Access pricing and market structure

Information Economics and Policy 13 (2001) 77–93 www.elsevier.nl / locate / econbase

Access pricing and market structure Koji Domon a , *, Koshiro Ota b b

a School of Social Sciences, Waseda University, Tokyo, Japan Faculty of Economic Sciences, Hiroshima Shudo University, Hiroshima-shi Japan

Received 31 October 1998; received in revised form 8 November 2000; accepted 8 November 2000

Abstract In telecommunications industries access charge problems are important issues during deregulation. In Japan and the US, deregulation also involves the issue of industrial structures as integration or divestiture of a long-distance sector. This paper analyzes access charge problems by introducing effects of the divestiture on cost functions. We show how the effects influence economic welfare under the integration and the divestiture in the Stackelberg model. The main result is that, without regulation, welfare losses, caused by an effect of double marginalization in the divestiture case, are not crucial when an entrant and a divested long-distance firm can make use of an efficient cost function. We also obtain a relationship between Ramsey access charges and the Efficient Component Pricing Rule.  2001 Elsevier Science B.V. All rights reserved. Keywords: Access pricing; Vertical integration; Divestiture effects; Efficient Component Pricing Rule JEL Classification: L51; L13; L96

1. Introduction Formerly public utilities were monopolies, due to huge fixed facilities needed to supply services. Even with current technology, we cannot do without such facilities, which are normally huge networks for the distribution of services from gas pipelines, electric wires, and telecommunication circuits. Furthermore, public utilities are integrated organizations. In many counties such * Corresponding author. Tel.: 181-3-5286-1451; fax: 181-3-5286-1451. E-mail address: [email protected] (K. Domon). 0167-6245 / 01 / $ – see front matter  2001 Elsevier Science B.V. All rights reserved. PII: S0167-6245( 00 )00034-2

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public utilities have recently been deregulated since the basis for a natural monopoly has gradually disappeared due to technological advances, and the belief that competition is necessary for the social welfare. In such situations, upstream sectors with huge fixed facilities must be regulated, while downstream sectors do not need to be so. When the upstream sector supplies only distribution services and not the final services to consumers, the regulation problem resembles that of monopolies. In telecommunication industries, however, the upstream sector supplies services to both the downstream sector and the consumer. Such a situation complicates regulations because of access services and distorted competition. Regarding the access charge problem 1 , various authors have recently presented papers classified into three main categories: Ramsey pricing, the Efficient Component Pricing Rule (ECPR)2 , and long-run incremental cost. For instance, Armstrong (1998) and Laffont et al. (1998) considered situations such as the UK market in which an incumbent (British Telecom), an entrant (Mercury), and CATV companies compete. In order to expand and cover service areas each company must interconnect to each other. They used the Hotelling model of product differentiation, and the characteristic of their models was consideration of a mature market in which firms equally compete with each other. These papers assumed situations causing interconnection, that is, a two-way access.3 However, there is another situation to be analyzed. Baumol and Sidak (1994), Armstrong et al. (1996), and Sidak and Spulber (1997) considered a one-way access and insisted on efficiency of the ECPR. One-way access takes place in the transit from monopolistic to competitive situations. Whenever a new entry occurred, the US telecommunications industry has seriously considered access charge problems of the one-way access. A similar situation arose in the Japanese telecommunications industry. In 1999, Japanese giant common carrier, Nippon Telegraph and Telephone (NTT), was divided into two local carriers and a long-distance carrier. The aim of such a divestiture was to create equal competitive conditions for long-distance common carriers. Since NTT’s long-distance sector had the advantage of integration in competition, to remove this advantage was 1 Laffont and Tirole (1994) and Vickers (1995) argued access pricing from the point of a Bayesian incentive regulation. Their models have some theoretically strict assumptions, especially linearity, when solving their Bayesian games. As we consider more practical situations, our approach differs from theirs. 2 ECPR indicates an optimal input price in such a situation where two firms compete in a market of final goods and one supplies the other with intermediate goods to produce final goods. In this case the firm producing intermediate goods has an advantage in competition, because the firm can control the other firm’s costs through the price of intermediate goods. See Chapter 7 of Baumol and Sidak (1994), Chapter 8 of Sidak and Spulber (1997), and Baumol et al. (1997). These papers insist on the validity of ECPR. Concerning criticisms of ECPR, see Mitchell et al. (1995) and Laffont and Tirole (1996). 3 A similar situation of the interconnection exists in international telecommunications industries. That is called international accounting rate system, which recently faces many criticisms and is in need of reform. See Domon and Kiyono (1999) and Wright (1999) in detail.

