GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No.194

Access charges, vertical separation, and lobbying

Toshihiro Matsumura and Noriaki Matsushima

May 2011

GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

Access charges, vertical separation, and lobbying∗Toshihiro Matsumura†Institute of Social Science, University of Tokyo
and
Noriaki Matsushima‡
Institute of Social and Economic Research, Osaka University
May 2, 2011

Abstract
We examine how vertical separation affects the lobbying activities for the accesscharge of essential facilities. First, when investigating a model where the number of
new entrants is fixed, we find that vertical separation either increases or decreases theaccess charge, and that this depends on the relative efficiency between the incumbent
and the new entrants, and the number of entrants. Second, when investigating a freeentry market, we find that vertical separation always reduces the access charge in sucha market. The vertically integrated firm has a stronger incentive to lobby in this market
because a higher access charge reduces the number of competitors.

JEL classification numbers: L51, L13
Key words: network industry, access charge, manipulation of accounting, regulation∗

We would like to thank seminar participants at Osaka University and Kyoto University for their helpfulcomments. The authors gratefully acknowledge financial support from a Grant-in-Aid for Encouragementof Young Scientists and for Basic Research from the Japanese Ministry of Education, Science and Culture.
Needless to say, we are responsible for any remaining errors.
†
Toshihiro Matsumura, Institute of Social Science, University of Tokyo, Hongo 7-3-1, Bunkyo, Tokyo
113-0033, Japan. E-mail: matsumur@iss.u-tokyo.ac.jp‡
Corresponding author: Noriaki Matsushima, Institute of Social and Economic Research, Osaka
University, Mihogaoka 6-1, Ibaraki, Osaka 567-0047, Japan.
Phone: +81-6-6879-8571.
E-mail:nmatsush@iser.osaka-u.ac.jp1

1

Introduction

Competition between a firm holding essential facilities (usually, a dominant firm) and firms
not holding them has been widely observed in many industries such as overnight delivery,
telecommunications, electric power, and natural gas distribution. In particular, in Japan,
dominant firms are not vertically separated in telecommunications, electric power, and gas
distribution. Dominant firms were previously legal monopolists, and they have had tocompete against new entrants after the liberalization of these markets. New entrants pay
an access fee to the dominant firms. The access charge (the price of using essential facilities
that is also an input price for new entrants) affects the new entrants’ marginal costs, andthus significantly affects the performance of the markets.
The access charge is typically regulated by the government. Considerable literature on
the desirable and/or existing rules for levying the access charge, such as efficient component
pricing rule (ECPR), total element long-run incremental cost (TELRIC), and a historicalcost approach, exist;1 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 traditional local telecommunications, while the historical cost approach has been adopted in
optical fiber networks, electric power, and natural gas distribution. In the EU, although
the rules are different for different countries, cost-based approaches have been adopted inmost industries and in most countries.
In practice, however, firms often influence the access charge by lobbying and/or manipulating the accounting costs, whereas in principle, the rule for calculating the access charge isdetermined by a neutral government, and there is no room for manipulation.2 For example,
1

For the general aspects of the access charge, see Vogelsang (2003) and Rey and Tirole (2007). See

also Laffont and Tirole (1994), Economides and White (1995), Hausman (1997), Armstrong and Vickers(1998), Ida (2001), Sappington (2006), and Higgins and Mukherjee (2010). Further, see 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).

2

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 for gas
distribution pipeline networks. They made substantial efforts to rationalize their argumentin front of the Gas Energy Committee of the Advisory Committee for Natural Resourceand Energy, which is the agency 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 observed intelecommunications and electric power distribution in Japan. In this paper, we consider asituation wherein the access charge is influenced by the firms through lobbying activities.
Another important topic in policy is whether dominant firms should be allowed to holdessential facilities. Vertical separation is always an important policy issue in this field, andownership unbundling has been widely observed, especially in the EU. It is often insisted
that vertical separation is beneficial because it deters manipulation by vertically integrated
firms.
In this paper, we discuss the manner in which vertical separation affects the accesscharge. First, we formulate a model where n firms compete in a final product market andone monopoly input supplier, firm 0, holds an essential facility. We compare two situations,firms 0 and 1 are vertically integrated (vertical integration case), and no firm is verticallyintegrated (vertical separation case).
We find that the effect of vertical separation on lobbying activities are ambiguous. It
depends on the number of firms and the cost structure. When the number of firms is large,
vertical separation decreases (increases) the lobbying activities and consequently the accesscharge if the incumbent is more efficient than or as efficient as the new entrants (if theincumbent is considerably less efficient than the new entrants). On the contrary, when thenumber of firms is small, vertical separation increases (decrease) the access charge if theincumbent is more efficient than or as efficient as the new entrants (if the incumbent is
considerably less efficient than the new entrants). We also discuss the welfare effects. We

