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UBRAR^ES - DEWEY
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HB31
.M415
working paper
department
of economics
ACCESS PRICING AND COMPETITION
Jean-Jaques Laffont
Jean Tirole
94-31
July 1994
massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 02139
ACCESS PRICING AND COMPETITION
Jean-Jaques Laffont
Jean Tirole
94-31
July 1994
Access Pricing and Competition^
Jean- Jacques Laffont^and Jean Tirole^
July
"We thank
Jerry
Hausman and John
6,
1994
Vickers for helpful comments.
Unstitut Universitaire de France, and Institut d'Economie Industrielle, Toulouse,
France
^Institut
bridge,
d'Economie
MA USA
Industrielle, Toulouse, France;
CERAS,
Paris;
and MIT, Cam-
Abstract
In
many
industries (electricity, telecommunications, railways), the
network can be described as a natural monopoly. A central issue
is how to combine the necessary regulation of the network with the
organization of competition in activities which use the network as an
input and are potentially competitive (generation of electricity, valueadded services, road transportation).
In this paper we derive access-pricing formulas in the framework of
an optimal regulation under incomplete information. First, we study
how access-pricing formulas take into account the fixed costs of the
network and the incentive constraints of the natural monopoly over
the network. Second, we examine the difficulties coming from the accounting impossibility to disentajigle costs of the network and costs
of the monopoly's competitive goods. Third, the analysis is extended
to the cases where governmental transfers are prohibited, where the
competitors have market power, and where competitors are not regulated. Fourth, the possibility some consumers bypass the network
is
taken into account. Finally the role of access pricing for inducing
is assessed. The conclusion summarizes our
the best market structure
results
and suggests avenues of further research.
Introduction
1
many
In
scribed
industries (electricity, telecommunications, railways), the network can be de-
cLS
a natural monopoly.
However,
many
activities
which use the network as an
input are potentially competitive (generation of electricity, value added services, road
transportation).
A
central issue
is
how
to
work with the organization of competition
Two
different types of policies
combine the necessary regulation of the netin those activities.
can be observed. In the USA, the local network mo-
nopolies in the telephone industry have been prevented from entering the value added
markets as well as the long distance market because of the Department of Justice's belief
that
in
is
it
impossible to define access rules to the network which create
those markets'*.
The argument here
is
that
the network to provide unfair advantages to
R
superior quality of access,
D
iS2
cost auditing. In the language of
it is
its
subsidies...)
competition
too easy for the monopoly in charge of
own products
even
if
(favorable access charges,
subsidieiries are created to
modern regulatory economics, asymmetries
between the regulator and the monopoly are so large that
tion
fair
fair
improve
of informa-
competition
is
not
possible.
The
alternative policy of defining access charges
common. The long
also
(BT)
to reach
market.
The
and
regulatory choice of the access charges
regulatory review of 1991,
its
European Community
BT
is
BT in the long distance
complex.
For instance, in the
has argued that the current setting of access charges creates
competitor (Cave (1992)). Note also that
it is
the goal of the
to define "reasonable" access charges to organize the competition
of electricity generation in Europe.
Other examples of
computer reservation systems and gas
It is difficult
is
distance operator Mercury pays access charges to British Telecom
consumers through the local loops and compete with
unfair advantages for
monopoly compete
letting the
activities
with regulated access are
pipelines.
to appraise the difficulties of regulating access
if all
the imperfections of
regulatory processes are taken into account simultaneously. In this paper,
we
start
from
an optimal benevolent regulation of a network monopoly facing a competive fringe in the
potentially competitive markets
focus
and we successively introduce various imperfections. To
on access we neglect the relevant
incorporated into our modeling.
policy.
a
first
of a
The modeling
step,
we choose
of the costs
to focus
more general theory
in
issue of network externalities,
which could be easily
Perhaps more importantly, we ignore the divestiture
and benefits of
on the
vertical integration
is
complex, and, in
vertically integrated structure as a building block
which breakups might be desirable.
'"DOJ... did not believe chat judicial and regulatory rules could be effective in preventing amonopolist
from advantaging an affiliate that provided competitive products and services" Noll (1989).
,
The
existing theoretical Uterature on network access pricing includes two papers build-
on contestable markets theory. Willig (1979) studies interconnection by competing
ing
He
suppUers.
may
stresses the fact that strategic behavior
deter socially beneficial entry (for example to expand
regulation)
and analyses the extent
to
its
lead the network operator to
rate base under rate of return
which Ramsey pricing
market structure. Baumol (1983) discusses similar
is
compatible with the best
issues in the framewTark of railroad ac-
cess pricing. Vickers (1989) addresses the access pricing issue within the
model
of regulation under incomplete information.
monopoly (network plus
integrated
sector of services with
commodity
services) with the case of
in particular a vertically
an imperfectly competitive
and without participation of the network operator.
Section 2 describes the model.
olized
He compares
Baron- Myerson
A
monopoly operates a network.
(for concreteness, local telephone), as well
It
produces a monop-
another conmaodity (long
distance telephone) which faces a competitively produced imperfect substitute.
The
long
distance operators require access to the local network in order to reach the final consumers.
That
the potentially competitive market needs to use the monopolized commodity as
is,
The purpose
an input.
access.
We
start
of the paper
is
normative theory of how to price
to develop a
by postulating that the regulator has complete information and faces a
social cost for public funds associated with the deadweight loss of taxation.
must then exceed marginal
price
deficit. Equivalently, access
The
access
cost in order to contribute to the reduction of the overall
can be priced at marginal cost and a tax levied on access. Sec-
tion 3 studies the impact of the regulator's incomplete information about the monopoly's
cost structure
for a further
any,
is
meant
on the monopoly's informational
Incomplete information
rents.
departure from marginal cost pricing of access.
The
may
call
further distortion,
if
to reduce the monopoly's rent. Section 4 explores conditions under which
the observability of the monopoly's subcosts, namely the cost related to the monopolized
good and the
The
analysis
ceive any
its
cost related to the competitive
is
extended
good
respectively, improves social welfare.
in Section 5 to the case
where the monopoly does not
monetary transfer from the regulator and therefore must cover
revenue.
The
access charge
is
cost with
then higher or lower than in the absence of a firm-level
budget constraint, depending on whether the monopoly's fixed cost
6 generalizes our access pricing formula to the case in
is
its
re-
is
high or low. Section
which the substitute commodity
produced by a competitor with market power rather than by a competitive industry
and Section
7 considers the case in
competitive segment at
all
which the regulator has no mandate to regulate the
(including the production of the competitive good by the
monopoly.)
Sections 6 and 7 emphasize the complexity of regulating a competitive segment with
limited instruments.
when consumers
Limitations on regulatory instruments are particularly penalizing
of the competitive
commodity can bypass the use
of the monopolized
good
The determination
(local telephone).
of the access price
conflicting goals of limiting inefficient bypass
it
approximate the
efficient level of
off
the
and of contributing to budget balance (be
the State's or the firm's). Unless the regulator
distance market to raise funds to cover the
must then trade
is
able to simultaneously tax the long
firm.'s fixed
cost
and use the access charge
to
bypass, only a rough balance between these objectives
can be achieved. The separation of the regulatory function from the teixation authorities
creates serious difficulties in the presence of bypEiss (Section 8).
Section 9 links the determination of the access charge with the choice of a market
structure and with the promotion of entry in the competitive segment.
ponent pricing rule recently advocated by some economists
is
The
efficient
com-
assessed in the light of our
normative treatment. Section 10 compares the theoretical precepts with two regulatory
practices,
namely the
British Telecom.
fully allocated cost
method and the
Oftel access pricing rule for
summary
of our analysis and discusses
The Conclusion provides a
brief
avenues of further research.
The Model
2
A
monopoly operates a network with
Co
Q
where
of
c.d.f.
effort
F{.)
With
>
/3 is
,
on
[^, ^]
:
Coeo
<
Cog
,
>
0,
(1)
a parameter of productivity, and
a level
eo
exerted by the firm in operating the network.
with a
is
private information of the firm
strictly positive density function /.
rate assumption {jg[F{0)/f{l3)]
>
We make
;
l3
has
the classical
0]).
the network the firm produces a quantity ^o of a monopolized
telephone).
let
Co0
,
a parameter of adverse selection which
monotone hazard
and
Co{^,eo,Q)
the level of network activity,
nonmonetary
,3 is
a
is
=
cost function
commodity
(local
Let us assume that ^o units of this commodity require qo units of network
S{qo) be consumers' utility for this good, with S'
The monopoly produces
also a
good
1
>
0,
S" <
0.
(long distance telephone) in quantity
qi.
This
other production has an imperfect substitute produced in quantity 92 by a competitive
fringe. Let V{qi,q2)
be consumers'
utility for these
two commodities.
In addition to the network input the production of
Ci
where
ex is
=
good
1
also generates a cost
(2)
Ci(/i,ei,9i)
the effort e.xerted to reduce the cost of producing
good
1.
The
disutility of
effort
is i/;(eo
+
ej)
with 0'
>
0,
0"
>
and
>
^p'"
0.