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Fig. 1. Market structure in the transition from monopoly to competition.

significantly important for new entrants. In Fig. 1 we present a course from monopoly to competition. The US chose the lower course in the 1996 Telecommunication Act, and the UK did the same, but skipped the partial integration and the complete divestiture. Japan started deregulation from the partial integration and is now at the stage of complete divestiture.4 We need to note here that no researcher has theoretically considered divestiture and integration effects of quasi-public utilities such as telecommunication industries. These effects are associated with network access. In this paper we consider a key factor, an effect of the divestiture on cost functions. Our analysis proceeds as follows: In Section 2, we set up a basic model and explain the effect of divestiture on cost functions. In Section 3, we consider situations with no regulation and compare welfare under two market structures: the partial integration and the divestiture cases. In Section 4, we obtain Ramsey prices, make it clear how the Ramsey access charge is related to ECPR. In final section, we summarize our considerations. 4 NTT’s local sector was divided into the eastern and western sections, but the monopoly in each area is nearly maintained. So we depict the current situation of the local markets as monopoly in Fig. 1. Furthermore, we note that NTT’s holding company includes the two local companies and a longdistance company. Therefore, the divestiture of NTT is not complete, and there are still strong managerial relationships between the local and long-distance companies.

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2. A model We consider two cases. The first case is that of an integrated firm (firm 1) which supplies services in an upstream (local telephone service) market, while firm 1 and firm 2 supply services in an downstream (long-distance telephone service) market. The second case is that of firm 0 which supplies services in an upstream market, while firm 1 and 2 supply services in an downstream market. In the second situation the divestiture of firm 1 is considered. In the first case, firm 1 supplies services to both an upstream and a downstream 1 market, that is, it is integrated. The cost function of firm 1 is denoted as Cˆ (q, Q 1 , Q 2 ), where q is the quantity of the upstream services, Q i (i 5 1,2) is the quantity supplied by firm i in the downstream market. In the downstream market, firm 2 needs access to upstream networks in order to supply services. We denote the cost function of firm 2 as C 2 (Q 2 ) 1 aQ 2 , where a is a price of the access service 5 to upstream networks: an access charge. Social welfare function under integration is, therefore, defined as S I 5 vˆ 1 Vˆ 1 pˆ 1 1 pˆ 2 1 5 vˆ 1 Vˆ 1s pq 1 PQ 1 2 Cˆ (q, Q 1 , Q 2 ) 1 aQ 2d

1sPQ 2 2 C 2 (Q 2 ) 2 aQ 2d

(1)

where p and P are respectively the price of the upstream market and the downstream market. vˆ and Vˆ represent respectively the consumers surplus in each market. In the second case, after firm 1 is divested of an upstream sector, the cost function of firm 1 becomes the same as firm 2’s: C 1 (Q 1 ) 1 aQ 1 (C 1 (Q 1 ) 5 C 2 (Q 2 )). The cost function of the divested firm, which is firm 0, is denoted as 0 C˜ (q, Q), where Q 5 Q 1 1 Q 2 . In this case the social welfare function is defined as S D 5 v˜ 1 V˜ 1 p˜ 0 1 p˜ 1 1 p˜ 2 0 5 v˜ 1 V˜ 1s pq 2 C˜ (q, Q) 1 a ? Qd

1sPQ 1 2 C 1 (Q 1 ) 2 aQ 1d 1sPQ 2 2 C 2 (Q 2 ) 2 aQ 2d

(2)

where v˜ and V˜ represent respectively the consumers surplus in the upstream and the downstream market under the divestiture case. We make the following assumptions for simplicity of analysis: 5 Concerning types of access charges, Laffont and Tirole (1998) and Armstrong (1998) distinguish a reciprocal access charge from a non-reciprocal one. In the vertical structure here we do not need to consider them. In the general analysis, see Domon and Okochi (2000).