3find that vertical separation can be harmful for welfare.
Second, we investigate a free-entry market of new entrants.3 We obtain a contrasting
clear-cut result. We find that vertical separation reduces the access charge in the free-entry
market. The vertically integrated firm has a stronger incentive to increase the access charge
in a free-entry market because a higher access charge reduces the number of competitors.
Such a strategic effect disappears under vertical separation.
We now review related papers. The aim of this paper is to investigate the relationshipbetween the incentive to raise the access charge and vertical separation/integration.4 In theliterature on vertically related industries, many works have already pointed out that vertically integrated firms have strong incentives to raise their rivals’ costs. Economides (1998)
investigates Cournot competition in a downstream market and shows that the verticallyintegrated firm has an incentive to exclude the rivals through a prohibitive access charge.
Mandy and Sappington (2007) show that the vertically integrated firm has an incentive
to engage in cost-increasing sabotage regardless of whether there is Cournot or Bertrand
competition in the downstream market, but has a weak (strong) incentive to engage indemand-reducing sabotage when there is Bertrand (Cournot) competition. The discussions
on increasing the rivals’ costs and cost-increasing sabotage in this context are also provided by Beard et al. (2001) (see also the papers cited by them). Bustos and Galetovic(2009) discuss a case in which a bottleneck monopoly endogenously determines its verticalstructure (integration or separation) and the degree of sabotage.
The setting of lobbing activity in this paper is closely related to the cost-increasing
sabotage discussed in the previous researches, but there is one crucial difference. Undervertical separation, the upstream firm has no incentive to engage in sabotage activities
because these activities never increase the revenue of the upstream firm (Beard et al. (2001)
and Mandy and Sappington (2007)). Thus, vertical separation never facilitates sabotage
3

Free entry markets often yield completely different economic implications (Lahiri and Ono (1995),

Davidson and Mukherjee (2007), Etro (2007), Marjit and Mukherjee (2008), and Ino and Matsumura (2010)).
4

Armstrong and Sappington (2006) provide a comprehensive survey for deregulation policy.

4

activities. On the contrary, the vertically separated upstream firm still has an incentive tolobby because an increase in the access charge can increase its profits. As a result, verticalseparation can facilitate lobbying activities. Another difference is that all works mentioned
above assume that the number of firms is given exogenously, while we consider a free-entry
market.5
The remainder of this paper is organized as follows. Section 2 formulates the model andprovides the basic calculus to derive the main result. Section 3 presents the main results.
Section 4 discusses a free-entry market. Section 5 concludes the paper.

2

The Model

We consider two cases: (1) a vertically integrated firm holding an essential facility and(2) vertical separation undertaken by the government. We call the firm holding an essential facility the integrated (separated) facility firm in the integration (separation) case,respectively.

2.1

Vertical integration case

We consider an oligopoly model. Firm 1 is an integrated facility firm, and firm i (i =2, . . . , n) is a new entrant. Firm i accesses the essential facility held by firm 1 and pays ayi
to firm 1, where a is the per unit access charge and yi is firm i’s output.6
In the first stage, the access charge (input price) a is determined. Let L(a) denote firm
1’s effort costs (costs incurred for the lobbying activity, manipulation of the access charge
5

The model formulation is also related to that in Buehler et al. (2006). They consider the effects of policy

instruments to a public utility which supplies an essential input to downstream firms and engages in quality
investment: (i) market structure regulation (vertical separation/integration with downstream competition
and monopoly vertical integration) and (ii) access charge regulation. They mainly focus on how verticalseparation/integration with downstream competition and the level of access charge change the price in thedownstream market and the service quality. This is different from the main concern in our paper.
6

In many countries, the sales and production departments of a vertically integrated firm pay ay1 to theirown network department that holds the essential facilities. However, this accounting system does not affectthe optimal output in an integrated firm as long as it maximizes the joint profit of both departments.