In addition to the network input the production of
c
common
is
good
2 generates a cost cq2 where
knowledge. Because we wish to focus on the network monopoly's incentive
to provide access,
we need not
Total network activity
investigate incentive issues in the fringe.
therefore
is
Q=
?o
+ ?i + 92-
Let a denote the access unit charge
The
paid by the competitive fringe to the monopoly.
fringe's level of profit
is
then
:
n = P292 - cq2 - aq-i.
(3)
Under complete information, the utiUtarian regulator observes
and
effort levels.
lator.
We make
Let
t
prices, quantities, costs,
denote the net transfer received by the monopoly from the regu-
the accounting convention that the regulator reimburses costs, receives
directly the revenue
from the
sale of the competitive
good and network good to the con-
sumers, and that the firm receives the access charges. This obviously involves no loss of
generality.
The monopoly's
utility level
then
is
:
U = - iPieo + ei) + aq2.
t
The
1
-f-
regulator must raise
A (where A
S{qo)
+
>
t
+ Co + Ci— poqo — pi^i
(4)
with a shadow price of public funds
because of distortive tcixation). The consumers'/taxpayers' utiUty
V{qi,q2)
-
poqo
- Pi?i - /'2?2 -
+
(1
^){i
+
Co
+
Ci
- poqo - Piqi).
is
(5)
Under complete information an utiUtarian regulator would maximise
f'>)+fi)^ (^)
-_
S{qo)
+
V{qi,q2)
- Poqo - Pl9i - P2?2 -
+ [t-
0(eo
+
ei)
+
aqz]
(1
+
+
A)(<
P292
+ Co + Ci - poqo - Pi9i)
-
cq2
-
a^j]
(6)
under the individual rationality (IR) constraints of the monopoly and the fringe
U=
t-ri;{eo
n=
P292
-
+
ei)
C92
—
+ aq2>0
(7)
>
(8)
a<}2
0.
Since public funds are costly, the monopoly's IR constraint
can be rewritten
is
binding and social welfare
+
5(^0 )
-
+
(1
Similarly, raising
V{qi,q2)
+
A)(0(eo
ei)
Apo9o
Api9i
The
(9), social
S{qo)
-
(1
+
A)(^(eo
Assuming that S and
is
+
V
+
+ ?i + gj) + Ci{/3,ei,qi)).
access charge
=
is
ei)
+
p2
—
(10)
+
Coil3,eo,qo
are concave
+ Piqi + P2q-i)
A(po?o
+ qi + ?2) +
= ^^-=^ =
=
Pi
-
^°Q
172
1
+
ei)
we can write
^J_
I
1
+
+
A
(?7l^2
7/2
=
-Ci,,.
=
^70
a-nd
'7i'72
+
T}\'n2
+
72=772
dm
= — r^
Pi
uPi
'7.
.
-^12'72l)
(13)
At/x
-Co«o
Straightforward computations show that ^0
(12)
7/0
- ^1.1 ^
=
(11)
in {eQ,ei,qi,Q), optimal
are (respectively) the price superelasticities of goods 0, 1, 2,
0'(eo
,
+ cgj).
r^^
+A
P2
771,
C'i(/3,ei,gi)
and Co and Ci convex
Pi
77
chosen to saturate the fringe's IR
characterized by the first-order conditions, that
^
,
valuable (see
c.
^'O
where
is
(9)
welfare takes the final form
V{qi, q2)
Lo
770,
cq2
:
Substituting (10) in
where
+ Xaq2 -
the access charge from the fringe
a
regulation
+
Co{/3,eo,qo
money through
the term Xaq2 in social welfare).
constraint
+
+
and
(15)
^^
(,f•^
<T]2
['')
'7i'7i2
;
'72721
=
'?.;
1^-
J^^
The benchmark
i
,
=
l,2
pricing rules are
=
z
,
Ramsey
l,2.
>
pricing rules because A
0.
The
access
charge can be rewritten
^
n-r
Access
fi^^^y
2
is
(18)
priced above marginal cost because deficits are socially costly.
is
can be viewed as a tax used to raise money.
low or
when
issues raised
If
P2
a.
the social cost of funds
is
high
It is
when the
high. In the next section
elasticity of
we address
good
various
by asymmetric information.
the regulator has two instruments, the access price and a tax on good
(14) can
The term
+
be rewritten a
T2
=
Cqq
+ yta^
Furthermore,
marginal cost of access.
it
is
2, r2,
equation
can obviously be taken equal to the
^.nd a
clear that
if
the regulator had access to a
nondistortive (lump sum) tax, marginal cost pricing of commodities and access would be
optimal.
Access Pricing and Incentives
3
The
first
issue
we
consider
is
the extent to which asymmetric information
pricing. Let us consider the case
where accounting
cifFects
access
rules enable the regulator to observe
separately Co and Ci.
Let Eo{t3,CQ,Q) denote the solution in eo of Co
the solution in
Ci of
Ci
=
t
Ci{/3,ei,qi).
The
{f(/3),
which
Co(/?),
CM,
we
Co(/5, eo,(5) ^.nd let £'i(/?, Ci,?i)
firm's utility
+ a92-^(^o(/3,Co,g) +
.Appealing to the revelation principle
=
can be written
consider a revelation
qiih q,{h
specifies the transfer received, the sub-costs to
produced, and the access price to be received
if
(19)
^i(/?,Ci,9i)).
Qih
mechanism
m]
(20)
be realized, the quantities to be
the firm announces a characteristic ^.
Neglecting momentarily second-order conditions, and using the rent variable
^(^)
=
i(/3)
+
a(/?)<72(/3)-V(£'o(/?, Co(/3),
Qm +
E,{P, Ci(/?),
?i(/?))),
monopoly can be written
the incentive constraint of the
t-(^)=-,'(e„^eO(f.f).
Since -g^
>
^>
and
>
(IR) constraint {U{3)
the rent
0,
decreasing in
is
down
for all /3) boils
Ui0)
Optimal regulation
>
and the individual rationaUty
to
0.
(22)
from the maximization, subject to (21) and
results
{s{qoiPom) +V{q,{pM,pM),
I'
/3
(21)
q,{pri/3),
(22), of
:
pM))
+x[po{i3)qo{pom+pmqi{pm,P2m+P2{0)q2{pm,P2m]
-(1
+
+
We
+
X)[4^{eoil3)
e,m + Co(^,eo(/?),9o(po(y3)) + 9i(pi(^),P2(^)) + 92 (Pi(/?),P2 (/?)))
C^{^,e,i|3),q,{p,{0),p,i|3)))+cq,{p^i0),p2m]-XU{0)yF{0).
obtain (see appendix
1).
Po-CoQ ^
Pi
-
Cqq
-
A
l
+
X f
F
A
1
xh'
d
Coe{/3,eo,Q) \
f
_
Cl^^
A
pAoQi
X
1
A
771
Co.o(/?,eo,g)i
P2-C0Q-C _
P2
J^
+
1
Pi
'^
(23)
+
A
F vy_^(
w' d f _
A
J_
l
172
+
5?i I
X f
/
p^dQX
p2dQ
Ci,.(/3,ei,5i)/y'
CW(/g,eo,g)
Coai/3, eo, Q)
^~
'
^
^
|
Coeo(/3,eo,g)i'
All prices are modified by an incentive correction related to the sub-cost function Cq
and
pi has
The
an additional correction associated with C\.
access charge can
now be
\
+
written
X
r]2
Let us analyse the new term, which
that there
is
no correction
for
1
is
+
A
/
dQl
Coeo
J
due to incentive constraints.
the most efficient tv-pe as F(/?)
=
0.
First,
we observe
Second,
^^ —
3(3
—Coff/Coeo
the
same
is
the rate at which the firm must substitute effort and productivity to keep
level of cost for the
to determine the firm's
is
The
rent.
we
(21),
see that
if it is negative.
The
it is
a crucial term
regulator wants to Hmit this costly rent.
he raises the access price and therefore reduces quantities
positive,
conversely
network acivity. From
If
^(-^)
to extract rent
and
on the access charge thus depends on
effect of incentives
fine characteristics of the cost function.
Access charges must be increased (decreased) for incentive reasons
of the network
Co
is
<«
>-
—
CoeaQCog
>
CquqCoco
"Spence-Mirrlees"' condition on cost, Copq
clear positive sign
is
obtained
if
Intuitively, production
>
and our previous assumptions, a
marginal cost. However,
effort increases the
is
must be decreased (increased)
increases (decreases) the "ability" of the firm to
0-
(<)
reasonable, effort decreases the marginal cost, the effect
terms,
the cost function
such that
>«
With the
if
lie
about
if,
as
is
more
ambiguous.
if
an increase
Q
in the level of
its characteristics (in elasticity
the quantity elasticity of the marginal effect on cost of the productivity charac-
if
teristics
is
larger (smaller) than the quantity elasticity of the marginal effect
on cost
of
effort).
