Market Structure and Consumer Surplus in the
Mobile Industry∗
Georges V. Houngbonon†
Francois Jeanjean‡
17th January 2017
Abstract
Merger reviews often require an analysis of the effect of market structure,
that is the number of firms, on welfare. This analysis is not straightforward in
the mobile industry due to investment to improve quality and reduce marginal
cost. In this paper, we develop a simple Cournot model with investment in
cost-reducing technologies and a structural estimation approach to estimate the
effects of market structure on consumer surplus in symmetric mobile markets.
We find that the relationship between market structure and consumer surplus
in the mobile industry depends on the magnitude of demand elasticity and the
effects of investment on marginal cost. Depending on demand elasticity, consumer
surplus is maximized with 3 or 4 symmetric operators. These findings are robust
when we consider a horizontal differentiation model in the tradition of Salop with
quality differentiation. They suggest a case-by-case merger reviews in the mobile
industry.
Keywords: Market structure, Investment, Mobile Telecommunications.
JEL Classification: D21, D22, L13, L40.
∗
Early version of this paper was presented at the 27th European Regional Conference in Cambridge (UK) in September 2016. The authors are grateful to the participants for the comments and
suggestions. The usual disclaimer applies.
†
Paris School of Economics, [email protected]
‡
Orange, [email protected]
1
1
Introduction
Telecommunications services generate significant benefits for the whole economy.1 Meanwhile, market structure, that is the number of firms, is regulated in the mobile industry.
Operators can only enter the mobile market after having purchased license awarded by
the government, and their mergers must be approved by antitrust authorities. Yet, as
epitomized by recent mergers reviews, the effects of these changes in market structure
on consumer surplus is not yet clear-cut. For instance, mergers between Telefonica
and E-Plus in Germany, and Telefonica and Hutchinson in Ireland in 2014 were approved, whereas the proposed merger between Telefonica and Hutchinson in the UK
was blocked.2
Contrary to other industries, price is not the only strategic variable in the mobile
industry. Indeed, the provision of mobile services requires significant investment in
mobile network technologies. This investment can benefit consumers in terms of higher
quality and lower marginal cost of production, but is affected by market structure
as shown by Genakos et al. (2015) and Jeanjean & Houngbonon (2016). Typically,
investment in mobile networks falls with the number of mobile operators. As a result,
change in market structure generates positive effects on consumer surplus due to lower
prices, but also negative effects on consumer surplus due to lower investment, the overall
effect is not straightforward.
In this paper, we estimate a Cournot model with investment in cost-reducing technologies in order to analyze the effects of market structure on consumer surplus in symmetric
mobile markets. The Cournot model defined mobile data services as the transmission
of homogeneous information (bytes). It relies on a constant-elasticity demand model
and a marginal cost function which depends on investment through a power function.
Operators simultaneously set output, that is the volume of data traffic, and investment
and the market clears. At the symmetric equilibrium, this simple model yields the essential features of pricing and investment in the mobile industry as shown by previous
studies. In particular, investment falls with the number of operators, and the effect of
the number of operators on price and consumer surplus depends on a tradeoff between
static effects, stemming from change in market power, and dynamic effects, stemming
1
See Roller & Waverman (2001) and Czernich et al. (2011) who find significant positive effects of
telecommunications infrastructure on Gross Domestic Product.
2
See the EU Commission decisions on these mergers: M7018, M6992 and M7612.
2
from change in the incentive to invest.
Using data on the volume of traffic from 27 European mobile markets, as well as data
on operators market share and investment, we are able to recover estimates of demand
elasticity per market. We use demand elasticity to obtain estimates of marginal cost
under the assumption of Cournot competition. We employ a non-parametric approach,
namely the locally weighted scatter-plot smoother (Lowess) to identify a power relationship between marginal cost and investment. The parameters of the marginal cost
function have been estimated using the Generalized Method of Moments estimator
(GMM), with population size as an instrument for investment. The estimates of demand and cost parameters determine the relationship between investment and market
structure.