5accounting, etc.). We implicitly assume that the per unit access charge is zero if firm 1 does
not make any effort. That is, the access charge is regulated but can be affected by firm 1’sefforts. Moreover, we only consider the cases in which only the integrated/separated facility
firm engages in lobbying activities. This is because we would like to clarify how vertical
integration/separation affects firm 1’s incentive to lobby. In the discussion on lobbying
activities, this simple functional form is often employed. For instance, Long and Soubeyran(1996), Pecorino (1998), and Yamazaki (2004) among others assume that in the context
of international trade, the tariff rate t is a function of the domestic firms’ total lobbying
efforts/expenditures or the industry-wide labor devoted to lobbying, and that the tariffPfunction t = t(Z) satisfies t0 > 0 and t00 < 0, where Z = ni=1 zi , and zi is the effective
lobbying effort/expenditure of the domestic firm i. We think that this simple assumption
clarifies how the main results in this paper are derived.7
In the second stage, the firms engage in Cournot competition. They simultaneously
produce perfectly homogeneous products for which the market demand function is givenby p(Y ) = v − Y , where v is a positive constant and Y is the total output of the firms(price as a function of quantity). Firm i’s production cost (except for the access charge) is
normalized to zero and firm 1’s marginal production cost is denoted by c. If c is positive(negative), firm 1 is less (more) efficient than firm i (i = 2, . . . , n). Firm 1’s profit and firmi’s profit are given as (i = 2, . . . , n)π1 = (p(Y ) − c)y1 + anXyj − L(a),πi = (p(Y ) − a)yi .

j=2

We assume that L0 (a) ≥ 0 and that L00 (a) > 0 in order to ensure the concavity of
7

It might be possible to formulate these lobbying activities by other models. For instance, lobbying

activities are often formulated by the rent-seeking model of Tullock (1980), which is also related to patent
race games (e.g., Loury (1979), Dasgupta and Stiglitz (1980), and Clark et al. (2010)). In these models, it isoften assumed that each player engages in lobbying activities and that the winner of the rent-seeking game(patent race game) is probabilistically determined. As the effort (investment) level of a player increases,
his/her winning probability increases. This property is somewhat similar to that formulated in this paper
although the access charge is deterministically set by the effort level of the integrated/separated facility
firm.

6

firm 1’s payoff function. We assume that L0 (0) = 0 in order to ensure interior solutions in
the first stage. We also assume interior solutions in the second stage (production stage)
discussed below.
Consider the second stage. The reaction functions of the firms in the second stage are
given by
R1 (Y−1 ) =

v−c−

Pn

j=2 yj2, Ri (Y−i ) =

v−a−

P

2

j6=i yj.

The resulting equilibrium outputs and profits are as follows (i = 2, 3, . . . , n):ny1IS =

Xv + c − 2anv − c − (n − 1)av − nc + (n − 1)a, yiIS =, Y IS ≡yjIS =
,
n+1
n+1
n+1
j=1

π1IS =(v − nc + (n − 1)a)2(n + 1)2+(v − 2a + c)2a(n − 1)(v + c − 2a)− L(a), πiIS =.
n+1(n + 1)2where the superscript IS denotes the equilibrium outcome under vertical integration in thesecond stage. The resulting total social surplus (consumer surplus plus the profits of thefirms) is given by8
W IS =(nv − c − (n − 1)a)((n + 2)v + c + (n − 1)a) c(v − nc + (n − 1)a)−
− L(a). (1)2(n + 1)2
n+1

In the first stage, firm 1 maximizes π1IS with respect to a. The first-order condition is∂π1IS2(n − 1)(v − nc + (n − 1)a) (n − 1)(v + c − 4a)=+− L0 (a) = 0.
∂a(n + 1)2
n+1(2)

Let the superscript I denote the subgame perfect Nash equilibrium (SPNE) outcomes undervertical integration. aI is derived from (2).

