REVIEW OF ECONOMIC PERSPECTIVES – NÁRODOHOSPODÁŘSKÝ OBZOR,
VOL. 12, ISSUE 1, 2012, pp. 22–41, DOI: 10.2478/v10135-012-0002-x
Access Pricing Under Imperfect Competition1
M. Burak Onemli2
Abstract: The study investigates optimal access charges when the downstream markets
are imperfectly competitive. Optimal access charges have been examined in the
literature mainly under the condition where only the incumbent has market power.
However, network industries tend to exhibit an oligopolistic market structure.
Therefore, the optimal access charge under imperfect competition is an important
consideration when regulators determine access charges. This essay investigates some
general principles for setting optimal access charges when downstream markets are
imperfectly competitive. One of the primary objectives of this essay is to show the
importance of the break-even constraint when first-best access charges are not feasible.
Specifically, we show that when the first-best access charges are not feasible, the
imposition of the break-even constraint on only the upstream profit of the incumbent is
superior to the case where break-even constraint applies to overall incumbent profit,
where the latter is the most commonly used constraint in the access pricing literature.
Bypass and its implications for optimal access charges and welfare are also explored.
Key words: Optimal Access Charges, Non-negativity Constraint, Regulation
JEL Classification: L13, L51, L97
Introduction
Industries such as telecommunications, electricity, natural gas, railroads, water, and the
postal service all have both naturally monopolistic and potentially competitive segments.
Hence, these industries can be viewed as having a vertical integrated structure. In the
telecommunications industry, local loops can be regarded as the naturally monopolistic
segment, whereas long distance and the value-added services can be regarded as
potentially competitive. In the electric power industry, transmission and distribution are
naturally monopolistic segments, while electricity generation is potentially a
competitive segment. Similarly, in the natural gas industry, pipelines are the naturally
monopolistic segment whereas extraction can be classified as a potentially competitive
segment. In the railroad industry, tracks and stations are in the naturally monopolistic
segment while passenger and freight services are potentially in the competitive segment.
All of these industries are similar in the sense that they contain both potentially
competitive segments and natural monopolistic segments.
1
The author wishes to thank Dennis L. Weisman and Joel Potter and two anonymous referees for
helpful comments and suggestions.
2
Kansas State University, Department of Statistics, Dickens Hall Manhattan, KS, 66506, USA,
e-mail: mbonemli@ksu.edu
Volume 12, Issue 1, 2012
23
Naturally monopolistic segments of these industries are often referred to as bottleneck
segments. Therefore, effective potential competition requires the non-discriminatory
access to bottleneck segments. Without question, unbundling and/or access pricing is
the main policy instrument for introducing competition in these industries. In other
words, access pricing is a critical policy for deregulation of industries where a vertically
integrated dominant firm controls the supply of a bottleneck input.
Access pricing is not a new issue in regulatory economics. Its roots derive from the
essential facilities doctrine that dates back to a U.S. Supreme Court decision for
railroads in the early 20th century. In 1912, the Supreme Court forced the Terminal
Railroad Association to allow its competitors to use its terminal facilities.3,4
As Sherman
(2008, p. 266) observed following the Supreme Court decision, when a firm has
monopolistic power over a facility that is required by other firms in order to compete, it
has been argued that other suppliers should have access to the facility on nondiscriminatory
terms and conditions.5
Access pricing became the main policy instrument for regulators after vertically
integrated monopolies were deregulated. Increased criticism of regulation in the 1970s
and 1980s led to network unbundling with the goal of increased competition. For
example, in Britain before privatizing the national railway in 1994, the railways were
sold to approximately seventy companies, and the most important company, Railtrack,
owned and maintained the infrastructure.6
In the United States, the most recent example
of unbundling as an industrial policy is the 1996 Telecommunications Act.7
Section 251
(d) (2) of the 1996 Telecommunications Act directs the Federal Communications
Commission (FCC) to determine the specific network elements that incumbent local
exchange carriers (ILECs) must provide to their competitors on an unbundled basis at
“cost-based” rates. 8
Nevertheless, the ILECs and the competitive local exchange
carriers’ (CLECs) are at odds with respect to the pricing of unbundled network elements
(UNEs) at cost-based rates. The ILECs contend that economic efficiency requires that
prices for UNEs be based on the actual, forward-looking costs. Conversely, the CLECs
contends that economic efficiency demands that prices for UNEs be based on the
forward-looking costs of an ideally efficient ILEC as this standard is consistent with the
competitive market structure that the 1996 Telecommunications Act envisioned.9
3
See United States v. Terminal Railroad Ass’n, 224 U.S. 383 (1912) and 236 U.S. 194 (1915).
4
The Terminal Railroad Association was an organization of railroads that owned a railroad bridge
and other facilities in St. Louis, Missouri.
5
See Lipsky and Sidak (1999) and Robinson and Weisman (2008) for detailed review of the
essential facilities doctrine.
6
For more detailed discussion, see Gómez-Ibáñez J. A. (2003, p. 247, 264-297).
7
The 1996 Telecommunication Act Section 251 (d) (2): In determining what network elements
should be made available for purposes of subsection (c) (3), the Commission shall consider, at a
minimum, whether
(A) access to such network elements as are proprietary in nature is necessary; and
(B) the failure to provide access to such network elements would impair the ability of the
telecommunications carrier seeking access to provide the services that it seeks to offer.
8
See Kahn,Tardiff and Weisman (1999) for a comprehensive discussion of the economics
underlying the 1996 Telecommunications Act.
9
See Weisman (2002) and Weisman (2000).
REVIEW OF ECONOMIC PERSPECTIVES
24
Both approaches can be criticized on various grounds. First, ILECs may have incentives
to misreport their actual costs. Whether the inefficiencies of ILECs should be reflected
in UNE prices is another point of criticism. Moreover, the ILEC might not have proper
incentives to achieve efficiency if UNE prices are based on actual costs. On the other
hand, the definition for the ideally efficient ILEC is unclear, and the proper standard to
determine what constitutes “an ideally efficient” ILEC is a difficult question to answer.