From
Leontief 's theorem
charge (and on good
1)
we know^
disappears
iff
Co
If
there
furthermore Ci
is
is
in addition that the incentive effect
there exists a function ( such that
= Com,eo),Q).
separable in
on the access
(/3,
(28)
on the one hand, and
ej)
no incentive distortion on any commodity
:
qi
on the other hand,
the dichotomy between pricing rules
(unaffected) and the cost reimbursement rules (see below) holds.
The
access pricing rule can then be rewritten
:
"^
a
=
Cog
(29)
-r
1
Note that
Pi
~ Cqq —
Oiqi
_
+
Hi
A^2
a
P2
Pi
It
is
also possible to find conditions
conclusions for the incentive correction
— Cqq
on the cost function that yield nonambiguous
when
it
exists.
For instance, the following class of
cost functions leads to a well defined sign of the incentive correction in the access charge
^From Leontief s iheorem we know
that
^^^ independent
function ^(.) such that (20) holds (see Laffont-Tirole (1990a)).
10
of
Q
is
:
equivalent to the existence of a
cnl>
Co=/3Q'-elQ
If
d
>
b{d
<
now
Let us
6),
the inceatiye correction
consider the effort levels (in the case of dichotomy) obtained by maximizing
under (21) and
(23)
positive (negative).
is
(22) with respect to (eo,ei).
V''(eo
2AF
O + A)/
(eo
+
e,)
ei)
+
ei)
-Coeo
=
(eo
Equations (30) and (31) can be interpreted
+ eO^^^Coeo
(30)
-Ciei
dEi\
.fdEo
\ ,,.
=
(^ + ^j +
^'(eo
2XF
+
We obtain
cis
,,,
cost
,
^
d'^E^
reimbursement
(31)
rules.
If
the con-
ditions underlying the irrelevance of subcost observability (see Section 4) hold, one can
obtain sufficient conditions for the optimal contract to be implementable through a
gle
menu
of linear sharing rules
share of the total cost which
is
^
= A — B{Cq
reimbursed.
-h
Ci) where
B =
From
(30), (31),
and F{0^
the most efficient type receives from the regulator a
tract)
and equates
its disutility
lump sum
=
tp'^^
=
V''fc^
we
0,
is
sin-
the
see that
transfer (fixed price con-
of effort to the marginal cost reduction as
under complete
information.
REMARKS
1. -
for
The most
relevant cost functions
seem
to be such that higher production levels call
higher effort levels and therefore induce higher rents. Incentive considerations raise
marginal costs and therefore indirectly
call for
a general reduction of quantities. Access
prices are increased for the competitor but simultaneously the
high prices for
its
own product and
own
the competitor's, the current model
misrepresentation.
efficiency of its
this link
2. - If
is
is
products. Because access costs are the
The
may
is
penalized by
for the
monopoHst's
monopoly
same
understate the incentives for
firm cannot claim simultcineously high access costs and high
own products
(see Laffont-Tirole (1993,
Chapter
5) for
an example where
suppressed).
the fringe
is
not regulated but
is
competitive, the same results obtain
;
p2
=
a
+
c
then ensured by competition rather than by the existence of a shadow cost of public
funds.
11
3.
Let us consider implementation of the optimal revelation mechanism with the follow-
-
ing specification
:
=
CQ
Ho{l3-eo)iqo
Ci
The
where
now
includes
t
-
,32)
i7:(/3-ei)9i.
(33)
monopoly can be rewritten
objective function of the
m
=
+ qi + q2)
V(
-
V.(2/3
V
yqa
the access charge.
^^\
+ + q^J)
- ^r^(-))
\q\Jy
qi
The second-order
(34)
condition of incentive compat-
ibility is
and the revelation mechanism
The
price
firm
now
is
equivalent to a nonUnear reward function
is
free to choose its access charge but
and the quantity of good
{&s well
1
access price defined in formula (27) since
same weighted
An
cost,
which determines
alternative implementation
Co, Ci, production levels ^ot
the conditional
demand
is
cis
good
it is
indifferent
2, 92
=
^2(911
it
chooses.
for e.xample)
service (good 1)
which
selects the level of
among
is
c-|- a)
= -Q +
=
prices leading to the
Col,i3,eo,Q)
-iqi -HCi(/?,ei,9i).
12
For this purpose consider
and substitute
in (36). It
some unobservable action
:
Ci
all
decreasing in the access charge
raises the cost for the network,
Co
will affect the
can be advised to choose the
picks.
it
easy to check that the transfer received by the firm
vestment
it
obtained by writing the transfer as a function of costs
function of good
Suppose that the monopoly
knows that
its rent.
is
4. -
It
2).
and access charge a
?i
it
:
i
(an in-
but decreases the cost of
its
Under complete information the optimal investment
=
is i
level,
which minimizes total
cost,
qi/Q. Under incomplete information, the moral hazard constraint on investment
is
or
qidEJdCr
QdEo/dCo'
To decrease the
Co and Ci,
(implying
exist
may
|^
7^
rent of asymmetric information the regulator,
use cost
reimbursement rules with different rates
|^) and
this
may
who
observes both
for sharing overruns
lead to a distortion of investment (which would not
the regulator were not observing separately sub-costs Co and Ci as in the next
if
section).
If
1
i
is
too low (too high), the access price
good
(favor
2)
and
may be viewed by
is
to foster
is
increased (decreased) in order to favor good
an increase (decrease) of investment.
the firm as a nonrecognition of
On
low access charge
investment costs in the network.
its
indeed low to decrease those types of investment which
4
A
may be
It
excessive.
Sub- Cost Observability
Section 3 derived the optimal regulation under the assumption that the regulator could
audit the costs of the regulated
monopoly
from the cost of the commodity produced
Using Ck instead of
A
e^ in the
well
enough
to separate the cost of the
network
in the competitive sector.
optimization leading to (30) and (31), we have
high-powered scheme on activity k corresponds to a case where the transfer received
by the firm
is
highly dependent on cost Ck,
i.e.
where
(
— |f^)
is
high.
Indeed
if
^
is
high in absolute value, marginal cost reductions on activity k per unit of effort are small
and therefore the firm
is
already induced to exert a large effort on activity
for further reference that if the cross
If
terms
^^ vanish
sub-costs are not observable, the firm minimizes
chooses
{cfc} or,
equivalently {Ck}, so as to minimize
13
k.
Also, note
the terms (-ffj-) are equal.
its effort for
any cost
ELo ^k{/3, Ck, Qk)
target.
subject to Co
It
+
= C
Ci
(with the convention
= Q,Qi =
Qo
Hence, in the absence of sub-cost
9i)-
observation the marginal effort levels to reduce sub-costs {—-g^) are equahzed®.
Whether the
on the
in the ca^e of sub-cost observability hinges
that this expression
is
/?
determinant of the firm's rent.
no point
and
If
different activities
^^
cross-partiiil derivatives
A
in absolute value proportional to g^
which the firm can substitute
rate, there is
on
regulator wants to give differentiated incentives
effort in activity k (see
-^
).
(note
measures the rate at
Section 3) and
it is
the main
the level of cost or the level of effort does not affect this
in using sub-cost observability to try to affect the firm's allocation
of effort to minimize cost in order to reduce rents.
More
formally, let us
subject to Cq
+
=C
Ci
solution to the system
{
assume that the minimization of
has a unique solution
|^ = |^
ejt
for all {k,i)
=
total effort
Ek{0,
C',
+
Ci
and Co
=C
Solving for the optimal regulation we obtain (see appendix 2)
Under sub-cost
observability
the firm faces uniform incentives
ii)
is
useless if
This result
d^Ek/dCkd^
tells
•£^fc(/?,
is
Ck, Qk)
the unique
}.
:
:
the firm faces higher incentives
i)
HJ-q
Qq, Qi), which
=
on those
on
activities for
all activities
K for all k
which low costs reduce rents
and therefore sub-cost
observability
and some constant K.
us that the incentive constraints of the firm are identical with or
without sub-cost observability when d^Ek/dCkd/3
=
constant for k
=
the optimal pricing rules and in particular the optimal access pricing
0,1. Consequently
unaffected in this
is
case by sub-cost unobservability.
A
characterization of the subclass of cost functions satisfying the sub-cost-irrelevance
property with
that
K
=
is
all k,
the subcost functions must be such
:
,^^ = 0for/t = 0.1 ^
for
For
easily obtained.
some functions Hk and Gk
On
for
i-
ek
=
=
0, 1
Ek{P,Ck,Qk)
and, since Ce^
=
<
Hki0,Qk)
0, Cjt
=
the other hand, recall that the dichotomy property holds
Ck
= Ck{W.tk),Qk)
for
A;
=
+ Gk{Ck,Qk)
Ck{Qk, Hk{0, Qk)-tk)-
when
:
0,1.
costs evaluated
"'Then, the theory of access pricing is similax to the one of Section 3 but for marginal
observable.
not
at the effort levels induced by the incentive scheme defined when sub-costs are
14
These related conditions are
dQk
different.
00
\
The dichotomy
'
dCkd/3 dQk
J
requires
dQkd/3
while the irrelevance of sub-cost observation requires
d^Ek
=
dCkd0
The
satisfies
class of cost functions
the sub-cost irrelevance property for any dk, b^ (with Ckq^
property for dk
On
Kiora.\[k.
