Price cap regulation in the Mexican telephone industry

INFORMATION

www.elsevier.com/locate/econbase

Information Economics and Policy 17 (2005) 231–246

ECONOMICSAND POLICY

Price cap regulation in the Mexicantelephone industry

Daniel Flores

Facultad de Economıa, Universidad Autonoma de Nuevo Leon, Loma Redonda 1515 Pte., Col. Loma

Larga, 64710 Monterrey, Mexico

Received 1 January 2001; received in revised form 18 May 2004; accepted 3 June 2004

Available online 23 August 2004

Abstract

This paper presents a model to analyze price cap regulation of the Mexican telephone

industry. There is a vertically integrated firm that is a monopolist in the local service market

and a duopolist in the long-distance service market. A regulator sets the access price and a

price cap on the basket of final services provided by the integrated firm. We show that this type

of price cap can increase the profits of this firm in the downstream market. Moreover, this con-

straint can actually increase its overall profits and reduce the profits of the downstream rival.

� 2004 Elsevier B.V. All rights reserved.

JEL classification: D42; D43; L51

Keywords: Access; Price cap regulation; Telecommunications

1. Introduction

The Mexican telephone industry was privatized and opened to competition during

the nineties. At the beginning of the decade, regulation was established to privatize

the state-owned company Telefonos de Mexico (TELMEX). After privatization,

TELMEX remained as the sole provider of local and long-distance telephone

0167-6245/$ - see front matter � 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.infoecopol.2004.06.002

E-mail addresses: [email protected], [email protected].

mailto:[email protected].

232 D. Flores / Information Economics and Policy 17 (2005) 231–246

services for several years. This was part of an agreement where TELMEX was

granted a temporal monopoly in exchange for the compromise to expand and im-

prove the local telephone network. 1 However, the monopoly in the long-distance

market ended in 1997 when other firms were allowed to enter the market and com-

pete with TELMEX�s long-distance service subsidiary.The basic problem in the Mexican telephone industry, since the moment long-dis-

tance service was opened to competition, has been to regulate a firm that owns the

local telephone network and competes with other firms in the long-distance market.

Since the local network is essential to produce long-distance service, there is concern

on the incentive that TELMEX has to provide itself competitive advantage in the

downstream market.

When competition was introduced, the regulatory framework for TELMEX in-

cluded a combination of an access price, a price cap and price floors. A national reg-ulator (Comision Federal de Telecomunicaciones or COFETEL) was in charge of

setting the price at which TELMEX provides access to its downstream rivals; 2

the maximum price for a basket of services that TELMEX provides to final consum-

ers, including local and long-distance telephone services; and minimum prices for

each of the services in the basket based on long run incremental costs. 3

TELMEX�s downstream competitors complained about the regulatory frame-

work, arguing that it was designed to favor TELMEX. By September 2000, after

a long legal process, COFETEL issued additional regulation for TELMEX in an at-tempt to foster downstream competition. Among other things, COFETEL estab-

lished a new criterion for calculating price floors for national and international

long-distance services. The new regulation stated that the weighted average price

of national (international) long-distance services should not be lower than its total

average cost, including the cost of capital. Apparently, price floors calculated on

TELMEX�s long run incremental cost were not high enough to prevent a price

squeeze.

It is easy to understand that the access price generates a conflict between accessseekers and TELMEX. Also, that price floors are useful to avoid predation. 4 But

other aspects of the regulation are difficult to understand. For examples, the effects

of a price cap, like the one faced by TELMEX, when there is imperfect competition

in the downstream market. Torre (2000) claims that the price cap is an important

flaw in the Mexican regulatory framework because it harms TELMEX�s downstreamcompetitors. However, there is no formal analysis to support this statement.

1 A similar privatization process took place in Argentina. However, the market for local telephone

service was divided in two parts, each licensed to a different firm for a period of 7 years. See Baumol and

Beker (1998) for an analysis on the privatization of telephone industry in Argentina.2 Before this regulation was established, TELMEX and access seekers had the opportunity to negotiate

the terms of access. However, negotiations were not successful and COFETEL ended up determining the

terms of access. See King and Maddock (1999) for a study of access based on negotiation.3 See Weisman (2002) for an explanation on price floors or imputation constraints.4 See Sappington and Weisman (1996).