Moreover as Weisman (2000, p. 196) observed “If regulators had sufficient information
to implement the efficient–firm cost standard, competition would be wholly
unnecessary.”
Therefore, the complex issue of optimal access charges lies at the core of deregulation
efforts in network industries. In other words, a sound access pricing policy is crucial for
the efficient development of competition in industries with bottleneck inputs. Moreover,
Laffont and Tirole (2001, p. 98-99) observed that an optimal access charge policy must
serve numerous purposes. It must generate efficient use of networks, encourage
incumbents to invest, promote cost minimization, and create an efficient amount of
entry into infrastructure, and do all this at a reasonable regulatory cost.
Realizing all of these objectives simultaneously with a single policy instrument is
complex. As Laffont and Tirole (2001, p. 99) point out, the access price is critical in
order to give incumbents the correct signals for their choices of investment in
infrastructure and induce potential competitors to enter into socially desirable segments.
Optimal access pricing has become one of the central topics in modern regulatory
economics. In the access pricing literature, there is a distinction between one-way
access pricing and two-way access pricing. In one-way access, pricing only competitors
require vital inputs from the monopolistic incumbent. In the case of two-way access
pricing, all firms in the market need to purchase critical inputs from each other. In this
study we focus on one-way access pricing.10
The purpose of this study is to examine optimal access charges under an oligopolistic
market structure. Although formerly regulated industries post-deregulation exhibit
properties that are closer to an oligopolistic market structure, most of the optimal access
pricing literature focuses on contestable/perfect competition models. In this respect, we
study key characteristics of optimal access charges in a simple Cournot competition
model where only one input is necessary for the downstream production. This is a
simple framework and many complicated real-word issues such as asymmetric
information, investment decisions, and dynamics are suppressed. Nonetheless, this
analysis provides a useful starting point for the analysis and future research.
As Vickers (1995) observed, Cournot competition results in market outputs with
positive markups. Hence, a vertically integrated firm has a markup over the marginal
cost of the input while a competitor will have a markup over the price of the critical
(essential) input. These are downstream markups. On the other hand, if the access price
exceeds marginal cost, then there would be a second markup from the upstream market.
Hence, determining the optimal access charge requires regulators to address these two
markups within the Cournot framework.
10
See Chapter 5 in Laffont and Tirole (2001), Armstong (2002, p. 350-379), and Chapters 5 and
6 in Dewenter and Haucap (2007) for studies that examine two-way access pricing.
Volume 12, Issue 1, 2012
25
Optimal access charges are closely related to the concepts of the first-best and the
second-best efficiency. When the non-negativity profit constraint of the vertically
integrated incumbent is not taken into account, optimal access prices are the first-best
access prices. However, first-best access pricing may result in negative profit for the
vertically integrated incumbent threatening its financial viability. This is the case when
the incumbent’s break-even constraint is binding at the social optimum. Therefore, the
effects of the profit constraint must be explicitly taken into account. Taking into account
the profit constraint of the incumbent gives rise to the concept of second-best access
pricing.
The non-negativity profit constraint of the incumbent is extensively used in the access
pricing literature. The general approach is to examine a non-negativity constraint that
applies to the overall profit of the incumbent. However, this potentially distorts
competition in the downstream market since applying a non-negativity profit constraint
to the overall profit of the incumbent guarantees normal profit for the incumbent in both
the regulated upstream market and the competitive downstream market. This might tend
to create a bias that favors the incumbent’s downstream production. Guaranteeing a
normal profit for the incumbent provider leads to a distortion in the retail market by
suppressing at least some of the advantages expected of competition. Moreover, it might
be the case that the incumbent’s inefficiencies are passed on to the retail market. In the
competitive/contestable market framework with retail price regulation, guaranteeing
non-negative overall profit may not create a serious distortion compared with the firstbest
output. However, in an oligopolistic market structure the non-negativity assumption
leads to a potentially large deviation from first-best output levels.
One solution for the given problem would be to impose a non-negativity constraint to
the incumbent’s upstream profit only while deregulating the downstream segment of the
industry. One of the objectives of this paper is to compare the welfare effects of these
two policies. To that end, we evaluate the welfare properties within the Cournot model
and show that imposing the non-negativity constraint on only upstream profits provides
higher total welfare than imposing the non-negativity constraint on overall profits.
Our simple framework is also used to examine the effect of bypass. Bypass arises when
the competitor – rather than using the incumbent’s network – uses an alternative source
for the bottleneck input. We show that under certain conditions bypass can be welfare-
enhancing.
The organization of the remainder of this essay is as follows. Section 2 provides a
literature review. Although there is a voluminous literature on the topic, the focus here
is primarily on studies that explore optimal access charges. Section 3 discusses the main
elements of the model. The first–best and second–best access prices in an oligopolistic
market structure are derived in Section 4. This section also includes the welfare
comparisons of two possible policies regarding the non-negativity constraint of the
vertically integrated provider. In Section 5, the possibility of bypass and its effects on
optimal access charges are examined. Section 6 contains the conclusion.
Literature Review
Since network unbundling has developed into a key policy instrument for introducing
competition into previously regulated industries, the topic has attracted significant
REVIEW OF ECONOMIC PERSPECTIVES
26
interest from researchers. As a result, a voluminous access pricing literature has
emerged. However, since our objective is to investigate general principles for optimal
access charges under an oligopolistic market structure, we limit the discussion to studies
that focus on properties of optimal access charges.
Perhaps one of the most important results in the optimal access charge literature is
known as the Baumol-Willig efficient component pricing rule (ECPR). Willig (1979)
and Baumol (1983) advocate the ECPR.11
Their analyses depend on contestable markets
which can be treated as part of a perfect competition framework. The optimal access
price of a bottleneck input based on the ECPR should be equal to the direct incremental
cost of access plus the opportunity cost borne by the integrated access provider in
supplying access. The opportunity cost is the decrease in the incumbent’s profit caused
by the provision of the bottleneck input to a rival. Therefore, the access charge can be
higher than the direct incremental cost by a substantial margin. The ILECs generally
favor such an access pricing policy. However, the fact that previously regulated
industries are far from being competitive is a serious point of criticism. Moreover, the
inclusion of the opportunity cost term in this form of access pricing means that lessefficient
incumbents will receive higher prices for their input, ceteris paribus.