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Assumption 1. Demand for long-distance services is independent to that of local services. Assumption 2. Consumers surplus functions and profit functions are twicecontinuously differentiable and strictly concave. To consider the impact of divestiture on the social welfare, we define an effect of the divestiture as follows:

r (q, Q 1 , Q 2 ) 5 S D 2 S I 1 0 5 Cˆ (q, Q 1 , Q 2 ) 2 C˜ (q, Q 1 , Q 2 ) 2 C 1 (Q 1 ).

(3)

Assumption 3. r is strictly increasing or decreasing and a convex function. 0 1 Because of r 1 C˜ 1 C 1 5 Cˆ , convexity of r is a sufficient condition for that 1 of Cˆ . Under that assumption we can classify the effect of the divestiture as follows:

Positive divestiture effect: r $ 0 for ;q, Q 1 , Q 2 . Negative divestiture effect: r # 0 for ;q, Q 1 , Q 2 . Quasi-positive divestiture effect: r (0, 0, 0) , 0 and r 5 0 for 'q, Q 1 , Q 2 . Quasi-negative divestiture effect: r (0, 0, 0) . 0 and r 5 0 for 'q, Q 1 , Q 2 . In the above definitions, quasi-positive (quasi-negative) divestiture effects mean that the amount of supply must be beyond some level in order for positive (negative) effects to work. In addition to such cases, there is a special case as depicted in Fig. 2: Decreasing positive divestiture effect: r $ 0 for ;q, Q 1 , Q 2 , and r is a decreasing function. We exclude the decreasing positive divestiture effect and assume Assumption 4. ri . 0 (or ri , 0) if r . 0 (or r , 0) for (i 5 q, 1, 2). In this assumption rq ; ≠r / ≠q and ri ; ≠r / ≠Q i (i 5 1, 2). 3. Analysis with no regulation

3.1. A partial integration case We set up a game structure in the partial integration case. An incumbent governing whole local and partial long-distance telephone service markets is a Stackelberg leader, first determining arguments of q, Q 1 , and a. A new entrant, a

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Fig. 2. Decreasing positive divestiture effect.

follower, after looking at the leader’s actions, determines the quantity of a long-distance telephone service. To calculate a solution to this game, we check the conditions for the new entry. The first-order condition for the new entrant is

pˆ 22 5 PQ Q 2 1 P 2 C 22 2 a # 0.

(4) 2

2

We denote the reaction function obtained by the condition as Qˆ 5 Rˆ (a, Q 1 ) and 2 assume pˆ 221 , 0.6 Under this assumption, Rˆ 1 5 2 pˆ 221 / pˆ 222 , 0 holds. Further2 2 more, we obtain Rˆ a 5 2 1 / pˆ 22 , 0. The domain (a, Q 1 ) [ R 1 3 R 1 that permits new entry is defined as 2 E 5h(a, Q 1 )uRˆ $ 0j.

(5)

If a point for maximizing the incumbent’s profit is outside E, that results in entry deterrence created by an access charge and a long-distance service. We cannot deny the possibility of this entry deterrence. In the following consideration, however, we shall focus on how the incumbent strategically behaves under the entry. The profit function of the incumbent is 2 pˆ 1 5 pq 1 P(Q 1 1 Qˆ (a, Q 1 )) ? Q 1 1 2 2 2 Cˆ (q, Q 1 , Qˆ (a, Q 1 )) 1 a ? Qˆ (a, Q 1 )

and the first-order conditions for profit maximization are 6

In the divestiture case the assumption means strategic substitutes.

