2009-11

Access charge, vertical separation, and lobbying
Toshihiro Matsumura
Noriaki Matsushima

Access Charge, Vertical Separation, and Lobbying
Toshihiro Matsumura
Institute of Social Science, University of Tokyo
and
Noriaki Matsushima∗
Graduate School of Business Administration, Kobe University
March 11, 2009

Abstract
We investigate the manner in which vertical separation affects lobbying activities as wellas the access charges for essential facilities. We find that vertical separation either increases ordecreases the access charge, and this depends on the relative efficiency between the incumbent
and new entrants.

JEL classification numbers: L51, L13
Key words: network industry, access charge, manipulation of accounting, regulation∗ Correspondence author: Noriaki Matsushima, Graduate School of Business Administration, Kobe University,
Rokkodai 2-1, Nada, Kobe, Hyogo 657-8501, Japan. Phone: +81-78-803-6981, Fax: +81-78-803-6977, E-mail:nmatsush@kobe-u.ac.jp1

1

Introduction

Competition between a firm holding essential facilities (usually, a dominant firm) and firms notholding them has been widely observed in many industries such as overnight delivery, telecommunication, electric power, and natural gas distribution industries. In particular, in Japan, dominantfirms are not vertically separated in telecommunication, electric power, and gas distribution industries. Dominant firms were previously legal monopolists, and they have had to compete against
new entrants after the liberalization of these markets. New entrants pay an access charge to thedominant firms. The rate of this charge affects the new entrants’ marginal costs, and hence, it
significantly affects the performance of the markets.
The rate of access charge (input price) is typically regulated by the government. Considerable
literature on the desirable and/or existing rules for levying access charges, such as efficient component pricing rule (ECPR), total element long run incremental cost (TELRIC), and a historical cost
approach, exists1 ; moreover, currently, charges based on the costs of essential facilities are levied
all over the world. For example, in Japan, TELRIC has been adopted in the traditional local
telecommunication network, and the historical cost approach has been adopted in the optical fiber
network, electric power, and natural gas distribution industries. In the EU, although the rules aredifferent for different countries, the cost-based approach has been adopted in most industries andin most countries.
In principle, the rule for calculating the rate of charge is determined by a neutral government,
and there is no room for manipulation. In practice, however, firms often influence the access charge
through lobbying and/or manipulation of accounting costs.2 For example, in Japan, integrated gas
companies insisted that the costs of vaporizers and pumps of liquidated natural gas (LNG) tanks
should be included in the access charge accounting of gas distribution pipeline networks. They
made substantial efforts to rationalize their argument at the government committee (Gas Energy
Committee in the Advisory Committee for Natural Resource and Energy) that determines the rules
for access charge accounting. Eventually, they succeeded in persuading the committee to adopt a
resolution to include these costs in the current access charge. Similar instances have been widely
1 See, among others, Laffont and Tirole (1994), Economides and White (1995), Armstrong et al. (1996), Hausman(1997), and Sappington (2006). See also Hori and Mizuno (2006), Mizuno and Shinkai (2006), Ida and Anbashi(2008), and Gautier and Mitra (2008) for the dynamic efficiency of access charge rules.
2 For discussions on these activities in the general context of regulation policies, see Viscusi et al. (2005).

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observed in the telecommunication and electric power distribution industries in Japan. In thispaper, we consider a situation wherein the access charge is influenced by firms through lobbying
activities.
Another important topic in policy is whether a dominant firm should be allowed to hold an
essential facility. Vertical separation is always an important policy issue in this field, and ownership unbundling has been widely observed, especially in the EU. It is often insisted that verticalseparation is beneficial because it deters manipulation by vertically integrated firms.
In this paper, we discuss the manner in which vertical separation affects the rate of accesscharge. We find that vertical separation decreases the lobbying activities and thereby reduces therate of access charge if the incumbent is considerably less efficient than the new entrant. However,this result is ambiguous when the cost differences between the firms is small, and it is possible thatvertical separation increases lobbying activities and thereby increases the rate of access charge. We
also find that vertical separation can be harmful for welfare.

2

The Model

We consider two cases: (1) a vertically integrated firm holding an essential facility and (2) verticalseparation undertaken by the government.

2.1

Vertically integrated case

We consider a duopoly model. Firm 1 is a vertically integrated firm holding an essential facility(dominant firm), and firm 2 is a new entrant. Firm 2 accesses the essential facility held by firm 1
and pays an access charge ry2 to firm 1, where r ∈ [0, r̄] is per unit access charge and yi is firm i’s
output.3
In the first stage, the per unit access charge (input price) r is determined. Let L(r) denote
firm 1’s effort costs (costs incurred for lobbying activity, manipulation of access charge accounting,etc.). In the second stage, firms engage in Cournot competition. They simultaneously produce
perfectly homogeneous products for which the market demand function is given by p = a−Y (priceas a function of quantity), where Y is the total output of the duopolists. Firm 2’s production cost
3 In many countries, the sales and productions departments in the vertically integrated firms pay access charges

to their own network departments which hold essential facilities in accounting. However, this accounting system does
not affect the optimal outputs in the integrated firms as long as they maximize the joint profits of both departments.