2.2

Vertical separation case

We consider the situation wherein vertical separation is undertaken by the government. In
the previous subsection, firm 1 holds the essential facility and supplies the final products.
In this subsection, firms 0 and 1 are separated. Firm 0 holds the essential facility but does
not supply the final products. It obtains access revenue from n firms including firm 1.
8

If the lobbying costs are not real social costs but only income transfers from the firm to the regulatorsor lawyers, it might be better not to subtract L(a) in (1).

7

In the first stage, firm 0 chooses a with cost L(a). After observing a, n firms compete interms of output. Firm 0’s profit, firm 1’s profit, and firm i’s profit are given by (i = 2, . . . , n)π0 = a ·nXyi − L(a),π1 = (p(Y ) − c − a)y1 ,

πi = (p(Y ) − a)yi .

i=1

Again, in the second stage, n firms engage in Cournot competition.
We discuss the second stage subgame where a is given exogenously. The equilibrium
outputs are as follows (i = 2, 3, . . . , n):y1SS =

v − nc − av+c−anv − c − na
, yiSS =, Y SS =
,
n+1
n+1
n+1

where the superscript SS denotes the equilibrium outcome under vertical separation in thesecond stage. The resulting profits of the firms are given by (i = 2, 3, . . . , n)π0SS =a(nv − c − na)(v − nc − a)2(v + c − a)2SS− L(a), π1SS =
,
π
=
.
i
n+1
(n + 1)2(n + 1)2

The resulting total social surplus is given by
W SS =(nv − c − na)((n + 2)v + c + na) c(v − nc − a)−− L(a).
2(n + 1)2
n+1

In the first stage, firm 0 maximizes its profit with respect to a. The first-order conditionis given bynv − c − 2na∂π0SS=− L0 (a) = 0.
∂a
n+1

(3)

Let the superscript S denote the SPNE outcomes under vertical separation. aS is derived
from (3).

3Results

We now present the results.
Proposition 1 (i) If n < 3, there exists c̃(n) such that aS > aI if and only if c < c̃(n).
(ii) If n = 3, aS = aI regardless of c.
(iii) If n > 3, there exists c̄(n) such that aS > aI if and only if c > c̄(n).
8Proof: See Appendix.
The following figures are helpful for understanding Proposition 1. In the figures, π̄iindicates the profit of firm i before subtracting lobbying cost L(a). ∂ π̄1IS /∂a and ∂ π̄0SS /∂arespectively denote the marginal gains of raising a for the facility firms in the integrationand the separation cases. L0 (a) denotes the marginal cost of raising a in both cases. Figures
1(a), 1(b), 1(c), and 1(d) indicate the cases in which n is small and c is large, both n andc are large, both n and c are small, and n is large and c is small, respectively. They show
the equilibrium access charge levels in each case.
[Figure 1 here]
A key property behind Proposition 1 is that the slope of ∂ π̄/∂a depends on the number offirms. Figure 1 shows that |∂ 2 π̄1IS /∂a2 | > |∂ 2 π̄0SS /∂a2 | (resp. |∂ 2 π̄1IS /∂a2 | < |∂ 2 π̄0SS /∂a2 |)holds if n is large (resp. small). We now discuss the intuition behind this property.
We rewrite the marginal gains of raising a for the facility firms in the two cases (integration and separation cases) as follows:
¶
n
n µ
X
X
∂yiIS (a) IS∂yiIS (a)∂ π̄1IS0IS= p (Y )y1 (a) +yi (a) + a
,
∂a
∂a
∂a
i=2
i=2
¶
n µ
SS (a)X∂ π̄0SS∂y=yiSS (a) + a i
.
∂a
∂a
i=1