Spencer and Brander (1983) focus on departures from marginal cost pricing induced by
imperfect competition in industries that require publicly-produced inputs. As they
assumed the public enterprise has a vertically-integrated structure, their analysis is
conducted with and without the non-negative profit constraint imposed on the public
enterprise. They show that in order to induce the socially desirable output under
imperfect competition, the first best access charge requires an input price set below the
marginal cost of the input. However, when the profit constraint is introduced, the
second-best input price exceeds the marginal cost of the input.
Vickers (1995) examines a vertically integrated industry structure with naturally
monopolistic and competitive segments. He examines whether the upstream monopolist
should be allowed to operate in the deregulated competitive sector. Vickers employs a
Cournot model in an asymmetric-information environment, and compares total welfare
under linear and unit-elastic demand functions in the cases of vertical integration and
vertical separation. Vickers’ analysis reveals that the access charge should be higher or
lower than marginal cost depends on whether the number of firms in the downstream
competition is sensitive to the level of the access charge. In particular, his analysis
suggests that when the number of firms is sensitive to the level of the access price, the
optimal access charge should be above the marginal cost, and vertical integration yields
higher welfare in this case. Conversely, if the number of firms in the downstream
market is insensitive to the access charge, the optimal access price should be set below
marginal cost, and vertical separation produces higher welfare results in this case.
Laffont and Tirole (1994) investigate optimal access prices in a competitive fringe
model using a principal-agent framework. In their analysis, the key assumption is that
the regulator can make up any possible earnings deficiency for the incumbent using
public funds. The authors show that the first-best access pricing should be marginal cost
pricing. However, when marginal cost pricing results in an earnings shortfall for the
11
See also Chapter 7 in Baumol and Sidak (1994).
Volume 12, Issue 1, 2012
27
incumbent provider, competitors should contribute to the fixed cost of the network. The
authors state that the contribution takes the form of an access charge exceeding the
marginal cost of the input.
Armstrong, Doyle and Vickers (1996) use a competitive fringe model to show that the
ECPR can be a useful benchmark for determining optimal access charges. They analyze
the precise meaning of ‘opportunity cost’ under differing demand and supply conditions.
Throughout their analysis, they assume that the price for the downstream product is a
choice variable for the regulator while competitors take this price as given. In the
benchmark case, they show that the optimal access charge should be equal to the
marginal cost of the bottleneck input when the incumbent’s break-even constraint is not
binding at the social optimum. Conversely, if the break-even constraint is binding at the
social optimum, the optimal access price should exceed marginal cost. Moreover, their
results reveal that the latter benchmark case with price regulation implies an optimal
charge fully consistent with the ECPR.
Armstrong and Vickers (1998) extend the analysis of Armstrong et al. (1996) to the case
where there is a retail price deregulation. The authors analyze a model for a
homogeneous product and price-taking rivals. They find that the optimal access charge
can be above, below or equal to the marginal cost of the bottleneck input. In particular,
when the demand and rival supply for the downstream product is linear, the authors
show that the optimal access price should be set equal to marginal cost as long as the
break-even constraint is not binding. However, based on the demand and the
competitors’ supply functions, the optimal access charge can be above or below
marginal cost.
Armstrong (2002) provides one of the most comprehensive studies to date in the access
pricing literature. By making use of unit demand, competitive fringe, perfect retail
competition, and partial deregulation models, Armstrong examines topics such as the
foreclosure problem, fixed retail prices, unregulated prices and bypass. In this study, he
sheds light on topics such as access charges, dynamic issues and two-way access pricing
in the telecommunications industry.
Model
The incumbent is a vertically integrated producer in this model, and a monopolist in the
production of the essential input. The essential input is assumed to be the sole input
necessary for the production of the downstream product. The incumbent’s downstream
affiliate and (n-1) competitors produce and market the retail product. The upstream and
downstream production technologies are assumed to exhibit constant returns to scale.
The incumbent’s marginal cost is c . The incumbent sells the essential input to its rivals
at unit price w . The price of the essential input is determined by the regulator. The
incumbent’s and a representative competitor’s downstream production are denoted by
1
I
q and iq , respectively. For simplicity, we assume that a linear inverse demand function
is given by 1 2
nI
ii
P q q
=
 + 
 ∑ , where '( ) 0P ⋅ < and ''( ) 0P ⋅ = .
REVIEW OF ECONOMIC PERSPECTIVES
28
The incumbent and the (n-1) competitors are assumed to engage in Cournot competition
in the downstream market. The profit functions of the incumbent and the representative
competitor are given, respectively, by:
( )1 1
1
( ) ( )
n
I I
i
i
w c q P Q c q
≠
Π = − + −∑ , and (1)
( )( )i iP Q w qΠ = − , (2)
where I
Π and iΠ are profits of the incumbent and the representative competitor. The
first term in (1) is the upstream profit that the incumbent realizes from selling the
essential input to the competitors. The second term is the incumbent’s profit from its
downstream operations. The essential input cost is assumed to be identical for the
incumbent’s upstream and downstream affiliates.12
The regulator has full information regarding the demand, cost structure and the nature of
competition. The following two-stage game is considered based on these assumptions.
In the first stage, the regulator’s objective is to establish an optimal access charge. In the
second stage, the incumbent and the (n-1) competitors take the input price as given and
engage in quantity competition in the downstream market. Finally, consumers make
their purchase decisions after observing the market price.
Main Findings
Assuming an interior solution, the first order necessary conditions of the incumbent and
the representative competitor for the profit maximization are the equality of marginal
revenue and marginal cost: 1' I
P q P c+ = and ' iP q P w+ = . Totally differentiating the
first-order conditions and allowing for an infinitesimal change in the price of essential
input yields:
1 1 2
' '( ). 0
nI I
ii
P dq P dq dq
=
 + ⋅ + = 
 ∑ and 1 2
' '( ).
nI
i ii
P dq P dq dq dw
=
 + ⋅ + = 
 ∑ .