We use these parameters to simulate the effects of market structure on price, investment
and consumer surplus in symmetric mobile markets. Price and investment fall with the
number of operators. However, the effect on consumer surplus is very sensitive to
the magnitude of demand elasticity and the effect of investment on marginal cost. In
general, consumer surplus is maximized in markets with 3 or 4 symmetric operators.
To test the robustness of this findings, particularly with respect to the assumption of
homogeneous mobile data services, we also develop a Salop model, whereby operators
propose horizontally differentiated products with quality differentiation. Using data on
operators’ accounting profit and market shares we are able to recover an estimate of the
horizontal differentiation parameter. In addition, the model also provides an estimate
of the parameter which determines the effect of investment on quality. We use these
parameters in conjunction with the estimates from Jeanjean & Houngbonon (2016) to
simulate the effects of market structure on consumer surplus and social welfare. We
also find an inverted-U relationship between the number of operators and welfare. In
particular, consumer surplus is maximized in markets with 3 or 4 symmetric operators.
The findings of this paper contribute to the literature on the effects of market structure
in dynamic frameworks as in Vives (2008) and Schmutzler (2013). In particular, it
provides a piece of evidence to the strand of the literature which investigates regulation
in the mobile industry. Gagnepain & Pereira (2007) is the closest to this paper. Gagnepain and Pereira show that consumer surplus increases with entry in the Portuguese
mobile market. However, their analysis focuses on the years 1992-2003, a period when
investment in mobile data, which brings about most of the dynamic efficiencies, was not
3
significant. Houngbonon & Jeanjean (2016) and Jeanjean & Houngbonon (2016) investigate the effects of competition and more specifically market structure on investment
in the mobile industry, but they do not evaluate the magnitude of static and dynamic
efficiencies.
The remaining of the paper is organized as follows. Section 2 presents some background
information about investment and pricing in the mobile industry. Section 3 presents
data sources and variables used in the estimation. Sections 4 and 5 present the outcome
of the structural modeling under the assumption of mobile services as homogeneous
and differentiated products, respectively. Finally section 6 concludes along with some
discussions of the findings.
2
Background on the mobile industry
The mobile industry is characterized by a significant rate of technological progress,
driving regular investment in mobile networks. According to Koh & Magee (2006), the
annual rate of technological progress in the transmission of information was 35 percent between 1940 and 2006. This is far greater than the annual rate of technological
progress in energy transportation (13.2 percent) (Koh & Magee, 2008). Every year,
equipment providers innovate and release new technologies for mobile telecommunications networks.
Operators adopt these new technologies by investing regularly, for instance in the second, third and fourth generation of mobile networks (2G, 3G and 4G). Investment in
these new technologies reduces marginal cost of production due to lower cost of equipment, as a result of technological progress. In addition, it also raises quality as new
technologies come with faster data transmission speed, enabling consumers to access
more valuable internet contents such as videos and online conferences.
Technological progress also drives the variety of offers proposed by mobile operators.
Historically, mobile telecommunications services mainly consist of the supply of voice
services, including short or multimedia message services. These services can be purchased under either a prepaid or a postpaid contract. Under a prepaid contract, the
customer typically pays for an allowance of voice services before consuming. The set of
prepaid contracts proposed by a firm is equivalent to a menu of pairs of quantity and
4
tariff, without any commitment required from the customer. Under a postpaid contract,
the customer pays a tariff periodically (monthly, in general) for a given allowance, with
a minimum duration of commitment. Some postpaid plans include unlimited voice or
data services, sold separately (standalone) or in a package (bundle).
For mobile plans with limited voice allowance, the customer pays a price per unit to
use the service in excess of the initial allowance. Because of these features, the tariff
structure of a mobile plan is in general considered as a three-part tariff (Lambrecht
et al. , 2007). The first part is an access price intended to recover the fixed cost of
investment or to extract consumer surplus. The second part corresponds to the usage
allowance and the third part is a variable price charged for every additional unit of the
service consumed in excess of the allowance.