We call the first term in the first equation “the strategic effect.” This represents the
incentive of the integrated facility firm for reducing its rivals’ outputs. We call the remaining
effects in the two equations “the input-market effect.” This represents the incentives of the
facility firms in both cases for obtaining access charge revenues. Note that in the separationcase, only the input-market effect exists.
We now investigate the condition that |∂ 2 π̄1IS /∂a2 | > |∂ 2 π̄0SS /∂a2 |. First, we discuss
the input-market effect. In both integration and separation cases, a higher a leads to alower output of firms paying the access charge (we call them service-based firms) because
it increases their marginal costs (direct effect). In the integration case, a higher a leads
9to a higher output of firm 1, and it further reduces the total output of the service-based
firms (indirect effect), while no such additional indirect effect exists in the separation case.
This means that an increase in a reduces the total output of service-based firms morein the integration case than in the separation case. Thus, an increase in a weakens the
input-market effect more in the integration case than in the separation case. Therefore,|∂ 2 π̄1IS /∂a2 | > |∂ 2 π̄0SS /∂a2 | holds unless the input-market effect is dominated by the strategic effect, which is discussed below.
Next, we discuss the strategic effect. There is no strategic effect in the separation case.
However, in the integration case, a higher a leads to a higher y1IS (a), which strengthens
the strategic effect. In other words, an increase in a enhances the marginal gain of raisinga from the strategic effect. Therefore, |∂ 2 π̄1IS /∂a2 | < |∂ 2 π̄0SS /∂a2 | holds as long as thestrategic effect dominates the input-market effect discussed above.
We now discuss how n affects these two effects. An increase in n increases the total output of service-based firms. Thus, it strengthens the input-market effect. The effect on thePstrategic effect is complicated. On the one hand, an increase in n increases i6=1 ∂yiIS (a)/∂aand strengthens the strategic effect. On the other hand, an increase in n reduces y1IS (a) andweakens the strategic effect. The above two effects are mutually canceled out, and the net
effect is weak. Under these conditions, the input-market effect is more likely to dominate
the strategic effect when n is larger. Hence, |∂ 2 π̄1IS /∂a2 | > |∂ 2 π̄0SS /∂a2 | holds unless n issmall enough.
Another key property behind Proposition 1 is that the intersection of the two curves ofmarginal gains in the two cases is ((v − nc)/2, (n − 1)c). The location of the intersection
depends on the efficiency of firm 1, c, and the number of firms, n. A decrease in c shifts thetwo curves of marginal gains toward the northeast. The shift of ∂ π̄1SS /∂a is larger (resp.
smaller) than that of ∂ π̄0IS /∂a when n is small (resp. large). The shifts of the two curves
induce the intersection to move toward the southeast (compare (a) with (c), and (b) with(d)). We explain the intuition behind the property of these shifts.
10First, we explain how a decrease in c increases the marginal gains in both cases andyields the upward shifts of both curves, ∂ π̄1SS /∂a and ∂ π̄0IS /∂a. A higher efficiency of theintegrated facility firm (a lower c) leads to its higher quantity y1IS (a). The strategic effect isstrong when the quantity supplied by the integrated facility firm (y1IS (a)) is large. Thus, adecrease in c strengthens the strategic effect in the integration case, resulting in an upward
shift of the curve, ∂ π̄0IS /∂a. In the separation case, a lower c leads to a higher total output
Pof the service-based firms ( ni=1 yiSS (a)). A lower c implies that the average of the firms’
marginal costs is smaller. As Salant and Shaffer (1999) show, it yields a larger total output.
Thus, a decrease in c strengthens the input-market effect in the separation case, resulting
in an upward shift of the curve, ∂ π̄1SS /∂a.
Next, we explain how a decrease in c yields a smaller shift of the curve in the separationcase when n is large. The impact of a decrease in c on the average marginal cost is smallerwhen n is large, and consequently, the marginal gain in the separation case is less sensitive
to c. On the contrary, in the integration case, the impact of a decrease in c on the strategic
effect is stronger when n is large. The impact of a decrease in c on y1IS is stronger whenn is larger. In fact, |∂y1IS /∂c| = n/(n + 1), and this is increasing in n. The rest of theparts consisting the strategic effect do not depend on c.9 As a result, the marginal gainin the integration case is more sensitive to c when n is large. Under these conditions, theupward shift of the curve, ∂ π̄0IS /∂a, which is caused by a decrease of c in the integrationcase, dominates that of ∂ π̄1SS /∂a in the separation case when n is large, resulting in theright-down shift of the intersection (see Figures 1(b) and 1(d)).
We briefly discuss the welfare implications of vertical separation. Vertical separation
yields a double-marginalization problem in firm 1 and reduces its output. Although it
increases the other firms’ outputs, the total output decreases by vertical separation. Givena, vertical separation reduces y1 and Y , and hence reduces welfare. Suppose that c ≤ 0.
9This property would depend on the assumption of the inverse demand function. We consider that the

weak relation between the rest of the parts and c holds, even though we use a more general inverse demand
function.

