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Merger Simulation in an Open Economy
Jay Pil Choi and Jae Nahm∗
March 2009
Abstract
Since the mid-1990s, antitrust authorities and courts in the U.S and the EU use several
merger simulation models to evaluate unilateral effects of horizontal mergers. Merger
simulation models combine game theoretic models with some premerger market data such as
demand elasticity to predict the impact of the merger on price, consumers' surplus and total
welfare. However, standard merger simulation tools are developed for a closed economy and
do not consider the role of exports. In an open economy or export-oriented economy, a
typical manufacturing industry exhibits quite high export shares. The welfare effects of
merger would be quite different between an open economy and a closed economy because of
export volumes. This article provides a framework on how to incorporate the export role in a
standard Cournot merger simulation model.
∗ Department of Economics, Michigan State University, 101 Marshall-Adams Hall, East
Lansing, Michigan 48824-1038, Tel: 517-353-7281, E-mail: choijay@msu.edu,
Department of Economics, Korea University, Shung-buk Gu Anam-dong, Seoul. , Tel: 82-2-
3229-2221, E-mail: shnahm@korea.ac.kr
1. Introduction
Antitrust law in several countries prohibits mergers that would substantially lessen
competition. Evaluation of anticompetitive effects of mergers has been largely based on
structural approaches such as market shares and market definition. For instance, the FTC
merger guideline has an initial screening of proposed mergers based on Herfindhal Index. If
the change of the index is large, it is most likely that the antitrust agency blocks the proposed
merger.
In the calculation of domestic market shares, antitrust agencies consider import volumes as
one of the domestic suppliers and calculate market shares because import volumes can be a
good substitute for domestic output. However, the role of export on the merger effects has not
been well incorporated in the merger evaluation.
The market structural approaches (market shares and market delineation) are based on the
implicit assumption that the extent of market share changes caused by a merger is a good
predictor of market power changes by the merger. However, there is no underlying
relationship between marker shares changes and consumer/social welfare changes.
Several alternative approaches combined with game theoretic tools and econometrics has
been developed to evaluate the effects of merger. One of the approaches is merger simulation.
Merger simulation is a simple tool to ‘simulate’ mergers. Once we have data on demand and
cost functions, by using a game theoretic tool, we can predict price/welfare changes with
regard to mergers. For instance, suppose that the demand for a product is p=1-Q, and the
marginal production costs are all zero. Then, by using a Cournot goods competition model,
we can predict the amount of price change when the number of firms decreases from N to N-
1.
Several merger simulation tools have been developed for homogeneous and differential
products model, such as Cournot model, Antitrust Logit Model, AIDS (almost ideal demand
system) model, PCAIDS (proportional calibrated AIDS), BLP model.
In a closed economy or large economy such as United States, manufacturing’s export shares
are not large. However, in a small, open economy or export-oriented economy, a typical
manufacturing industry exhibits quite high export shares. Usually, more than 40% of industry
outputs are exported abroad in Korea. The welfare effects of merger would be quite different
between industries with different export volumes. In this article we modify a Cournot merger
simulation model in order to incorporate effects of exports.
In our model, there are N firms in an open economy. Firms do price discrimination between
domestic and foreign export markets. Firms face horizontal foreign export price and down-
slope domestic demand curve. Firms are engaged in Cournot competition in the domestic
market. As the standard third degree price discrimination, firms choose their domestic and
export output levels such that their marginal revenues in domestic and in foreign markets are
equal. Suppose that two of the N firms merge with each other. As the standard Cournot model,
the two firms becomes one, and the other firms would expand their outputs. In the open
economy, firms export some volumes of their production outputs. When the merging firms
restrict their outputs, the domestic price increases, and the other firms can reallocate their
outputs between domestic sales and exports without increasing their output levels. In the
standard Cournot model without export, firms increase their outputs along their marginal cost
curves. However, in an open economy, if they want, firms can increase their domestic output
levels simply by reshuffling their outputs between domestic and export markets. We find that
the merger effects on price, consumer surplus and social welfare are quite different depending
on the pre- merger export shares out of the total output level.
This article consists of two parts. In the first part, in a symmetric Cournot model with export,
we analyze how merger effects change depending on the export market. We show that the
export market has huge effects on the merger, which indicates that we cannot apply the
antitrust tools developed in a closed economy to an open economy without some
modifications. In the second part, we allow asymmetry among firms and devise a Cournot
merger simulation model, which incorporate the role of exports.
