Universal Service Obligations in Developing
Countries
Antonio Estache JeanJacques La¤onty Xinzhu Zhangz
August, 2004
Abstract
This paper develops a model to analyze the impacts of asymmetric
information on optimal universal service policy in the public utilities of
developing countries. Optimal universal service policy is implemented
using two regulatory instruments: pricing and network investment. Under
discriminatory pricing asymmetric information leads to a higher price and
smaller network in the rural area than under full information. Under
uniform pricing the price is also lower but the network is even smaller. In
addition, under both pricing regimes not only the ...rm but also taxpayers
have incentives to collude with the regulator.
Keywords: Universal service obligations; Asymmetric information; Col
lusion
JEL Classi...cation: L43; D82; O12
1 Introduction
Universal service obligations have played a prominent role in policy debates on
public utilities in developed economies.1 In the United States, for instance, a
large part of the 1996 Telecommunications Act is devoted to reforming univer
sal service obligations, and the Federal Communications Commission has made
enormous e¤orts to implement these obligations. Governments in developing
Corresponding author. World Bank, Washington, D.C. 20433 and ECARES, Univer
site Libre de Bruxelles. Tel.: +12024581442; fax: +12025222961. Email Address: aes
tache@worldbank.org (A. Estache).
yIDEI and Université des Sciences Sociales, Place Anatole, 31042 Toulouse Cedex, France.
Professor La¤ont passed away on May 1, 2004.
zResearch Center for Regulation and Competition, Chinese Academy of Social Sciences,
Beijing 100732, P. R. China.
1For recent overview of the economics of USO, see Cremer and et al. (2001).
1
countries have also viewed these obligations as an important social commit
ment and implemented universal service policies to varying degrees as part
of regulatory reforms (see Clarke and Wallsten (2002) for an overview). For
developing countries universal service obligations are broadly viewed by politi
cians and policy makers as a necessary component of equitable development
strategies redistribution toward the poor and the underdeveloped regions as
part of USOs.
Still, universal service obligations have created considerable controversies in
reform processes and raised many practical and theoretical issues two of which
are especially relevant to developing countries.2 The ...rst is how best to pro
mote network expansion. Unlike in industrial countries, where penetration of
basic infrastructure services is no longer an issue,3 in developing countries many
people still lack these services, particularly in rural areas. Thus network expan
sion remains an essential dimension of universal service policies in developing
countries.
The other important issue in developing countries is the design of pricing
policy instruments to support universal service obligations. Because the neces
sary ...scal instruments are often not available, policy makers have traditionally
tended to rely mostly on simple pricing policies to achieve both allocative ef
...ciency and redistribution goals. USOs have indeed often been ...nanced by
crosssubsidies across clients of the monopoly responsible for service delivery.
But this historical approach needs to be reassessed once competition is intro
duced in a sector and regulatory decisions associated with the speci...c economic
characteristics of the sector and the service users need to be designed. This is a
particularly di¢ cult challenge in developing countries which generally have lim
ited experience in regulating infrastructure in a competitive environment and
where regulatory capture risks may be associated with institutional limitations.
2There is very little academic literature on universal services obligations in developing
countries. For an overview of the developing countries experience in adopting USO, see Chisari
et al. (2003), ClarkeWallsten (2002), Estache et al. (2003), La¤ont and N'Gbo (2000) or
Gasmi et al. (1999).
3People might object that what is "basic" get rede...ned. So "Internet access has now
become a subject of debate as many now still don't have access to broadband access in
developed countries.
2
The main contribution of this paper is to use incentive theory to analyze
these speci...c policy issues in developing countries. It provides a ...rst step to
ward understanding the theoretical foundations of universal service policies from
a normative point of view, and the associated features of political economy in
developing countries. To do so, the paper develops a simple model based on
asymmetric information, in which a developing country government lacks infor
mation about a monopolistic ...rm's marginal cost of providing an infrastructure
service in a rural area. The model is used to analyze the impacts of asymmetric
information and the threat of regulatory capture on optimal universal service
policy in the public utilities of developing countries. Here optimal universal
service policy is implemented using two regulatory instruments: pricing and
network investment. The analysis is conducted under both discriminatory pric
ing (between urban and rural areas) and uniform pricing. The results show that
under both pricing regimes, asymmetric information results in a higher price
and smaller network in the rural area than does complete information. More
importantly, although uniform pricing leads to a lower price in the rural area,
the network size is smaller than under discriminatory pricing.
When considering the possibilities of collusion between various actors, the
analysis here relies on the hard information structure used in Tirole (1986) and
La¤ont and Tirole (1993). An important feature of our model is that multiple
interest groups have incentives to collude with the regulator. The ...rm, which
obtains an information rent if the regulator does not reveal its private informa
tion, has incentives to collude with the regulator if it is relying on a lowcost
technology. At the same time, taxpayers may bene...t from information hiding
by the regulator (by paying less taxes) if the ...rm uses a highcost technology.4
Although collusion between the regulator and taxpayers may be di¢ cult since
taxpayers are often not well organized our analysis points out the stakes that
taxpayers may have in a speci...c universal service policy. Preventing collusion
between the regulator and the ...rm requires increasing the price and reducing
the size of the network for the rural area. But prevention of collusion between
4In developed countries and some developing economies, USO cost is usually born by users
in other regions or richer users rather than by taxpayers. So the relevant collusion would be
with a roundtable of metropolitan areas rather than with taxpayers.
3
the regulator and taxpayers needs opposite regulatory responses. Therefore,
the existence of taxpayers as an interest group hardens the coalition incentive
constraint for the regulator and the ...rm.
The rest of the paper is organized as follows: Section 2 establishes the basic
setting for the analysis and the resulting model. After that optimal regulation
of pricing is considered, with analysis of discriminatory pricing in Section 3 and
uniform pricing in Section 4. We analyze the impacts of the threat of collusion
in section 5. Section 6 then concludes.
2 The Basic Setting
Consider a simple principalagent relationship between a benevolent government
and a monopolistic ...rm that is regulated when providing, for instance, telecom
munications services in a speci...c territory. The ...rm's territory is divided into
two areas: a lowcost urban one and a highcost rural one. Let 1 be the share
of the population in the urban area and 2 the share in the rural area, with
1 + 2 = 1:
Assume that the marginal cost of providing services in the urban area is c1;
which is common knowledge. One can think of this assumption as a reduced
form of competition in the urban sector. But the government has asymmetric
information about c2; the marginal cost of providing services in the rural area.