More recently, innovations in new generations of mobile networks, notably the third
and the fourth generations (3G and 4G), have spurred the supply and demand for
mobile data services. For instance, the share of mobile data in the revenue of Western
European mobile operators has tripled from 15% in 2007 to almost 45% in 2013. The
emergence of mobile data services has been accompanied by the bundling of both mobile
voice and data services. Since the first quarter of 2014, half of European Union mobile
users purchase voice and data services in bundles (E-communications surveys N0 414).
On top of these features, a postpaid mobile contract may also include several add-ons
such as a subsidy for the handset, a premium quality service for business customers,
international roaming services, and inter-temporal discounts. This variety of mobile
plans makes it more reasonable to use a horizontally differentiated demand model.
However, all different plans purport to supply a service of information transmission. In
this setting, information, measured in byte, is homogeneous.
Besides, the market structure of the mobile industry is strongly regulated. Entry into
the mobile market depends on the allocation of radio frequency bands by the regulator.
In addition, the industry is somehow concentrated compared to other industries. As a
result, mergers are subjected to the approval of antitrust authorities.
5
3
Data
We estimate the demand for mobile data services using a dataset provided by the
consultancy firm Analysys Mason on the basis of figures released by national regulators.
This dataset provides aggregate traffic data for 27 European markets over 9 years, from
2007 to 2015. We obtain monthly data consumption per user by dividing the aggregate
data traffic by the number of data users and 12 months. The number of data users
has been estimated using the penetration rate of 3G and 4G technologies as provided
by the World Cellular Information Services (WCIS), an online database managed by
Ovum, a consultancy firm.
Estimates of the average price per megabyte of mobile data are obtained by dividing
the market level average monthly revenue per user of mobile data (ARPU) over the
monthly data consumption per user. The ARPU data comes from WCIS and cover
the 27 European markets from 2007 to 2015. We complement this information with
data on industry investment provided by WCIS, and a proxy for income, namely Gross
Domestic Product per capita (GDP), retrieved from the World Development Indicator
database (WDI), a publicly available and managed by the World Bank.
To estimate marginal cost parameters, we use data on market shares of mobile data
provided by WCIS on 72 operators from the 27 European markets between 2007 and
2015. We also use data on investment per operator defined as capital expenditures from
the same source. Capital expenditures is limited to mobile networks, but may include
license fees. Additional data include GDP per capita, and population size as provided
in the WDI.
Table 1 in the appendix presents the main variables along with the data sources. These
data sources are proprietary, but widely used in academic research as in Whalley &
Curwen (2014), Kim et al. (2011) and Hazlett et al. (2014). On top of these data, we
also rely on estimates from Jeanjean & Houngbonon (2016). The final sample covers
27 European mobile markets with 72 mobile operators, observed from 2007 to 2015.
6
4
Mobile services as homogeneous products
This section develops a Cournot model with investment in cost-reducing technologies
to estimate the effect of market structure on consumer surplus in symmetric markets.
This model follows from the one developed in Dasgupta & Stiglitz (1980).
4.1
Settings of the model
We consider N ≥ 2 mobile operators, exogenously given by regulation, that supply
a transmission service of electronic signals for end-users. Electronic signals are measured in bytes and correspond to mobile data. Irrespective of the operator, signals are
homogeneous. We assume that aggregate demand for bytes is iso-elastic and can be
expressed as:
Q = αP −β
(1)
Q= N
i=1 qi is the aggregate volume of bytes transmitted and qi is the volume supplied
by operator i. P is the market price. As such, β corresponds to the absolute elasticity
of demand.