=
>
0)
and the dichotomy
6^ only.
the other hand, Ck{0-,tk,qk)
=
^
satisfies
the dichotomy property but not the
sub-cost irrelevance property.
Optimal Access Pricing
ernment Transfers
5
We now
us for
cLssume that the regulator
is
prohibited from transferring
example consider a constant returns
irrelevance of subcost observability hold
Co
and
let cq
=
i/o(/5
— eo)
Cx
,
=
=
Hq{0
to scale case
-
eo)(9o
+
<7i(Pi,a
to the firm. Let
where the dichotomy and the
+ 9i + 92)
fixed cost for notational simplicity).
Under symmetric information, the budget constraint
-co(<7o(Po)
money
:
Hi{0 — ti) (we omit the
Po<?o(Po)
Absence of Gov-
in the
+ Pi9i(Pi, a +
c)
+ c)-h92(Pi,a +
15
of the
monopoly
is
+ 092(^1,0 + c)
c))
-
Ci9i(pi, a
-f-
c)
- >
i
0,
(38)
where
t
must now be interpreted
consumer charges
The
= —
[so if
as the firm's manager's
v{eo
t
+
compensation and
is
paid from
ei)).
regulator wishes to maximize, for each value of
Cq,
Cj,
f,
social welfare
:
S{qo{po))+V(^qi{pi,a + c),q2{pi,a + c}j-poqQ{pQ)-piqi{pi,a + c)-{a+c)q2{pi,a + c) + U
subject to constraint (38) (where
U
the firm's welfare).
is
Under asymmetric information, the
U{I3)
leads to the incentive
=
m
- rPieom + e^m,
and individual rationality constraints
U{|3)
=
-^J;'{eo{^)
>
U{0)
The budget
constraint
is,
for
each
-co{qoipom +
The
qi{px{i3),a{0)
ci9i(pi(,3), a{0)
regulator's optimization
+ c) =
program
is
j-0
max
f
[5(9o(po(3)))
+
:
+ e^m
(39)
(40)
0.
:
Po{0)qo{pom+Px{l3)qi{pm,ai0)
-
namely
firm's rent,
V(?i(pi(/3),a(/3)
+ c) + <i(/3)92(pi(/?),a(/3) + c)
+
c)
t/(/?)
+
+
q2{pi{0),a{l3)
0(eo(/?)
+
+
c))
(41)
e,{/3)).
:
+ c),g2(pi(;9),a(/3) + c)) - Po(^)9o(M/5))
l0
-Pi(/?)9i(pi(/3),a(^)
s.t.
+ c)
-P2(^)92(pi(/3),a(^)
+ c) +
W)]^W)
(39), (40), (41).
Let
/^(/?)
be the Pontryagin multiplier of the state variable
multiplier of the budget constraint. Optimizing over prices
as in Section
2 with
sality condition /z(^)
U
and
we obtain
(1
the
'\{,d)
replacing A. Using the Pontryagin principle
=
we have
0,
16
+
\{/3))f{P) the
same equations
and the transver-
Optimizing over
effort levels
we
get finally
:
and
When the
^^^^^
(i+A)/U
dichotomy does not hold, formulae similar to those of Section 3 are obtained
replaced by
jr\0)md0
(l
+
A(;3))/(^)'
In particular the access pricing equation
becomes
(42)
Under the assumption
of dichotomy, the ratios of Lerner indices are unaffected
lack of transfers, but the whole price structure
on how binding the budget constraint
is.
is
shifted
upwards or downwards depending
Consequently, the access charge
than in the absence of budget constraint when the fixed cost
6
is
is
higher (lower)
high (low).
Access Pricing and Competitor with Market Power
Competition
for
by the
in the
markets using the network as an input
is
often imperfect, as
is
the case
competition in long distance telecommunications, or competition in the generation of
electricity in
England. To account
analysis of Section 5 with the
for this
market power we pursue the balanced- budget
same technology (guaranteeing the dichotomy and the
irrelevance of sub-cost observation).
17
the competitor has market power and
If
is
unregulated, the mciximization of expected
welfare must be carried under the constraint that the competitor chooses price so as to
maximize
its profit
:
+ P2-^{puP2) -
q2iPuP2)
From
+ a)-^{p^,P2) = OJ
{c
ap2
(43)
Cfp2
the first-order condition of this maximization program (see appendix 3)
obtain the access pricing rule
a
:
\{,d)p2
P2
=
L'oQ
we
=
1
f
P2m^,(^)+Pini2i^{^)
1
(44)
<
1
+
A(^)lr/^
=
72
75
T]2
Vi'n2-m2r}2\
with
l2
Equation (44)
•
complex, but can be given a natural interpretation. The two terms
is
the derivatives of the elasticity of
in
and
in pi
p2
t^j
if 77217712
corrected for market power.
>
71(^2
—
!)•
>
budget (reflected in A
to A
is
To explain
It
demand
for
0) calls for a higher final price
notice that the
this,
-).
More
changes
interesting
case
good
(7721
2),
=
7712
=
0),
the
is
exceeds the regular superelasticity
demand
elasticity
—
effects of
772
772
<
if
^2
the need to balance the
than in the absence of monopoly
monopoly power amounts
to a social loss equal
times the monopoly's profit P2<}2/V2, OQce the standard subsidy P2<l2/^2 (see (44))
made
to offset the
increase in p2 (that
monopoly
expression of
in the
in the access price) reduces this
is,
7/2
Because marginal revenue
distortion.
However, with dependent demands, there
the
good 2 describe the
In the independent
and therefore (assuming a constant
power.
for
on the mark up or monopoly power 1/(1
superelasticity
and only
demand
:
)
pi
is
is
monopoly
decreasing, an
is
profit.
Hence
t/j
a second eifect (described by the term
<
^2-
77217712
reduced to lower the monopoly profit P2q2/V2- To rebalance
consumers' choice between the two substitutes. p2 must also be reduced, and so must
be the access charge.
If
the social welfare function did not include the competitor's profit (an extreme way
of depicting the redistribution problem), similar calculations
a
= ^
CoQ
,
-I
M3)
P2
T~~::~
P27i9f7(;^)+Pi7i2af7(;^)
1+A(i)j?2
".A.n
alternative formula
would yield
would be obtained
7172
if
-
:
+ ^_
^2-
'/12'721
a nonlinear access pricing rule was used.
conclusion.
18
See the
Restricted Regulation
7
In practice, the regulator
may
be instructed to
let (or
good and the access
set its charges
the natured monopoly select his
and regulate only the price of the monop-
pricing behavior in the "competitive mzirket"
olized
let)
on value added
services. This section studies the design
of such restricted regulation under simplifying assumptions.
a competitive fringe.
We
an announcement
prices Pq{$)
/?
Telecom
price to the network. For instance, France
We come
free to
and consequences
back to the case of
consider the class of regulatory mechanisms that associate with
and a{$). The managerial compensation t{$)
defined as a residual by the balanced budget constraint, once efforts Cq
Pi
is
and
ej
is
then
and price
have been chosen.
The
monopoly has an additional
analysis proceeds as in Section 5 except that the
moral hazard variable pi which leads to the first-order equation, that the monopoly's
marginal profit be equal to zero
=
.V/P
91
:
+ 1^ [p: -
Co
- ci]
-H
dpi
we make the following assumptions
Concavity of profit
:
^
c]
0.
<
:
^¥^ >
0.
condition for strategic complementeirity
d[qi
+
j^lpi
-
Co
is
- Ci]]/Jp2 >
0.
Here, the monopolist also receives income from giving access.
for
=
:
Generalized strategic complements
The standard
- Co 1^
[P2
dpi
generahzed strategic complementarity
is
A
sufficient condition
strategic complementarity plus the condition
that the marginal profit on access increases with p2 (condition that holds with hnear
demand and constant
Appendix
returns to scale).
shadow
6 shows that for a given
price, the access price is lowered relative to
the unrestricted control case, in order to reduce the
strategic
raises pi.
The
complementarity for a given
On
the other hand, monopoly power on good
To rebalance the consumers' choice between the two goods,
effect of restricted regulation
However,
pi.
monopoly price through (generalized)
in the case of linear
on the access price
demand, for
remains the formula of full regulation.
19
is
therefore
the optimal pi,
p2
must be
ambiguous
1
raised.
in general.
the access pricing
formula
Access Pricing and Bypass
8
A
practical
problem encountered
ing access to the network
may
in the
useful as
is
telecommunications sector
is
the following
giv-
:
expands the space of commodities offered and
it
decrease the rents of asymmetric information by shrinking the incumbent's scale of
More
operation.
the incumbent
cations for
directly
may
it
also
be useful
for yardstick recisons
if
the technology of
correlated with the monopolist's technology. However, in teleconmiuni-
is
example giving access
to the
network to long distance operators leads to the
possibiHty of bypass of the local loop by large consumers to connect with these operators.