For simplicity assume that there are only two possible cost levels or two types
that is, c2 2 fc2;c2g and c2 > c1; with probability distribution Pr(c2 = c2) =
and Pr(c2 = c2) = 1 . Let c2 c2 c2 > 0:
Assume also that full service coverage has been achieved in the urban area
but that the rural area is only partially connected. Denote < 1 the proportion
of households in the rural area which are connected. Because some people
in the rural area are not connected, the government imposes universal service
obligations on the monopolistic ...rm in the form of speci...ed pricing and network
expansion in the rural area. Assume that the cost of network investment C( )
is a convex function satisfying C0( ) > 0 and C00( ) > 0:
4
Let S(q) be the gross social surplus for subscribers, derived from consump
tion of the service in both lowcost and highcost areas, and P(q) the corre
sponding inverse demand function. Assume that jS00j is large enough through
out the paper so that the optimization programs are concave. To simplify our
analysis, we do not consider consumers'connection decisions, which means that
consumers derive the entire surplus from consumption of services and all ca
pacities are used immediately, because we focus on linear pricing which is one
way of getting users to enjoy a rent from getting connected; alternatively, users
could be heterogeneous and non linear pricing could be used. We also assume
for simplicity that consumers have a demand with constant absolute elasticity
> 1:
The timing of events is as follows. After the ...rm learns its private informa
tion about c2; the government determines regulatory policies for services prices
and network sizes in both urban and rural areas. The ...rm then invests to
expand the rural network, and consumers make decisions about consumption.
3 Optimal Regulation Under Price Discrimina
tion
This section considers the case where price discrimination is allowed, so that the
regulator sets di¤erent prices (p1 and p2) for each area and consumers consume
q1 and q2 accordingly. In that case the ...rm's utility function is:
U = t + 1 P(q1)q1 + 2 P(q2)q2 [ 1 1
c q(p1) + 2 c2q(p2)] C( ); (1)
where t is the monetary transfer obtained from the government since we do not
constrain the ...rm to balance its budget.5
We assume that the benevolent regulator has a utilitarian social welfare
5Alternatively, the ...rm could have ...xed costs and face a budget constraint. Then nothing
changes except: (1) that is the shadow cost of the budget constraint; (2) collusion is then
with users in the urban area rather than with taxpayers, and (3) things will de...nitely be more
complicated.
5
function. Then,
W = 1 [S(q(p1)) p1q(p1)] + 2 [S(q(p2)) p2q(p2)] (1 + )t + U; (2)
where > 0 is the shadow cost of public funds, which is exogenous. Substituting
from (1) the transfer t, we can rewrite the objective function as:
W = 1[S(q(p1)) + p1q(p1)] + 2 [S(q(p2)) + p2q(p2)]
(1 + )[ 1 1
c q(p1) + 2 c2q(p2) + C( )] U: (3)
For expositional simplicity the following notation is introduced:
pi; qi and pi; qi
are the price and quantity when c2 is c2 and c2, respectively; and similarly
t = t(c2) t = t(c2)
= (c2) = (c2):
Before proceeding further, we derive the benchmark result under full infor
mation. The following participation constraints have to be satis...ed to induce
voluntary participation for the highcost (or badtype) ...rm:
t + 1 p1q1 + 2 p2q2 ( 1 1
c q1 + 2 c2q2) C( ) 0; (4)
and for the lowcost (or goodtype) ...rm:
t + 1 p q + 2 p q ( 1 1
c q + 2
1 1 2 2 1 c2q2) C( ) 0: (5)
So, the government's optimal regulatory policy under complete information can
be obtained by solving the following program:
Max
fq1;q2; ;U; q1;q2; ;Ug f (S(q1) + p1q1) +
1 2 (S(q ) + p q ) (1 + )( 1 1
c q + 2
2 2 2 1 c2q2
+C( )) Ug + (1 )f (S(q1 + p1q1) +
1 2 (S(q2) + p2q2)
(1 + )( 1 1
c q1 + 2 c2q2 + C( )) Ug
s.t. (4) and (5).
Optimal regulation then entails:
6
Proposition 1 : Under complete information and discriminatory pricing the
optimal prices follow the Ramsey rule and the optimal size of the network is
such that the social marginal cost of network expansion is equal to the social
marginal gain. More precisely,
p c1 1
1 p1 c1
= =
p p1 1 +
1
p c2 1
2 p2 c2
= =
p p2 1 +
2
(1 + )C0( ) = 2[S(q ) + p q
2 2 2 (1 + )c2q2]
(1 + )C0( ) = 2 [S(q2) + p2q2 (1 + )c2q2] :
Proof: See the Appendix.
Under complete information the regulator needs only to satisfy the partici
pation constraints of the monopolistic ...rm so that no information rent is left to
the ...rm. The optimal prices are set according to Ramsey principles. Markups
above marginal costs are due to the social cost of public funds.
To determine the optimal size of the network, one needs to take into account
two types of bene...ts from providing services in the rural area. The net surplus
e¤ect, S(q2) (1+ )c2q2, represents the net bene...ts from consumption obtained
by those connected to the rural network. The revenue e¤ect, p2q2, is the social
gain of revenues from those same consumers. Simple inspection of the ...rstorder
conditions shows that p = p1 = p1 and p2 < p2: Moreover, > . In other
1
words, a higher marginal cost leads to a higher price and smaller network for
the rural area.
By di¤erentiating the network investment equation with respect to , one
can ...nd that the network size is a decreasing function of the social cost of public
funds that is, d < 0: So in a typical developing country, where is larger
d
than in industrial economies, network should be smaller from a normative point
of view.