P
Operators produce under constant marginal cost c(z) which can be lowered by investment in new technologies:
∂c(z)
<0
∂z
Due to technological progress, investment lowers marginal cost by allowing more traffic
to be conveyed at the same cost. As investment increases the speed at which mobile
data can be consumed, it also raises the quality of the mobile data from the perspective
of the consumer. However, it is not possible to distinguish between quality increasing
and cost-reducing investment. We assume that the effect of investment is to reduce
marginal cost.
To obtain an analytically tractable expression of investment as a function of the number
of operators, we express marginal cost as a power function of investment:
7
c(z) = α0 z −β
0
In the next sections, this relationship will be first identified using a non-parametric
methodology before being estimated.
Operators simultaneously choose investment zi and output qi to maximize their profit.
This latter can be expressed as:
πi = [P − c(zi )]qi − zi − F
F denotes fixed costs of entry, which will be set to zero.
Under these conditions, the symmetric equilibrium investment can be expressed as3 :
∗
z =
h
β 0 β1 0 β1 −1 1 i 1−β0β(β−1)
α
1−
αN
βN
(2)
The first-order conditions of the choice of output are:
P − c(zi )
φi
=
P
β
(3)
Where φi = qQi is the market share of operator i. An equilibrium exists if and only
if φβi < 1 for all i. In symmetric markets, this condition is equivalent to stating that
β > 21 . Therefore, we will assume that 12 < β < 1. Let P̂ and Q̂ denote respectively
equilibrium price and quantity. They both satisfy equation (3).
Consumer surplus in symmetric markets writes:
CS =
ZQ̂
[P (Q) − P̂ ]dQ
(4)
a
Where a is a constant which ensures that demand is never nil. Change in consumer
surplus is not sensitive to the choice of this constant. It is set to 1, meaning that Q ≥ 1.
3
See Dasgupta & Stiglitz (1980)
8
It can be shown with simple algebra that:
CS = P̂ −
1
β
P̂ Q̂ +
1−β
1−β
(5)
Plugging the expression of price from equation (3) into the equation (5), the derivative
of consumer surplus can be expressed as:
∂CS
=
∂N
c(z)
βN 2
−
∂c(z) ∂z(N )
(1
∂z
∂N
2
1
1 − βN
−
1
)
βN
(Q̂ − 1)
(6)
Given that Q ≥ 1, Q̂ ≥ 1 and,
sign{
∂CS
c(z)
∂c(z) ∂z(N )
1
} = sign{
−
(1 −
)}
2
∂N
βN
∂z ∂N
βN
(7)
Two observations stand out from this equation. First, the sign of the effect of the
number of operators on consumer surplus depends on the number of operators N .
Therefore, change in consumer surplus is not necessarily monotonous. Second, this sign
is characterized by two terms, one corresponding to a positive market power effect,
∂z(N )
c(z)
, and the other corresponding to a negative effect due to investment, − ∂c(z)
.
βN 2
∂z
∂N
As a result, the effect of the number of operators on consumer surplus depends on the
magnitude of the elasticity of demand, β, the shape of the marginal cost function, ∂c(z)
,
∂z
∂z(N )
1
and the magnitude of the effect of the number of operators on investment, ∂N (1− βN
).
The remaining of this section provides empirical estimates for these parameters in order
to analyze the effect of the number of operators on consumer surplus.
4.2
Estimation of the demand for mobile services
Drawing upon equation (1), the aggregate demand for mobile services can be estimated
on the basis of the following model:
ln Qjt = α − β ln Pjt + εjt
9
(8)
ln denotes the natural logarithm. Qjt and Pjt are respectively the aggregate output and
price in market j in year t. εjt correspond to the unobserved determinants of demand
for mobile services. Due to consumers heterogeneity in terms of income, we need to
include a proxy for income into this equation. Let y denotes this proxy. In addition, as
suggested by the theoretical settings, price and quantity can be jointly determined by
quality, through investment. Therefore, we shall also include a measure of investment
into the demand model. Moreover, the model also includes time-invariant unobserved
market and year-specific effects. Unobserved market-specific effects are interacted with
the price variable in order to obtain market-specific elasticity of demand. The resulting
model writes:
ln Qjt = α − βj µj ∗ ln Pjt + δ ln zjt + γyjt + µt + µjt
(9)
Qjt is measured as the monthly volume of mobile data traffic per user. At this stage, we
focus on mobile data as the demand for mobile voice is rather flat. Pjt is measured as
the price per megabyte of mobile data. It corresponds to the ratio of aggregate mobile
data revenues to the aggregate volume of mobile data consumption. zjt is the capital
expenditures per user and yjt is the monthly estimate of GDP per capita. µj is a set of
dummy variables for each market in our sample and µt is set of yearly dummies. Table
2 presents summary statistics of the main variables.
