Download Oligopolistic Competition on Local Markets with Product

Oligopolistic Competition on Local Markets with Product Differentiation
Mateusz Zawisza1, Bogumił Kamiński
1
1Warsaw School of Economics, Al. Niepodległości 162,
02-554 Warsaw, Poland
Abstract. Contemporary multinational and multiproduct conglomerates compete with each
other at different geographical locations. Mutual forbearance hypothesis suggests that such
firms don‟t compete fiercely on any of regional markets, because they fear rivals‟ retaliation
actions on other local markets. As a result, companies follow a live-and-let-live policy, which
deteriorates a market competition. This paper investigates how multiple contacts on different
geographical locations influence the market competitiveness. We show that the geographical
market structure matters and identify determinants of average market price. We evaluate
the performance of this type of local market competition and compare it to the single market
structure. Finally, we suggest recommendations for antitrust agencies, concerning
the appropriate measures of market concentration in the context of local market competition.
We apply simulation methodology to generate different market structures and employ a
game-theoretical framework to calculate equilibrium prices on each of simulated market.
Keywords: local market
oligopoly pricing, simulation.
1.
competition,
multimarket
contact,
mutual
forbearance,
Introduction
Contemporary national or multinational conglomerates, especially in local infrastructure intensive
industries, operate on segmented local markets and compete with other conglomerates as well as
smaller regional companies. It creates interdependence of price behavior between companies.
Competing in one region has its repercussion on other local markets. Company, which sets one
common price for all local markets, has to take into account its effects on all regions. Exploiting one
region with its monopoly power can destroy its competitiveness on other local markets. On the other
hand, harsh competition with other firms on some local markets, would not let to harvest monopoly
profits on the other markets.
Classical standard economics models assume single global market with free entry and treat each
regional market as independent. In fact, the number of companies in each region varies and it depends
on both the demand and the cost of entry, e.g. new infrastructure investments. Moreover, since
companies set one common price, there is a strong interdependence between local markets as they
cannot be treated separately. For example on Polish telecommunication market there is one incumbent
company providing its services in most of the regions, several challenging companies and over one
thousand of local companies, see UKE (2011). Fig. 1 shows the percentage of towns with
telecommunication services with only one telecommunication service provider by voivodeship in
Poland. It can be clearly seen that although there are many services providers the problem of local
monopolies is very strong. The second thing to notice is that the percentage of monopolies is highly
variable regionally. Following this observation the market leader has its prices regulated and is not
allowed to discriminate them geographically. The aim of this paper is to verify if such a policy
towards market regulation is beneficial for the customers.
Multimarket competition is associated with the mutual forbearance hypothesis, which was first
raised by Edwards (1955). According to this hypothesis, firms which encounter each other at
numerous local markets, have no incentive to launch an aggressive pricing on one market, because
such a behavior could trigger the retaliation of its rivals on the other markets. Potential gains from
winning one local market can be relatively small to the loss caused by retaliatory actions of opponents.
Therefore, as stated by Edwards (1964): “conglomerates may develop a live-and-let-live policy
designed to stabilize the whole market structure of the competitive relationship”.
Fig. 1. Percentage of monopolies in towns with telecommunication services by voivodeships in
Poland; on map of Poland voivodeships are colored according to monopolization level; white: below
60%, light grey: 60% - 80%, dark grey: over 80%. Data source: UKE (2011).
Empirical evidence supports the mutual forbearance hypothesis. Heggestad and Rhoades (1978)
proved the mutual forbearance effect in the context of American banking sector industry. They
demonstrated that multi-market meetings between dominant banks adversely affect the degree of
rivalry within markets. They argue that the acquisition by dominant firms outside their traditional
geographic markets is likely to be detrimental to competition and performance in the markets where
they operate. Other empirical evidence suggesting the validity of mutual forbearance hypothesis were
performed for the airline industry – Evans and Kessides (1994), cement industry – Jans and
Rosenbaum (1996) or hotel industry – Fernandez and Marin (1998). There are also some theoretical
results suggesting that the potential for mutual forbearance exists, see Berheim and Whinston (1990).