D. Flores / Information Economics and Policy 17 (2005) 231–246 233

This paper uses a Cournot model to analyze the effects of price cap regulation in

the Mexican telephone industry. TELMEX will be represented by a vertically inte-

grated firm. This firm is a monopolist in the upstream market and a duopolist in

the downstream market. We find that a small decrease of the price cap can increase

the profits of this firm in the downstream market. Moreover, it can actually in-crease the overall profits of this firm and reduce the profits of its downstream

competitor.

This paper differs from most of the literature on the regulation of telephone indus-

try in several ways. The main difference is that most of the literature studies optimal

access price design but this paper will examine the effects of access price changes or

price cap changes on firms� profits. The motivation for this approach is to identify

potential ways in which a regulator can use common regulatory tools, such as the

access price or the price cap, to benefit a vertically integrated firm. The main resultsof the paper can be related to the works of Economides (1998), King and Maddock

(1999) and Mandy (2000) on sabotage; similarly, to the work of Bulow et al. (1985)

on the behavior of multi-market oligopolies.

The remaining of the paper is organized as follows. Section 2 presents the basic

elements of the model. Section 3 considers a benchmark setting with no price cap

to analyze whether a vertically integrated firm would increase the access price to ex-

clude its downstream rival from the market. Section 4 derives the main result of the

paper regarding the effects of a price cap reduction on firms� profits. Section 5 illus-trates this result with a numerical example. Section 6 summarizes the results of the

paper.

2. The model

There is a vertically integrated firm, hereinafter called the operator, that provides

local and long-distance telephone services. There is also a firm called the rival. Thisfirm requires access to the local network of the operator in order to provide long-

distance service. Assume that consumers regard local and long-distance services as

independent goods. In particular, suppose that inverse market demand for local

telephone service is

plðqlÞ ¼ max 0; al � bl � qlf g; ð1Þ

where ql denotes the output of the operator. Similarly, that inverse market demandfor long-distance telephone service is

pðqo þ qrÞ ¼ max 0; a� b � qo þ qrð Þf g; ð2Þ

where qo and qr represent the output of the operator and the rival, respectively.

The cost structure is shown in Fig. 1. For simplicity, we ignore fixed costs and as-

sume that each unit of long-distance service requires a unit of local service. The oper-

ator provides local telephone service at constant marginal cost cl and long-distance

lc

w

Local network

Operator

rc

Rival

oc

External network

lc

Fig. 1. The cost structure.


service at cl + co. The rival provides long-distance service at constant marginal cost

w + cr,5 where w is the regulated access price. Note that the operator receives w � cl

as net payment for each unit of long-distance service that its rival sells.We model competition in the downstream market as a Cournot game where firms

choose output levels simultaneously. Each firm takes its output to the market and

sells it at the market-clearing price. It is beyond the scope of this paper to determine

whether a Bertrand or Cournot framework is more appropriate to model imperfect

competition in the telephone industry. Some authors like Lewis and Sappington

(1999) model downstream competition as a Bertrand game with differentiated prod-

ucts, others like Weisman and Kang (2001) or Mandy (2000) follow Economides

(1998) by considering a Cournot game instead. It is not difficult to argue in favorof either model. For instance, we recognize in favor of Bertrand�s model that firms

choosing prices seems a more natural assumption than firms choosing output levels.

However, it also seems natural to assume that firms providing long-distance tele-

phone services produce perfect substitutes. If this is the case, Cournot�s model yields

a more convincing result than Bertrand�s. 6

In addition to the access price, a national regulator determines the maximum

price, �p, for a basket of services that the operator provides to final consumers. As-

sume for simplicity that this basket contains one unit of local service and one unitof long-distance service. 7 In the context of this model, the constraint on prices im-

plies that the operator has to choose ql and qo to keep the sum of its corresponding

prices below certain value (i.e., plðqlÞ þ pðqo þ qrÞ6 �p).Let po and pr denote profits of the operator and the rival, respectively. The oper-

ator chooses ql and qo to maximize

5 Si6 K

first ch

use of7 F

and Ti

po ¼ pl qlð Þ � cl½ �ql þ p qo þ qrð Þ � cl � co½ �qo þ w� clð Þqr ð3Þ
subject to plðqlÞ þ pðqo þ qrÞ6 �p, while the rival chooses qr to maximize
milar cost structure is adopted in Laffont and Tirole (1996) and Lewis and Sappington (1999).