2. Model
There are N firms in a small economy. The firms sell their outputs in two separated
markets, domestic and export markets. The foreign market is much more competitive than the
domestic market. For simplicity, we assume that the foreign market is perfectly elastic at
price PF. That is, the firms can export their outputs at PF, and the export price is exogenously
given.1 The export output levels by the N firms is denoted by
{}
12
,,,
N
x
xx x ′
=L
In the domestic market, the firms face a down-slope demand, pD(Q), and each firm
engages in Cournot competition. The output levels by the N firms is denoted by
{}
12
,,,
N
qqq q
′
=Land the total quantity is 1
D
N
Qq q
=
+L
Each firm’s cost function is denoted by 2
()
2
i
iii
Cqx
α
=+, which indicates the
marginal cost is ( )
ii i
qx
α
+, where αi measures each firm’s production efficiency. Also,
besides the production efficiency, these firms have different domestic sales advantages. These
domestic strengths are denoted by θi. Each firm’s profit function is as follows,
2
()
2
i
iDiFi ii ii
Pq Px q x q
α
π
θ
=+− +− (1)
Different firms have different θi, which reflects each firm’s domestic sales strengths. θi
measures each firm’s relative strength of domestic sales over its export market.
Each firm maximizes the profit function by choosing qi and xi. The first-order-
conditions w. r. t qi and xi are as follows,
F. O .C:
() 0
iD
Diiiii
ii
P
Pqqx
qq
π
αθ
∂∂
=
+−+−=
∂∂ , for 1, 2, 3, , .iN
=
L (2)
()0
iFiii
i
Pqx
x
π
α
∂=− +=
∂ , for 1, 2, 3, , .iN
=
L (3)
It is one application of the standard 3rd degree price discrimination. Each firm would sell its
1 Even though we relax the assumption that the export market is perfectly elastic, we still get the
same qualitative results as long as the export market is more elastic than the domestic market. In
order to simplify the analysis, we assume the perfectly elastic export market.
output in domestic and foreign markets such that the marginal revenue in the domestic market
is the same as the marginal revenue in the export market and the marginal revenue is equal to
the marginal cost.
By arranging equations (2) and (3), we have the following condition.
()
D
D
ii iii F
i
P
Pq qxp
q
θα
∂
+−=−+=
∂
(4)
Since the marginal revenue in the export market is pF, the domestic output level is set such
that the domestic market’s marginal revenue minus θi is equal to pF. The export volume is set
such that the marginal cost at the total production volume is equal to pF. The following figure
shows each firm’s optimal domestic and export outputs.
[Figure 1 here]
For instance, as pF gets higher, the export volume increases, and the domestic output
level decreases. Also, if export were prohibited, the domestic output levels would increase,
and domestic consumers would pay a lower price for the product.
Given pF, we can calculate the equilibrium domestic output levels and export volumes. For
simplicity, we assume a linear domestic demand curve, p=a-bQ. The first order conditions
above can be represented by a Matrix form.
1
()
iNiiF
abq q q bq P
θ
−++ −−=LL
=> 1
1()(2)
Fi i N
aP q q q
b
θ
−− = ++ +LL
=>
11
22
21 1
12 1 1
11 2
F
F
NFN
qaP
qaP
b
qaP
θ
θ
θ
−−
⎡
⎤⎡ ⎤
⎡⎤
⎢
⎥⎢ ⎥
⎢⎥−−
⎢
⎥⎢ ⎥
⎢⎥
=
⎢
⎥⎢ ⎥
⎢⎥
⎢
⎥⎢ ⎥
⎢⎥−−
⎣⎦
⎣
⎦⎣ ⎦
L
L
MM
MMOM
L
⇔ 1
qb
Λ
=Ω --- (5)
where Λ=
21 1
12 1
11 2
⎡⎤
⎢⎥
⎢⎥
⎢⎥
⎢⎥
⎣⎦
L
L
MMOM
L
and
Ω
=
1
2
F
F
FN
aP
aP
aP
θ
θ
θ
−−
⎡
⎤
⎢
⎥
−−
⎢
⎥
⎢
⎥
⎢
⎥
−−
⎣
⎦
M
We get the equilibrium domestic output levels, *1
1
qb−
=
ΛΩ
.
From equation (3), we get x*.
xi* = Fi
i
pq
α
−
----- (6)
3. Merger Effects in symmetric case
For a simple comparison, we look at the symmetric case, in which all N firms have
the same α, ,and all θi are zero.