Using a game-theoretical framework, they show conditions under which multimarket contact can
facilitate a collusion. Also experiments of multimarket contact across two Cournot duopoly markets
were performed, see Phillilps and Mason (1992). They find that the multimarket contact causes
the price in their „monopolistic‟ market to fall and the price in the other market to rise.
Perloff and Salop (1985) introduced a model of product differentiation which combines elements of
both spatial and representative consumer formulations. It demonstrates how customers' preferences are
formed and what is customers' decision mechanism. Finally, they derive analytically an equilibrium
price formula for a single market. For the purpose of this research, we extend the model of Perloff and
Salop (1985) by introducing: (1) geographically segmented market (2) inelastic demand and (3)
the parameter controlling the strength of product homogeneity. Geographically segmented market alter
directly firms‟ profit functions, which change their price behavior in comparison to Perloff and
Salop (1985). Introduced inelastic demand means that customers can refrain from purchasing any of
products if none of them meet their expectations. Finally, introducing the strength of product
homogeneity makes our model the wider class of models, which encompasses the special case of
homogenous product Bertrand competition.
In this research we investigate the influence of market regional structure on price behavior from:
(1) global perspective (2) firm perspective and (3) regional perspective. We test numerous measures of
concentration to indicate the most useful for antitrust agencies in determining an average price in
multimarket context. We evaluate the performance of regulated versus unregulated market and suggest
recommendations for antitrust regulators. In order to take into account the regionally segmented
market structure we apply simulation methodology to generate different market structures and employ
a game-theoretical analysis to calculate equilibrium prices on each of simulated market.
The article is organized as follows. In next Section 2, it presents the extended model of Perloff
and Salop (1985) and numerical procedure of finding equilibrium prices. Then in Section 3., we
demonstrate a simulation experiment setup as well as results from three different points of view:
(1) global view in Subsection 3.1 (2) firm‟s view in Subsection 3.2 and (3) regional view in
Subsection 3.3. Additionally, we compare the performance of regulated market to unregulated market
in Subsection 3.4. The paper concludes in Section 4. with recommendations for antitrust agencies and
suggestions for the future research.
2. Model of Local Market Oligopoly
Following model is the extension of Perloff and Salop (1985) model of product differentiation.
The extension consists in (1) including local market segmentation (2) introducing elastic demand for
products and (3) incorporating the parameter controlling the strength of product homogeneity.
The model consists of two types of agents (1) firms, which offer one product in selected local markets
and (2) customers, who are assigned to the specific local market and buy no more than one unit of
product from chosen company, which is available in their region. Such a setup is typical for cable TV
or internet access competition. Companies in order to be able to compete on a local market have to
invest in local infrastructure and customers usually will not sign more than one contract for such
services.
There are
firms and
local markets. At least one company is present in each region.
,
Market structure is described by binary matrix
, where:
{
Notice that sums of columns ∑
company is present, and sums of rows ∑
at given region.
informs about the number of local markets, at which given
informs about the number of firms, which are present
We want to simulate a situation with different sizes of companies on the market – ranging from
global player to local challengers. Therefore matrix A is generated for each simulation according to
the following probability distribution:
⋀ (
)
It follows that firm is expected to be active in
regional markets. In particular, first
firm
is present in each region, which guarantees that each region has at least one company and
makes first company a dominant one. If we treat
as a firm size and assume that a firm size is
Zipf distribution random variable, see Axtell (2001), then the following statement should be satisfied:
(
)
, which is exactly the distribution of firm sizes in our model. It
implies that suggested generating process of market structure results in Zipf distribution of firm sizes,
which is empirically proved to be a valid distribution of firm sizes, see Axtell (2001).
Each customer has its own preferences for brands, which are available in his region. This takes into
account non-price aspects of available offers, for example product quality or customer service level.