So
far
we had no need
of long distance,
to distinguish
between producer prices and consumer prices
and we could assume without
was
loss of generality that access pricing
the only tool used to oblige the competitor to participate in the fixed costs of the local
loop. However,
when bypass
feasible high access prices required for funding these costs
is
induce inefficient bypass.
may
help mitigate this dilemma*. But,
of dealing with this
problem which amounts to discon-
Nonlinear prices for local telecommunication
there
is
a
much more
way
efficient
necting consumer prices and producer prices^.
The monopolist has marginal
The
fringe has marginal cost C2^°.
cost cq for the local
network and
Ci for
Consider the case of a continuum
long distance.
[0,1] of
consumers
with identical preferences V{qi,q2)- Let V{pi,p2) be the indirect utility function. The
bypass technology
b is
the
Let
same
T2
is
characterized by a fixed cost 6
for everyone, 9
be a tax on good
With a competitive
=
P2
The
price of
good 2 charged
to those
P2
The marginal
price of
good
[0,
oo)
and a
(low) mctrginal cost
b.
distributed according to a c.d.f. G[9).
is
2.
€
—
a
-h C2 4- T2
a
=
C2
local loop
2
is
then
:
is
+ T2.
through bypass
= P2 + ^ -
given that consumer 6 has paid a fixed cost
good
.
who bypass the
2 obtained
P2
fringe the price of
is
de facto
a
6.
*See Laffont-Tirole (1990b) for a different example of the use of nonlinear prices to fight bypass.
^However, this option is rarely available to regulators.
'°The dichotomy property is assumed so that we can study pricing issues independently of incentives
issues.
20
For given prices
who bypass
P2,a) consumers
(pi,
are those with 9 lower than 9'
defined by
V{pi,P2)
Leaving aside good
Max
[v{puP2
^
+
=
-9'
Vipi,p2
+ b-a)-9 +
[V{pi,P2)
+
(1
+
{l
+
X)[{pi
X)[{pi
- Ci -
?i
Let
=
=
qiiPuP2
demand
+ b-a)
92(a)
Let
AR
2)
AR =
is
-
(pi
ci
-
Co)(9i(a)
effect.
when a consumer
It is
-
qi)
+
{p2
-
a
-
C2)q2{a)]]dG{9)
(45)
AR
<
+ b - a)
?2(Pl,P2)-
demand
-
a
and
and revenues associated
let
171, 772, ^712,
'721,-^1, -^2
functions 91,52-
- 03)92(0) -
(P2
-
C2
-
£0)92-
the loss of profits (including access charge and
switches to bypass.
means that
less
This should favor a lower access price than
If
we
it is
tcix
on
think of the difference between prices
the difference of "collected taxes"
taxes are collected
when no switch
when
when
the switch occurs.
occurs (see equation A5.3 in
5).
seems
difficult to predict
AR Si 0".
the sign of
AR. So we wiU
Then, from appendix 5 we have
A
I
Pl
P2-C2--Qd
+
1
At/i
A
1
P2
give the complete results only
:
Pi-ci--Co
where
q2{pi,P2
^i(a))-R2(a) be the elasticities
costs as taxes for raising funds,
the switch occurs.
appendix
=
functions qi{a),q2{a) and the prices pi,p2
an income
and marginal
=
?2
the elasticities and revenues associated with the
for
(pj
-ci- Co)qi + {P2 -C2- Co)q2]]dG{9)
<ll{Pl,P2)
771(a), ^2(0)1 '712(a), '721(0)5
with the
It
+
co)qi{a)
:
for ease of notation
?i(a)
good
+ b-a).
optimal pricing and access pricing are then the solution of
0,
J^^
where
+
+
1
A
7/2
fi, ^2 ^^^ superelasticity formulas for the hybrid population of
bypass and those
''Note that
if
who do
consumers who
not.
in addition a direct
subsidy (or tax) for bypass was available this effect would disappear.
21
The
deviation of the access price from the marginal cost
a
-
A
Co
1
P2
If elasticities
where
is
^2
mation
are constant,
if
+A W2
72(a)
TiiT]2{a)!'
the proportion of those
who bypass
the classical super-elasticity and similarly ^^
w
^1)^^,
is
smeill
(then fj
we obtain the
Pricing access at marginal cost
approxi-
is
Co.
then appropriate.
have assumed here the existence of transfers.
If
there
is
no transfer, similar
hold as long as the tax revenue on good 2 goes to the monopoly.
If not,
bypass
inefficient
is
:
The
The concern was the
cost.
The optimal
now
that the competitor
access pricing rule
for
some
services
efficiency of supply of services given existing
words we have assumed that the regulated firm's
the access price. Suppose
Compo-
Efficient
So far we have focussed on pricing access when there exist competitors
firms. In other
and very
be expected.
to
Access Pricing and Entry
nent Pricing Rule.
which need access.
results
access prices
participate strongly in raising funds to pay for the fixed costs of the local loop
9
*^ V2
:
act
We
then
is
may be
must pay a
affected
rival enters regardless of
fixed entry or operating
by the existence of
this fixed cost,
because the entrant does not internalize the consumer surplus created by the introduction
of
good
Ideally one
2.
would hke to use
direct entry subsidies to deal optimcdly with the
entry decision. [Under incomplete information about the entrant's cost, one would need a
nonlinear transfer function of the quantity to be produced
is
about the variable
fixed cost
if
cost,
induce a better entry
.Also,
it
the asymmetry of information
and a stochastic decision of entry as a function of the announced
the asymmetry of information
alternative instruments
if
is
may be optimal
about the fixed
cost]. In
the absence of such
to lower the access price obtained so far to
decision^"'.
concerned with entry decisions, Baumol has proposed a simple and influential
'-In the absence of these assumptions different taxes for those
who bypass and
those
who do not would
be desirable.
'•^The relatively favorable interconnect prices levied
are a
dynamic version
marivet structure.
A
on Mercury to access British Telecom's network
widely believed that they were designed to realise a pcirticular
different but related reason for low access prices is the high switching costs of
of this point.
It is
consumers.
22
access pricing rule
^*,
component pricing
called the "'efficient
(ECP
rule"
rule)
which
foUows from the precepts of contestability theory.
In our notation, this rule
the monopoly's price and
its
recommends an
marginal cost in the competitive mairket
a
The
if
idea
and only
is
ECP
more
if it is
rule
:
= pi- ci.
(46)
that an entrant with marginal cost c on the competitive segment will enter
efficient
P2
•
access price equal to the difference between
:
=a+c=
(pi
-
ci)
under perfect substitutes
+c<
The
:
pi
«c<
Ci.
following assumptions
make
this rule
optimal. First, the monopoly's and the entrant's goods are perfect substitutes. Otherwise
entry by a less efficient entrant
may be
Second, the regulator observes the
desirable.
monopoly's marginal cost on the competitive market. Third, the entrant has no monopoly
power. Otherwise, the choice of pi not only determines the access price, but also constrains
the entrant's
monopoly power. Fourth, and
relatedly, the technologies exhibit constant
returns to scale. Fixed entry costs for instance would create severed difficulties with the
Baumol
On
in
rule.
On
the one hand, the no-monopoly-power assumption would be streched.
the other hand, the entrant might not enter because he does not internalise the increase
consumer surplus created by
[Incidentally,
pricing.
But, p2
=
a
-h c is
entry. Fifth, the
Baumol seems
lower than the
On
to
benchmark pricing
recommend Ramsey
Ramsey
rule
is
marginal cost
pricing as the benchmark.
price for cost (co -H c)
if
pi
the
is
Ramsey
the other hand,
if
those five conditions are satisfied,
argued that the access pricing rule (46)
is
irrelevant.
for cost (co
-f-
ci).]
should supply only access
(pi is irrelevant)
;
or c
>
ci
Either c
<
Ci
it
price
can be
and the monopoly
and no access should be given
(a
is
irrelevant).
•
ECP
rule under imperfect substitutes
differentiation (as
we have done
the competitive segment.
To
we assume constant returns
entrants,
until
now)
:
In the rest of this section
to justify the presence of several firms in
retain the spirit of the
for the
much
as possible,
known marginal
cost for the
Baumol
to scale, competitive entrants,
and the dichotomy property
we introduce
rule as
monopoly's cost function. For instance, we
can take the sub-cost functions assumed in Section
5.
The dichotomy
ensures that the
pricing rules will not be affected by incentive corrections.
"If a component of a product is offered by a single supplier who also competes
••See Baumol (1993)
with others in offering the remaining product component, the single-supplier component's price should
cover its incremental cost plus the opportunity cost incurred when a rival supplies the final product".
:
23
model the Baumol
In our
amounts
rule
to
a(;3)=Pi(/3)-cx=pi(/3)-^.
Competition
= Pi{/3) + c —
competitive segment implies that p^iP)
in the
Ci.
Optimizing expected social welfare under constraint (46) and under the incentive constraints (see
appendix
6),
we obtain the
=
a
where
an "average
is
772
.
V2
=
P2
qi
——'71
P2
(47)
+ 92
to the formula a
?2
+
9i
=
+
Cqq +
772
,
— —T~"'?21 -
-
-7/2
here of dichotomy), the elasticity used
The
A(/?)