(a) Closed Economy
Suppose that two of the N firms merge with each other. In the closed economy, the effects of
merger on domestic price depend on the number of firms and the production efficiency. For
numerical results, we assume that the domestic demand curve is p=1-Q. The following table
shows the effect of mergers on domestic price.
Table 1. The amount of price changes in a closed economy
when two firms merge with each other
α
N 0.3 0.5 1 2 3
3 30.3% 28.6% 25.0% 20.0% 16.7%
4 23.3% 22.2% 20.0% 16.7% 14.3%
5 18.9% 18.2% 16.7% 14.3% 12.5%
6 15.9% 15.4% 14.3% 12.5% 11.1%
7 13.7% 13.3% 12.5% 11.1% 10.0%
8 12.0% 11.8% 11.1% 10.0% 9.1%
9 10.8% 10.5% 10.0% 9.1% 8.3%
10 9.7% 9.5% 9.1% 8.3% 7.7%
11 8.8% 8.7% 8.3% 7.7% 7.1%
For instance, when two firms merge with each other, the domestic price increases by 30.3%
when the initial number of firms is 3, and the value of α is 0.3. The effect on price changes
gets higher as α gets higher. The explanation is as follows. α measures the marginal
production cost. When two firms merge with each other and becomes one firm, the output
level by the two firms decreases, and the market price increases. Since the market price gets
higher, other firms want to increase its output. The amount of output increase by the other
firms depends on the marginal production cost. When α is high, the marginal production cost
is high, and, thus, the amount of output increase by the other firms is small. Thus, the price
increase by the merger gets larger.
(b) Open economy
We would investigate the effects of merger on the domestic price in the open economy.
Post merger, the merged firm could restrict its output level. Then, the domestic price
increases, which is equivalent to an individual firm’s marginal revenue increase. Since the
individual firm’s residual marginal revenue increases, other firms can expand their outputs. In
the closed economy, firms increase their outputs along their marginal costs. However, in an
open economy, they can reshuffle between exports and the domestic sales. In the latter case,
firms with export volumes behave as if their marginal cost curve is flat. The following figure
shows the differences.
[figure 2 here]
Thus, when the merged firm restricts its output level, in the open economy with export
volumes other firms more easily expand their output level, which nullifies the initial output
reductions. The following table shows the size of the amount of the domestic price increase
as the foreign export price changes.
Table 2. Domestic price increase in an open economy
N pF 0.2 0.3 0.4 0.5
3 16.7% 12.3% 5.2% 4.3%
4 11.1% 8.0% 3.1% 2.5%
58.0%5.6%2.0%1.7%
66.1%4.2%1.4%1.2%
74.8%3.2%1.1%0.9%
83.8%2.6%0.8%0.7%
93.2%2.1%0.7%0.6%
10 2.7% 1.8% 0.5% 0.5%
11 2.3% 1.5% 0.5% 0.4%
For instance, suppose that the export price is 0.5 and the number of firms is three.
When two firms merge with each other, the domestic price increases only by 4.3%. The
extent of the price increases in the open economy with export volumes is much smaller than
that of the price increase in the closed economy.
4. Merger Simulation in an open economy
Merger simulation has been developed and widely used in order to evaluate the welfare
effects of merger in US and Europe antitrust cases. Merger simulation models combine game
theoretic models with some premerger market data such as demand elasticity to predict the
impact of the merger on price, consumers' surplus and total welfare. There merger simulation
models are varying on the market competition modes (such as Cournot competition or
Bertrand pricing competition) and demand estimates estimation/calibrations method. The
simplest model is a Cournot merger simulation designed for homogenous goods. Here, we
modify the Cournot merger simulation model in order to incorporate the export volume.
Usually, merger simulation consists of two parts. The first part is to get industry parameters.
From observed industry data such as industry outputs, price, demand elasticity, export price
and export volumes, we have to recover industry parameters such as cost efficiency, demand
curves, domestic competition strength by using firms’ first order conditions. Second, by using
the recovered parameters, we ‘simulate’ the merger and predict the merger outcomes. Thus,
the inputs for the simulation in this paper are {pD, pF , x, Q,, ε }, where ε denotes the
domestic demand elasticity at price pD. The parameters to be estimated are {αi,θi}. We assume
that pF does not change between before-and after- merger. By using the parameters, we
simulate the modified Cournot model to predict the Post merger price, domestic production,
and export volume, {pD, x, Q}.2
The detailed steps are as follows.
(1) Recovering demand curve.