(6)

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pˆ 5 C 1q 2 pq q

(7)

1 2 2 aˆ 5 Cˆ 2 2 PQ Q 1 2 Qˆ /Qˆ a

(8)

1 2 2 2 Pˆ 5 Cˆ 1 2 PQ Q 1 1 (Qˆ /Qˆ a )Qˆ 1 .

(9)

ˆ the first term in Eq. (8) is the marginal cost for supplying an Concerning a, access service, and the second is interpreted as an effect of the access charge on 2 marginal revenue in a long-distance market. That is, the access charge affects Qˆ , and the influence on the marginal revenue in the long-distance market is expressed 2 2 as 2 PQ Q 1 . The final term, 2 Qˆ /Qˆ a , is an effect of monopolistic marginalization based on the monopolistic supply of an access service. ˆ the first term is the marginal cost for supplying a long-distance Concerning P, service, and the second is the effect of monopolistic marginalization based on 2 2 2 monopolistic supply of an long-distance service. The third, (Qˆ /Qˆ a )Qˆ 1 , is 2 interpreted as the effect of the first-mover advantage, because Qˆ 1 is caused by the Stackelberg leader of firm 1. This reflects a characteristic of partial integration.

3.2. A divestiture case In a divestiture case, firm 0, supplying an access service and a local telephone service, first determines the level of the access charge and the local telephone service price. After that, symmetric firm 1 and firm 2 deploy Nash competition in the long-distance market. The profit function of firm i is

p˜ i 5 PQ i 2 C i (Q i ) 2 aQ i . (i 5 1, 2)

(10)

The first-order condition for the profit maximization is

p˜ ii 5 PQ Q i 1 P 2 C ii 2 a 5 0 (i 5 1, 2)

(11)

i i and we denote the reaction function as Q˜ 5 R˜ (Q j ; a) and Nash equilibrium in the i long-distance market as Q˜ * (a). The profit function of firm 0 is 0

p˜ 0 5 pq 2 C˜ (q, Q˜ *) 1 a ? Q˜ *

(12)

1 2 where Q˜ * 5 Q˜ * 1 Q˜ * . From the first-order conditions for the profit maximization we get 0

p˜ 5 C˜ q 2 pq q 0 i i a˜ 5 C˜ Q 2 Q˜ * /Q˜ a*

(13) (i 5 1, 2)

(14)

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K. Domon, K. Ota / Information Economics and Policy 13 (2001) 77 – 93 0 i i P˜ 5 C˜ Q 1 C ii 2 Q˜ * /Q˜ a* 2 PQ Q i * . (i 5 1, 2)

(15)

The above conditions show typical double marginalization. In determining an i i access charge the first monopolistic marginalization, 2 Q˜ * /Q˜ a* , appears, and in Nash competition of the long-distance market the second monopolistic marginalization, 2 PQ Q i * , appears. Furthermore, we can check effects of divestiture on 0 1 0 1 prices. Because of C˜ Q 5 Cˆ i 2 C 1i 2 ri and C˜ q 5 Cˆ q 2 rq , positive (negative) divestiture effects have power to decrease (increase) the prices in the divestiture case.

3.3. Welfare comparison To derive intuitive implication of the partial integration considered above, we shall set up a linear model. Demand functions are p5b2c? q

(16)

P5 A2B?Q

(17)

where all parameters are strictly positive. Cost functions are 1 Cˆ 5 aˆ ? q 1 bˆ ? Q 1 gˆ ? Q 1

(18)

0 C˜ 5 a˜ ? q 1 b˜ ? Q

(19)

Ci 5 g ? Qi

(20)

(i 5 1, 2)

where a and b are costs associated with local networks, g is a cost associated with long-distance networks, and all are strictly positive. An effect of incumbent divestiture is

r 5 ( aˆ ? q 1 bˆ ? Q 1 gˆ ? Q 1 ) 2 ( a˜ ? q 1 b˜ ? Q 1 g ? Q 1 ) 5 ( aˆ 2 a˜ )q 1 ( bˆ 2 b˜ )Q 1 ( gˆ 2 g )Q 1 .