reps and Scheinkman (1983) show that Cournot outcome can arise in a two-stage game where firms

oose production capacities and then compete in prices. This can be used as an argument to favor the

Cournot�s model.

or an analysis of different price cap regulation plans see Sappington and Weisman (1996) or Laffont

role (1996).


pr ¼ p qo þ qrð Þ � w� cr½ �qr: ð4Þ

3. Benchmark setting with no price cap

In this section, we consider a benchmark setting where the integrated firm faces

either no price cap regulation or a non-binding price cap. If this occurs, the operator

can choose ql and qo independently. The optimal local service output is

ql clð Þ ¼ al � cl2bl

: ð5Þ

The optimal long-distance service output for each firm depends on the choice of

its competitor. Simple calculations lead to the reaction functions:

qo qr; cl; coð Þ ¼ a� bqr � cl � co2b

; ð6Þ

and

qr qo;w; crð Þ ¼ a� bqo � w� cr2b

: ð7Þ

The Nash equilibrium is a pair (qo, qr) that solves (6) and (7) simultaneously, thatis

qo w; cr; cl; coð Þ ¼ aþ wþ cr � 2 cl þ coð Þ3b

; ð8Þ

and

qr w; cr; cl; coð Þ ¼ aþ cl þ co � 2 wþ crð Þ3b

: ð9Þ

Some implications of this benchmark model are obvious from Eqs. (8) and (9).

For example, a higher (lower, respectively) access price allows the operator (rival,

respectively) to increase its share of total output in the long-distance market. In addi-

tion, it reduces (increases, respectively) total output. It is straightforward to deter-

mine the effect of a change in total output on the price of long-distance service.

Proposition 1. A decrease in the access price lowers the price of long-distance service

but has no effect on the price of local service (assuming the price cap is not binding

before and after the change in the access price).

Proof. Eqs. (8) and (9) imply that total long-distance output increases. Thus Eq. (2)

implies a lower price. It follows from Eqs. (1) and (5) that the optimal price for local

service does not depend on the access price. h

The intuition behind the first part of the result is simple, a change in the access

price is equivalent to a change in the marginal cost of the rival. Thus, a reductionin the rival�s marginal cost leads to an increase in total output and consequently to

a lower price. The second part of the result, that a change in the access price has

no effect on the price of local service, is not difficult to understand. A multiproduct


firm alters the price it charges in one market in response to a shock in other market

when there is market interdependence. There are three ways in which markets could

be interdependent: demand interdependence, cost interdependence and a composite

binding price cap. 8 None of these alternatives takes place in the model so far.

Several issues can be addressed with this model before considering a binding pricecap: among others, whether the integrated firm would maximize profits by setting an

access price that is high enough to exclude its competitor from the long-distance

market. 9 This can be an important issue, in spite of access price regulation, if there

is sufficient evidence to believe that regulatory capture is taking place. A similar con-

cern arises when an upstream monopolist is able to increase the marginal cost of its

downstream rivals, presumably through quality degradation. In this context, Econo-

mides (1998) claims that regardless of the relative efficiency of competitors with re-

spect to its downstream subsidiary, the monopolist has an incentive to increase thecost of its competitors until they are driven out of the market. 10

In the current model, the relative efficiency of the operator and the rival in the

production of long-distance service is crucial to determine whether the vertically inte-

grated firm has an incentive to exclude its rival from the market.

Proposition 2. Let w be the minimum access price that drives the rival out of the

market. 11If the operator is allowed to set the access price, w, then it would choose:

(i) cl < w < w, not excluding its rival from the market, if the rival is relatively more

efficient in the production of long-distance service (i.e, cr < co),

(ii) w P w, excluding its rival from the market, if the rival is relatively less efficient in

the production of long-distance service (i.e., cr P co).