+
Cqq
elasticity"
Pi 9i
Compared
access pricing rule
92
P2
92
Pi 9i
+ 92
9i
J/n-
^L ^ obtained in Section 5
t
(in the case
- ^12 '721
'7i'72 + '72'72i
^71^2
=
772'
difference between the two formulas (assuming that there
Baumol
is
rule ties the
no need
P2
-c-
Co
=
pi
-
ci
-
costs.
One then
for
=
771
772
and
c
=
Ci.
an
in-
:
These imply that
Co, or
a
Thus
has
for
two prices on the
competitive segment. Let us compare the two rules in some specific cases
Symmetric demands and
assumed
not the correct one, namely
is
centive correction) stems from the fact that the
-
(48)
91+92
symmetric demands and
= pi- ci.
costs, the efficient
component pricing
rule
is
consis-
tent with optimal regulation.
-
Linear demands, symmetric
costs,
and captive customers.
ous symmetry assumption in one respect
:
the monopoly has captive customers while
competitors do not. Under hnear demands, the
with d
<h
and
02
<
ai.
demand
(7i
=
ai
-
bpi
+
q2
=
0,2
—
bp2
+ dpi
>
P2
and
24
a
<
functions are
dp2
Marginal costs are identical
Pi
Let us alter the previ-
pi
:
—
ci
=
C\.
c.
Our formulas then
yield
The
intuition
that the
is
monopoly must charge a higher price
because captive customers make markup relatively
turn, this high
efficient
-
markup on good
component
efficient in
covering the fixed cost. In
can be viewed as an access subsidy relative to the
1
pricing rule.
Linear symmetric demands, cost superiority of monopoly.
previous example that ci
=
03,
but
ci
<
P2
Pi
The
intuition
now
is
<
Then our formulas
c.
and
that under linear
—
partially reflect the cost differential C2
a
<
demand
Ci.
price cap
Price Caps
:
—
pi
Let us assume in the
yield
:
Ci.
the price differential p2
There
"cost absorption".
is
must therefore be lower than that recommended the
Remark on
thcin its competitors
efficient
Suppose that the monopoly
is
— Pi must
The
only
access price
component pricing
rule.
regulated according to the
:
aopo
with the access pricing rule
+ aipt < p,
(49)
:
a
= pi-ci
or
P2=Pl-Ci+ C.
This of course
lator
If
makes use
is
not pure price cap regulation (neither
is
practice) because the regu-
of the cost information ci.
the weights Qq and Oi are chosen approximately equal to qo and
we obtain
(see
appendix
7)
Po
-
Cqq
_
(1
Po
Pi
-
i^)
lo
- Cqq -
Ci^,
_
1
Pi
where u
is
qi 4- 92 respectively
-
V
V2
the multiplier of the price cap constraint and
a
=
Uoo
H
fj^
is
given by (49).
Then
•
Tz
^2
Comparing with
—i^. On
we
notice two differences. First
the other hand, under a price cap, effort
production level
effort level
(48)
qo
+
(^i
+
?2
and therefore Cqq
than under optimal regulation.
25
is
is
1
-
1/
will in general differ
from
optimal conditionally on the total
evaluated at a (conditionally) higher
Access Pricing in Practice
10
To assess current practice
Co
=
+
CqQ
Fully distributed costs
a)
:
markup above marginal
^^^^^
Po
1
=
Co
+ -,
=
Ci
ko,
=
=
C-i
cq2.
method
populeir
of pricing access consists
products in a mechanistic way. For instance, a
may be uniform
cost
pi
and
Ciqi
The most
in allocating the fixed cost to the firm's
product's
model, assume that
in the light of the theoretical
(ci
+
Co)
This accounting rule generates "'excess" revenue
+ -,
:
a
=
Co
+ -.
=^ + ^^ + ^^ =
A:o,
that covers the
fixed cost.
It
interesting to note that this accounting rule satisfies the efficient
is
component
pricing rule, as
Pi
-
=
ci
a.
This of course need not be the case for alternative methods of distributing the fixed
For example, a markup proportional to marginal cost, namely
cost.
Po
where S
=
Co(l
+
Pi
<^),
=
(co
Pi
is
—
Ci
demand and
proper cost,
>
—
The
Ci)qi,
Oftel rule
and B2
=
long distance, access).
The
=
co(l
+ S),
a.
is
{a
entry considerations.
:
—
The
idea of the rule
fully distributed costs. Let
arbitrary and has no reason to reflect the
The
access rule designed
Telecom's (BT) network can be sketched as follows
Co
a
no point dwelling on the conceptual drawbacks of
us just recall that the fixed cost allocation
b)
<J),
chosen so as to ensure budget balance, yields
is
There
+ Ci)(l +
is
Co)?2
:
by Oftel
Let So
denote BT's profits in
AD
"access deficit"
is
its
=
for the access to British
(po
—
<^)%i ^i
to set a usage-based price of access to
is
(Pi
—
various product lines (local,
here equal to the fixed cost
.\amely the margin above the cost of giving access
=
BT's
ko.
local network.
proportional to the access deficit
per unit of BT's output in this activity and to the share of BT's variable profits provided
by this activity. For the long distance activity, one thus has
a
—
Co
=
AD
qi
:
Bi
Bq
26
+
Bi
+ B2
(50)
Note that B2
depends on the access price and that
itself
mination of access prices under
fully distributed costs)
(as
is
the case for the deter-
formula (50) involves a fixed point.
In practice (again as in the case of fully distributed costs), the access price
outcome of a dynamic tatonnement, whose path ought to be studied
If
the budget
balanced (that
is
AD =
is, if
in
must be the
more
^o+^i-f ^2), the Oftel formula
detail.
interestingly
reduces to
= pi-ci
a
which
under budget balance the
yields
To
there
exactly the "opportunity cost" of
is
is
is
Oftel formula thus
rule.
usage -and not only cost- based, suppose that
competition not only on the long distance domestic market (goods
but also on the international market (good 93 produced by
competitors).
its
The
in the activity.
component pricing
efficient
see that the access pricing rule
BT
The
BT
and good
q^
qi
and
92)?
produced by
Oftel rule then defines different access prices for competitors, 02 on
the domestic long distance market and 04 on the international mcirket despite identical
access costs^^.With obvious notation,
02
and
—
Co
=
AD —5Bx —
so
02
04
The markups
The
Oftel rule
is
—
_,
and
a^
— cq =
Co
Bi/qi
Co
^3/93
AD
B3
(51)
are thus proportional to BT's unit revenues on the competitive segments.
therefore related to our access pricing formula, in that both are usage-
revenue imposed by competitors on the network provider. The
based and
reflect the loss of
difference
between the Oftel rule and our formula (29)
is
that the unit revenues replace
the superelasticities.
11
Conclusion
In a first best world, access pricing to a
network (hke any other pricing) should be marginal
cost pricing. In practice the appropriate rule departs
from the
first
best
and depends on
the constraints and on the available instruments.
First, the provision of the
nondistortive
lump sum
•For the sake
ta.xes.
network imposes fixed costs which cannot be financed by
Competitors should then contribute to the fixed cost of
In practice, a domestic call uses two domestic local loops while an
Further, the access price peak load structure can only be coarse, and
differ for the two types of calls if their timing stuctures differ within pricing
of the argument.
international call uses only one.
iherelbre network costs
may
bands.
27
the network. This contribution, which takes the form of an access price above marginal
cost, reduces either the financial
burden of the regulator
(in
the case of transfers) or the
price distortions associated with the firm's budget constraint.
Second, asymmetric information of the regulator about the firm's costs
may
introduce
other standard distortions, because informational rrats must be taken into account
defining proper marginal costs.
may be
Further distortions
desirable
if
when
network and
competitive segment subcosts cannot be disentangled.
When
taxation of the competitive goods
is
feasible, access
can be priced at margined
cost while taxes contribute to covering the fixed cost. [Note nevertheless that the marginal
cost referred to
firm,
and
is
is
the marginal cost which arises from the optimal regulation of the
in general different
from the
first
best marginal cost because effort
This disconnection of consumer and producer prices
very handy
is
competitive segment can bypass the network.
By
and taxation mandates reduces the
number
price
regulators'
if
pricing rules
to the coverage of fixed costs.
become more and more complex
to use access prices, rather
lower].
consumers on the
contrast, a separation of regulatory
of instruments,
must then arbitrate very imperfectly between the goals of limiting
and participating
is
It is
clear
and the access
ineflScient bjT)ass
more generally that
access
as well as inefficient as the regulator tries
than complementary instruments, in order to meet various
market structure goals such as inducing proper entry or reducing monopoly power
in the
competitive segment or to achieve distributive objectives.
Last,
we have shown that our
analysis can shed substantial light on the effectiveness
component pricing
of policy proposals such as the efficient
rule
and of existing poUcies
such as the Oftel rule for British Telecom.
Looking forward, our analysis can be pursued in several directions. With a proper
regulatory model of predatory behavior, one should be able to investigate the conjecture
that access pricing
products.