3(except for access charge) is normalized to zero and firm 1’s marginal production cost is denotedby c. If c is positive (negative), firm 1 is less (more) efficient than firm 2. Let yi denote the output
of firm i. Firm 1’s profit is π1 = (p(Y ) − c)y1 + ry2 − L(r), and firm 2’s profit is π2 = (p(Y ) − r)y2 .
We assume that L0 (r) ≥ 0 and that L00 (r) is positive and sufficiently large in order to ensure theconcavity of firm 1’s payoff function. We assume that L0 (0) = 0 and that L0 (r̄) is sufficiently large
in order to ensure interior solutions in the first stage (i.e., the equilibrium r ∈ (0, r̄)). We also
assume that −(a − 2r̄) < c < a/2 to ensure interior solutions in the second stage (production
stage).
Consider the second stage. The reaction functions of firms at the second stage are given by
R1 (y2 ) =a − c − y2,2

R2 (y1 ) =a − r − y1
.
2

(1)

The resulting equilibrium outputs and profits are as follows:
y1IS =

a − 2c + r,
3π1IS =y2IS =

a − 2r + c,
3

Y IS ≡ y1IS + y2IS =(a − 2c + r)2r(a − 2r + c)+
− L(r),
93π2IS =

2a − r − c,3(a − 2r + c)2
,
9

(2)
(3)

where the superscript IS denotes the equilibrium outcomes under vertical integration at the second
stage. The resulting total social surplus (consumer surplus plus the profits of the two firms) is
given by4
W IS =

8a2 − 2a(r + c) − (r + c)2c(a − 2c + r)−
− L(r).
18
3(4)

In the first stage, firm 1 maximizes π1IS with respect to r. The first-order condition is∂π1IS5(a − 2r) c=− − L0 (r) = 0.
∂r
9
9

(5)

Let the superscript I denote the subgame perfect Nash equilibrium (SPNE) outcomes under vertical
integration. rI is derived from (5).

2.2

Vertically separated case

We consider the situation wherein vertical separation is undertaken by the government. Firm 0
holds the essential facility, and firms 1 and 2 pay access charges to firm 0. In the first stage, firm
0 chooses r with cost L(r). After observing r, firms 1 and 2 compete in terms of output. Firm 0’s
4 If the lobbying costs are not real social costs but only income transfers from the firm to regulators or lawyers,

it might be better not to subtract L(r) in (4). All our results hold true if we do not subtract L(r) from welfare.

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profit is given by π0 = r(y1 + y2 ) − L(r), firm 1’s profit is given by π1 = (p(Y ) − c − r)y1 , andfirm 2’s profit is given by π2 = (p(Y ) − r)y2 . Again, in the second stage, firms 1 and 2 engage in
Cournot competition.
We discuss the second stage subgame where r is given exogenously. The equilibrium outputs
are as follows:
y1SS =

a − 2c − r,
3y2SS =a−r+c,
3

Y SS =

2a − 2r − c
,
3

(6)

where the superscript SS denotes the equilibrium outcome under vertical separation at the second
stage game. The resulting profits of firms 0–2 are given by
π0SS =

r(2a − 2r − c)− L(r),
3

π1SS =(a − 2c − r)2,9π2SS =(a − r + c)2
.
9

(7)

The resulting total social surplus is given by
W SS =c(a − 2c − r)
8a2 − 2a(2r + c) − (2r + c)2−− L(r).
18
3(8)

In the first stage, firm 0 maximizes its profit with respect to r. The first-order condition is
given by
∂π0SS
2(a − 2r) c=− − L0 (r) = 0.
∂r
3
3

(9)

Let the superscript S denote the SPNE outcomes under vertical integration. rS is derived from
(9).

3

Results

Proposition 1 (i) If c ≤ 0, then rS ≥ rI . (ii) If c is sufficiently large, then rS < rI .
Proof: Comparing (5) with (9), we obtain rS > rI when c ≤ 0, and rS < rI for large c. Q.E.D.
Firm 0 obtains access charge revenue from firms 1 and 2 under vertical separation, while firm 1
obtains access charge revenue from one firm (firm 2) only.5 Thus, vertical separation increases thesize of input market. As a result, firm 0 has a stronger incentive for increasing r than the integrated
firm, firm 1 (input-market enhancing effect). On the other hand, under vertical integration, firm 1
5 In the model of vertical integration, the network department of firm 1 might obtain access charge revenue fromthe retail department of firm 1. However, this merely indicates income transfer within the same firm; thus, firm 1
does not care about this transfer when it chooses r.