Solving the previous n equation system yields:
1
1
( 1) '
I n
dq dw
n P
−
= −
+
, and (3)
2
( 1) '
idq dw
n P
=
+
. (4)
The measure of total welfare employed here is the unweighted sum of consumer surplus
and total industry profits, or, 1 2
nI
ii
W CS
=
= + Π + Π∑ , where consumer surplus (CS) is
given by 1 1
2 2
()
n nI I
i ii i
U q q P q q
= =
   + − ⋅ +   
   ∑ ∑ .
12
The regulators impose parity requirements on vertically integrated producers in order to prevent
sabotage. See Sappington and Weisman (2005, p. 156) footnote 3.
Volume 12, Issue 1, 2012
29
Proposition 1 specifies the general principles regarding the optimal access charge under
the stated assumptions.
Proposition 1: At the welfare optimizing essential input price, (i) the downstream
product price equals the marginal cost of the essential input in the downstream market,
and (ii) the optimal access charge is lower than the marginal cost of access under
specified assumptions.
Proposition 1 (i) states that the welfare-optimizing access price in our simple Cournot
framework enables market price to equal marginal cost for the critical input. In a sense
this is the first-best access charge. Therefore, allocative efficiency can be attained at the
optimal access charge.
Two observations are instructive regarding the first-best optimal access charge. First,
when price equals marginal cost, the incumbent’s downstream production is zero
according to the necessary first-order condition for the incumbent.13
This result is
consistent with Vickers (1995).14
Second, based on the first-order condition of the
competitor, its downstream production is positive if and only if the optimal access
charge is lower than the marginal cost of access. This result is identical to Spencer and
Brander (1983). They showed that in the case of first-best pricing of a publicly
produced input with imperfect downstream competition, the input price should be lower
than marginal cost of the input and downstream product price equals marginal cost.15
Based on these observations and Proposition 1, it follows that the regulator uses the
upstream markup to achieve the first-best output level in the retail market. In other
words, by charging less than the marginal cost for the bottleneck input, the regulator is
subsidizing access to harmonize the downstream product price with the marginal cost of
production. The key point here is that the regulator compensates for downstream market
power by reducing the critical input price below marginal cost to increase output in the
retail market.
Henceforth, for analytical convenience and clarity in comparisons of various regulatory
policies, the market inverse demand function for the downstream product is assumed to
have the general form:
Assumption 1: ( )1 2( ) I
nP Q Q q q qα β α β= − = − + + +L
,
where 0α > and 0.β >
13
One logical question concerns why the incumbent firm’s downstream production is zero at the
first-best access charge. In other words, is the incumbent able to reduce its losses in the upstream
market by producing positive output in the downstream market? To answer this question, note
that the first-best access charge results in market price equal marginal cost (c) in the equilibrium.
Therefore, if the incumbent firm produces some positive quantity for the downstream market at
the optimal access charge, the market price for the downstream product should be lower. Hence,
producing positive output actually increases the incumbent’s losses in this case.
14
Vickers shows that in the case of linear demand, when the vertically integrated producer is
allowed into the downstream market, welfare is lower than the case where it is not allowed into
the downstream market. Hence, Vickers’ result can be interpreted as the incumbent’s downstream
production is zero at the optimal access price.
15
See Spencer and Brander (1983) Proposition 1.
REVIEW OF ECONOMIC PERSPECTIVES
30
To solve the sub-game perfect Nash equilibrium of the two stage game, backward
induction is employed. In this respect, we first solve for the equilibrium values in the
second stage. The incumbent’s and a representative competitor’s profits under
assumption 1 are:
1 1 1
1 1
( )
n n
I I I
i i
i i
w c q q q c qα β β
≠ ≠
 
Π = − + − − − 
 
∑ ∑ ,
and
(5)
1,
n
i i j i
j j i
q q w qα β β
= ≠
 
Π = − − − 
 
∑ . (6)
Lemma 1 summarizes industry profit and consumer surplus for the specified model.
Lemma 1: When Assumption 1 holds and the downstream market is characterized by
Cournot competition, the equilibrium incumbent’s profit, representative competitors’
profit and consumer surplus are given, respectively, by:
( )2
1 2
( 1)2
( )( 1) ;
( 1) ( 1)
I nc n wc w
w c n
n n
αα
β β
− + −+ −
Π = − − +
+ +
(7)
( )2
2
2
( 1) 2
;
( 1)
n
i
i
n c w
n
α
β=
− + −
Π =
+
∑ and (8)
( )2
2
( 1)
2 ( 1)
n c n w
CS
n
α
β
− − −
= ⋅
+ (9)
Total welfare (W) is assumed to be the unweighted summation of (7), (8) and (9). The
optimal access charge (w*
) for the essential input can be found by maximizing total
welfare (W) with respect to the access price (w). Hence, the optimal access charge is
given by *
( ) ( 1)w nc nα= − − .16
Note that *
w is the access charge that allows the
market price for the downstream product to equal the marginal cost of the input. This is
the first-best access pricing policy and *
( ) ( 1)w nc nα= − − is lower than marginal cost
of the input. Hence at the first-best access price the incumbent makes negative profit
from the upstream market. In addition, as previously stated, the optimal access charge
16
Notice that the first-best access charge, *
1
nc
w
n
α−
=
−
, increases with the number of firms (n).
Moreover, *
lim
1n
nc
w c
n
α
+→∞
−
= =
−
implies that as the number of firms approaches to infinity, the firstbest
access charge approaches the marginal cost of the input. This result is not surprising since as
n approaches to infinity, the firms become price takers and the results of the model become
consistent with the perfect competition models. In other words, as n grows large, the regulator
needs be concerned less with downstream market power, and hence w approaches to c.
Volume 12, Issue 1, 2012
31
leads the incumbent’s downstream affiliate to not produce any output in the downstream
market. Therefore, the vertically integrated producer makes negative profit at the
essential input price *
w since the incumbent’s break-even constraint will bind at the
social optimum. In the case where no lump-sum transfers are available to cover the
incumbent’s losses, this access charge is not feasible.