Now assume that the regulator has asymmetric information about c2: Using
the revelation principle, we can without loss of generality restrict our atten
7
tion to regulatory rules that are direct revelation mechanisms. Here a direct
revelation mechanism is characterized by:
where e2 is the monopolist's report to the government about its c2.
c fp1(e2);p2(e2); (e2);t(e2)g with e2 2 fc2;c2g
c c c c c
For incentive compatibility, the following incentive constraints must be sat
is...ed for the highcost (badtype) ...rm:
t + 1p1q1 + 2 p2q2 ( 1 1
c q1 + 2 c2q2) C( )
t + 1p q + 2 p q ( 1 1
c q + 2 C( ) (6)
1 1 2 2 1 c2q2)
and for the lowcost (goodtype) ...rm:
t + 1p q + 2 p q ( 1 1
c q + 2 C( )
1 1 2 2 1 c2q2)
t + 1p1q1 + 2 p2q2 ( 1 1
c q1 + 2c2 q2) C( ): (7)
Thus the government's program is:
Max
fq1;q2; ;U; q1;q2; ;Ug f (S(q1) + p1q1) +
1 2 (S(q ) + p q ) (1 + )( 1 1
c q + 2
2 2 2 1 c2q2
+C( )) U)g + (1 )f (S(q1) + p1q1) +
1 2 (S(q2) + p2q2)
(1 + )( 1 1
c q1 + 2 c2q2 + C( )) Ug
s.t. (4), (5), (6), and (7).
That leads to the following result:
Proposition 2 : Under asymmetric information and discriminatory pricing
the optimal regulatory policy entails:
(1) If c2 = c2, the optimal price and network size for the rural area are the
same as under complete information;
(2) If c2 = c2, asymmetric information leads to a higher price and smaller
network for the rural area than under complete information.
More speci...cally,
pSB = pSB = p1;pSB = p2; SB =
1 1 2
8
pSB 1
2 c2 c2
= +
pSB 1 + 1 + 1 pSB
2 2
(1 + )C0( SB ) = 2 S(qSB) + pSBqSB
2 2 2 (1 + )c2qSB2 c2qSB :
1 2
Proof: See the Appendix.
Under asymmetric information the regulator has to give up an information
rent = 2 c2q2 to the e¢ cient ...rm to satisfy incentive compatibility. Both
the optimal price and the optimal network size for the rural area when c2 = c2
are distorted to mitigate this rent. Indeed, the optimal price in the rural area
p2 is increased (consumption q2 decreased) and the optimal network size 2
decreased relative to the ...rstbest allocations. Therefore, there are two e¤ects
distorting the optimal network size away from the ...rstbest level if > 0: (1)
q2 is reduced, which leads to a reduction in ; and (2) itself is reduced to
2 2
lower the rent.
Proposition 2 says that when price discrimination is allowed, under asym
metric information rural consumers face a higher price due to the information
cost and so consume a lower level of services. Moreover, people without con
nections are less likely to be connected because the information rent increases
the investment cost. Thus asymmetric information adversely a¤ects both the
connected and unconnected consumers in the rural area.
4 Optimal Regulation Under Uniform Pricing
This section derives the optimal regulatory policy under uniform pricing. As
before, we ...rst consider the benchmark case in which there is complete informa
tion about the cost of providing services in the rural area, c2: For expositional
simplicity, more notation is introduced: p = p(c2); q = q(p); p = p(c2); and
q = q(p). Other notational conventions are de...ned as in the previous section.
Under complete information the following participation constraints must be
satis...ed for the highcost (badtype) ...rm:
t + ( 1+ 2 )pq ( 1 1
c + 2 2
c )q C( ) 0; (8)
9
and for the lowcost (goodtype) ...rm:
t + ( 1 + 2 )pq ( 1 1
c + 2c2 )q C( ) 0: (9)
The government optimizes the following objective function:
max W = + 2 )(S(q) + pq) (1 + )[( 1 1
c + 2 c2)q + C( )]
(p; ;p; ) f( 1 Ug
+ (1 )f( 1+ 2 )(S(q) + pq) (1 + )[( 1 1
c + 2 c2)q + C( )] Ug
subject to constraints (8) and (9).
Then optimal regulation entails:
Proposition 3 : Suppose that the government has complete information about
c2. Then uniform pricing reduces both the price and the network size for the
rural area relative to those under price discrimination. More speci...cally,
1 1
c +
p 2c2
p 1 1
c + 2 2
c
1
1+ 2 1+ 2
= =
p p 1 +
(1 + )C0( ) = 2[S(q ) + p q (1 + )c2q ]
(1 + )C0( ) = 2 [S(q ) + p q (1 + )c2q ] :
Proof: See the Appendix.
Under complete information the optimal allocation under uniform pricing
can be implemented without giving up any information rent. Again, the prices
are determined by the Ramsey rule. When the marginal cost in the rural area
1 1
c +
is c2 (resp. c2); the relevant cost is the average marginal cost 2c2 (resp.
1 + 2
), which is lower than c2 (resp. c2) but higher than the marginal
1 1
c + 2 2
c
1 + 2
cost in the urban area, c1. Thus uniform pricing leads to the redistributive
outcome of a lower price for the rural area and a higher price for the urban area
regardless of the network size that is, p1 < p < p and p1 < p < p2 . But
2
as we will see soon, pricing favoritism towards the rural area is achieved with a
distortion resulting in a smaller network.
10
When the monopolistic ...rm is endowed with a highcost technology (that
is c2 = c2), C0( ) is the marginal cost of network expansion in the rural area.
As before, two bene...ts of network expansion must be taken into account. One
is the net surplus e¤ect from consumption, S(q) (1 + )qc2; the other is the
revenue e¤ect resulting from the social cost of public funds. But unlike under
price discrimination, the net e¤ect entails that S(q) + pq (1 + )qc2 is a
decreasing function of q at q rather than a constant function. The reason is
that uniform pricing creates a distortion resulting in a lower price in the rural
area, which causes a distortion toward the size of the network. Thus <
and < :
A few remarks about uniform pricing are in order. Universal service oblig
ations are often implemented using uniform pricing (such as for postal or tele
phone services). Although this regulatory policy may have political advantages,
it is not necessarily the right approach to favor the rural area. For instance, the
government could take a di¤erent approach to the design of its redistributive
policy by changing the weights of consumers in di¤erent areas in the objective
function. To illustrate this point, assume that the government puts a weight
! > 1 on the net consumer surplus in the rural area, which implies that it places
a higher value on the surplus of these consumers. By simple manipulation the
government's objective function can be written as:
W = 1(S(q1) p1q1) + 2 !(S(q2) p2q2) (1 + )t + U
1 +
= 1(S(q1) + p1q1) + 2 ![S(q2) + ( 1)p2q2] (1 + )( 1 1 1
c q + 2 2
c q2 + C( )):
!