Proof. Consider the derivative of the operator�s profits with respect to the access

price. It follows from the envelope theorem that

8 B

affect t9 F

that th

thereb10 O

(2000)

accord

efficien

price d11 It

dpo

dw¼ 2q�o

3þ q�r �

2

3bw� clð Þ: ð�Þ

It is not difficult to see that the derivative is positive for any w 6 cl and that the prof-

it function po(w) is concave (i.e., p00oðwÞ ¼ �10=9b) as long as q�o > 0 and q�r > 0.

Thus, the operator will always choose w > cl. Note also that increasing the access

price is inconsequential once the access price is high enough to drive the rival out

ulow et al. consider demand or cost interdependence to explain that a shock in one market may

he profits of a multimarket firm by influencing rivals� strategies in a second market.

or instance, ‘‘If the network operator is also a supplier of final products, there is the obvious danger

is integrated firm will seek to exclude competing final product suppliers by setting high access prices,

y raising rival�s cost’’ (Armstrong et al. (1996, p. 131)).

ther authors use similar models to explain that this claim is not generally true. For instance, Mandy

says that the incentive to non-price discriminate is theoretically ambiguous but likely to occur

ing to US telecommunications industry data, while Weisman and Kang (2001) find that large

cy superiority of downstream rivals is required to eliminate the incentives of the monopolist to non-

iscriminate.

is not difficult to find that q�r ¼ 0 implies w � aþclþco2

� cr.


of the market, that is, w > w is equivalent to w = w). Thus, the problem of the oper-

ator can be simplified to the choice of w2(cl,w].Evaluate (*) at w = w (remember that q�r ¼ 0 in this case) and substitute Eq. (8) to

find

12 It

dpo

dw

��w¼w

¼ 2q�o3

� 2

3bw� clð Þ ¼ 2

9baþ cl � 2co � 2wþ crð Þ: ð��Þ

Since w ¼ aþclþco2

� cr it follows that

dpo

dw

��w¼w

¼ 2

3bcr � coð Þ:

The concavity of po(w) implies that the operator sets w < w, not excluding its rival

from the market, if cr < co; similarly, that it sets wP w, excluding its rival from

the market, if crP co. h

In principle, it is not difficult to see that a higher access price does not necessarily

benefits the operator. This firm profits from three sources: local, long-distance and

access services. Profits from local service can be ignored because they do not depend

on the access price. Profits from long-distance service increase because a higher ac-

cess price raises the marginal cost of the rival. However, the effect on access profits is

ambiguous because the access price is higher but the rival�s output is lower. Thus, itis possible that higher profits from the downstream market are not sufficient to com-

pensate lower profits from access services.Why is relative efficiency crucial to determine whether the operator excludes its

downstream competitor? Consider an integrated firm that increases the access price

to the point where its competitor exits from the downstream market (i.e., w = w). If

this is the case, the operator sets the monopoly price pm for long-distance service. 12

The surplus of this firm for each unit of long-distance service it sells is pm � co � cl.

However, by letting its rival produce long-distance service instead of its subsidiary at

the margin, the operator could make w � cl. Since w = pm � cr, it follows that

w � cl = pm � cr � cl. In other words, the operator can use the access price to extractall the surplus of its downstream rival at the margin. This surplus is higher than the

one the operator currently obtains if and only if the rival is relatively more efficient.

In spite of the similarity between access price and quality degradation as tools the

upstream monopolist can use to increase the rival�s cost, there is no conflict between

Proposition 2 in the current paper and the claim in Economides (1998). There is a

fundamental difference between the two variables in question. While the only effect

of quality degradation is to increase the rival�s marginal cost, a higher access price

has the additional effect of increasing the marginal profitability of access services.Therefore, the upstream monopolist has less incentive to exclude its downstream riv-

al from the market by increasing the access price than by increasing its marginal cost

through quality degradation.

is not difficult to find that pm ¼ aþclþco2

.