11

According to Proposition 1(i), vertical separation increases a when n = 2, which results in a
welfare loss. Because both effects reduce welfare, vertical separation unambiguously reduces
welfare. When n = 3, the second effect disappears, but the first effect is still present. Thus,
vertical separation unambiguously reduces welfare when n = 3. These yield the following
proposition:
Proposition 2 If n ≤ 3, vertical separation reduces welfare when c ≤ 0.
When c is positive, however, the implications on welfare are ambiguous even when n ≤ 3.
When c is large, a reduction in firm 1’s output and an increase in the outputs of the otherdownstream firms improve welfare because the other firms are more efficient than firm 1(total production costs are economized). This effect is known as the welfare-improving
production substitution effect.10 Moreover, vertical separation decreases a (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, whether theformer welfare-improving effect dominates the latter welfare-reducing effect is ambiguous.
When n > 3, the welfare implication of vertical separation becomes further complicated.
Suppose that c ≤ 0. Given a, vertical separation reduces firm 1’s output and increases theother firms’ outputs. However, because it reduces the total output, it reduces welfare as in
the case where n ≤ 3. According to Proposition 1(iv), if c ≤ 0, vertical separation decreases
a when n > 3, which results in a welfare gain. Thus, whether the latter welfare-improving
effect dominates the former welfare-reducing effect is ambiguous.
We now specify L(a) = φa2 /2 and present a numerical result where φ is a positive
constant. Suppose that c = 0. Figure 2 indicates the condition wherein vertical separation
reduces welfare. This figure indicates that when n or φ is large, vertical separation improves
welfare.
10

See Lahiri and Ono (1988, 1998, 1999). Production substitution plays a crucial role in the discussions

on public policies. See, among others, Ono (1990), Ushio (2000), Matsushima (2001), Matsumura (2003),
Matsushima and Matsumura (2003), and Ishida et al. (2010).

12

[Figure 2 here]
The larger the value of n, the weaker the double marginalization effect discussed above(the welfare-reducing effect of vertical separation). Thus, vertical separation is more likely
to improve welfare when n is larger. The larger the value of φ, the larger the lobbying cost
L(a) = φa2 /2, given a fixed a. Although the absolute values of aI and aS decrease with φ,
the difference between aI and aS affects the welfare difference between the two cases (notethat aI > aS ). Thus, vertical separation is more likely to improve welfare when φ is large.
RemarkIn our model, vertical separation reduces welfare when c ≤ 0 and n ≤ 3 (Propo-

sition 2). However, we should not excessively emphasize this result. We have assumed thatthe facility firms in the two cases have the same manipulation cost function L(a). This assumption may not be realistic. Under vertical separation, the cost structure becomes moretransparent and the disintegrated upstream firm faces more difficulties in manipulating theaccounting costs. In such situations, the access charge is lower than that predicted by ourmodel. Thus, our model might underestimate the gains from vertical separation.

4

Free entry

In the previous section, the number of firms in the product market is given exogenously.
However, if we consider the entries of independent firms, the results may change. Undervertical separation, the separated facility firm has an incentive to reduce the access charge
in order to stimulate new entries. On the contrary, the integrated facility firm has an
opposite strategic incentive. It strategically increases the access charge in order to deter
further entries. Thus, if we consider a possible further new entry, vertical separation might
reduce the access charge even when the incumbent is as efficient as the new entrants. In
this section, we examine this problem.11
11

In this paper, we consider the situation in which a is determined before entry. If a is determined after

entry, the basic principle discussed in the previous section can also apply to the free-entry market case. Thus,
vertical separation can either increase or decrease the access charge, depending on the relative production