OLS estimates of equation (9) would be biased due to unobserved horizontal differentiation. We implement a Generalized Method of Moments estimator using lagged price
of mobile data and lagged investment as instruments. Serial autocorrelation statistics
are presented to test the validity of these lags as instruments. Estimation relies on 243
observations from 26 European markets from 2007 to 2015. Due to the use of lags the
final sample includes 175 observations. The outcome of the estimation is presented in
table 3. Demand elasticities are all negative as expected. As discussed in section 4.3
below, market-specific demand elasticities will be useful for the estimation of marginal
cost. Average demand elasticity is −0.9 and will be used in the simulation of the effect
of the number of operators on consumer surplus.
10
4.3
Estimation of marginal cost of production
In this section, we first recover marginal cost from the first-order condition of the
Cournot equilibrium, that is equation (3) in the theoretical section. With data on
market-specific demand elasticities, price per megabyte and market shares, marginal
cost can be calculated using the following formula:
c(zijt ) = pijt ∗ 1 −
φijt βj
(10)
This formula yields estimates of the marginal cost experienced by each mobile operator under the assumption that they compete in output. These estimates have been
combined with operators’ investment in order to determine marginal cost function c(z).
As the effect of market structure on consumer surplus depends on the nature of this
function we first employ a non-parametric strategy to identify the functional form and
then estimate the parameters of this function.
Non-parametric identification of c(z)
We employ the locally weighted scatterplot smoothing (Lowess), a non-parametric algorithm proposed by Cleveland (1979). This algorithm traces a curve through the
scatterplot of two variables, from locally fitted curves identified by regressing one variable over the other. The algorithm runs as follows:
First, it derives the residuals of the regressions of the marginal cost and investment
on operator’s fixed effects. This procedure follows from the Frish-Waugh Theorem
(Frisch & Waugh, 1933), which basically states that a regression between two variables
with additional controls is equivalent to regressing their residuals obtained from their
regressions on the controls. Let’s crk and zkr denotes the residuals of marginal cost and
investment respectively.
For a given value of investment zkr , let’s define a bandwidth b around this point. This
r
r
r
bandwidth determines a subset of pairs (crl , zlr ) such that zk−
. The
b ≤ zl ≤ z
k+ 2b
2
corresponding Lowess smoother of the marginal cost crk is the predicted value of the
following weighted OLS regression:
11
crl = σ ∗ wl ∗ zlr + µl
(11)
l ∈ [k − 2b ; k + 2b ].
wl is a weight attached to the observations indexed by l. Several kernel weighting
functions can be used. The non-parametric smoothing relies in particular on the tricube
weighting function, a robust kernel widely used in the literature on non-parametric
methodologies.4
The Lowess smoother of marginal cost associated with the investment zkr is determined
as:
cˆrk = σ̂ ∗ wl ∗ zkr
The same procedure is replicated for all k, that is, for all observations of investment.
The Lowess smoother is a graphical representation of the set of points (cˆrk , zkr ). Figure
1 presents the outcome of the non-parametric algorithm. It shows a downward sloping
relationship between marginal cost and investment.