The customer derives utility form given brand
*
+ according to his reservation price
,
which is drawn from normal distribution with expected value of and standard deviation of :
(
)
Where
denotes normal distribution. Additionally, we take account for the strength of product
homogeneity by drawing vector
from multivariate normal distribution (
) with
correlation and corresponding covariance matrix:
[
]
The higher correlation coefficient , the more similar are products to customers. Notice that limiting
case with
results in homogenous product Bertand competition. Parameter
might be also
interpreted in terms of price obfuscation conducted by companies, see Latek and Kaminski (2009).
Given price of -th firm
, customer can earn surplus from buying -th product, which is equal
to:
Client chooses the brand with the largest surplus, which is available to him, provided it is
nonnegative:
*
(
)
+
Where () is an indicator function, which informs whether firm
(
)
is present in the region of client :
{
Notice that if the largest surplus is negative, client restrains from buying the product. It introduces
elastic demand, which is not present in the original model of Perloff and Salop (1985).
In the special case of two companies and , the probability that
(
)
(
)
is chosen by client is given by:
(
)
(
(
)
√
)
Where is cumulative standard normal distribution function. In general case probability of product
being the best choice according to client is given by:
(
⋀
*(
) (
)
)
+
∫
(
∏
)
*
(
(
* (
)
√
+
)
)+
Notice that unlike the original model Perloff and Sallop (1985) the sum of these probabilities over
not necessarily sums to unity. The outstanding mass probability is the probability that client refrains
from buying.
We assume that each local market is equally populated by infinite number of agents and local
market is identified by an agent. Hence, we can interpret (
) as the quantity share gained
by firm in the market of client . Therefore quantity sold by company on the local market is
proportional to the probability of choosing brand by client from market :
(
)
(
)
Profit function of company , given its own price and rivals‟ prices, is the sum of profits over all
regions:
(
Where
)
∑ (
)(
(
∑
)
)(
)
is the marginal cost of supplying the good to the customer.
Company sets price, which maximizes its profit at given prices of competitors, according to
the best response function:
(
)
(
)
function
()
set
to random values
set
to zeros
(|
|)
while
set
for each company
*
+
set
(
)
end for
end while
return
end function
Table 1. Function equilibrium() which returns equilibrium prices
Equilibrium finding is conducted numerically by applying procedure
Table 1.
() presented in
3. Experiment Setup and Results
The experiment setup procedure is presented in Table 2. In order to capture the influence of
regional distribution of companies, we generate new market structure at each simulation run . Given
specified market structure we perform
() procedure, which calculates an equilibrium price
vector. For purposes of further analyses some statistics are computed concerning characteristics of
market structure at (a) global, (b) firm and (c) regional level. Additionally, for comparison purposes
we calculate equilibrium prices in a single market for each number of companies on such a market.
for each simulation run
*
+
generate new binary matrix of market structure
calculate equilibrium prices by
() procedure
calculate statistics for analysis from a global perspective (dataset with rows)
calculate statistics for analysis from a firm perspective (dataset with
rows)
calculate statistics for analysis from a regional perspective (dataset with
rows)
end for
for each market size
*
+
generate one-row binary matrix
,⏞
-, corresponding to a single market with
calculate equilibrium prices by
() procedure
end
firms
Table 2. Simulation experiment setup
Simulation parameters are fixed and presented in Table 3. Further research requires performing
a sensitivity analysis across some crucial parameters concerning market structure and customer
preferences. The simulation is implemented in GNU R statistical environment, see R Development
Core Team (2011).