4. Analysis of a setting with a binding price cap

A composite price cap can establish a link between two apparently unrelated mar-

kets. For instance, once the operator chooses output for the long-distance market,

the price cap and the choice of its rival automatically determine output in the othermarket. That is,

pl qlð Þ þ p qo þ qrð Þ ¼ al � blql þ a� b qo þ qrð Þ ¼ �p ð10Þ
implies:
ql �p; qo þ qrð Þ ¼ al � �p þ a� b qo þ qrð Þbl

: ð11Þ

If the problem is defined in this manner, the equilibrium is a pair (qo, qr) such that

qo is an optimal response to qr, and vice versa. Since the rival is not subject to the

price cap, it still maximizes (4) and its reaction function is still (7). However, the

operator�s reaction function is now

qo qr; cl; co; �pð Þ ¼ 2bþ blð Þ a� bqrð Þ þ bal � 2b�p � cl bl � bð Þ � cobl2b bþ blð Þ : ð12Þ

The Nash equilibrium is given by:

q�o ¼2b aþ wþ cr þ cl þ alð Þ þ bl aþ wþ cr � 2co � 2clð Þ � 4b�p

b 2bþ 3blð Þ ð13Þ

and

q�r ¼bl aþ co þ cl � 2w� 2crð Þ � b al þ cl þ 2wþ 2crð Þ þ 2b�p

b 2bþ 3blð Þ ; ð14Þ

which can be used to find the equilibrium price of long-distance service

p� ¼ bl aþ co þ cl þ wþ crð Þ � b al þ clð Þ þ 2b�p2bþ 3bl

; ð15Þ

the price of local service

p�l ¼b al þ clð Þ � bl aþ co þ cl þ wþ crð Þ þ 3bl�p

2bþ 3blð16Þ

and finally, to calculate the equilibrium local service output

q�l ¼b al � clð Þ þ bl aþ co þ cl þ wþ cr þ 3alð Þ � 3bl�p

bl 2bþ 3blð Þ : ð17Þ

As mentioned before, the price cap links the two markets. Thus a shock in one of

the markets, for example a change in the access price, can affect the operator�s behav-ior in the other market.

Proposition 3. A decrease in the access price generates a lower price for long-distance

service but a higher price for local service (assuming the price ceiling is binding before

and after the change in the access price).


Proof. Eq. (15) implies that the price for long-distance services decreases and Eq.

(16) that the price for local services increases. h

It is not difficult to provide an intuitive explanation of this result. When the price

cap is binding, the operator is forced to provide more output than the unconstrained

optimum in the local service market. Since a lower access price generates a lowerprice for long-distance service, it allows the operator to reduce output in the local

service market and approach the unconstrained optimum.

The main point of this paper is to analyze the effect of a price cap on firms� profits.A constraint is usually considered a disadvantage for the firm and in most of the

cases it is. However, the opposite can occur in the context of an oligopoly model

due to the strategic effect. A firm can actually obtain higher profits when facing a

constraint because its rival�s strategy changes once it knows that the firm has to sat-

isfy the constraint. A similar argument is used to explain the counterintuitive resultin Bulow et al. where the total profits of an integrated firm are reduced when it re-

ceives a per unit subsidy in its monopoly market. In their example, market demands

are independent but the integrated firm has joint diseconomies of scope.

Before showing that a price cap can increase the overall profits of the incumbent,

it is useful to define B as the point where the price cap just binds and poð�pÞ as themaximized profits function of the incumbent under a binding price cap. 13 That is

13 In

�p ¼ B

B � 13aþ wþ cr þ coð Þ þ 5

6cl þ

al2; ð18Þ

and

po �pð Þ � p�l �pð Þ � cl� �

q�l �pð Þ þ p� �pð Þ � cl � co½ �q�o �pð Þ þ w� clð Þq�r �pð Þ; ð19Þ

Note that profits with and without the price cap are equal at the point where the

constraint just binds. In other words, we can obtain unconstrained maximized profits

by evaluating (19) at �p ¼ B. For the purpose of this analysis, imposing a price cap is

equivalent to reducing it from the point where it just binds.The first step towards the main result of the paper is to establish the shape of the

maximized profit function under the constraint.

Proposition 4. The profit function of the incumbent under a binding price cap, poð�pÞ, isstrictly concave.