Parametric identification of c(z)
In order to get an estimate of the magnitude of the effect of investment on marginal
cost, we formulate the following equation that provides the best statistical fit to the
relationship between marginal cost and investment.
ln c(zijt ) = α0 − β 0 ln zijt + γ 0 yjt + νi + νt + νijt
(13)
c(zijt ) are estimated from equation (10). zijt is investment, measured by capital expenditures, of operator i in market j at time t. yjt is an estimate of the monthly GDP per
capita. νi is a set of operators dummy variables. νt corresponds to year-specific effects.
4
The tricube weighting function is defined as follows:
K(u) =
70
1 − u3 )3
81
For all u such that |u| ≤ 1, u = l − k.
12
(12)
Figure 1: Non-parametric marginal cost curve
Finally, νijt represents the residuals. Table 4 presents summary statistics of the main
variables.
OLS estimate of β 0 can be biased due to the unobserved horizontal differentiation
parameters or time-variant efficiency parameters. As a result, equation (13) is estimated
by the Generalized Methods of Moments with instrumental variable strategy. We use
population size as an instrument for investment, the intuition being that investment per
operator is higher in more populated markets, whereas population size is exogenous.
The outcome of the estimation is presented in table 3. It turns out that investment in
mobile network significantly reduces marginal cost of mobile data. The magnitude is
such that 1% increase in investment lowers marginal cost by 2.3%, on average.
4.4
Counterfactual analysis
This section presents the outcome of a counterfactual analysis of the effects of market
structure on consumer surplus in a representative European market. This representative
market has the average characteristics of all European mobile market and is symmetric.
13
This estimate provides the second row of table 5, showing that investment per operator
falls with the number of operators. The estimates of equation (13) in conjunction with
the simulated investment yields the simulated marginal cost in the third row of table
5. As expected, marginal cost increases with the number of operators.
We use the average demand elasticity and the simulated marginal cost to recover the
corresponding price per GB of mobile data. The formula writes:
P (N ) =
c[z(N )]
1
1 − N ∗β
j
(14)
It turns out that starting from 3 operators, market power reduction effect of an additional entry is not strong enough to compensate the dynamic effect stemming from
investment. As a result, price per unit rises with the number of operators. As shown
in the fourth row of table 5, price per gigabyte rises from 27 cents dollars with three
operators to 40 cents dollars with five operators. Correspondingly, monthly data consumption per user decreases. And as a result consumer surplus falls with the number
of operators.
However, price per unit falls when going from 2 to 3 operators. As a result, data
consumption increases and consumer surplus rises. This result reflects the fact that
static effects outweigh dynamic effects between 2 and 3 operators.
These results are very sensitive to the elasticity of demand and the effect of investment
on marginal cost. For instance, price per unit rises and consumer surplus falls with the
number of operators when demand elasticity is lower, say 0.8.
5
Mobile services as differentiated products
This section provides a robustness check analysis of the Cournot framework by considering mobile services as differentiated products in a Salop model.
14
5.1
Settings of the model
We use the Salop model with vertical quality differentiation developed in Jeanjean
& Houngbonon (2016). In this model, N operators compete in price. In symmetric
markets, the incentive to invest zi to reach quality di can be expressed as:
∂zi
β0 (N )
=2
∂di
N
(15)
Where the parameter β0 (N ) can be expressed as:
√ N
3 +1
β0 = 1 − √ √ N
3 2+ 3 −1
2+
Consumer surplus (CS) and social welfare (W) are respectively expressed as:
CS = d −
W =d−
5h
4N
t
−N
4N
Marginal effect of the number of operators on consumer surplus and welfare can be
expressed as:
∂CS
∂d
5h
=
+
∂N
∂N
4N 2
(16)
∂W
∂d
h
=
(1 − 2β0 ) − z − F +
∂N
∂N
4N 2
(17)
and
Equations (16) and (17) show the trade-off between static and dynamic effects. Terms
∂d
∂d
with ∂N
are the dynamic effects. ∂N
is negative and represents the decrease in quality
caused by an increase in the number of firms, as investment declines with the number of
15
operators. Terms with h are the static effects, they represent the decrease in consumers
transportation costs caused by a higher number of operators. As transportation costs
have a negative impact on consumer surplus and welfare, its reduction has a positive
one, hence the positive sign.