13

We now consider a case in which new entrants freely enter the market after the valueof a is determined. The input price a is common among the final product suppliers. Let F√
be the entry cost of each new entrant. We assume that c < F . Otherwise, the incumbent
exits from the final product market in both the vertical integration case and the verticalseparation case; thus, vertical separation never affects the equilibrium access charge.12
Vertical integration

We consider the vertical integration case with free-entry. First,

we consider the equilibrium in the second stage (quantity competition stage). The resulting
equilibrium outputs and profits are the same as fixed n case except that (i = 2, 3, . . . , n)πiIS =(v − 2a + c)2− F,(n + 1)2where F is the entry cost of each independent firm. From the free-entry condition (zeroprofit condition), we have the equilibrium number of firms:√
v + c − 2a − F√.
n=FThe resulting equilibrium outputs and profits are as follows (i = 2, 3, . . . , n):√√
F + (a − c), yiIS = F , Y IS = v − F − a,√π1IS = ( F − c)2 + (v − c)a − a2 − L(a), πiIS = 0,√√(v − F − a)2ISW =+ ( F − c)2 + (v − c)a − a2 − L(a).
2y1IS =√

Second, we consider the first stage. The integrated facility firm maximizes π1IS withrespect to a. The first-order condition is∂π1IS= v − c − 2a − L0 (a) = 0.
∂a(4)

Let the superscript I denote the subgame perfect Nash equilibrium (SPNE) outcomes undervertical integration. aI is derived from (4).
efficiency between the incumbent and the new entrants, and the entry cost that affects the equilibrium
number of entrants.
12

Under vertical separation, we can see this from y1SS in (5). Under vertical integration, we can showthat exiting from the final product market before the entry of rival firms increases the profit of firm 1 if and√only if c ≥ F . Thus, even here, firm 1 is not active in the final product market.

14Vertical separation

We consider the vertical separation case with free-entry. Fist, weconsider the equilibrium outcome in the second stage. The resulting equilibrium outputs
and profits are the same as fixed n case except for (i = 2, 3, . . . , n)πiSS =(v + c − a)2− F.
(n + 1)2

From the free-entry condition, we have the equilibrium number of firms:√
v+c−a− F√n=.
F
The resulting equilibrium outputs and profits are as follows (i = 2, 3, . . . , n):√√
F − c, yiSS = F , Y SS = (v − a) − F ,√√π0SS = (v − F − a)a − L(a), π1SS = ( F − c)2 , πiSS = 0,√√√(v − F − a)2
SS+ ( F − c)2 + (v − F )a − a2 − L(a).
W =2y1SS =√(5)

In the first stage, firm 0 maximizes its profit with respect to a. The first-order conditionis given by√∂π0SS= v − F − 2a − L0 (a) = 0.
∂a

(6)

Let the superscript S denote the SPNE outcomes under vertical separation. aS is derived
from (6).
Because we assume that c <√F , from (4) and (6), we have the following proposition:13

Proposition 3 aS < aI . That is, the input price decrease under vertical separation.
Under free-entry, an additional strategic effect emerges. Under vertical integration, a higher
input price diminishes the incentive of the new entrants to enter the market. This higher
price protects the integrated downstream incumbent. Thus, the integrated facility firm has
a strong incentive to raise a. This strategic effect disappears under vertical separation. In
addition, under vertical separation, the separated facility firm has the opposite incentive.
In the free-entry market, a reduction in a stimulates new entries and increases the aggregate
quantity supplied. Thus, the separated facility firm has a weaker incentive to raise a.
13

As is noted in the second paragraph of this section, aS = aI if c ≥

15

√

F.