We thus obtain:
p! ! 1
2 c2
= (1 )
p! 1 +
2
1 +
(1 + )C0( !) = ! !
2[!(S(q2 ) + ( 1)p!q!) (1 + )c2q2 ]:
! 2 2
To compare these results with those under uniform pricing, we substitute
p! = p into the above pricing function to get ! = (1 + )[1 p c2 ]: One
2 p
can show that !(S(q ) + (1+ 1)p q (1 + )c2q > S(q ) + p q
!
11
(1 + )c2q :6 In other words, uniform pricing induces a smaller network with
the same price for rural areas and achieves a lower level of social welfare with
a weight, !; that induces the same price in rural areas. We can therefore con
clude that, under complete information, favoring rural areas with proper price
discrimination is a better way of implementing redistribution than using uniform
pricing, if it is politically feasible.7
Assume now that the social planner has asymmetric information about c2:
The regulatory policy under uniform pricing (with ! = 1) can be de...ned as the
following direct revelation mechanism:
fp(e2); e(e2);t(e2)g with e2 in fc2;c2g:
c c c c
Then the following incentive constraints need to be satis...ed for the highcost
(badtype) ...rm:
t+( 1+ 2 )pq ( 1 1
c + 2 2
c )q C( ) t+( 1+ 2 )pq ( 1 1
c + 2 c2)q C( )
(10)
and for the lowcost (goodtype) ...rm:
t+( 1+ 2 )pq ( 1 1
c + 2 c2 )q C( ) t+( 1+ 2 )pq ( 1 1
c + 2 c2)q C( ):
(11)
The government needs to solve the following program for the optimal regulatory
policy:
Max
fq; ;U;q; ;Ug f( 1 + 2 )(S(q) + pq) (1 + )(( 1 1
c + 2c2 )q + C( )) Ug
+(1 )f( 1+ 2 )(S(q) + pq) (1 + )[( 1 1
c + 2 2
c )q + C( )] Ug
s.t. (8), (9), (10), and (11).
We can now state the next result:
Proposition 4 : Suppose that the government has asymmetric information
about c2 and uses uniform pricing. Then:
6Since p c2 1 1 p
p 1+ < 0, by collecting terms one has (1+ c2)[S(q ) p q ] >
p
0.
7However, since our focus is on pricing as a way of redistribution, we remain the assumption
of ! = 1 throughout the paper.
12
(1) When the size of information asymmetry c2 is large enough:
i) If c2 = c2, the optimal regulatory rule is the same as under complete
information with uniform pricing; and
ii) If c2 = c2, the price is higher and the network size smaller in the rural
area than under complete information with uniform pricing. Moreover, the price
is lower and the network smaller than under asymmetric information with dis
criminatory pricing.
More speci...cally,
pUSB = p1 ; USB =
1
USB
pUSB 1 1
c + 2 2
c USB
1 c2 1
1 + USB
2 2
= +
pUSB 1 + 1 + 1 USB USB
1 + 2 p
(1+ )C0( USB ) = 2 S(qUSB) + pUSBqUSB (1 + )c2qUSB c2qUSB ;
1
(2) When the size of information asymmetry c2 is small enough, bunching
occurs and optimal regulation entails:
USB
pUSB 1 1
c + 2[ c2+(1 )c2]
USB
1 c2 1
1+ USB
2 2
= +
pUSB 1 + 1 + 1 + USB USB
2 p
S(qUSB) + pUSBqUSB
C0( USB ) = 2[ ( c2+(1 )c2)qUSB c2qUSB]:
1 + 1 +
Proof: See the Appendix.
Under uniform pricing and asymmetric information, the optimal regulatory
rule is obtained when c2 = c2 that is, there is no distortion at top. But since
the government has to give up an information rent, 2 c2q; to the ...rm in
order to induce truthful revelation of its information, both the price and the
network size are distorted as a result of the e¢ ciencyrentextraction tradeo¤
when the ...rm has a highcost technology.
Uniform pricing under asymmetric information has two e¤ects on the pricing
decision. One is the direct e¤ect of asymmetric information, which leads to a
higher price. The other is the average marginal cost e¤ect caused by uniform
13
pricing, which tends to induce a lower price. The net e¤ect is in general am
biguous because the ...rstorder conditions are simultaneous equations of p and
. But if the size of information asymmetry c2 is large enough, under uniform
pricing the price for the rural area is higher than under complete information.
To determine the optimal network investment, one needs now to take into
account three e¤ects: In addition to the surplus e¤ect and the revenue e¤ect,
there is a direct e¤ect of asymmetric information that calls for a reduction of
the network size. The net e¤ect is to induce a smaller network if c2 is large
enough.
Next we compare these results with those under discriminatory pricing.
There are two e¤ects that need to be considered. In addition to the average
marginal cost e¤ect, which leads to a decrease in price, there is another e¤ect
which, by reducing information cost, also induces a lower price. Therefore, the
price under uniform pricing is always lower than under discriminatory pricing.
More speci...cally, denote p 1 1
p + 2 p2 as the average price under price dis
1+ 2
crimination, one can obtain that the price under uniform pricing is equal to
the average price under discrimination (p = pUSB) for a given size of the net
work. As a result the size of the network under uniform pricing is smaller than
under discriminatory pricing. We thus conclude that, while under asymmetric
information, uniform pricing does favor the rural people contrary to what was
observed under full information, it does so at the expense of network expansion,
therefore penalizing unconnected users (as well as future users).
An interesting additional result under uniform pricing is that bunching oc
curs if c2 is small enough. In that case optimization of the social welfare
calls for consumption and network investment to be decreasing functions of c2:8
But in the presence of asymmetric information, if c2 is small enough, the
secondorder condition of truthtelling requires both the consumption and the
network size be increasing functions of c2.9 These opposite monotonic con
ditions required by the optimization of the objective function and the imple
8Note that in the optimal allocation under complete information, monotonicity is satis...ed
if 1is large enough.
9Here the action space is two dimensional.