Since the first-best access pricing policy is inconsistent with the financial viability of
the incumbent provider, the regulator may opt to determine the optimal access charge
under the break-even constraint. There are two possibilities regarding the break-even
constraint from the regulator’s perspective. The first policy option is that the break-even
constraint for the incumbent applies to the incumbent’s overall profits. The second
policy option entails applying the break-even constraint to the incumbent’s upstream
activities only. Vickers (1995, p. 14) summarizes these two possibilities in the following
statement in which he contemplates extensions of his analysis:
“It has been assumed that the participation constraint for M (vertically integrated
incumbent) applies to its profits overall, including profits from the downstream
competitive activity… Indeed, it is more in the spirit of deregulation to allow the firm
independently to take it chances along with other competitors in deregulated activities,
and not to prejudge the outcome of competition there... This suggests that a more
realistic formulation might be to require that M at least break even in its upstream
regulated activities.”
However, Vickers does not actually conduct the formal analysis that he contemplates.
Throughout the vast optimal access pricing literature that focuses on the non-negativity
constraint of the incumbent’s overall profit, to our knowledge there is no study that
concentrates on a non-negativity constraint applied exclusively to the incumbent’s
upstream profit. One reason for this is that the models used in the previous studies
include perfect downstream competition with price regulation. In these models, there is
no business-stealing-effect unless there is product differentiation. When downstream
competition is imperfect, implying that each firm in the downstream market has some
degree of market power, a one-for-one displacement of outputs from the incumbent to
the competitors typically does not hold in equilibrium. Therefore, the regulator solves
the following problem:
0..
)(max
11
11
1
≥Π+Π
Π+Π+Π+ ∑≠
I
d
I
u
I
d
I
u
n
i
i
ts
CS
θ
(10)
where [ ]0,1θ ∈ , λ > 0 is the Lagrange multiplier and 1
I
uΠ and 1
I
dΠ denote upstream
and downstream profits of the vertically-integrated incumbent, respectively. The
boundary points on this closed interval characterize two possible break-even constraints
under examination. When 0θ = , the break-even constraint applies to only incumbent’s
upstream market. Conversely, when 1θ = , the break-even constraint is implemented for
the total (upstream and downstream) profits of the incumbent.
Finding the optimal access charge for the incumbent’s profit constraint requires solving
the regulator’s constrained maximization problem in (10). The second-order conditions
REVIEW OF ECONOMIC PERSPECTIVES
32
are assumed to hold, hence, the focus is on an interior solution here. The optimal access
price can be found by setting the derivative of the Lagrange function equal to zero and
solving it for the access charge (w).17
The optimal access charge is given by:
( )( ) ( )( )
( )
*
2 1 ( 1) 3 2 1 3 ( 1) 3
( 1) 3 2 (1 ) 4 ( 1)
n n n n c
w
n n
θ λ λ α θ λ λ
θ λ λ
+ + + − − + − + −
=
− − + + +
(11)
The optimal access charge in (11) is the second-best access charge. Notice that the
optimal access charge exceeds the marginal cost of access.18
This implies that the
second-best optimal access price allows the incumbent’s downstream production to be
positive.
Lemma 2 summarizes industry profit and consumer surplus in the model at the optimal
access charge when the incumbent’s profit constraint is binding at the social optimum.
Lemma 2: When Assumption 1 holds and the incumbent’s profit constraint is binding at
the optimal access charge, the equilibrium value of the incumbent’s profit, the
competitors’ profit and the consumer surplus are given by:
( )( )
( )
( )
2
1 2
2
2 (1 ) ( 1) 3 3 2 2 (1 )1
( )
( 1) 3 2 (1 ) 4 ( 1)
1 ( 3)( )
;
( 1) 3 2 (1 ) 4 ( 1)
I nn
c
n n
n c
n n
θ λ λ λ θ λ
α
β θ λ λ
λ α
β θ λ λ
+ + + − + − +−
Π = −
 − − + + + 
 + −
+  
− − + + +  
(12)
( )
( )
2
2
3 2 2 (1 ) ( )1
( 1) 3 2 (1 ) 4 ( 1)
n
i
i
cn
n n
λ θ λ α
β θ λ λ=
 + − + −−
Π =  
− − + + +  
∑ ; and (13)
( )
( )
2
( 1) 3 2 (1 ) (3 1) ( )1
2 ( 1) 3 2 (1 ) 4 ( 1)
n n c
CS
n n
θ λ λ α
β θ λ λ
  − − + + + −  = ⋅
− − + + +  
(14)
Equations (12) – (14) define total social welfare under the optimal access charge.
Specifically, when 1θ = , equations (12) – (14) denote total welfare under the secondbest
optimal access charge when the break even constraint applies to the incumbent’s
17
The focus here is an interior solution where the non-negativity profit constraint is binding at
social optimum. Therefore, we only discuss the results of Kuhn-Tucker conditions where λ>0. In
the case where λ=0, we have unconstrained optimization whose results have already been
discussed above.
18
The mark-up in producing the bottleneck input at the optimal access price for the incumbent is
given by , where the
denominator is unambiguously positive. Hence, the optimal access charge exceeds marginal cost
if 2 (1 ) ( 1) 3 0nθ λ λ+ + + − > . Since θ is a positive exogenous value determined by the regulator,
there always exists a positive value of λ for different θ’s that satisfy this inequality.
Volume 12, Issue 1, 2012
33
overall profit. Conversely, when 0θ = , equations (12) – (14) define total social welfare
under the second-best optimal access price when the break-even constraint for the
incumbent applies to its upstream profit only. Proposition 2 provides a comparison of
the two possibilities regarding the break-even constraint for the incumbent.
Proposition 2: Assume that Assumption 1 holds and the downstream market is
characterized by Cournot competition,
(i) The incumbent’s profit is higher when the break-even constraint for the incumbent
applies to its overall profits ( 1)θ = ,
(ii) The consumer surplus, the competitors’ profit and total welfare are higher when the
break-even constraint for the incumbent applies to its upstream profit only ( 0)θ = .