The
is
a
intuition
more
is
efficient tool to
the following
:
A
prey than the pricing of the competitive
low price
for the
competitive product signals
a high efficiency. This information can be used by the regulator to extract the monopoly's
rent in the future.
On
the other hand, a high ciccess price seems
immune
to ratcheting.
Next, one could substitute to the optimal regulation various types of current regulations (price cap, rate of return)
and analyze how the deviations from optimal regulation
impact on the access pricing formulas (see
for
example the Remark
could even depart from the regulatory context and see
in Section 9).
how competition
One
policy alone would
deal with access pricing. Excessive access prices could be considered as a predatory tool
to eliminate
competition as has been claimed in the ATi:T case before divestiture.
Our framework
also enables us to discuss a current debate in Europe. Telecormnuni-
cation companies are required to offer universal service of local telephone (here good zero)
28
at a
low price. Their budget constraint would normally force them to increase the price of
their other services as well as the price of access to the network.
A concurrent
low-access-
Community might demand marginal
charge constraint (for example the European
cost
pricing in order to increase competition) then forces the network firm to further increase
the price of
its
other services and and to lose
its
competitive edge.
We
are not then
very far from the solution adopted by the U.S. courts, which prohibits the network from
offering competitive services.
There, universal service
charges to the network instead of the profits
made by
is
financed by appropriate access
the network firm on
its
additional
services as in Europe.
We
have not discussed nonlinear access pricing
rules, for
long as the fixed part of the tariff plays the role of a
to raise the
money needed
lump sum
tax,
it is
some
example Laffont-Tirole (1993)
tariffs.
As
an excellent tool
to pay for the fixed cost of the network. However,
take in account the fact that beyond
rate (see for
example two-part
one must
level the fixed charge lowers the connection
ch.
2).
Similarly
we have not
discussed the
important practical issue of peak load access pricing.
Finally, let us stress that, to a large extent,
we have
left
aside various
dynamic
issues
:
investments (in particular unobservable specific ones) for network development (see however
Remark
4 in Section 3), consequences of regulators' limited
well as regulation of entry. Inefficient
commitment power,
as
developement of the network, more costly rents of
asymmetric information, and inadequate entry behavior are then to be expected. These
questions can be addressed within our general regulatory framework (see ch. 1,9, and 13
in Laffont-Tirole (1993) for
the basic principles).
29
APPENDIX
Let
/i(/3)
1
:
Optimal regulatory rule (Section
be the co-state variable associated with U. From the Pontryagin principle
=
/i(/3)
Using the transversality condition
fi{0)
/x(/3)
The
=
=
we have
AF(/?).
{S{qo{poim + V{qi{pi{0),P2m,q2{pM,P2{m
+a[po(/5)?o(Po(/3))
+
A/(^).
differentiation of the Hamiltonian
H=
-(1
3)
A)[0(eo(^)
+
e,i/3))
+
+ Pi(/3)gi(pi(/3),P2(/5))
Co(/?,eo(/3),9o(Po(/3))
+P2(/?)92(Pi(/5),P2(/?))]
+ ?i(pi(/3),P2(^)) + 92(pi(/?),P2(/3)))
-M(/3)0'(eo(/?)+e:(/3)){^(/?,Co(/3,eo(/3),9o(po(/?))+9i(pi(/5),P2(/3))+92(Pi(/?),P2(/3))),
qoipom + qi{pm,P2m + q2{p,m.P2m)
with respect to po, pi, P2 gives (24), (25) and (26) and with respect to
and
(31).
30
eo,
ci gives (30)
APPENDIX
Part
(i)
dCkd0 =
is the same
/?
—
results
from
ioT k
=
Sub-cost observability
To prove that sub-cost observation
(37).
is
useless
1,2 note that, at the optimal regulatory policy,
That
for all k.
{t{/3),C(/3) ,Qi/3),qi{/3)}
This incentive scheme
to its
:
is,
when d^Ekl
{—dEk/dCk)
given the firm's scheme under sub-cost observability,
{t{/3),Co(^) ,Ci(l3),Q{0),qi{0)} consider the associated incentive scheme
>•
type
2
/3
announces ^
it
is
under sub-cost unobservability, where C{0)
incentive compatible.
will
To show
=
Co(/3)
this, it suflBces to
-I-
—
Ci(/3).
show that
if
choose the sub-cost cdlocation {Co(/3),Ci(/3)} corresponding
announcement, even though the regulator cannot control sub-costs. Note that from
(37), there exists
a such
that
^(/?,C,(/3),(3,(^))
=a
k
=
0,l
and
Coi0)
where Qq
=Q
and Qi
=
+ C,0) =
C{^),
q\.
But the condition d^Ek/dCk
5/?
=
impHes that
^0,Ck0),Qk0)) = a
for all k,
as well.
/3
From our assumption, {Cq{^) + Ci{0) = C{0)} is the imique cost minimizer for type
when it announces /3. We can thus implement the same allocation when sub-costs are
unobservable as when they are.
31
APPENDIX
3
:
Competitor market power
Because of the dichotomy assumption, the optimization with respect to the access
price can be carried out under complete information
max^ {S{qo{po))
+
:
V{qi{pi,p2),qi{pi,p2))
vo
-
-PiqiiPi,P2)
(a
- poqoipo)
+ c)q2{pi,P2)}
(A3.1)
s.t.
PoqoiPo)
+ Piqi(pi,P:i) + aq2{pi,P2) -Ciqi{pi,P2)
q2{puP2)
From
P2
I
+ ei)
(A3.2)
+ P2-^{puP2) -{a + c)-^{pi,p2) =
ap2
+c=
p2
+
(A3.3)
0.
Op2
g2(PliP2)
-9——!
^iPl,P2)
Substituting into (A3.1), (A3. 2)
max
X
i^{eo
+ 9i(pi,P2) + 92(^1, P2))
(A3. 3)
a
PO>Pl
>
Co(?o(po)
= P2(l -
l/r]2{puP2))-
we have
S{qo{po))+V{qi{pi,p2),q2{pi,P2))-Poqo{Po)-PiqiiPi,P2)-P2q2iPi,P2)+
^
^
^'
^
V2[Pl,P2)
L
s.t.
Po9o(Po)
+ Pl?l(Pl,P2) + P2q2{Pl,P2) -
-Ciqi{pi,P2)
cq2{pi,P2)
+ qiipi,P2) + ?2(Pl,P2))
Coiqoipo)
>
r + ^(^0 + ^l)-
-,
V2{P\,P2)
Let
1
+ A(/3)
denote the multiplier of the contraint.
We substitute A
convenience.
Maximizing with respect to (^1,^2) we obtain
:
dV
dqx
dV
dq2
dq]_
dqi
dpi
dq2 dpi
dpi
^(1+A)
.
_
dq2_
dpi
dqi
dq2
fdqi
dq2
opi
dpi
\dpi
dpi
32
to A(/3)
below
for
i
J
dq2
dqi
-CiOPi
c-^—
dpii
dV
dV^ dq^
dqx dp2
+(1
+
A)
dpi \
dq2
dq
iSl
op2
ap2
dp2
dq2
dp2
dp2
dq,
?2
dp2
„ 9qi
dqi
-
dq2
dqi
dp2 dp2
-
Pi
dpi dpi
P2
— + -^^
dp2\
P2
Co
-
T]2
5p2/
J
Ci
-Co -c
1
-
Co
.
—Co —
Ci
1
C
+
+
A
1
El
+
The second term
I
J^
dp2 \
r]2
J
A
dq2
1
-1
_d_fm2\
dpi\
dqi dq2
d (P2q2\
dp2\ T/2 /
dp2 dp2
_
dq2_
^21
921.
dpi
dq2
'
dn
dq2
^
_
T}2
J
^31. i33.
9pa
d
f
1
9pi
\
dp 1V772/
\dp2'dpi
dpi'dp2
P2_
fdq]_ dq2
dqi dq2
dqi__d_n\
\dpi' dp2
dp2'dpi
dpidp2\r]2J
B2.
11
+
J
dpi dpi
T}2
I
r]2
of the right-rand side equals
1
P2 fdq2_ dq2
dpi \
+A
V2
T]2
dp2
Cn(
\dp2
dqi
-
-P2
dq2
dqi
Pi
J
dqi
dq2 dp2
.
T]2
^
.dp2
dq2
d
dpidp2\T]2^
dpidp2 \r]2
dp2dpi\i)2)
Pii2i^{^)+P2mii;{^) +
'7i72 - '7i2'72i
A
El
th^i4(^)+P^'?"af7(i). +
'7i'72 - 7i2'72i
33
dq2 g2
dpiT]2
+
dqi q2
dpi
r/2
.
Pi
-
Co
-
Pi 72
Ci
Pi
P2
-
-
Co
=
Since a
a
A
1
+
7172
'/I
A
1
1
72
72
I
2li
72
- 712721
P^'?^afc(^)+P^^"a^(^
—+—
C
P2
where Rk
+
1
t{^)+P2m.^{^)
7i72
- 712721
Pkqk-
=
P2
=^
uoQ
—
c
—
P2
we have
22.