14
mentability of allocations or by satisfying incentive compatibility lead to the
nonresponsiveness result. That is, screening is no longer possible with uniform
pricing.10
5 Universal Service Policy Under Collusion
We now consider the possibility of collusion, to illustrate in a very simple setting
the impact of collusion on the optimal regulatory policy. For this purpose we
add to the basic principalagent relationship between the government and the
monopolist ...rm a hierarchical level representing the regulator of the ...rm. We
also consider other interest groups which have stakes in regulation. Indeed, a
special feature of this paper is that in addition to the threat of collusion between
the regulator and the ...rm, collusion may arise between the regulator and other
interest groups such as taxpayers and rural consumers.
Following Tirole (1986), we assume that the regulator's role is to bridge
the government's information gap about c2. Suppose the regulator has utility
function:
R(s) = s and s 0; (12)
where s is the regulator's reward. The regulator is risk neutral but is protected
by limited liability. Therefore, to obtain the regulator's participation he should
get at least his reservation utility level, which is normalized to be zero.
Assume that the regulator is endowed with an information technology that
he uses to obtain a private signal ( = c2) about the monopolist's cost in
the rural area with probability and learns nothing ( = ) with probability
1 : For simplicity we assume that the regulator's information is known to
the monopolistic ...rm and other possible interest groups. In other words, side
contracting is assumed to take place under complete information.11 To make
use of the regulator's information ; the government asks him to report the
10For an exposition of this non responsiveness result in a model with a single action see
La¤ont and Martimort (2002, p. 53).
11One can think of the principal as the public opinion and the regulator is an independent
regulator. Thus it is possible that many people such as the ...rm, urban and rural users, and
taxpayers are informed but the government is not.
15
signal he has received that is, r 2 fc2;c2; g: The critical assumption is that
the signal the regulator reports to the government is hard information when a
signal is reported to the government, it is hard evidence. But the regulator can
hide information and report that the signal is . If the regulator learns nothing,
he must report = : Thus the regulator has discretion only when he receives
a signal that reveals the ...rm's private information. The regulator's information
technology is summarized in the following table describing the probability of
each state of nature.
type c2 type c2
= c2 0
= (1 ) (1 )(1 )
= c2 0 (1 )
The timing of the regulatory game in the presence of a collusion threat
between the regulator and the monopolist and other interest groups is as follows.
The government o¤ers a grand contract after the regulator, the ...rm, and other
interest groups learn their respective information12. The regulator then makes
a takeitorleaveit o¤er to the ...rm and other interest groups and they decide
whether to accept this sidecontract. The government then asks the regulator
for a report about the monopolist's cost. When evidence is reported by the
regulator, the regulatory contract is chosen under complete information. But
when the regulator reports that he has learned nothing, the revelation game
under asymmetric information is played as in the previous section. Finally, the
...rm decides whether to accept the grand contract, and both the grand contract
and the side contract will be executed if they are accepted.13
To simplify exposition, the following notation is introduced: qc2 = q(c2 =
12One may be worried about the possibility of Maskin games (Maskin, 1999) that is,
pushing one group against another to verify information. Indeed, there might exist a more
general class of mechanisms (perhaps bizarre) such as asking urban users to predict what
the regulator would announce and give a small discount if they get it right and use this
information to regulate. However, as is standard in the literature, we will be restricting
attention to mechanisms in which is announced by the regulator and c2 by the ...rm.
13Note that under our assumption about the regulator's information technology, the poste
rior beliefs after an inconclusive signal (;) are identical to the prior beliefs:
(1 )
^ = = :
(1 ) + (1 )(1 )
16
c2; = c2); qc2 = q(c2 = c2; = c2); qc2 = q(c2 = c2; = ); and qc2 = q(c2 =
c2; = ). Other notation such as c; c ; c ; and c is similarly de...ned.
To analyze when collusion matters, assume that the secondbest contract
under discriminatory pricing is still o¤ered under the threat of collusion. Let us
look ...rst at what happens if the state of nature is c2 = c2 and = c2: In this
case the ...rm gets an information rent of SB
2 c2qSB if the regulator hides
2
the information that the ...rm is e¢ cient. So there is scope for collusion the
goodtype ...rm may bribe the regulator for his silence. Thus the government
has to satisfy the following coalition incentive constraint to induce the regulator
to tell the truth:
sf > k1 c
2 c2 qc2 ; (13)
where sf is the reward of the regulator if he reveals that the ...rm is type c2;
and k1 = 1 where represents the transaction cost between the regulator
1+ 1
1
and the ...rm. To focus on the interesting case we assume 1 > .14 Extending
Proposition 2 to take into account the cost of collusionproofness, we know that
for c2 = c2 the price and the network size are not distorted regardless of the
regulator's report. Thus consumers in the rural area are not a¤ected by the
presence of collusion in this state of nature. Similarly, urban consumers will not
collude with the regulator because of complete information about c1: Another
potential interest group is taxpayers, who are obliged to fund any de...cit due to
the lack of budget constraint for the ...rm. Nevertheless, because neither the price
nor the network size are distorted by the presence of asymmetric information,
taxpayers will pay the same amount of taxes under asymmetric information as
under complete information. So, taxpayers do not want to collude with the
regulator either. Thus sf > 0 is the only incentive payment to the regulator to
induce his truthful report:
Suppose the state of nature is c2 = c2 and = c2. In this case the ...rm does
not obtain any information rent even if the regulator hides the evidence. So,
the monopolistic ...rm does not want to collude with the regulator. Similarly,
urban consumers do not collude with the regulator. Moreover, we know from
14Otherwise, sidecontracting incurs a lower transaction cost than the social cost of public
funds and it is optimal to let collusion take place. So avoiding collusion is not an issue.
17
Proposition 2 that rural consumers would get a surplus of SB
2 (S(qSB)
2
pSBqSB) if the signal were concealed by the regulator, and
2 2 2 (S(q2) p2q2)
if the signal were truthfully revealed. Since asymmetric information leads to a
higher price and smaller network for the rural area under price discrimination
and S(q) pq is an increasing function of q in the relevant region, rural consumers
would obtain less surplus from collusion and so do not have any incentive to
collude with the regulator.