5.2
Evaluation of the optimal number of operators
The evaluation of the optimal number of operators relies on the effects of market structure on investment presented in Jeanjean & Houngbonon (2016). As the observed
markets are not symmetric, we first need to calculate zs, the investment at operator
level as if the market were symmetrical. To do so, we use the relationship between
investment and market structure as presented in Jeanjean & Houngbonon (2016) to
subtract the effect of asymmetry from the actual investment z:
ln zsijt = ln zijt − δ∆ijt
which leads to
zsjt = zijt e−δ∆ijt
At the industry level,
N
X
i=1
zsjt =
N
X
zijt e−δ∆ijt
i=1
As zsijt does not depend on the operators since market is symmetrical, we can write:
N
1 X
zijt e−δ∆ijt
zsjt =
N i=1
We use Ebitdaijt (earnings before interest, taxes, depreciation, and amortization) as a
proxy for profit, Ebitdaijt = πi∗ + zi + F = σi2 h. At the industry level,
16
N
X
Ebitdaijt = HHIjt .hjt
i=1
The value of the transportation cost, hjt is thus:
N
P
hjt =
Then we can calculate the value of
∂CS
∂N
ebitdaijt
i=1
HHIjt
and
∂W
∂N
for all the observations of the database.
As a result, equations (16) and (17) can be written:
θlr zsN
5h
∂CS
(N ) =
+
∂N
2β0
4N 2
(18)
∂W
θlr zsN
h
(N ) =
− (θlr N + 1) zs +
−F
∂N
2β0
4N 2
(19)
2
2
∂ W
∂CS
∂W
We can easily check that ∂∂NCS
2 and ∂N 2 are negative, as a result, ∂N = 0 or ∂N = 0
represent the maximums. The number of operators which is the closest respectively
= 0 or ∂W
= 0 is thus the one that maximizes respectively consumer surplus
from ∂CS
∂N
∂N
or welfare.
As the dynamic term includes zs and the static one includes h, the ratio
be a good index of the trade-off between static and dynamic effects.
zs
h
seems to
∂CS
zs
−5β0
= 0 =⇒
=
∂N
h
2θlr N 3
In the database, we do not observe the fixed cost F incurred by operators to enter the
market which has a decreasing impact on welfare. Neglecting F leads to overestimate
the number of operators that maximizes welfare.
∂W
zs
−β0
= 0 =⇒
=
∂N
h
2θlr N 3 (1 − 2β0 ) + 4β0 N 2
17
From these two equations, we can obtain the value of the ration zs
as a function of the
h
number of operators. Figure 2 below represents the relationship between zs
and N .
h
Figure 2: Ratio
zs
h
maximizing consumer Surplus and Welfare.
For all the countries in the sample and each year, we can calculate the ratio
−β0
0
compares it to 2θ−5β
3 and 2θ N 3 (1−2β )+4β N 2 .
0
0
lr N
lr
zs
h
and
−5β0
∂CS
zs
0
0
When zs
than from 2θ−5β
< 2θ−5β
3 then ∂N > 0, in such case, if h is closer to
3,
h
2θlr (N +1)3
lr N
lr N
then the current number of operator is below the number of operator that maximizes
consumer surplus. Otherwise, it is the one that maximizes consumer surplus.
∂CS
h
0
0
> 2θ−5β
< 0. If zs
is closer to 2θ −5β
Similarly, when zs
3 than from
3 , then
h
∂N
lr N
lr (N −1)
−5β0
, then the current number of operator is greater than the number of operator
2θlr N 3
that maximizes consumer surplus. Otherwise, it is the one that maximizes consumer
surplus.
Similar reasoning shows whether the current number of operator is greater than, equal
to or below the one that maximizes the welfare.