Parameter
ϕ
µ
σ
ρ
ε
Simulation values
Interpretation
Oligopolistic Local Market Structure
5
The number of firms
400
The number of local markets
0
Marginal Cost of unit production
Customer Preferences
Normal distribution
Probability density function of customer utility
5
Expected value of customer utility
1
Standard deviation of customer utility
0
Correlation of customer utilities between brands
Simulation Setup
100
The number of times whole simulation is run
0.01
Desired accuracy
Table 3. Model parameters and their values
In the following sections we inspect determinants of price. Price mechanism from a global
perspective follows in subsection 4.1. Firms‟ price behavior is investigated in subsection 4.2. Price
determinants at a regional level are presented in subsection 4.3. Finally, in subsection 4.4 we compare
regimes of regulated and unregulated market.
3.1 Global perspective
*
+
For the purpose of the analysis from a global perspective we treat each simulation run
as one data observation point, which results in the dataset with
rows. In this analysis, we are
interested in explaining determinants of average market price weighted by market shares. For each
simulation , average market price is calculated as follows:
∑
Fig. 2 (a) shows that an average price varies from 1.7 to 2.1. Since the only difference across
simulation runs is a market structure given by matrix , it follows that market structure matters. For
comparison, notice that monopoly price on the single market is c.a.
, duopoly price is c.a.
and triopoly price is c.a.
. Our market with
unequally distributed companies results in
an average prices dispersion which covers duopoly price, but is definitely lower than a monopoly price
and higher than triopoly case. Moreover, note that the average number of companies in a region is
c.a.
(
), which might mistakenly suggest that price should fall
between duopoly and triopoly, which is not the case. Further figures explores this market structure
impact.
Indeed, average number of companies per region is an important factor in explaining differences in
average price across simulation runs, see Fig. 2 (b). As we may see, the average number of firms
varies between
and
, centered around its average
. The higher average number of
companies, the lower is the average market price. But still, there is much unexplained variance of
33%.
It seems that better predictor of average market price is the fraction of regions with monopoly,
i.e. regions with only one company, see Fig. 2 (c). This fraction varies between
and
and can
explain 95% variance of average market price. The importance of this factor shows that the fraction of
regions occupied by a dominant firm is far more important than the average number of firms per
region.
It can be found out that the main driver of average market price is the weighted average of
Herfindahl-Hirschman Index (HHI). HHI is the measure of market concentration and is calculated as
the sum of squared market shares, see Tirole (1994). The higher HHI, the more concentrated is
the market. HHI takes values from ( -. HHI is equal to , if there is a monopoly. HHI is near ,
if there are many companies with small (equal) market shares. However, we calculate HHI on each
regional level and average it afterwards. Next, we show how we calculate regional HHI.
Fig. 2. Market price histogram (a) and its correlates (b-d).
In order to calculate market share of company in region we have to normalize firms‟ quantity.
Note that the sum of firms‟ quantity does not have to sum to unity. It is caused by an introduced elastic
demand, which makes some customers to refrain from buying any product. Therefore we calculate
the total amount of products sold in region as follows:
∑
We get the market share of company
in region
(
)
by normalizing its quantity:
(
Herfindahl-Hirschman Index in region
)
is the sum of squared market shares in region
∑
Finally, regional HHI is weighted sum of HHIs in all
regions:
∑
∑
:
As we may see in Fig. 2 (d), regional HHI explains 99% variance of average market price.
varies between 50% and 64%. Note that duopoly with equal market shares results in
HHI of
(
), wheras monopoly has HHI of
Hence, regional HHI of
is between duopoly and monopoly cases, which is congruent with price comparisons.
Regional
can explain 99%, whereas global
(without taking into account regional
markets) is statistically insignificant in explaining average market price (
). It is
an important implication for antitrust agencies, which regularly calculate
indices. It shows that, in
the context of fragmented regional markets, it is crucial to calculate regional
in order to properly
evaluate the performance of agency‟s measures aimed at improving market competition.
3.2 Firm perspective
In this section we want to take a firm perspective and find out determinants of its price. In our
model we have
firms which compete with each other at
(or less) regional markets.
We have one major company, which is present in each region and other companies, which are
operating at selected local markets. In this analysis, we threat one company in each simulation run as
one data point, which results in
observations.