5

Concluding remarks

Firms often influence the access charge by lobbying and/or manipulating the accounting
costs in practice, whereas the rule for calculating the access charge is determined by aneutral government, and there is no room for manipulation in principle. In this paper, weconsider a situation wherein the access charge is influenced by the firms through lobbying
activities. Under the situation, we mainly discuss the manner in which vertical separation
affects the access charge. We find that it is ambiguous as to whether or not verticalseparation decreases the lobbying activities and consequently lowers the access charge.
When the number of new entrants is large (small) and the incumbent is as efficient as the
new entrants, vertical separation decreases (increases) the access charge. We also find thatvertical separation can be harmful for welfare. In free-entry markets, however, the resultof the equilibrium access charge is clearer. Vertical separation always decreases lobbying
activities and consequently lowers the equilibrium access charge.
In this paper, we assume that the lobbying function is given exogenously and investigate whether or not vertical separation reduces the incentive to lobby. Endogenizing therelationship between lobbying activity and the resulting access charge under vertical integration and vertical separation and/or introducing lobbying by multiple players remains aninteresting topic for future research.

16

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19

Appendix
Proof of Proposition 1

First, we show (ii). Given a, the difference between ∂π0SS /∂ain (3) and ∂π1IS /∂a in (2) is given as
D≡−(n − 3)(v − nc − 2a).
(n + 1)2

If n = 3, D = 0 regardless of the parameters. This implies aS = aI .
Next, we show (i) and (iii). We show the following three properties:
(a)
(b)
(c)

∂ π̄1IS /∂a = ∂ π̄0SS /∂a = (n − 1)c when a = (v − nc)/2;∂ 2 π̄1IS /∂a2 < 0 and ∂ 2 π̄0SS /∂a2 < 0;
∂ 2 π̄1IS /∂a2 < ∂ 2 π̄0SS /∂a2 holds if n < 3,
∂ 2 π̄1IS /∂a2 > ∂ 2 π̄0SS /∂a2 holds if n > 3.

If the three properties hold, from Figure 1, it is clear that Proposition 1(i) and Proposition
1(iii) hold.
We first show that (a) holds. ∂ π̄1IS /∂a and ∂ π̄0SS /∂a are given as∂ π̄1IS∂a∂ π̄0SS∂a==2(n − 1)(v − nc + (n − 1)a) (n − 1)(v + c − 4a)+,(n + 1)2
n+1
nv − c − 2na.
n+1

Substituting a = (v − nc)/2 into these two equations yields ∂ π̄1IS /∂a = ∂ π̄0SS /∂a = (n − 1)c.
This implies (a).
Second, we show that (b) holds. Differentiating ∂ π̄1IS /∂a and ∂ π̄0SS /∂a with respect toa, we have
∂ 2 π̄1IS
2(n − 1)(n + 3)
=−
< 0,
2
∂a
(n + 1)2∂ 2 π̄0SS
2n
=−
< 0.
2
∂a
n+1

Thus, (b) holds.
Finally, we show that (c) holds. The difference between ∂ 2 π̄1IS /∂a2 and ∂ 2 π̄0SS /∂a2 isgiven as∂ π̄0SS∂ 2 π̄1IS
2(3 − n)
−
.
=
2
∂a
∂a
(n + 1)2
Thus, (c) holds.

Q.E.D.
20∂ π̄/∂a, L0 (a)∂ π̄/∂a, L0 (a)L0 (a)L0 (a)∂ π̄0IS /∂a∂ π̄1SS /∂aM
M∂ π̄0IS /∂a∂ π̄1SS /∂a
a

aS

a

aI

aI

(a) c is large, n = 2

aS(b) c is large, n > 3∂ π̄/∂a, L0 (a)∂ π̄/∂a, L0 (a)L0 (a)L0 (a)∂ π̄0IS /∂a∂ π̄1SS /∂aM∂ π̄0IS /∂a

M

a
aI

∂ π̄1SS /∂a
a

aS

aS

(c) c is small, n = 2

aI(d) c is small, n > 3

Figure 1: The marginal gain and cost of raising a.
Horizontal axis: The access charge level, a,Vertical axis: The marginal gain and cost of raising a, ∂π0IS /∂a and ∂π1SS /∂a, L0 (a),M : The intersection of the two curves, (a, ∂ π̄/∂a) = ((v − nc)/2, (n − 1)c).

21

10

8

6

4

2

2

4

6

8

10

Figure 2: The condition wherein vertical separation reduces welfare
Horizontal axis: The number of firms (n),Vertical axis: The parameter of the investment function (φ),
Shaded area is that the condition holds.

22