The average ratio zs
on the sample is 0.031 with a standard deviation according the
h
countries equals to 0.012. In the graph above, the solid line represents the average ratio
zs
and the dotted lines represent the confidence interval.
h
The solid line crosses the curve of consumer surplus between 3 and 4 symmetric operators. The curve of Welfare crosses the solid line just below the symmetric duopoly.
18
6
Conclusion
Our analysis shows that consumer surplus tends to be maximized in markets with 3
or 4 symmetric mobile operators. This finding suggests that dynamic effects stemming
from investment tend to outweigh static effects in markets with more than 4 operators.
In general, the effect of market structure on consumer surplus in the mobile industry is
sensitive to consumer preferences and the effect of investment on marginal cost. Therefore, a case-by-case analysis is necessary when analyzing the optimal market structure
in merger reviews.
This analysis is conducted for symmetric markets. The effect of market structure on
consumer surplus is clearer in this setting, however the role of asymmetry is still unknown. Asymmetry affects both the static and dynamic component of surplus in an
ambiguous way. Smaller level of asymmetry can increase the industry investment while
higher level of asymmetry decreases it. In addition, more asymmetry increases market
power of some operators while reducing it for others.
Another limitation of this analysis is the fact that we only account for differentiation
across operators, assuming that operators are single product firms. Yet, in practice
operators are multiproduct firms and consumers’ preferences for varieties as well as the
way in which changes in market structure affect operators products line is not clear-cut.
Future work need to account for asymmetry and products variety.
19
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21
A
Appendix
Table 1: Datasets and variables
Original variables
Comments
Unit of observation
Data source
Capital expenditures
in millions US dollars
operator level
WCIS, Ovum
operator level
WCIS, Ovum
market level
WCIS, Ovum
Ebitda
Mobile data revenue
in millions US dollars
Subscribers
operator level
WCIS, Ovum
Mobile data market share
operator level
WCIS, Ovum
market level
Analysys Mason
Mobile data traffic
in Terabytes
Gross domestic product
in thousands US dollars
market level
WDI
Population size
in million
market level
WDI
WCIS: World cellular Information Services by Ovum,
WDI: World Development Indicators. All variables are observed at the year level.
Table 2: Summary statistics for the demand estimation
Obs
Mean
Std. Dev.
Min
Max
lndatatpu
175
7.80
1.42
3.59
11.01
lnprice
175
-3.95
1.18
-6.64
-0.61
lninvpu
175
3.70
0.60
2.28
5.74
gdppcpm
175
1940.84
1091.93
459.36
5386.31
22
Table 3: Estimation results
Average elasticity
lninvpu
Log. MB per user
-0.900
Log. marg. cost
2.608
(9.461)
lninv
gdppcpm
-0.000
(0.002)
Operators FE
Year FE
_cons
X
-7.406
(33.325)
175
28
N
Instruments
hansenp
ar2p
ar3p
ar4p
weak id. test
-2.339∗∗
(0.947)
-1.329∗
(0.775)
X
X
9.851∗∗∗
(3.793)
366
1
0.80
0.79
0.95
14.17
Table 4: Summary statistics for the marginal cost estimation
lncost
capex_
gdppcpm
pop
Obs
Mean
Std. Dev.
Min
Max
366
366
366
366
-4.11
292.42
1.99
26.27
1.43
376.93
1.09
27.54
-9.00
1.05
0.45
1.32
0.28
2665.57
5.38
82.21
Table 5: Counterfactual results
Number of operators
Yearly investment per operator (million US dollars)
Marginal cost per GB (US dollars)
Price per GB (US dollars)
Monthly data traffic per user (MB)
Variation in consumer surplus (US dollars)
23
2
3
4
5
116.7
0.14
0.32
1.38
108.3
0.17
0.27
1.62
0.025
94.8
0.23
0.32
1.38
-0.025
83.5
0.31
0.40
1.13
-0.020