(21)

In this linear model we graphically analyze the effect of the divestiture on the social welfare. To do this we first show basic results. The reaction function of firm 2, in both the partial integration and the divestiture cases, is 1 A2g 2a R 2 (Q 1 , a) 5 2 ] Q 1 1 ]]]. 2 2B

(22)

Access charges are calculated as 1 1 2 2 1 2 aˆ 5 Cˆ 2 2 PQ Q 1 2 Qˆ /Qˆ a 5 bˆ 1 BQˆ 1 2BQˆ 5 ] ( bˆ 1 A 2 g ) 2

(23)

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1 0 i i a˜ 5 C˜ Q 2 Q˜ /Q˜ a 5 b˜ 1 (A 2 g 2 a˜ ) 5 ]( b˜ 1 A 2 g ). 2

85

(24)

In this linear model an effect of structural difference on an access charge is caused only by an divestiture effect on cost functions. If there is no divestiture ˜ This means that the monopolistic marginalizaeffect, that is, bˆ 5 b˜ , then aˆ 5 a. tion’s effect on an access charge under the divestiture is equal to that effect plus the effect of an access charge on marginal revenue in a long-distance market. By using this result, we can easily analyze the divestiture effects of cost functions on the social welfare. We first obtain the following results: 7 Remark 1. If there are no or negative divestiture effects on cost functions, the social welfare in the partial integration is higher than that in the divestiture ˜ without regulation, due to Qˆ . Q˜ and qˆ $ q. With no divestiture effect on cost functions, the reaction function of firm 2, under the partial integration, is the same as that under divestiture. The quantities in i the long-distance market under the partial integration are depicted as Qˆ (i 5 1, 2) i in Fig. 3, and those under the divestiture separation as Qˆ (i 5 1, 2). Since the stability condition for Nash equilibrium, uR iju , 1 (i, j 5 1, 2; i ± j), is satisfied,

Fig. 3. Comparison with no divestiture effects. 7

Regarding the proof, see Appendix.

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Qˆ . Q˜ is obvious. This result demonstrates the superiority of the partial integration from the position of an incumbent firm, that is, the Stackelberg leader. The advantages caused by this incumbent position outweighs the damages caused by double marginalization from the divestiture. Next we obtain 8 Remark 2. If there are positive divestiture effects on cost functions and the level of an access charge is less than a¯ (in Fig. 4), the social welfare in the divestiture is higher than that in the partial integration under no regulation, due to Qˆ # Q˜ ˜ and qˆ , q. Negative divestiture effects causing a˜ . aˆ ensure the superiority of the partial integration in both the long-distance and local markets. However, if positive divestiture effects take place, then qˆ , q˜ holds. Moreover, reaction functions under the divestiture move upward because of lower access charges, and the quantity of the long-distance market, at Nash equilibrium, increases. If the access ¯ depicted in Fig. 4, then Qˆ # Q˜ holds. As a result, charge is less than the level of a, the social welfare is improved by the divestiture. There is an ambiguous zone at the level of a in regarding the social welfare. The zone is between a¯ and the level of access charge under no integration effect. Within this zone, the divestiture leads to an increase of local services and a decrease of long-distance services. The zone is created by the first-mover advantage of the incumbent in the partial integration. To make the divestiture

Fig. 4. Comparison with positive divestiture effects. 8

We can prove Remark 2 in the same way as in Remark 1.

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valuable, positive divestiture effects of cost functions must outweigh the firstmover advantages under the partial integration.9 We can summarize the divestiture effect on the social welfare. Although double marginalization’s effects in the divestiture case incur welfare loss, it is negated if an efficient new entry occurs and a divested firm uses an efficient technology more advanced than the incumbent’s. This appears to explains the phenomenon occurring in the real market.