For taxpayers, however, if = c2 is reported to the government, they will
pay:
Tc = 1 q1(c1 p1) + 2 q2(c2 p2) + C( )
and
Tc = 1qSB(c1 pSB) + SB SB pSB) + C( SB )
1 1 2 q2 (c2 2
if is hidden. Since asymmetric information induces a higher price and smaller
network in the rural area, one can check that Tc < Tc. In other words,
taxpayers pay less to fund the de...cit if the regulator hides the information that
= c2. Thus taxpayers want to collude with the regulator if they can overcome
the organizational costs involved and ask the regulator to hide the signal = c2
in order to save a tax payment of Tc T : In this case the government has to
satisfy the following coalition incentive constraint:
st > k2(Tc Tc ); (14)
where k2 = 1 and denotes the transaction cost of sidecontracting between
1+ 2
2
the regulator and taxpayers. Again, we assume 2> to focus on the interesting
case where collusion is an issue. Assume also that the government's program
remains concave.
Let WFI(q1;q2;c c c) and WFI(q1 ;q2 ;
c c c ) denote the expected welfare un
der full information and under asymmetric information, respectively. The gov
ernment optimizes the following program to solve for the optimal regulatory
policy under the threat of collusion:
Max ) + (1 )WFI(q1 ;q2 ;
c c c )
fqc1;qc2;qc2 ;c c
; ;qc1;qc2;qc2 ;c c
; g f WFI(q1;q2;
c c c
k1 c
2 c2 qc2 (1 ) k2(Tc Tc )g
18
subject to constraints (7),(8),(9),(10),(13), and (14).
Note that when the state of nature is c2 = c2 and = c2; the government
does not need to give up any information rent but has to o¤er an incentive
payment, k1 c
2 c2 qc2 ; to the regulator in order to induce truthful revelation
of information. In that case regulation is made under complete information.
When the state of nature is c2 = c2 and = ; regulatory policies are made
under asymmetric information. In this case the government not only has to pay
the regulator's reservation utility level but has to give up an information rent,
c
2 c2 qc2 ; to the goodtype ...rm.
When the state of nature is c2 = c2 and = c2; the monopolistic ...rm does
not get any information rent. But the regulator receives an incentive payment
of st = 1 (Tc Tc ) to reveal his information.
1+ 2
We thus obtain the following result:
Proposition 5 : Assume that the government has asymmetric information
about c2 and uses discriminatory pricing15. Then the optimal regulatory re
sponse to the threat of collusion calls for:
i) When c2 = c2; the price and the network size in the rural area are the
same as ...rstbest allocations;
ii) When the state of nature is c2 = c2 and = , The regulatory response
is to reduce not only the information rent available to the ...rm but also the tax
savings to taxpayers. The optimal size of the rural network is smaller than
without the threat of collusion. Moreover, the optimal price for the rural area is
higher than in the absence of collusion if k1 > (1 1)k2=(1 1 ).
1+ 1+
iii) When the state of nature is c2 = c2 and = c2, The regulatory response
is to reduce the tax savings available to taxpayers. The optimal price for the
rural area is higher and the optimal size of the rural network is smaller than in
the absence of collusion.
15For simplicity we also assume that the secondorder condition for thuthtelling is satis...ed.
Otherwise, bunching occurs and collusion leads to less screening.
19
More speci...cally, the optimal regulatory policy entails:
pc = pc = p ; c = c =
2 2 2
pc2 c2 [1 + k2] = 1 1 [ k2 + (1 )]
pc2 1+ 1 1+ 1
+1+ 1 c2[ k1 + (1 )]
1 1 pc2
pc2 c2(1 1
+ k2) = (1 + k2)
pc2 1 + 1 +
C0( c )[(1 + ) k2] =
1 2 [S(qc2 ) + pc2 qc2 (1 + )c2qc2
qc2 c2 (k1 + (1 )) c2)
1 1 1 k2qc2 (pc2
C0( )[(1 + ) + k2] =
c
2[S(qc2) + pc2qc2 (1 + )c2qc2 + k2qc2(pc2 c2)]:
Proof: The proof of Proposition 5 is straightforward so it is omitted.
Under our assumptions the binding constraints are the participation con
straint of the badtype, the incentive constraint of the goodtype, and the
collusionproof constraints (13) and (14). When the state of nature is c2 = c2
and = c2; since the goodtype ...rm obtains an information rent of c
2 c2 qc2
if the regulator reports r = , the optimal regulatory response to the threat of
collusion between the ...rm and the regulator is to raise the price pc2 and reduce
the network size c . In other words, incentives given to the ...rm are weakened
to reduce the stake of collusion.
But when the state of nature is c2 = c2 and = c2; taxpayers receives a tax
saving of Tc Tc if the regulator conceals his information. In this case pre
vention of collusion requires lowering the price pc2 and raising the network size
c on the one hand, and raising the price pc2 and reducing the network size c
on the other, to reduce taxpayers'incentives in regulation. Since both incentive
payments to the regulator, sf and st; depend on the output qc2 , we have an
interesting case where, from the government's point of view, the monopolistic
...rm and taxpayers have similar incentives to collude with the regulator both
have stakes in ine¢ cient regulation. As a result the existence of one coalition in
centive constraint hardens the other one, even though these coalition constraints
are associated with di¤erent states of nature. Indeed, satisfying the coalition
20
incentive constraint between the regulator and taxpayers requires that the in
centive for taxpayers are weakened ( c and qc2 are increased); but raising c
and qc2 strengthens the incentives o¤ered to the ...rm which are socially costly.
However, it turns out that the need to reduce the stake of collusion between the
regulator and the ...rm dominates that between the regulator and taxpayers if
k1 is large or 1 small. The intuition is simple if the transaction cost between
the regulator and the ...rm is small, the collusion threat is then more likely to
be an issue than that between the regulator and taxpayers. Consequently, the
price in the rural area will be higher than without collusion. Conversely, the
presence of collusion induces a lower price for the rural area if k1 is small.16
At this stage one may wonder whether the result about collusion under dis
criminatory pricing also holds under uniform pricing. We show this robustness
result in the appendix and limit ourselves only with collecting the result below.