A(/3)
r
72
1
+
P2—
A(^)^ 72
with
72
A(/?)
1
.
=
l
+
A(/3)
P27ia^fe)+pi7i2gf7(;^)
7i72
— 712721
+ 72172 - 721712 7i72
72-
27172
34
7i
-
P2
712721
APPENDIX
The dichotomy
4
Restricted regulation
:
implies that price formulae can be obtained as in the full information
case. Let
W = S{qo) + V{qi,
92)
- poqo - Piqi - P2?2
denote the consumer net surplus, and
MP =
q^
+ p^[p^-Co-c^] + p-\p,-Co-c]
Opi
OPl
denote the monopoHst's marginal profit and
let
P
denote
its profit.
The planner
solves
:
W
max
{P0,Pl,P7}
subject to
P -y; =
(BB)
po9o
+ Piqi +
{p2
-
MP =
Let
(1
+
hand
side of
to pi
is
A)
and v denote the shadow
(B5)
Cxq\
- V" =
and
0.
prices of the
maximized with respect
is
- CqQ -
0)92
two constraints. Because the
left-
to pi, the first-order condition with respect
:
dW
f
dp\
\ dpx
Because the net consumer surplus
sumption on
profit,
we obtain
1/
<
0.
dMP \
decreaises
The
)
with prices, and from our concavity as-
derivative of the Lagrangian with respect to pi
yields
dW
-
dp2
The
ing.
dP_
dp2
dMP _
dp2
first-two terms are the standard terms obtained in the
The
correction in the access pricing formula {a
d{MP)/dp2, which
is
is
p2
—
c)
also increased
and the
p2,
and therefore the access
result aimbiguous.
However,
functions and constant returns to scale both effects cancel, giving the
formula as
in the case of full regulation.
35
pric-
depends on the sign of
positive under generahzed strategic complementarity.
equation shows that for a given pi the price
lowered. But pi
=
absence of monopoly
price,
This last
should be
for linear
same
demand
access pricing
APPENDIX
=
Let e- be defined by 9'
V{pi,p2
+b-
-
a)
5
V{pi,p2).
Hence
dO'
^=
de'
91
-
gx(a)
=
?2
-
?2(a)
=
92(a)-
+
ip2
dp2
dO'
da
Let
AR =
(pi
-
-
ci
Co)(gi(a)
-
qi))
Maximizing (45) with respect to pi,p2,a
0(9') \q,{a)
+(i-G(n)
yields
+
A) [ip,
A91
+
(1
+
+(1-G(n)
+
(1
+
A92
+
A) [(pi
-
Ci
'
-
A92(a)
-
(1
(P2
-
C2
A) (^^
(l
+
+
(P2
-
Co
-
C2)|^]]
'^^a^^'^)
(A5.1)
+ (P2 - a - C2)^(a)]]
A)
A) [(p:
- ci -
+
A)Air:
co)||(a)
+
A)Ai2
=
+
(p2
(A5.2)
-
a
- C2)|^(«)]]
=
Hence
G{9') A9i(a)
+
-(1-G(5-)) A9i
+^(^-)(l
(1
+
+
(l
A)(p,
+ A)(px-Ci-Co)|^(a)
-
c,
-co)^(a)J^-;^^-^_
+ (1+A)
+
co)92-
+ A)Ai2 =
-''-
+^(^*)?2(a)(l
-(A,2(a)
-
:
- Co)|| +
+5(n[92-92(a)](l
G(5-)
- 02)92(0) -
-c- Co)||(a) + (P2 " a - ^2)^(0)]]
+5(^')(9i-9i(a))(l
G{9') A92(a)
a
dq2
(1
+
-
A)Ai? 9i-9x(a)-92(a)^^^/^^^^^)|-0,
36
(A5.3)
and
[l-G{e')]^Xq,
+ {l+\) (p,_e,-co)|l + (p,-c.-co)|l]]
+9iO')q2{l
Given the ambiguity of the sign of
+
A)Ai?
AR, we
=
0.
will consider
the case
AR = 0.
-Ci-co)
(Pi
(1
+
A)
iP2-Co-
C2)
-{l-G)Xq2
or
{l+X)A
Pl-Ci-Co
P2- Co- C2
OCX
"2
.
9n
det
n _
- GfA
A = G{\- G)^^A{a)A^
+ (1
with
A _
^9i^<?2
^92 591
a?!
5?2,
dpi ^p2
5pi ap2
dpi
dp2
A-'
=
dqx
dq2
dp2
dpi
i^-G)t -i^-G)'^
-i^-G)t
+ (^-G)t
lS^.
dpi
'^"1
Bi-)
apjV
1
det
X
A
This yields
-A[G'(9i(a)
Pi
-
Ci
-
Co
- 92(a)l{^) +
(1
-
G)?:](l
- G)|^ +
{1
- G)^A92|^
=
(1+A) (l-G)2A + G(l-G')A(a)fe/g^(a)
A[G(<7i(a)-<72(a)#|^)+(l-G)9il(l-G)|^-A(l-(?)g2
P2
— C2 — Co
=
'dp
'}P7
(1
+
A)
(l-C?)2A + G(l-G)A(a)(|^/|^(a)
37
Pi
1
,,-c,-c
{^^•('^- +
A
1
P2
+
GA{a);^^ + {l-G)A
+ A-
l
+ Xrfi
^^^ + ii!}) + (l-G)(,. + ,.,)^_
GA(a);^^ + (l-G)A
A-
1
with
A=
=
A(a)
These formulas reduce to the
From
771772
-
771(0)772(0)
7/127721
-
7712(0)7721(0),
classical superelasticity formulais
when
G = 0.
(A5.3)
Cq-q _
~
P2
A
1
+
1
A
Pi
-Ci -Co
772(a)
A
^
l
+
pi
f
7712(0) i?i(o)
772(0)
1
^
R^ia)
_772i(o)
j
^1772(0)
^2'''
I
Al772(o)
38
_
,
P2
-
C2
p2
- Co
+
,
A^,
APPENDIX
The
6
:
Implications of the Efficient
program
regulator's
then
is
Component
Pricing rule
:
max^''[5(9o(;'o(/3)))+l/(gi(pi(;5),pi(/3)-^i(/3-ei(;3))+c),92(pa(^),Pi(;3)-tfi(/9-ei(^))+c)
-Po{0)qo{pom - pMqiipii/3),pi{0) - H,i0 -
eri0))
+ c)
-{pM -H,{^- eM) + c)q2{pi{/3),p,{/3) - H,{^ - ei(/3)) + c) + U{0)]dF{l3)
s.t.
Um >
0,
and
Po(^)?o(Po(/?))
+ Pi{/3)qi{pi{(3),pi{0) -
+ [px(/3) - H^{0 -
e^m]q2{p^i0),p^{0)
Hr{/3
^i(/3
+92(pi(^),Pi(/3)-^i(/3-ei(^))
-//i(/3
-
ei(/3))9i(;7i(/3),pi(/3)
Proceeding as
in Section 5
0'(eo
-
ei)
=
-
^i(/?
-
+ c) -
ei(/3))
+
ei)
=
//o(?o
H[q,
- CoQ -
e^) + c)
-
ei(/3))
+ c)
+ c))
W) -
+ 91 + 92) -
~
+
V(eo(y9)
+
-
j[mmd0
—
-=
=
r
,
C, ^
^'"(eo
V"(eo
^+
+ eO
OP2i
\{0)
A(/3)
i
.
I
-((?!
1
+ 'xm r-'
39
+
ei)
A{p))j[p)
dp2
Pi
+ c)
we obtain
(1
w'(eo
ei(/?))
- H,{P -
- eomiqoipM) + qi{pxm,Pxm -
-i7o(/5
-
+ «72)
p
A(/?)
92
ei(/3))
=
0.
with
V91
+ 92/
P2\qi
+ q2/
Hence
a(/3)=pi(/?)-/ri(^-ei(/3))
A(/3)
,
with
ri^
=
p,
^T,".
40
_
m
p2
APPENDIX
7
The Lagrangian
:
The
Component Pricing
Efficient
monopoly's optimization problem
of the
rule
under price caps
is
Poqo{po)-Ho{/3-eo){qo{po) + qi{puPi-Hi{^-ei{^)) + c) + q2{pi,pi-Hi{0-ei{^)) + c))
+(p:
-Hr{l3-
ei)){qiipuPi
- H^{0 -
-V-Ceo
The
first-order conditions
e,{0))
+ c) + q2{pi,Pi -
+ ei) + j/(p - aopo - OiPi).
with respect to pq and p\ are
bo - Cd)^— + 90 =
olqv
dpo
.f9qi
(
If
oq
~
qo
and ai
~
^i
+ q2,
po
—
Co
w
Po
Pi
rj^
is
1
—
1/
Vo
Pl-Co-Ci
where
dq2\
dq2
dqi
\-Vp2
12
given by (47).
41
Pi
H,i/3
-
t^{0))
+ c))
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phone
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TIROLE
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VICKERS,
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42
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3
TDflo
DDfl^t.sl^
s
Date Due
,0.2
•#&-'
iCT,
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