5has an incentive to increase r so as to reduce its rival’s output. For this strategic purpose, firm 1
has a stronger incentive for increasing r than the vertically separated firm, firm 0 (strategic effect).
The significance of the input-market enhancing effect is measured by (y1SS + y2SS ) − y2IS . The
smaller c is, the larger (y1SS + y2SS ) − y2IS is (and hence the stronger the input-market enhancing
effect is). Thus, the input-market enhancing effect is more likely to dominate the strategic effectwhen c is smaller.6
Note that c ≤ 0 is a sufficient, but not a necessary condition under which vertical separation
increases the rate of access charge. Even with a positive c, it is possible that vertical separation
increases r.
Next, we briefly discuss the welfare implications of vertical separation. Vertical separation
yields a double-marginalization problem in firm 1 and then reduces firm 1’s output. Although it
increases firm 2’s output, the total output decreases. When c ≤ 0, the vertical separation reduces
y1 and Y and hence reduces welfare. According to Proposition 1(i), if c ≤ 0, vertical separation
increases r, which results in a welfare loss. Since both effects reduce welfare, vertical separation
unambiguously reduces welfare.
Proposition 2 Vertical separation reduces welfare when c ≤ 0.
However, when c is positive, the implications on welfare are ambiguous. When c is large, a
reduction in firm 1’s output and an increase in firm 2’s output improve welfare because firm 2
is more efficient than firm 1 (total production costs are economized). This effect is known as
the welfare-improving production substitution effect. Moreover, vertical separation decreases r(Proposition 1(ii)), resulting in a welfare gain. Although these two effects improve welfare, verticalseparation induces a decrease in the total output, which reduces welfare. Thus, it is ambiguouswhether the former welfare-improving effects dominate the latter welfare-reducing effect.
In our model, vertical separation reduces welfare when c ≤ 0 (Proposition 2). However, weshould not place excessive emphasis on this result. We have assumed that firm 0 (under verticalseparation) and firm 1 (under vertical integration) have the same manipulation cost function L(r).
This assumption may not be realistic. Under vertical separation, the cost structure becomes moretransparent and the disintegrated upstream firm has more difficulties in manipulating accounting
6 This result does not depends on the assumption of Cournot competition. If we consider Bertrand model withproduct differentiation, we can show that vertical separation increases (reduces) r when c is small (large) enough.

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costs. In such situations, the rate of access charge is lower than that predicted by our model. Thus,
our model might underestimate the gains of vertical separation.
Although the number of firms in the product market is given exogenously in this paper, the entries of independent firms (the long-run effect) must change the results. Under vertical separation,
the firm holding an essential facility (firm 0) has an incentive to reduce r in order to stimulate
new entries. On the contrary, the vertically integrated firm has an opposite strategic incentive. It
strategically increases r in order to deter further entries. Thus, if we consider a possible further
new entry, vertical separation might reduce r even when the incumbent is as efficient as the newentrants. This topic should also be examined in future research.
[2009.3.11 915]

References
Armstrong, M., Vickers, J., 1998. The access pricing problem with deregulation: a note. Journalof Industrial Economics 46, 115–121.
Beard, T. R., Kaserman, D. L., Mayo, J. W., 2001. Regulation, vertical integration and sabotage.
Journal of Industrial Economics 49, 319–333.
Economides, N., 1998. The incentive for non-price discrimination by an input monopolist. International Journal of Industrial Organization 16, 271–284.
Economides, N., White, L. J., 1995. Access and interconnection pricing: How efficient is theefficient component pricing rule. Antitrust Bulletin 40, 557–579.
Gautier, A., Mitra, M., 2008. Regulation of an open access essential facility. Economica 75,
662–682.
Hausman, J. A., 1997. Valuing the effect of regulation on new services in telecommunication.
Brooking Papers on Economic Activity, Microeconomics, 1–38.
Ida, T., Anbashi, M., 2008. Analysis of vertical separation of regulators under adverse selection.
Journal of Economics 93, 1–29.
Hori, K., Mizuno, K., 2006. Access pricing and investment with stochastically growing demand.
International Journal of Industrial Organization 24, 795–808.
Laffont, J. J., Tirole, J., 1994. Access pricing and competition. European Economic Review 38,
1673–1710.
Mandy, D. M., Sappington, D. E. M., 2007. Incentives for sabotage in vertically related industries.
Journal of Regulatory Economics 31, 235–260.

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Mizuno, K., Shinkai, T., 2006. Delegating infrastructure projects with open access. Journal of
Economics 88, 243–261.
Sappington, D. E. M., 2005. On the irrelevance of input prices for make or buy decisions. American Economic Review 95, 1631–1638.
Sappington, D. E. M., 2006. On the design of input prices: Can TELRIC prices ever be optimal?
Information Economics and Policy 18, 197–215.
Viscusi, W. K., Harrington, J. E., Vernon. J. M., 2005. Economics of Regulation and Antitrust
4th Edition, MIT Press.

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