Given the domestic demand elasticity and domestic price and quality, we recover the
shape of domestic demand curve. In order to recover the demand curve, we have to assume
demand function curvatures. In this model, for simplicity, we assume a linear demand curve,
p=a-bQ.3 We observe (ε, Q, p) in the domestic market. Then, from the ε=Qp p
b
p
QQ
∂=−
∂, we
can get the value of b. From p=a-bQ, we can get the value of a. Therefore, we can recover {a,
b}, the domestic demand curve.
a = p +bQ = p -εQ
p
b = - εQ
p
(2) Calibrating firms’ efficiency parameters (αi and θi).
Equations (5) and (6) tell us the relationship between an individual firm’s optimal
domestic production and efficiency parameter values. We have two equations (equations, 5
and 6) and two unknown parameters (αi and θi). Thus, from equations (5) and (6), we can get
αi and θi
(3) the merging firm’s efficiency gains.
2 As the domestic price changes, the demand elasticity changes along the curvature of the
demand function.
3 Alternatively, we can assume a constant elasticity demand curve.
The merging firm can enjoy merger specific efficiency gains. As usual, we would assume
either that the merging firm’s efficiency parameter is the lower value of the two firms’ pre-
merger efficiency parameters. Or the merging firm’s efficiency parameter is the weighted
average of the previous two efficiency values.
12
min( , )
m
θ
θθ
=,and 12
min( , )
m
α
αα
= or
12
12
12 12
mxx
x
xxx
θ
θθ
=+
++
, and 11 2 2
12
11 2 2 11 2 2
() ( )
()( )()( )
mqx qx
qx qx qx qx
α
αα
+
+
=+
+++ +++
(4) Computing post-merger equilibrium.
Post merger, there are two changes. First, the number of firms changes. Second, the merged
firm has a new efficiency parameter. Once the firm-specific efficiency parameters have been
recovered, we can simulate the post-merger equilibrium by calculating the new equilibrium
point. We can find the new equilibrium quantities and price satisfying equations (4) and (5)
with the new efficiency parameters.
By taking these four steps (1)-(4), we can conduct the merger simulation that
considers the role of exports in an open economy. We would compare the prediction by the
standard Cournot simulation model with the prediction by our Cournot merger simulation
mode with exports. For instance, we put the following data; q={65, 60,50,55}, x={60,50, 40,
35}, pd=60, and pF=40. The standard Cournot simulation model that does not consider the
role of exports predicts the post-merger domestic price to be 68, which implies the price
increases by 13%. However, the simulation model with exports predicts the post-merger
domestic price to be 63, and, thus, the predicted price change is 5%, which is dramatically
different from the prediction by the standard merger simulation.
References
Ashenfelter, O., D. Ashmore, J. B. Baker, S. Gleason, D. S. Hosken (2006),
“Empirical Methods in Merger Analysis: Econometric Analysis of Pricing in FTC vs.
Staples,” International Journal of the Economics of Business 13, 265-279
Baker, J. B. & D. L. Rubinfeld (1999), Empirical Methods in Antitrust Litigation:
Review and Critique, in: American Law and Economics Review, Vol. 1(1/2), pp. 386-435.
Baker, J. B. (1999a), Developments in Antitrust Economics, in: Journal of
Economic Perspectives, Vol. 13 (1), pp. 181-194
Berry, S.T., J. Levinsohn, and A. Pakes (1995), “Automobile Prices in Market
Equilibrium,” Econometrica 63, 841-890.
EC Commission (2000), “Case No COMP/M.1672 – Volvo/Scanina”
http://ec.europa.eu/comm/competition/mergers/cases/decisions/m1672_en.pdf
Epstein, J. R., and D. L. Rubinfeld (2004), “Effects of Mergers Involving
Differentiated Products,” Technical Report for EC Commission, COMP/B1/2003/07, October
7, 2004.
Nevo, A. (2000), “Mergers with Differentiated Products: The Case of the Ready-
to-Eat Cereal Industry,” Rand Journal of Economics 31, 395-421.
Shapiro, Carl (1995), “Mergers with Differentiated Products,” mimeo.
U.S. DOJ and FTC (1997), “1992 Horizontal Merger Guidelines [with April 8,
1997, Revisions to Section 7 on Efficiencies],”
http://www.usdoj.gov/atr/public/guidelines/horiz_book /hmg1.html
U.S. DOJ and FTC (2006), “Commentary on the Horizontal Merger Guidelines,”
March 2006.
Whinston, M.D (2007), “Antitrust Policy toward Horizontal Mergers,” Chapter 36
in: M. Armstrong and R.H. Porter, Handbook of Industrial Organization Volume 3, North-
Holland.