The findings of Proposition 2 are intuitive regarding the incumbent’s break-even
constraint. When the break-even constraint is introduced, the optimal access charge
results in a welfare reduction relative to the first-best optimal access charge. In addition,
the higher price-marginal cost markup for downstream output, the greater the welfare
loss, ceteris paribus. Applying the break-even constraint to the incumbent’s overall
profit including its profits from downstream activities leads to a higher markup over the
marginal cost compared to the case when the break-even constraint for the incumbent
applies to the upstream profit only. In other words, applying the break-even constraint
to the incumbent’s overall profit leads to a higher deviation from the first-best optimal
access charge than applying it to the incumbent’s upstream profit only. Therefore,
applying the break-even constraint to the incumbent’s upstream profit only yields both a
lower access charge and a market price closer to marginal cost, ceteris paribus.
Notice that the incumbent’s downstream production is positively related to the access
price. The same observation is also true for the incumbent’s overall profit due to the fact
that the second-best access price exceeds marginal cost of the bottleneck input. On the
other hand, a competitor’s downstream production and profit are inversely related to the
access price. Thus, as compared to the case where the non-negative profit constraint is
restricted to upstream profit, the incumbent’s downstream output and profit increases
when the non-negativity constraint applies to overall profit. For competitors, the
converse is true. In addition, the competitors’ production falls by more than the increase
in incumbent’s production. Therefore, higher access charges lead to a decrease in the
market equilibrium quantity. Hence, consumer surplus will be lower in the case where
the break-even constraint applies to the incumbent’s overall profit rather than its
upstream profit only. This implies that social welfare is lower due to the fact that the
overall decrease in the entrants’ profit and consumer surplus outweigh the increase in
the incumbent’s profit.
Hence, when the downstream market structure is oligopolistic rather than competitive,
regulators must exercise caution in applying the break-even constraint on the operations
of the incumbent provider. To wit, applying a break-even constraint to overall profits
rather than limiting it to upstream profits tends to result in higher market distortions and
hence larger reductions in social welfare.
REVIEW OF ECONOMIC PERSPECTIVES
34
Bypass
It is common in the access pricing literature to consider the effect of the entrants’ ability
to substitute away from the incumbent’s network. This concept is generally referred to
as bypass. Armstrong, Doyle and Vickers (1996) state two reasons why the fringe is
able to bypass the incumbent’s access service: (i) the fringe may supply the access
service itself or purchase it from a third party; and (ii) the technology used by the fringe
is a variable-coefficient technology and for high access charges the fringe may use
proportionately less of the bottleneck input. The competitive fringe model of Armstrong,
Doyle and Vickers reveals that the possibility of bypass reduces the optimal access
charge compared to the non-bypass scenario by reducing the displacement ratio.
Additionally, Armstrong (2002, pp. 323-324) suggests that when competitors have
bypass opportunities, both the market price for the final product and the access charge
are priced above marginal cost.
We assume that m of n-1 firms make their own input, and hence n-1-m firms buy the
bottleneck input from the incumbent. Note that the number of firms that make the input
is exogenous. Furthermore, for simplicity, we assume that the marginal cost of
producing the input is also c for the competitors who bypass the incumbent (i.e., make
their own input). One possible explanation for having the same marginal cost with the
incumbent would be the marginal cost is the result of cost minimizing production
technology of the bottleneck input. Therefore, the profit function for the incumbent, one
of m firms and one of n-m-1 firms are given as follows.
1 1 1
1 1
( )
n
I I I
i i
n m i
w c q q q c qα β β
− − ≠
 
Π = − + − − − 
 
 
∑ ∑ , (15)
1,
n
m
i i j i
j j i
q q c qα β β
= ≠
 
 Π = − − −
 
 
∑ , and (16)
1,
n
B
i i j i
j j i
q q w qα β β
= ≠
 
 Π = − − −
 
 
∑ . (17)
Lemma 3 summarizes the components of total social welfare in the case of bypass. In
this respect, we obtain total industry profit and consumer surplus at the equilibrium
when m of n-1 competitors can bypass the incumbent’s network.
Lemma 3: When Assumption 1 holds and the downstream market is characterized by
Cournot competition, the equilibrium incumbent’s profit, the competitors’ profit and
consumer surplus are given, respectively, by:
Volume 12, Issue 1, 2012
35
[ ]
1
2
2
( 1) ( 2)
( )( 1)
( 1)
( ) ( 1)1
;
( 1)
I m c m w
w c n m
n
n m c n m w
n
α
β
α
β
+ + − +
Π = − − −
+
− − + − −
+
+
(18)
[ ]2
2
( ) ( 1)
;
( 1)
M
i
m
n m c n m wm
n
α
β
− − + − −
Π =
+
∑ (19)
[ ]2
2
1
( 1) ( 2)1
;
( 1)
B
i
n m
m c m wn m
n
α
β− −
+ + − +− −
Π =
+
∑ and
(20)
[ ]2
2
( 1) ( 1)1
2 ( 1)
n m c n m w
CS
n
α
β
− + − − −
= ⋅
+
(21)
Summation of expressions (18) – (21) yields total social welfare. It is straightforward to
show that the optimal access charge when the incumbent’s budget constraint is not
binding at the social optimum. The first best optimal access charge is
)1())((* −−−−= mncmnw α in the bypass case. First, notice that when the
number of firms that make the input (m) is zero, w*
is equal to the first-best access
charge when bypass is not feasible.19
Second, w*
decreases with the number of firms
that can bypass.
Therefore, this optimal access charge would be the first-best optimal access price in this
case, and once more the first best optimal access charge equates the market price to the
marginal cost of the input, or c. However, the first-best optimal access charge leads to
the same qualitative results as in the non-bypass case. In other words, at the first-best
optimal access charge, the downstream production of the incumbent–and the
competitors that make the key input–is zero, since the optimal access charge is lower
than the marginal cost of the access. Hence, the incumbent’s financial viability is
threatened in the bypass case as well.