Proof. Consider the first and second derivatives of poð�pÞ with respect to �p. That is,

dpo �pð Þd�p

¼ p�l �pð Þ� cl� �oq�l �pð Þ

o�pþq�l �pð Þop

�l �pð Þo�p

þ p� �pð Þ� cl� co½ �oq�o �pð Þo�p

þq�o �pð Þop� �pð Þo�p

þ w� clð Þoq�r �pð Þo�p

and

other words, B is the least upper bound of the set of binding price caps. It is not difficult to see that

makes (5), (8) and (9) equal to (17), (13) and (14), respectively.


d2po �pð Þd�p2

¼ p�l �pð Þ � cl� � o2q�l �pð Þ

o�p2þ oq�l �pð Þ

o�pop�l �pð Þo�p

þ q�l �pð Þ o2p�l �pð Þo�p2

þ op�l �pð Þo�p

oq�l �pð Þo�p

þ q�o �pð Þ o2p� �pð Þo�p2

þ op� �pð Þo�p

oq�o �pð Þo�p

þ p� �pð Þ � cl � co½ � o2q�o �pð Þo�p2

þ oq�o �pð Þo�p

op� �pð Þo�p

þ w� clð Þ o2q�r �pð Þo�p2

;

respectively.It follows from (13)–(17) that q�l ; p�l ; q�o; q�r and p� are linear functions of the

price cap. Thus the second derivative can be simplified to:

d2po �pð Þd�p2

¼ 2oq�l �pð Þo�p

op�l �pð Þo�p

þ oq�o �pð Þo�p

op� �pð Þo�p

� �¼ �2

2bþ 3bl

9

2bþ 3blþ 2cobþ bl

� �

< 0: �

The second step is to establish the slope of the profit function at �p ¼ B. That is, atthe point where the price cap just binds.

Proposition 5. Suppose that the price cap is just binding at the current value of �p (i.e.,�p ¼ B). A small reduction of �p increases the operator�s profits if

2co + 2w � cl � cr � a < 0.

Proof. Eq. (19) can also be written as follows:

po ql �pð Þ þ qo �pð Þð Þ ¼ p�l ql �pð Þð Þ � cl� �

q�l �pð Þ þ p� q�o �pð Þ þ q�r �pð Þ� �

� cl � co� �

q�o �pð Þþ w� clð Þq�r �pð Þ:

Consider the derivative of this function with respect to �p,

dpo

d�p¼ p�l � cl þ q�l

op�loql

� oq�lo�p

þ p� � cl � co þ q�oop�

oqo

� oq�oo�p

þ q�oop�

oqrþ w� cl

� �oq�ro�p

: ð�Þ

Since the price cap is just binding at �p ¼ B, the envelope theorem implies that

dpo

d�p

��p¼B

¼ q�oop�

oqrþ w� cl

� �oq�ro�p

:

Eq. (14) implies that the partial derivative of q�r with respect to �p is positive. It fol-

lows from (2) and (8) that

signdpo

d�p

��p¼B

¼ sign 2co þ 2w� cl � cr � að Þ: �

This proposition presents a necessary and sufficient condition for the operator�sprofits to increase when the price cap is lowered from the point where it just becomes

binding. It is important to note that this condition is likely to be satisfied because

marginal costs and the access price are usually low figures in comparison to a.


The implications of Propositions 4 and 5 can be explained with the aid of Fig. 2.

The solid curve represents the maximized profit function of the incumbent under a

binding price cap. If the condition in Proposition 5 is satisfied, then the slope of

the profit function at �p ¼ B is negative. It follows that a price cap leads to higher

profits as long as A < �p < B.An intuitive explanation of the result is provided in the following. In response to a

lower price cap the operator has to increase output levels in both the local and the

long-distance markets. However, for small enough output variations the direct effect

on the operator�s profits is negligible. In contrast, the indirect effect of a small change

in the rival�s behavior alters the operator�s profits significantly. An increase of the

operator�s long-distance service output causes a reduction of the rival�s marginal rev-

enues, thus induces the rival to reduce output. This small output decrease may be

enough to increase the operator�s profits.The analysis above can also be explained in terms of reaction functions. The oper-

ator�s optimal strategy as a function of the rival�s strategy, qoðqr; �p; cl; coÞ, and the

rival�s optimal strategy as a function of the operator�s strategy, qr(qo, w, cr), are

shown in Fig. 3. The solid lines are firms� reaction functions for an initial price

cap, �p0, while the dotted line is the operator�s reaction function for a lower price

cap �p00. The initial Nash equilibrium is at e 0. Note that a lower price cap shifts out

the operator�s reaction function, making it more aggressive in the long-distance mar-

ket. That is, a lower price cap forces the operator to increase output in order to re-duce the price and satisfy the constraint. Since higher operator�s output implies lower

marginal revenues for the rival, the optimal response of the rival is to reduce output.