Proposition 6 : Assume that the government has asymmetric information
about c2 and uses uniform pricing. Then the optimal regulatory response to
the threat of collusion entails:
(1) When c2 = c2; the allocations are the same as under complete informa
tion;
(2) When the state of nature is c2 = c2 and = :
i) The price for the rural area is lower and the size of network is smaller
than under discriminatory pricing, and
ii) If k1 is large, the price for the rural area is higher and the network size
smaller than in the absence of collusion;
(2) When c2 = c2 and = c2, the price is higher and the network size
smaller in the rural area than in the absence of collusion.
Proof: See the Appendix.
16It is interesting to note that this result is similar to La¤ont and Tirole (1993, p. 490)
where the existence of a di¤erent interest group (environmentalists) increases the ...rm's rent.
In both cases the ...rm and taxpayers have a stake in making regulation ine¢ cient.
21
As for the case of discriminatory pricing, the monopolistic ...rm's incentives
are weakened by the existence of taxpayers as an interest group. Moreover,
allocations are distorted when c2 = c2 and the regulator learns this information
and then reports it to the government. But in both states of nature c2 = c2 and
= and c2 = c2 and = c2; the price for the rural area is lower and the size
of the network is smaller than those under discriminatory pricing.
6 Conclusion
This paper has built a formal model to analyze the optimal regulatory policy
associated with universal service obligations. In particular, it has examined
how optimal universal service policy is a¤ected by asymmetric information and
the threat of regulatory capture under both discriminatory pricing and uniform
pricing. The ...ndings show that under both types of pricing, asymmetric infor
mation leads to a higher price and smaller network in the rural area and the
collusion threat weakens the incentives given to the serviceproviding ...rm. In
addition, although uniform pricing may achieve the redistributive goal of a lower
price for the rural area, it is at the cost of a smaller network.
One of the main policy implications of these results is that when uniform
pricing is used to favor rural consumers, consumers who are not connected
may be adversely a¤ected because less investment is directed towards network
expansion. Thus uniform pricing may not achieve the goal claimed by policy
makers of promoting increased access to infrastructure services an urgent need
in developing countries. On the contrary, network expansion may be delayed
precisely because rural consumers are favored in pricing. Thus one general lesson
from this paper is that one cannot isolate the network investment problem from
pricing policy.
Because developing countries have not yet developed su¢ cient infrastructure
networks to provide services to all members of society, network expansion is an
extremely important development strategy for these countries. Indeed, in many
developing countries poor people are willing to pay a high price to access to
22
basic infrastructure services. But since there is no network in place, they are
deprived of the services. Thus governments in developing countries should pay
more attention to providing incentives for network investments rather than to
distorting prices.
Another contribution of the paper is to provide a better description of the
losers and winners in the universal service policy game. Furthermore, as the
agencybased theory of capture has shown, having a stake is a necessary but not
su¢ cient condition for an interest group to potentially be able to capture the
regulator. Accordingly, we have characterized the optimal regulatory responses.
Ultimately, one of the main results may be that the universal service policy is
easily manipulated.
Acknowledgements
We thank especially Jean Tirole for his very detailed comments and sugges
tions and the participants at the IO workshop at Guanghua Management School
of Beijing University for their comments.
23
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24
La¤ont, J.J., Tirole, J., 2002. Competition in Telecommunications. MIT
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.
25
Appendix
Proof of Proposition 1:
The ...rstorder conditions with respect to q1, q2, (and similarly for those
with respect to q , q , ) are:
1 2
1(S0(q1) + p01q1 + p1) (1 + ) 1 1
c = 0 (15)
2 (S0(q2) + p02q2 + p2) (1 + ) 2 c2 = 0 (16)
2(S(q2) + p2q2) (1 + )( 2 2
c q2 + C0( )) = 0: (17)
Since C00 > 0, a su¢ cient condition for the concavity of the objective function
is jS00j large enough.
The determination of p2 and is illustrated in Figure 1.
p2
6 (17)
(16)

Figure 1
Equation (16) determines q2 according to the Ramsey rule.17 For this level
17There is of course an one to one relationship between p2 and q2.
26
of q2, (17) determines .
Proof of Proposition 2:
Since only q2 and are a¤ected by asymmetric information, we only consider
the ...rstorder conditions with respect to q2 and :
2 c2 + (1 )[ 2(S0(q2) + p02q2 + p2) (1 + ) 2 2
c ] = (18)
0
2 c2q2 + (1 )[ 2 (S(q2) + p2q2) (1 + )(2 2
c q2 + C0( )] = (19)0
jS00j large enough ensures concavity.
Denote
U(c2;e( )1c1tq((ep1)(c+
c2 c2 1 1 c2 c
as the utility the ...rm obtains when its report about c2 is e2: Proceeding as if
e2)) +p (e2c)2q((pe(e2)) +c
c2 1 c 2
c2)q(p2(e2)))(e2Cp( ((ee)q(p2(e2))
c ) 2
c2))
c
c2 was a continuous variable, the ...rstorder condition for truthtelling is:
t_ + 1(p_1q10 p1 + p_1q1) + 2 _ p2q2 + 2(q2p_2 + p2p_2q20 )
( 1 1
c q10 p_1 + 2 2
c (_q2 + q20 p_2)) C0( )_ = 0:
The secondorder condition for truthtelling is:
2( _ q2 + q20 p_2) 0:
Since q20 < 0, a su¢ cient secondorder condition is _ < 0 and p_2 > 0. So,
the strategy is to solve the problem in the absence of the secondorder condition
and check ex post that the su¢ cient condition _ < 0 and p_2 > 0 is satis...ed (see
Guesnerie and La¤ont (1984)).
We can easily represent the impact of asymmetric information on Figure 1
by looking at equations (18) (19). We obtain Figure 2.
27
p2 (19)
(17)
6
(18)
(16)

Figure 2
Therefore pSB > p2 > p2 = pSB and SB < < = SB . So the
2 2
secondorder condition of incentive compatibility is satis...ed.
Proof of Proposition 3:
The ...rstorder conditions with respect to q and are:
( 1 + 2 )(S0(q) + p0q + p) (1 + )( 1 1
c + 2 2
c ) = 0 (20)
2(S(q) + pq) (1 + )( 2 2
c q + C0( )) = 0: (21)
From secondorder conditions, the objective function is concave if the fol
lowing conditions are satis...ed:
( 1+ 2 )(S00(q) + p00q + 2 p0) < 0
C00( )( 1 2 1
(c c2)
1 + 2 )(S00(q) + p00q + 2 p) > (1 + )[ ]2:
1+ 2
So a su¢ cient condition for the concavity of the objective function is jS00j large
enough.