4. Ramsey pricing In most countries, although competitive forces have been introduced, the incumbent is regulated. This means that there remains considerable monopoly power to lessen the merits of competition. In the previous section we considered how monopoly power damaged the social welfare under two market structures. In this section we shall consider regulatory issues, Ramsey prices, and compare them with prices under no regulation. To calculate Ramsey prices, we assume that policymakers regulate only an incumbent and face its break-even constraint. They do not intervene in the duopoly market, i.e., the long-distance market.10 This setting is the most realistic one. The problems to be solved are L I 5 S I 1 l I pˆ 1

(25)

L D 5 S D 1 l D p˜ 0 .

(26)

The first is the Lagrangean function in the partial integration case, and the break-even constraint is pˆ 1 $ 0. The second is one in the divestiture case and the break-even constraint is p˜ 0 $ 0. l i (i 5 I, S) is a Lagrangean multiplier. The solutions of Ramsey prices under the partial integration are

lI 1 ˆp R 5 Cˆ q 2 ]]I pq q 11l

(27)

Qˆ 2 1 1 1 aˆ R 5 Cˆ 2 2 PQ Q 1 2 ]2 2 ]I sP 2 Cˆ 2 2 C 22d ˆ Qa l

(28)

S

D

lI Qˆ 2 2 R 1 Pˆ 5 Cˆ 1 2 ]]I PQ Q 1 2 ]2 Qˆ 1 . 11l Qˆ a 9

(29)

Even though we can calculate the solution for the welfare comparison, the implications obtained by the solution do not differ from those mentioned here. 10 In spite that our model treats duopoly, the nature of results obtained here is not different from a general oligopoly case.

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R The Ramsey final service prices, pˆ R and Pˆ , can be interpreted as usual ones.11 That is, they are equal to a marginal cost plus a Ramsey term. Comparing respectively (27) and (29) with (7) and (9), we obtain a clear relationship between monopoly and Ramsey prices. An interesting result in the Ramsey access charge is that it consists of a monopoly price minus profit decreases per the competitor’s service quantity. We can rearrange as follows: 12

pˆ a1 1 1 2 ˆ 2 ]I sP 2 C 2 2 C 2d 5 ]2 l Qˆ a

(30)

where pˆ 1a 5 (S Ia /S Iq )pˆ 1q 5 (S Ia /S IQ )pˆ 1Q . pˆ 1a is a marginal profit with the increase of 2 an access charge and strictly positive since the constraint is binding, while Qˆ a is a marginal decrease of competitor’s service quantity with the increase of an access 2 charge. Therefore, pˆ a1 /Qˆ a ( , 0) demonstrates that profit decreases due to the increase of the competitor’s service quantity. Our results for the Ramsey access charge differ from the ECPR: ECPR 5 marginal cost plus opportunity cost for supplying access service.

(31)

The Ramsey access charge in our model is monopoly access charges minus profit decreases due to the increase of the competitor’s service quantity 13 . Next, we shall determine if the same results of the Ramsey access charge are also obtained under the divestiture case. The Ramsey prices in this case are

lD 0 p˜ R 5 C˜ q 2 ]] p q 1 1 lD q Q˜ i * 1 0 0 a˜ R 5 C˜ Q 2 ]] 2] P 2 C˜ Q 2 C ii D i ˜ Q a* l

S

p˜ a0 Q˜ i * 0 ˜ 5 C Q 2 ]] 1 ]]. (i 5 1, 2) Q˜ ia* Q˜ ia*

(32)

D (33)

Therefore, the difference in the Ramsey prices between two market structures is the same as that in the monopoly prices. 11

