Distributive and Regional Effects of Monopoly Power

Distributive and Regional Effects of Monopoly Power



Carlos M. Urzúa*



Documento de Trabajo
Working Paper

EGAP-2009-04




Tecnológico de Monterrey, Campus Ciudad de México





*EGAP, Calle del Puente 222, Col. Ejidos de Huipulco, 14380 Tlalpan, México, DF, MÉXICO
E-mail: curzua@itesm.mx

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DISTRIBUTIVE AND REGIONAL EFFECTS
OF MONOPOLY POWER


Carlos M. Urzúa*
Tecnológico de Monterrey, Campus Ciudad de México
May 2009

Abstract
This paper estimates the distributive and regional effects of firms with market power in
the case of Mexico. It presents evidence that the welfare losses due to the exercise of
monopoly power are not only significant, but also regressive. Moreover, the losses are
different for the urban and rural sectors, as well as for each of the states of Mexico, being
the inhabitants of the poorest ones the most affected by firms with market power.

JEL codes: L10, L40, L66

Keywords: monopoly, distributive effects, regional effects, income distribution, Mexico


*I thank Francisco Rodríguez for his computational help, Ernesto Estrada and Pascual García-Alba for their
very helpful comments, and Ignacio Navarro and Javier Núñez for their suggestions. This paper is the
English version of an unpublished (and larger) technical report prepared for the Mexican Federal
Competition Commission. I am indebted to the Commission for financing the project, as well as for the
comments of its reviewers. Needless to add, any opinions expressed in this paper are solely my own.

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“Despite the primary concern of economists with the resource allocation
effects of market arrangements, political officials are more often concerned
with distributive effects”. Comanor and Smiley (1975, p. 194).

At first glance it would seem natural to surmise that the welfare effects caused by firms
with a significant market power would vary according to the consumers’ income, or even
according to the regions where the firms sell their products; the latter especially in the
case of developing countries, where transportation costs tend to be high and consumers
are typically poorly informed. Nevertheless, there have been very few studies that explore
in detail the distributional consequences of monopoly power in any economy, whether
developed or underdeveloped. Among the general studies known to us are those of
Comanor and Smiley (1975), McKenzie (1983), and Creedy and Dixon (1998 and 1999);
while Hausman and Sidak (2004) explore the same issue for the particular case of long-
distance phone calls. In all those studies the verdict is the same: market power has a
significant distributive impact. In the case of Australia, for instance, Creedy and Dixon
(1998, p. 285) conclude that “whatever the size of the absolute welfare loss arising from
monopoly, there may be a substantial effect on the distribution of welfare”.

Our work not only follows those authors in analyzing the distributive impact of
firms with a significant market power, this time in the case of Mexico, but it also deals
with their regional effects. In order to accomplish this last task, we distinguish between
households living in urban and rural areas, and we calculate afterwards the welfare losses
due to market power for each of the thirty two Mexican states. Section 1 presents the
theoretical model to be used to estimate those welfare losses, which is based on the
assumption of oligopolies with conjectural variations. Section 2 details the household

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expenditure survey that is used in the paper, as well as the markets under study. These are
chosen according to two criteria: a presumption, from the part of the Mexican Federal
Competition Commission, that there could be market power from the part of the sellers,
and the availability of data on, both, households’ spending and unit values.

Since the expenditure surveys that are officially made in Mexico are not
longitudinal, it is not permissible to regard the reported unit values as prices. Strictly
speaking, those values reflect not only commodity prices but also the quality of them.
Thus, Section 3 uses the ingenious model of spatial variations proposed by Deaton (1987
and 1990) to circumvent that problem. Once the price elasticities of the demand for the
goods are estimated for both the urban and the rural sectors, the distributional and spatial
effects on social welfare are finally estimated in Section 4.

I. MEASURING WELFARE LOSSES DUE TO MARKET POWER

In this part we present the theoretical model that is used in a later section to estimate the
distributional consequences of market power. It is assumed from the beginning that the
social welfare cost of market power can be represented by the loss of consumers’ surplus.
Although it is well known that welfare losses are much better estimated using utility-
based measures, such as equivalent variations, these measures cannot be calculated here.
This is so because, as explained in Section 3 below, the econometric model that is used in
this paper to estimate the own-price elasticities is not a bona fide demand system, since it
is not derived from a utility function.

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Given a particular good, let m
p be the price charged to households by the firms
with market power. We assume that the marginal cost of the supplier, cm, is constant and
equal to the competitive price that would prevail under perfect competition, c
p . As in
Creedy and Dixon (1998), we further assume that the demand curve can be approximated
by a linear demand function, in such a way that the loss of consumers’ surplus, B, can be
calculated as:


( m
c
p ? p )( c
m
q ? q )
=
(1)
B
.
2

Denoting by ? the elasticity of the demand for the good relative to its own price, then


m
c
m
(q ? q ) / q
? =
(2)
,
m
c
m
( p ? p ) / p

and so, using (2) in (1), the welfare loss can be rewritten as:


2
? m
p ? c
p ?
m
m
p q ( ?
? )
(3)
B =
.
?
?

m
?
?
p
2
?
?


In order to calculate (3), we require not only an estimate of the elasticity, but also
of the amount spent on the good, which can be obtained from a survey, and the estimated

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increase in relative prices due to market power, which depends on the particular industrial
structure prevailing in the market. Following Creedy and Dixon (1999), we assume here
that the industries under study are made of oligopolies with conjectural variations.

