I f SR***°= IC and SR***i= IC, then SR***°= SR ***~. [-1
Lemma 2. SR ***° (SR***i)=IC if and only if Xo(P*o(IC,.))=Xi(P*(IC,.)). Proof.
=,Suppose SR*o** =IC>O. First-order necessary conditions reduce to d~-o(IC)
dSR
Xo(P*,,(IC,.)) + X~(P~ (IC,.)) <- 0
(A.7)
However, since S R * * * - I C > 0 , complementary slackness requires daro/dSR=O. ~ L i k e the proof of Proposition 3 a unique solution exists; and SR ***° =IC satisfies the first-order condition. I-I Proposition 4 is then an immediate consequence of Lemmas 1 and 2.
References Acton, J.E and I. Vogelsang 1992, Telephone demand over the Atlantic: Evidence from co,retry-pair data, Journal of Industrial Economics XL, 1-19. Appelbe, T.W., N.A. Snihur, C. Dineen, D. Fames and R. Giorano, 1988, Point-to-point modelling: An application to Canada-Canada and Canada-United States long distance calling, Information Economics and Policy 3, 311-331. Cave, M. and J. Michie, 1991, Developing competition in international telephone service, In: F. Klaver and E Slaa, eds., Telecommunication: New signposts to old roads (IOS Press, Amsterdam). Cheong, K. and M. Mullins, 1991, International telephone service imbalances, Telecommunications Policy, April, 107-118. Ergas, H. and E Paterson, 1991, International telecommunications settlement arrangements, Telecommunications Policy, Feb., 29-48. Eward, R., 1985, The deregulation of international telecommunications (RAND, Santa Monica, CA). Hakim, S.R. and D. Lu, 1993, Monopolistic settlement agreements in international telecommunications, Information Economics and Policy 5, 145-157. Johnson, L.L., 1989/91, Dealing with monopoly in international telephone service: A U.S. perspective, Information Economics and Policy, 225-234. Larson, A.C., D.E. Lehman and D.L. Weisman, 1990, A general theory of point-to-point long distance demand, In: A. deFontenay, M.H. Shugard and D.S. Sibley, eds., Telecommunications demand modelling (North-Holland, Amsterdam). Milgrom, E and J. Roberts, 1992, Economics organisation and management (Prentice Hall, New York). Nash, J., 1950, The bargaining problem, Econometrica 18, 155-62.
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OECD, 1995, International telecommunications practices and principles: A progress review tOECD, Paris). Sandbach, I., 1995, International telephone traffic, callback and policy implications, Mimeo. (NERA, London). Young, H.E, 1993, An evolutionary model of bargaining, Journal of Economic Theory 59, 145-168.