The regulator’s objective is therefore to determine the optimal access charge under the
non-negativity profit constraint for the incumbent’s profit. We previously showed that
applying the non-negativity constraint to the incumbent’s upstream profit only yields
higher welfare in the non-bypass case. Therefore, we assume that the regulator’s
objective is to determine the optimal access charge when the non-negativity profit
constraint applies only to the incumbent’s upstream profit. In this case, the regulator’s
problem is given by:
19
See page 11.
REVIEW OF ECONOMIC PERSPECTIVES
36
0..
)(max
1
11
1
≥Π
Π+Π+Π+ ∑≠
I
u
I
d
I
u
n
i
i
ts
CS
(22)
where 0λ > and 1
I
uΠ and 1
I
dΠ denote upstream and downstream profits of the
vertically-integrated incumbent, respectively.
The optimal access charge can be found by setting the derivative of the Lagrange
function equal to zero and solving it for the access charge (w). Therefore the optimal
access charge is given by
* ( ( 1) 1) (( ) ( 1)(3 2 ))
( 1) 2 ( 1)( 2)
n n m n m c
w
m n n m
λ λ
λ
+ − + − + + +
= ⋅
− − + + +
(23)
The expression in (23) characterizes the second-best access charge. Notice that the
second-best access price exceeds the marginal cost of the input.20
Hence, the incumbent
and the competitors that provide their own input realize positive downstream production
at the second-best access price.
Lemma 4 summarizes equilibrium industry profit and consumer surplus in the model at
the optimal access charge when the incumbent’s profit constraint is binding at the social
optimum.
Lemma 4: When Assumption 1 holds and the incumbent’s profit constraint is binding at
the optimal access charge, the equilibrium values of the incumbent’s profit, the
competitors’ profit and the consumer surplus are given, respectively, by:
( )( )
[ ]
2
1 2
2
( 1) 1 ( 2) 11
( )
( 1) 2 ( 1)( 2)
1 ( 3)( )
;
( 1) 2 ( 1)( 2)
I n mn m
c
n m n m
n m c
n m n m
λ λ
α
β λ
λ α
β λ
+ − + +− −
Π = −
− − + + +
 + + −
+  
− − + + + 
(24)
( )
2
3 ( )
( 1) 2 ( 1)( 2)
M
i
M
m n cm
n m n m
λ α
β λ
 + + −
Π =  
− − + + +  
∑ ; (25)
( )
2
( 2 1)( )1
( 1) 2 ( 1)( 2)
B
i
B
m cn m
n m n m
λ α
β λ
 + + −− −
Π =  
− − + + +  
∑ ; and (26)
20
The mark-up for the bottleneck input at the optimal access price for the incumbent is
( ( 1) 1)( )*
( 1) 2 ( 1)( 2)
n c
w c
n m n m
λ α
λ
+ − −
− =
− − + + +
, where the denominator is unambiguously positive. Hence, the
optimal access charge exceeds marginal cost if
1
1n
λ >
+
.
Volume 12, Issue 1, 2012
37
[ ]
( )
2
( 1) (3 2 1) ( )1
2 ( 1) 3 2 (1 ) 4 ( 1)
n m n m mn c
CS
n n
λ α
β θ λ λ
 − − + + + + −
= ⋅ 
− − + + +  
(27)
Expressions (24) – (27) define total welfare at the second-best optimal access charge.
Proposition 3 provides selected comparative statics for changes in the second-best
optimal access charge (w*
) and welfare (W*
) in the presence of bypass opportunities.
Proposition 3: Suppose that Assumption 1 holds and that downstream competition is
characterized by Cournot competition. At the second-best optimal access charge: (i)
*
0
w
m
∂
<
∂
and (ii)
*
0
W
m
∂
>
∂
.
First, it is straightforward to show that the second-best optimal access charge is
inversely related to bypass opportunities. In other words, as the number of firms that
makes their own input increases, the second-best optimal charge approaches the
marginal cost of access. This results in higher equilibrium market output. The rationale
for this finding is that there are fewer firms requiring the input from the incumbent
compared to the non-bypass case. Hence, there are more firms producing the
downstream output at a marginal cost c which is lower than the second-best optimal
access price. Therefore, the regulator can set a lower access charge compared to the
non-bypass case by lowering the mark-ups of all firms. Hence the effect of bypass is no
different than the effect of an industry-wide cost reduction under the Cournot
equilibrium.
Since the equilibrium market output is higher with bypass, the consumer surplus is also
unambiguously higher compared to the non-bypass case. The incumbent’s profit is
unambiguously lower in the bypass case. This can be shown by taking the derivative of
the expression given in equation (24) with respect to the number of firms that make the
input (m). Unlike the consumer surplus and the incumbent’s profit, the manner in which
bypass affects the competitors’ profit is ambiguous since it depends on the initial value
of m. However, total welfare unambiguously increases with bypass. This is due to the
effect of the lower markups discussed above.
Conclusion
Although deregulation typically results in market structures that are closer to oligopoly,
the access pricing literature has focused primarily on contestable/perfect competition
models. This essay addresses that issue with a simple Cournot competition model with
perfect information. This simple model yields some useful results concerning optimal
access pricing in imperfectly competitive markets. A vertically-integrated industry is
assumed to be deregulated and the formerly regulated firm is the only provider of the
bottleneck input in the upstream market and one of n competing firms in the
downstream or retail market in which all firms possess some market power.
When n firms engage in Cournot competition, the first best access charge equates the
market price of the downstream product to its marginal cost. However, the first-best
optimal access charge is not feasible without governmental transfers since it threatens
the financial viability of the vertically-integrated firm. On the other hand, the secondbest
optimal access charge exceeds the marginal cost of access. The regulator is
REVIEW OF ECONOMIC PERSPECTIVES
38
assumed to have two policy options for determining the second-best optimal access
charge: (1) The regulator could apply the non-negativity constraint to the incumbent’s
provider overall profit; or (2) The regulator could impose the constraint only on the
upstream profit of the incumbent provider. Our results suggest that the latter yields
higher social welfare. The policy implication of this result is that regulators should be
cautious in determining the access prices in imperfect markets when they are required to
satisfy a profit constraint for the vertically integrated firm. Specifically, imposing the
non-negativity profit constraint on the overall profit of the incumbent may introduce
distortions in the downstream product market and reduce economic welfare. We also
examine the effect of outsourcing by allowing some of the firms to bypass the
vertically-integrated firm’s network. With efficient bypass, our model reveals that
optimal access charges decrease and welfare increases, ceteris paribus.