Fig. 3. Firm price histogram (a) and its correlates (b-d).
As we can see on Fig. 3 (a), the dispersion of firms‟ prices is larger than for average market price.
Firms‟ prices vary from 1.4 to 2.6. Moreover, we see that the distribution of firm prices is bimodal.
The largest mass probability falls between
and
. The rest mass probability is located between
and
. As we can investigate in further pictures on Fig. 3 (b) - (d), this bimodality is created by
the fact that major company, which is a monopolist in some regions, sets systematically higher prices
than other companies.
As before in a global perspective, we see that the fraction of regions with monopoly is an important
factor in determining firm prices, see Fig 3 (b). Especially, it is a very good predictor of monopolist‟s
price. However, there is still a lot of noise in predicting price of the remaining minor companies.
Regional
, which is a perfect predictor in a global perspective, is not so good at predicting firm
behavior, see Fig. 3 (c). Its power in explaining firm price is similar to the fraction of regions with
monopoly.
Fig. 3 (d) shows that the main factor of firm price is its individual
. Firm specific
the average of
s from regions, in which firm is present. The following formula applies:
∑*
is
+
∑*
+
Notice, that since the major company is present in each region we have
. Therefore, Regional
is a good predictor only for monopoly company and not for
the remaining firms, as depicted in Fig. 3 (c).
3.3 Regional perspective
In this section we want to take a regional perspective and find out what characteristics of given
region and global market influence an average price in given region. In our model we have
local markets. In each region at least one major company operates. Maximum number of firms on
the local market is
. In this analysis, we threat each region as one data point, which results in
observations.
Fig. 4 Average regional price histogram (a) and its correlates (b-d).
On Fig. 4 (a) we observe that average price in regions varies from 1.6 to 2.6. Distribution is
bimodal. The largest part of probability mass is located between 1.6 and 2.0. The remaining part is
from 2.0 to 2.4. Prices from the latter range are charged by companies, which are the only player in
the region, see Fig. 4 (b) - (d).
Fig. 4 (b) depicts Box-and-Whisker plot and shows that the average price in region depends
negatively on the number of companies, which are present in this region. However, the relationship is
not linear and marginal impact on price is decreasing, i.e. the largest decrease in a price is resulted
from introducing 2-nd company, and the smallest decrease is attained by the entry of 5-th company.
Still, there is a lot of price variation, which is not explained by the number of firms.
As we may see in Fig. 4 (c), regional
is an important predictor within given number of firms
in the region. Higher
in the region makes an average price in this region higher, ceteris paribus.
Still, there is a lot of unexplained variation in prices. This high unexplained variance both on Fig. 4 (b)
and (c) shows that the price in the region cannot be explained fully by characteristics of this region.
Fig. 4 (d) shows that also external characteristics of the whole market play important role. It depicts
that the higher fraction of regions with monopoly, the higher regional prices given the number of firms
fixed. Hence, we see that monopolized regions create negative externalities on other monopolized and
not monopolized local markets. It is an important implication for antitrust agencies, because promoting
competition in monopolized regions can generate positive results in this region and the remaining part
of market.
3.4 Unregulated versus regulated market comparison
In previous sections we assume that each company sets one common price which applies to all
local markets. Such an assumption might be the part of antitrust regulations, which prevent companies
from a socially unbeneficial discriminatory pricing. We will call such a regime as ‘regulated market
regime’. On the other hand, if an antitrust agency let companies to set their prices freely on each of
their local markets, we will call such a regime as ‘unregulated market regime’. In this section we want
to compare both regimes.
Fig. 5. Comparison of prices and supplied quantity under regulated and unregulated regimes.
The only determinant of price on the unregulated market is the number of companies in the region.