More formally, consider an oligopoly that is constituted by K firms, all of them
producing the same homogeneous good. Let Q be the total production of the industry,
which is the sum of the production by firm k, denoted by qk , and the aggregate
production from the rest of the firms, denoted by q?k . Assuming that all the firms base
their decisions according to the conjectural variations hypothesis, the optimality condition
for each firm k is given by:


?
1 ?
m
(4)
cm = p
k
?
?1+
?
? ,
?
?k ?

where cm
?
k is the marginal cost for firm k, which is assumed to be constant, while
k is
the demand elasticity as perceived by the firm. The following expressions establish the
relationship between this last elasticity and the market elasticity:


?
dq / q
dq / q dQ / Q
dq / q
k
k
k
k
k
k
?
=
=
?
(5)
k
.
dp / p
dQ / Q dp / p
dQ / Q

The denominator on the right-hand side of (5) can be written as


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dQ
q dq
q
dq
k
k
?k
?k
=
+
(6)
,
Q
Q q
Q q
k
?k

which, if we denote the market share of firm k as sk , can be rewritten as


dQ
dq
dq
k
?k
= s
+ 1
( ? s
(7)
k
k )
.
Q
q
q
k
?k


Let us define the conjectural elasticity ? ? (dq
/ q ) /(dq / q )
k
?k
?k
k
k
, which
measures the degree to which firm k takes into account its rivals’ reactions to its own
changes in production. Using ?k , and inserting (7) in (5), we can obtain the firm’s
perceived conjectural elasticity in terms of the elasticity of market demand and the market
share as:


? = ? ?
1
where ? ?
.
(8)
k
k
k
s + 1
( ? s ?
k
k )
k

Assuming now that, for all firms, ? = ?
cm = p
k
and
c
k
(conditions that would be fulfilled
in particular if all firms were identical), then, after substituting (8) in (4), we can find that
the price margin due to market power can be expressed as:


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m
p ? c
p
1
= ?
(9)
.
m
p
??

Thus, using (9) in (3), the total consumers’ loss due to market power can be approximated
as


m m
p q
=
(10)
B ? ?? .
2


Note that this last equation just requires an estimate of the price elasticity and the
spending on each good, once the value of ? is established. It equals one in the case of a
monopoly, but the value depends in general on both the market shares and the conjectural
elasticities. If we further assume that the conjectural responses correspond to the Cournot
model, as we do in a later section, then ? = 0 and, by (8), ? is simply equal to K. Also
note that for the optimality condition in (4) to make sense, it is necessary that ? < 1
?
k
,
since the marginal cost is always positive. This requires that ? < 1
? /?k , which, in the
case of identical firms in a Cournot game, implies in turn that ? < 1
? / K .

Finally, in order to be able to establish comparisons across groups of individuals,
it is convenient to rescale the welfare loss given in (10). Let M be the number of goods
purchased by the consumers from firms with market power. A measure of the total
welfare loss in relative terms can be found after dividing the welfare loss on each item by
the total expenditure on the M goods:

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M
L = ? 1 ? wi
(11)
,
2
? ?
i=1
i i

where wi is the share of good i in total expenditure.

II. DATA AND MARKETS UNDER STUDY

The household income and expenditure survey to be used here is known in Mexico as the
Encuesta Nacional de Ingresos y Gastos de los Hogares, ENIGH for short. The most
recent ENIGH that was available at the moment of this writing was made in August-
November 2006 (INEGI, 2007). The sample consisted of 20,875 housing units, and it was
designed to provide reliable estimates at the national level, as well as at the urban and
rural levels (the urban sector consists of all localities with 2,500 or more inhabitants, and
the rural sector of the rest); furthermore, the 2006 survey was also representative for
some, but not all, of the 32 Mexican states. For reasons to be given in a later section, it is
important to add that the sampling process was stratified and multi-staged. Each primary
sampling unit was made of one or several “basic geostatistical areas” (these are similar to
the census tracts employed in other countries). The resulting 2,785 primary sampling
units were subject to a stratification based on socio-demographic variables to finally
produce 392 strata from which the sample was drawn.

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Turning now to the markets to be studied, their selection is facilitated by the fact
that in 2008 the Federal Competition Commission listed a number of sectors that it
wanted to examine closely (CFC, 2008). The goods mentioned by the Commission that
are also contemplated in the ENIGH are the following: corn tortilla; processed meats;
carbonated soft drinks; cow milk; chicken and eggs; beer; medicines; electricity; liquefied
gas; natural gas; and gasoline. On the other hand, the services included in that list that are
also recorded in the expenditure survey are: foreign bus transportation; air transportation;
private primary schools; private high schools; private universities; long-distance phone
calls; local phone calls; cell phones; internet; medical fees; hospital fees; and credit card
payments.

Even though all the goods and services mentioned above are reported in the
ENIGH, for most of them there is only information on household spending, not on unit
values. This is the case for both the services and the energy consumption goods. Since
this fact prevents us from a direct estimation of their corresponding price elasticities, in
this paper we focus solely on the following seven consumption goods for which unit
values are indeed reported: corn tortilla; processed meats (ham, bacon, sausage, etc.);
carbonated soft drinks (together with juices and bottled water); cow milk; chicken and
eggs; beer; and medicines (whether purchased with or without a prescription).

Having selected the goods markets, it remains to be decided whether or not each
of them can be treated as a single national market. In our context, this would be so if there
were no presumption of differing non-competitive practices across all regions in Mexico.
Although in the case of urban areas there is no such presumption, in the case of rural

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