The model developed in this paper uses a very simple framework and therefore
suppresses some complicated real-world issues. For example, throughout the analysis
the total number of competitors and the number of competitors that bypass the
incumbent firm’s network are assumed to be exogenous. Additionally, we assume the
regulator has perfect information regarding the cost and demand structures. We also
disavow the possibility that the vertically-integrated producer engages in sabotage or is
subject to moral hazard problems. Given that the assumptions of our model are
somewhat restrictive, developing more general models with less restrictive assumptions
would prove fruitful in terms of future research.
Appendix- Proofs for Propositions
Proof of Proposition 1: Total welfare is the unweighted sum of consumer surplus and
total industry profits, 1 2
nI
ii
W CS
=
= + Π + Π∑ , where consumer surplus is given by
1 1
2 2
()
n nI I
i ii i
U q q P q q
= =
   + − ⋅ +   
   ∑ ∑ . Totally differentiating total welfare yields
1
2
n
I
i
i
dW dCS d d
=
= + Π + Π∑ (A1)
( )( )1 1'( ) ( 1) ( 1)I I
i idCS P dq n dq q n q= − ⋅ + − + − (A2)
( )( )( )1
2
( 1) ' ( 1) ( 1) ( )
n
I
i i i i i
i
d n P dq n dq q n q dw P w dq
=
Π = − ⋅ + − − − + −∑ (A3)
( ) ( )( )1 1 1 1( 1) ( ) ' ( 1) ( )I I I I
i i id n q dw w c dq P dq n dq q P c dqΠ = − + − + ⋅ + − + − (A4)
Substituting (A2), (A3) and (A4) into (A1) by making use of (3) and (4) yields
Volume 12, Issue 1, 2012
39
( )1
( 1)
( ) ( 1) ( )
( 1) '
I
i
n
dW P c dq n dq P c dw
n P
−
= − + − = −
+
(A5)
and therefore
( 1)
( ) 0
( 1) '
dW n
P c
dw n P
−
= − =
+
. (A6)
Equation (A6) characterizes the welfare optimizing access price in our simple Cournot
model, one that equates the market price with the marginal cost of access. This
completes the proof part (a). To prove part (b), note that the first-order conditions for
the profit maximization condition of a representative competitor is ' iP q P w+ = . The
first-order condition with P c= implies that 0iq > if and only if w c< . This
completes the proof of part (b).
Proof of Proposition 2: In order to prove part (i), take the derivative of the
incumbent’s profit in (12) with respect to θ :
( )
( )
2 2
1
3
2 (1 )( 1)( 3) ( ) 3 2 (1 ) 2
0
( 1) 3 2 (1 ) 4 ( 1)
I n n c
n n
λ λ α θ λ λ
θ β θ λ λ
+ − + − − + +∂Π
= > ⋅
∂  − − + + + 
(A7)
Hence, the incumbent’s profit increases with θ . This implies that incumbent’s profit is
higher when the break-even constraint for the incumbent applies to its overall profits.
This completes part (i).
Similarly, to show that part (ii) holds we take the derivative of the competitors’ total
profit, given in equation (13), and of consumer surplus given in equation (14), with
respect to θ . Therefore:
( )
( )
2
2
3
8 (1 )( 1)( 3)( ) 3 2 (1 ) 2
0
( 1) 3 2 (1 ) 4 ( 1)
n
ii n n c
n n
λ λ α θ λ λ
θ β θ λ λ
=
 ∂ Π  + − + − − + +  = − < ⋅
∂  − − + + + 
∑ (A8)
Hence, the competitors’ total profit decreases with θ , so the competitors’ total profit is
higher when the break-even constraint for the incumbent applies only to its upstream
profits.
( )
( )
2
3
2 (1 )( 1)( 3)( ) ( 1) 3 2 (1 ) (3 1)
0
( 1) 3 2 (1 ) 4 ( 1)
n n c n nCS
n n
λ λ α θ λ λ
θ β θ λ λ
 + − + − − − + + +∂  = − < ⋅
∂  − − + + + 
(A9)
Similarly, consumer surplus is lower when the break-even constraint for the incumbent
applies to its overall profits since the consumer surplus is decreasing in θ .
Summing (12) – (14) yields economic welfare. Taking the derivative of economic
welfare with respect to θ yields
REVIEW OF ECONOMIC PERSPECTIVES
40
( )
2 2 2
3
2 (1 )( 1)( 3) ( )
0.
( 1) 3 2 (1 ) 4 ( 1)
W n n c
n n
λ λ α
θ β θ λ λ
∂ + − + −
= − <
∂  − − + + + 
(A10)
Hence, total welfare is decreasing in θ . This implies that total welfare is higher when
the break-even constraint for the incumbent applies only to its upstream profit. This
completes part (ii).
Proof of Proposition 3: Taking the derivative of (23) with respect to m yields:
( ( 1) 1)(2 ( 1) 1)
( ) 0.
( 1) 2 ( 1)( 2)
w n n
c
m n m n m
λ λ
α
λ
∂ + − + −
= − − <
∂ − − + + +
(A11)
Therefore, the second-best optimal access charge is decreasing in m
Summation of (24) – (27) gives the total welfare at the second-best optimal access
charge. Taking the derivative of total welfare with respect to m yields:
( )
2
2
3
2 ( 1)( 1)( 3)
( ) 0
( 1) 2 ( 1)( 2)
dW n n m n
c
dm n m n m
λ λ λ
α
β λ
+ + − + +
= − >
− − + + +
(A12)
Hence, total welfare increases with bypass, ceteris paribus.
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