This fact can be observed on Fig. 5 (a) of price histogram for both regimes. Under the unregulated
regime, there are only five unique prices, which correspond to the price of monopoly, duopoly,
triopoly, etc. We see that these prices vary from
i.e. the price in the region with five competitors,
to
, i.e. the monopoly price. The most frequent price is the duopoly price of
. Under
the regulated regime, price dispersion is lower, since prices change from
to
. It follows that
under the regulated regime, regions with only one company, can benefit at the cost of regions with
three and more companies, which have to pay higher prices than they would under the unregulated
regime, see Fig. 5 (c). The fraction of customers paying lower prices under the regulated market is
only c.a.
, see Fig. 5 (b). It means that c.a.
of customers would prefer to be in
the unregulated regime. However, Fig. 5 (d) shows that the benefit for 72% of population from
switching the regime would be lower than the loss for
of customers. The average price under
regulated regime is lower and supplied quantity is higher. This positive net effect is achieved mainly
thanks to much lower prices in regions with one company under the regulated market. In the regime
with freely set prices, the major company exercises its market power in the region without other
competitors by setting high monopoly price and supplying low quantity. Under the regulated market
with only one price per company, a monopoly company has still an incentive to compete on other
regional markets and therefore it suppresses its price, which is beneficial to regions occupied by
the single company.
The conclusion from this comparison is that market regulation does not strongly affect average
prices on the whole market under simulation parameters, but it serves as a tool allowing regulator to
improve price equality among customers in different geographical regions.
It is important to note that the obtained results concerning the performance of the regulated market
depend on the specific parameterization. Especially, parameters of customer preferences are crucial in
this context. Further research aimed at a detailed sensitivity analysis is required.
4 Conclusion
Herfindahl-Hirschman Index (HHI) is an important statistics calculated by antitrust agencies.
We find out that the way HHI is calculated is crucial for its ability to predict average market price.
Agencies, which are interested in lower prices on the geographically segmented market, should
calculate HHI for each region and average it afterwards, instead of calculating it on the global level.
We show that the former way predicts 99% of market price variability, whereas the latter has
no statistically significant impact. A good proxy for regional HHI is the fraction of regions with only
one company. Major company operating on a lot of local markets without other competitors can
concentrate on exploiting these local markets by setting high prices. Such a major company does not
have to compete fiercely on other local markets, which also softens competition in these other regions.
It implies that is important to strengthen the competition in regions of only one company.
On the firm level, we observe that firms' price distribution is bimodal and more dispersed than
average market price distribution. Bimodality is created by the fact that major company sets
systematically higher prices and their pricing behavior differs from minor companies. Monopolist
price can be predicted very well by the fraction of regions with one company and regional HHI,
whereas the behavior of small companies deviates from these relationships. We conclude that firm
price is accurately predicted by the firm specific HHI, but still the exact relationship is different for
a monopolist and the rest of companies.
From the regional perspective, the price in a given region depends on both its internal and external
characteristics. The main internal factors are (1) the number of firms and (2) HHI in the region.
However, regional price is also strongly influenced by the fraction of remaining regions occupied by
a single company. It implies that monopolized regions create negative externalities on the other parts
of market. It is an important implication for antitrust agencies, because promoting competition in
monopolized regions can generate positive results on the whole market.
The comparison of regulated and unregulated markets shows that no regime is Pareto-optimal,
i.e. under each of regime there are both winners and losers. Under the regulated regime, a price
dispersion is lower and regions with a single company can benefit at the cost of competitive regions
with more companies, which have to pay higher prices than they would under the unregulated regime.
The fraction of winners under the unregulated market is higher than losers. However, winners' gains
are relatively small to losers' losses. As a result, the average market price under the regulated regime is
slightly lower and supplied quantity is higher. Exact net effect of regime-switching depends strongly
on a parameterization setup.
Since the obtained results depend heavily on assumed parameters, it is important to perform
detailed sensitivity analysis across some key parameters, e.g. number of firms and distribution of
customers‟ utilities. Especially, it is of special interest to test different generating processes of market
structure. Employing some real data of market structure would be interesting. It would enable to
identifying companies‟ interdependence by assessing their best response functions.
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