At the new Nash equilibrium, e00, the operator�s output has increased and its rival�soutput decreased. While a small increase in the operator�s output has almost no effect

on its profits (i.e., at the point where the constraint just becomes binding profit max-

imization implies opo/oq0 = 0), a small reduction in the rival�s output may strictly in-

crease or decrease the operator�s profits (i.e., opo/oqr 6¼ 0 ).

A reduction in the rival�s output, at the point where the price cap just becomesbinding, affects the operator�s profits in two ways. On the one hand, it has a positive

poπ

A Bp

Boπ

( )

( ) ( )

poπ

Fig. 2. Maximized profits under a binding price cap.

( )

( )

( )

( )

( )

( )olro ccpqq ,,,

pqo ′*

ror cwqq ,,

rq

0

pqr ′*

pqr ″*

pqo ″*

e′

e″

oq

Fig. 3. Reaction functions.


indirect effect on long-distance service profits because it allows the operator to sellthe same output at a higher price. On the other hand, it has a negative direct effect

on access service profits. The condition in Proposition 5, that is, the sign of

2co + 2w � cl � cr � a, determines which of the two effects dominates.

If a price cap leads the operator to higher profits, then why can�t the operator

impose it on itself? In principle, the operator can impose the price cap on itself by

claiming that it will produce more output. However, it is key for this strategy to

work that the rival believes the operator will actually do it. In a sense, the setting

is similar to one in which a Cournot duopolist, say firm A, claims that it will pro-duce Stackelberg�s leader output instead of Cournot�s output. If the other duopol-

ist, say firm B, believes this is true, it would produce Stackelberg�s follower outputwhich is the best response to firm�s A claimed behavior. It seems that just by mak-

ing this threat firm A can make higher profits at the expense of firm B. The prob-

lem is that firm B may not believe that firm A will produce Stackelberg�s leader

output. If firm A anticipates this, then it would rather produce Cournot�s output.

In other words, the threat is not credible unless firm A is able to convince firm B

that it is committed to produce Stackelberg�s leader output. In Stackelberg�s model,the leader ‘‘convinces’’ the follower that it is committed to produce more than

Cournot�s output by doing it before the other firm is able to undertake any action.

In the current model, the commitment device is the regulator�s capacity to enforce

the constraint.

5. Numerical example

A numerical example can help to illustrate the result in Proposition 5. Suppose

that al = a = 100, bl = b = cl = 1, cr = co = 2 and w = 3. Firms� long-distance service

output and the operator�s profits for different price caps are shown in Table 1.

The first value corresponding to the price cap (i.e., 86.5) is the point where the

restriction just becomes binding. That is, the operator would freely choose q�o ¼ 33

Table 1

Production and benefits with a binding price cap

�p q�l q�o q�r p0 L.D. Local Access

86.5 49.5 33 31 3601 1089 2450.25 62

85.5 50.1 33.8 30.6 3613 1102 2449.89 61.2

75.5 56.1 41.8 26.6 3655 1195 2406.69 53.2

65.5 62.1 49.8 22.6 3562 1225 2291.49 45.2

55.5 68.1 57.8 18.6 3332 1191 2104.29 37.2

45.5 74.1 65.8 14.6 2967 1092 1845.09 29.2


and q�l ¼ 49:5, while its rival chooses q�r ¼ 31. It is important to emphasize that the

operator�s profits in this scenario (i.e., p0 = 3601) are equivalent to the profits that

this firm would obtain in the absence of price cap regulation.