If the break-even constraint does not bind, the Ramsey prices becomes the first-best solution: 1 1 R 1 1 pˆ 5 Cˆ q , aˆ R 5 Cˆ 2 , and Pˆ 5 Cˆ 2 1 C 22 5 Cˆ 1 . 12 1 1 1 1 1 1 1 We get the result from the following calculation. From L a 5 S a 1 l pˆ a , l 5 2 S a / pˆ a . 1 1 1 1 2 ˆ 2 2 1 ˆ 2 2 1 ˆ ˆ ˆ Moreover, from S a 5 (P 2 C 2 2 C 2 )Q a , P 2 C 2 2 C 2 5 S a /Q a . Therefore, 2 (P 2 C 2 2 C 2 ) /l 5 2 2 ( pˆ a1 /S a1 ) ? (S a1 /Qˆ a ) 5 pˆ a1 /Qˆ a . 13 Regarding general consideration, see Appendix. R

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5. Concluding remarks In this paper we presented two clear conclusions regarding divestiture effects of cost functions and difference in Ramsey access charges between two market structures. The first conclusion, concretely explained in the linear model, suggests that the positive divestiture effect is not a sufficient but a necessary condition. A relatively large positive effect is needed to improve the social welfare in the divestiture case. The second conclusion is that we must modify the efficient component-pricing rule in the partial integration case and cannot use it in the divestiture case. We obtained new formulas for each case. Market structures are drastically changing in the information industries. What determines them is impossible to explain. However, we must take into account proper regulations, especially in telecommunications industries of many countries which have various regulations regarding market structures. The considerations in this paper can be applied analyzing various situations.

Acknowledgements The first draft of this paper was presented at the annual conference of the Japanese Economic Association held in Ritsumeikan University, Japan, in September 1998. We are grateful to Toshihiko Hayashi and two anonymous referees for helpful comments. This paper has been partly supported by a Waseda University Grant for Special Research Project (99A-569).

Appendix Proof of Remark 1 Under no regulation, qˆ

31E 31E

SI 2 SD 5

q˜

2 1E

p dq 2 aˆ qˆ 2

0

˜ Q

ˆ Q

1

0

24 2 1E

p dq 2 a˜ q˜

0

1

P dQ 2 bˆ Qˆ 2 gˆ Qˆ 2 g Qˆ

2

2

0

P dQ 2 b˜ Q˜ 2 g Q˜

24

.

(A.1) Due to gˆ # g, there is d ( $ 0) satisfying gˆ 1 d 5 g. Therefore we can rearrange

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90

qˆ

31E 31E

SI 2 SD 5

q˜

2 1E

p dq 2 aˆ qˆ 2

0

24

˜ Q

ˆ Q

1

p dq 2 a˜ q˜

0

2 1E

P dQ 2 bˆ Qˆ 2 g Qˆ 2

0

P dQ 2 b˜ Q˜ 2 g Q˜

0

24

1

1 d Qˆ . (A.2)

˜ and qˆ $ q, ˜ then the first brackets is positive, the If aˆ # a˜ , bˆ # b˜ , gˆ # g, Qˆ . Q, 1 second bracket is strictly positive, and d Qˆ $ 0. Consequently we get S I . S D. The general formula for Ramsey access charges Suppose that there are two agents: agent 1 and 2. The agents can communicate with each other by interconnecting with each network. The payoff functions of the agents are P i 5 B i (m i , m j ) 2 C i (m i , m j ) (i, j 5 1, 2; i ± j) i

(A.3) i

where m is the amount of messages sent from agent i to agent j, B the benefit function, and C i the cost function. The payoff function does not include settlements caused by sending and receiving messages. We consider the reciprocal access charge system. The system is simple in that the agents settle the uniform compensation per unit message, which is called a reciprocal access charge. The system is expressed as S i 5 a ? (m j 2 m i ) (i, j 5 1, 2; i ± j)

(A.4)

where a is the reciprocal access charge, and S i the settlement amount of agent i for communication. Under the system, payoff functions are modified as P¯ i 5 P i 1 S i . (i, j 5 1, 2; i ± j)

(A.5)

Given a, the first-order condition for the payoff maximization is P¯ ii 5 P ii 2 a 5 0 (i, j 5 1, 2; i ± j)

(A.6)