Since < c2; we have p < p2 and p < p : Moreover, since p2
1 1
c + 2 2
c
1 + 2 2
maximizes S(q2)+ p2q2 S0(q )+ p 0q + p c2 < 0 by substituting
1+ c2q2 and 1+
the ...rstorder conditions, one obtains that < : Similarly, < .
28
Proof of Proposition 4:
The ...rstorder conditions are:
1 c2 +(1 )[( 1 + 2 )(S0(q)+ p0q + p) (1+ )( 1 1
c + 2 2
c )] = 0
1 c2q + (1 )[ 2(S(q) + pq) (1 + )( 2 2
c q + C0( ))] = 0:
One can show that a su¢ cient condition for the concavity of the objective
function is jS00j large enough.
c t(e2)+(
c 1+ 2 c c c 1 1
c + 2 2 c c
dition for truthtelling is (for a continuous variable c2):
C( (e2)) as the ...rm's utility when e2 is its report about c2. The ...rstorder con
Denote U(c2;e2)
c c (e2))p(q(e2))q(e2) ( c (e2))q(e2)
t_+ 2_ p(q)q + ( 1 + 2 )(p0qq + pq_)
_ 2 2
c _q ( 1 1
c + 2 2
c )q_ C0( )_ = 0:
The secondorder condition is:
2_ q 2 q_ 0:
A su¢ cient condition for the secondorder condition to be satis...ed is pUSB >
pUSB and USB < USB ; which implies:
USB USB c +
1 1
c + 2 2
c 2 c2 1 1 2 c2
+ >
USB 1 + 1 USB +
1 + 2 1 + 2 1 2
S(qUSB) + pUSBqUSB S(q ) + p q
qUSBc2 c2qUSB < q c2:
1 + 1 + 1 1 +
Thus a su¢ cient condition for the secondorder condition of truth telling to
be satis...ed is c2 large enough. However, if c2 small enough, we have pUSB <
pUSB and USB > USB : Then bunching occurs so that pUSB = pUSB = pUSB
and USB = USB = USB :
Let us now compute the condition that ensures pUSB > p and USB < .
From the ...rstorder conditions we have:
USB USB
1 1
c + 2 2
c 2 c2 1 1
c + 2 2c
+ >
USB 1 + 1 USB +
1 + 2 1 + 2 1 2
29
or pUSB > p if c2 is large enough. Similarly, USB < if c2 is large
USB USB
enough: Finally, since + is always smaller
1 1
c + 2 2
c 2 c2
1 + USB
2 1+ 1 1+ USB
2
than c2 + c2; we have pUSB < pSB. Moreover, since pSB optimizes
1+ 1 2 2
S(q2)+ p2q2 USB < SB :
1+ q2c2 1+ 1 c2q2; we have
Proof of Proposition 6:
De...ne quc = q(c2 = c2; = c2); quc = q(c2 = c2; = c2); quc = q(c2 =
c2; = ); and quc = q(c2 = c2; = ). Other notation such as uc; uc ; uc;
and uc is similarly de...ned.
If c2 = c2 and = c2; the good type ...rm will get an information rent of
c
2 c2 qc if the regulator hides the information. Thus the government has
to satisfy the following collusionproofness constraint to induce truthtelling by
the regulator:
suf > k1 uc
2 c2 quc : (22)
As with discriminatory pricing, rural consumers do not have any stake in
collusion because neither the price nor the size of the network is distorted if c2 =
c2. Since c1 is common knowledge, urban consumers cannot collude with the
regulator, even though they are adversely a¤ected by uniform pricing. Similarly,
taxpayers will pay the same amount of taxes regardless of the regulator's report.
Suppose the state of nature is c2 = c2 and = c2: The ...rm does not have
any stake in collusion any more because it does not get any information rent
when c2 = c2. We know from Proposition 4 that when asymmetric informa
tion is large enough, the price for the rural area is higher and the network
smaller if the regulator hides his information. Thus uc
2 (S(quc) pucquc)>
uc
2 (S(quc ) puc quc ) that is, rural consumers obtain less surplus if the
regulator does not report truthfully, so they have no incentive to collude. Sim
ilarly, collusion between urban consumers and the regulator is not an issue in
this state of nature.
Note that taxpayers pay Tuc = ( uc
1 1
c + 2 2
c )quc ( uc
1 + 2 )pucquc +
C( uc) if the signal is revealed and Tuc = ( c
1 1
c + 2 2
c )quc ( 1 +
30
uc
2 )puc quc +C( uc ) if not. Since ( 1 1
c + 2 2
c )q ( 1+ 2 )pq+C( ) >
0 if C0( ) is large enough, the taxpayers save a tax payment of Tuc Tuc > 0
if the regulator reports r = . So they have incentives to collude with the reg
ulator. Thus the government needs to satisfy the following collusionproofness
constraint:
sut > k2[( uc uc uc
1 1
c + 2 2
c )quc ( 1 + 2 )pucquc + C( )
( uc
1 1
c + 2 2
c )quc + ( uc
1 + 2 )puc quc uc
C( )]:(23)
Manipulation of ...rstorder conditions leads to the following result:
puc = puc = p , uc = uc =
pc 1c1+ 2c2 c
(1 k2)
1+ 2 c 1+ 1
=
pc
uc
1 + k2(1 1 ) + 1 [ k1 + (1 )]
2 c2 1
1+ 1+ 1 1+ 1 1 1+ uc
2 puc
uc
puc 1c1+ 2c2 (1 k2)
1+ 2 uc 1+ = 1 1)
puc k2(1
1+ 1+
C0( uc )(1 k2) = [S(quc )+ puc quc c2qc quc c2 (k1 + (1 ))
1+ 1 2 1+ 1+ 1 1
k2quc (puc c2)]
1+ 1
C0( uc)(1 + k2) = [S(quc)+ pucquc c2quc + k2quc(pc c2)]:
1+ 1 2 1+ 1+
31