Note that the overall profits of the operator increase for a small initial reduction

in the price cap. In this sense, it can be said that for values of �p within a certain

range, price cap regulation can result in higher profits for the operator in comparison

to profits under no price cap regulation. The last three columns in Table 1 decom-

pose profits into three parts that correspond to long-distance, local and access serv-ices. A lower price cap generates a minor decrease in profits from local and access

services but an increase in profits from long-distance service. However, if the price

cap continues to be lowered, profits from the three sources will eventually start

decreasing.

In order to illustrate the point, we can set the price cap at 75.5 and compare to the

situation where the price cap is not binding. When the price cap is 75.5, the incum-

bent chooses q�o ¼ 41:8 and q�l ¼ 56:1, while its rival chooses q�r ¼ 26:6. The opera-

tor�s profits increases from 3601 to 3655. One could argue that the incumbent isable to choose these quantities (i.e., q�o ¼ 41:8 and q�l ¼ 56:1) in the absence of the

price cap to increase profits. Why not doing it? Behaving as having a constraint is

not enough for the incumbent to increase profits. The rival needs to know that the

incumbent must meet the constraint and act accordingly. 14 Otherwise, the incum-

bent will be worse off.

The curve in Fig. 4 represents incumbent profits from local service. The initial

equilibrium given a non-binding price cap is at eo. It is clear that the incumbent�s freechoice production (i.e., ql = 49.5) maximizes profits. However, when the price cap isset at 75.5 the incumbent is forced to increase production. At the new equilibrium, e 0,

the incumbent produces more local service (i.e., ql = 56.1) than the optimum. Thus,

profits from this source are reduced.

14 Ross (2003) explains that: ‘‘. . .the Spanish conqueror Cortez, when landing in Mexico with a small

force who had good reason to fear their capacity to repel attack from the far more numerous Aztecs,

removed the risk that his troops might think their way into a retreat by burning the ships on which they

landed. With retreat having thus been rendered physically impossible, the Spanish soldiers had no better

course of action but to stand and fight.’’ Later on Ross adds: ‘‘. . .from Cortez�s point of view, his actionhad a discouraging effect on the motivation of Aztecs. He took care to burn the ships very visibly, so that

the Aztecs would be sure to see what he had done’’.

0

500

1000

1500

2000

2500

3000

30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72

ql

$

oe e ′

Fig. 4. Incumbent profits from local service.


The two curves in Fig. 5 represent incumbent profits from long-distance service.

The lower curve corresponds to a rival that produces 31 units of long-distance serv-

ice. In other words, a rival who thinks that the price cap is not binding and assumes

that the incumbent will produce 33 units of long-distance service. The other curverepresents profits given that the rival produces 26.6 units. That is, assuming that

the rival thinks the incumbent produces 41.8 instead of 33 to satisfy the constraint.

0

200

400

600

800

1000

1200

1400

20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62

qo

$

e′

e″oe

Fig. 5. Incumbent profits from long-distance service.


Note again that at the initial equilibrium, eo, the operator maximizes profits from

long-distance service. When the price cap is impossed, the incumbent increases pro-

duction of long-distance service above the optimum to meet the constraint. How-

ever, the rival�s reaction shifts out the incumbent�s long-distance profits function.

At the new equilibrium, e 0, the incumbent profits are higher in spite it is not produc-ing the unrestricted optimum. Note that profits would decrease, as in point e00, if the

incumbent increases production but the rival does not think it will actually happen.

6. Conclusion

In this paper, we introduced a theoretical framework to analyze the effects of price

cap regulation in the telephone industry. We considered a vertically integrated firmthat is a monopolist in the local service market and a duopolist in the long-distance

service market. We showed that the vertically integrated firm can benefit from price

cap regulation. In particular, that price cap regulation can lead the firm to higher

overall profits and its downstream rival to lower profits. We also showed that the

relative efficiency of the integrated firm and its rival in the production of long-dis-

tance service is crucial to determine whether the vertically integrated firm has an

incentive to increase the access price and exclude its rival from the downstream

market.

Acknowledgements

I am grateful to the editors and anonymous referees for their valuable comments.

Also to Alba Hernandez, Enrique Flores and Leo Torre for their help reading pre-

vious versions of this paper.

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Price cap regulation in the Mexican telephone industry

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