Nash equilibrium is obtained by solving the above equations. We denote the solutions as m i (a), and assume m ai , 0 14 to exclude unusual cases. Privately optimal reciprocal access charges at Nash competition are obtained as follows: P¯ ia (m i (a), m j (a)) 5 (a 1 P ij )m ja 1 (m j 2 m i ) 5 0

(A.7)

14 This assumption is equivalent to P jjj 2 P iji , 0. This is easily checked by totally differentiating i ˜ P i 5 0.

K. Domon, K. Ota / Information Economics and Policy 13 (2001) 77 – 93

m j 2 mi a i 5 2 P ij 2 ]]] m ja

91

(i, j 5 1, 2; i ± j)

(A.8)

i

where a represents a privately optimal reciprocal access charge of agent i (i 5 1, 2). It is obvious that the charge determined by negotiation, a N , exists in the following interval: m1 2 m2 m2 2 m1 N 1 ]]] ]]] a 5uP u 2 # a #uP 2u 2 5 a 1 or, m a1 m a2 2

2 1

(A.9)

m2 2 m1 m1 2 m2 N 2 ]]] a 5uP u 2 ]]] # a # u P u 2 5 a 2. 1 m a2 m a1 1

1 2

The difference between the interval of a N and that of a* maximizing P 1 1 P 2 is the factor of (m j 2 m i ) /m aj . For the agent i whose outbound messages are larger than inbound messages, which results in (m j 2 m i ) /m aj . 0, his optimal access charge is smaller than a marginal damage the agent j suffers by receiving a message. The reason is that the imbalance of messages causes the payment from the agent i to the agent j, and the payer inclines to decrease the payment. Conversely, in this case, agent j likes the higher settlement rate rather than a marginal damage to the agent i. Remark A.1. Under the reciprocal access charge system, the joint payoff P is maximized at Nash equilibrium in a private optimal settlement rate if P 21 5 P 12 and P 11 5 P 22 . 1

2

1

2

1

2

N

2

1

Proof. If P 1 5 P 2 , then m 5 m from (A.4). Therefore a 5 a 5 a 5uP 1u 5uP 2u if P 21 5 P 12 from (A.9), and Pi 5 P ii 1 P ij 5 a N 1 P ij 5 0 (i, j 5 1, 2; i ± j) at Nash equilibrium. h Let us assume B ij 5 0, that is, the demand is independent of the service quantity of the other agent. This case corresponds to international telecommunication markets. In this case a 5 C ij holds, and, when they face perfect competition, the maximum of joint payoff leads to a maximum social surplus. Even when they face imperfect competition, the settlement rate is the first-best solution under the reciprocal access charge system because the rate is equal to a marginal damage to the other firm. The problem in the imperfect competition is not in the level of the settlement rate but in the level of service prices. Next let us assume B ij , 0, that is, the demand decreases as a competitor supplies more services. This case corresponds to domestic horizontally competitive telecommunication markets. In this case a 5 C ij 2 B ij holds.

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The above consideration concerns a two-way access. In a one-way access, considered here, we modify the above model as follows: P 1 5 B 1 (m 1 , m 2 ) 2 C 1 (m 1 , m 2 ),

P 2 5 B 2 (m 2 , m 1 ) 2 C 2 (m 2 )

(A.10)

and, P¯ 1 5 P 1 1 am 2 , P¯ 2 5 P 2 2 am 2 .

(A.11)

The Ramsey access price is obtained by solving the following Lagrangean problem: L 5 P(m 1 , m 2 (a)) 1 lP¯ 1 (m 1 , m 2 (a), a).

(A.12)

From La 5 0 we get 2 2 P¯ a1 P¯ a1 m m R 1 1 1 a 5 2 P 2 2 ]2 1 ]2 5 C 2 2 B 2 2 ]2 1 ]2 . ma ma ma ma

(A.13)

This formula corresponds to the condition (28). The difference between this condition and that in a symmetric two-way access is that the first-best outcome is obtained in the symmetric two-way access while the second-best outcome is obtained in the one-way access.

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