Problem_Set_2
Horizontal Mergers
Horizontal merger: Two firms that compete against each other in the same
market merge with each other.
Examples: Ford and Volvo, MCI and Worldcom, AT&T and Cingular. Anheuse
Busch InBev & SABMille
Page 1
Lecture Outline
I. Data: Mergers are a common occu
ence.
II. Theory: Why do firms merge?
• Differentiated goods markets.
III. Department of Justice (DOJ) Merger Guidelines.
• Market definition.
• Herfindahl–Hirschman Index (HHI).
• Diversion ratios.
• Challenge criteria.
Page 2
I. Data Facts
Page 3
I. Data Fact 1
Figure: Mergers & Acquisitions in the United States
I Mergers are increasingly common (bars, left y-axis) and the overall value of
M&A activity is also increasing (red line, right y-axis).
I US M&A looks pro-cyclical: When times are bad (i.e., 90-91, 01, & 08-09
ecessions), M&A activity (number, value) seems to decrease. Why?
Page 4
I. Data Fact 2
Figure: Value of Announced Mergers & Acquisitions (2017)
Value of global M&A deals in billion U.S. dollars
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
339339
XXXXXXXXXX
XXXXXXXXXX
149149
XXXXXXXXXX
XXXXXXXXXX
Value of global mergers and acquisitions in 2017, by industry (in billion U.S.
dollars)
Additional Information:
Worldwide; Bloomberg; 2017
Financial
Consumer Non-cyclical
Communications
Industrial
Consumer Cyclical
Energy
Technology
Utilities
Basic Materials
Diversified
Source
Bloomberg
© Statista 2018
XXXXXXXXXX XXXXXXXXXX1 …
I Mergers are common across a variety of industries.
I In some of these industries firms produce homogeneous goods (e.g., energy, utilities)
while in other industries firms produce differentiated goods (e.g., consumer goods).
Page 5
II. Theory
Page 6
II. Theory: Why do competing firms choose to merge?
1. Reduce competition, raising prices and profits.
2. Coordination of prices or quantities.
3. Production efficiencies: lower fixed and/or marginal costs (greater economies of
scale or scope), leads to higher profits.
4. Other efficiencies: Eliminate inefficient competitors. Takeovers, or the threat of
takeovers, may discipline bad management.
Let’s start by focusing on the effects of mergers on competition.
Page 7
Horizontal Mergers in Differentiated Good Markets
Most markets are differentiated good markets. What are the gains to merging in
these kinds of markets?
Example: Three firms, three goods, marginal costs are zero and demands are
given by
y1 = 1− p1 + s(p2 + p3)
y2 = 1− p2 + s(p1 + p3)
y3 = 1− p3 + s(p1 + p2)
Assume substitutes so 1 > s > 0. Firms compete in prices.
Page 8
Benchmark Nash Equili
ium
Firm 1 chooses price to solve
max
p1
p1 ×
(
1− p1 + s(p2 + p3)
)
Differentiating and solving for best reply,
p1 =
1
2
[1 + s(p2 + p3)]
Imposing symmetry,
p? =
1
2(1− s)
, y? =
1
2(1− s)
, π? =
1
4(1− s)2
Page 9
Merger Nash Equili
ium
Suppose Firms 1 and 2 merge. In contrast to homogenous good case, the new
firm continues to produce both types of goods.
Firm 12 chooses p1 and p2 to maximize profits from both products:
max
p1,p2
{
p1
(
1− p1 + s(p2 + p3)
)
︸ ︷︷ ︸
π1(p1,p2,p3)
+ p2
(
1− p2 + s(p1 + p3)
)
︸ ︷︷ ︸
π2(p1,p2,p3)
}
Differentiating,
∂π12
∂p1
= 0⇒ 1− 2p1 + s(p2 + p3)︸ ︷︷ ︸
∂π1
∂p1
+sp2 = 0
∂π12
∂p2
= 0⇒ 1− 2p2 + s(p1 + p3)︸ ︷︷ ︸
∂π2
∂p2
+sp1 = 0
Page 10
What Effect Does the Merger Have on NE Prices and
Profits?
One Strategy: Solve the new NE and compare equili
ium prices and profits to
the benchmark case.
Alt. Strategy: Evaluate ∂π12∂p1 ,
∂π12
∂p2
at (p?1 , p
?
2 , p
?
3 ). This tells us whether the new
firm will increase prices at the old NE, ceteris paribus.
Note that ∂π1(p
?)
∂p? = 0,
∂π2(p
?)
∂p? = 0, and sp
? > 0 so the derivatives for firm 12 at
the old equili
ium prices are strictly greater than zero. To lower the value of the
derivatives,
I Firm 12 increases the prices of its goods (p1 ↑, p2 ↑) and
I Firm 3 responds by also raising its price (p3 ↑) because best replies are
strategic complements (look at the BRs).
Results:
1. Merger leads to higher prices.
2. Merger is profitable since profits for the merged firm are π1 + π2 and it can
generate the old equili
ium profits by choosing p?.
Page 11
A More General Model
I For simplicity, assume one market. If there are more than one, loop over the
markets to solve for prices.
I J products. Product r ∈ J produced with constant marginal cost cr .
I F multi-product firms. Firm f ∈ F has portfolio F . Denote the portfolio of a
firm f which produces product j as F j
I Each firm f chooses the vector of prices (p) in its portfolio to solve
πf (p
?) = max
p
{ ∑
∈F j
(pr − cr )× yr (p)
}
.
I Profit maximization implies the following FOC for firm f ’s product j :
yj(p) +
∑
∈F j
(
pr − c
)
× ∂y
∂pj
= 0 .
I In Bertrand-Nash equili
ium, J firm prices simultaneously satisfy all J FOCs.
Page 12
A More General Model
I For simplicity, assume one market. If there are more than one, loop over the
markets to solve for prices.
I J products. Product r ∈ J produced with constant marginal cost cr .
I F multi-product firms. Firm f ∈ F has portfolio F . Denote the portfolio of a
firm f which produces product j as F j
I Each firm f chooses the vector of prices (p) in its portfolio to solve
πf (p
?) = max
p
{ ∑
∈F j
(pr − cr )× yr (p)
}
.
I Profit maximization implies the following FOC for firm f ’s product j :
yj(p) +
∑
∈F j
(
pr − c
)
× ∂y
∂pj
= 0 .
I In Bertrand-Nash equili
ium, J firm prices simultaneously satisfy all J FOCs.
Page 12
III. Mergers and Acquisitions in
Practice: Government Guidelines
Page 13
III. DOJ Merger Guidelines: How is a merger evaluated?
I The Department of Justice (DOJ) is tasked with approving potential mergers
and acquisitions in order to ensure that such changes of ownership meet the
standards of antitrust law (e.g., Sherman, Clayton, Robinson-Patman).
I Usually, the DOJ has only a matter of months to understand the implications
of a merger and we’ve already established that each year there are thousands of
mergers across disparate industries.
I To increase efficiency, the DOJ simplifies things in two important ways:
1. It uses several “sufficient statistics” to simplify the analysis. Conducting a merge
analysis properly requires computing pre and post equili
ia which requires a lot of
time and data to do properly. Instead, the hope that is with a handful of simple
statistics (and perhaps a simple model), we can capture 80% of the truth.
2. It publishes guidelines for how it evaluates mergers. This is useful for prospective
firms since a merger between two firms can be costly and time-consuming. These
costs multiply when the government challenges the merger.
For example, both companies are required to submit detailed (and proprietary)
information about their business.
Making the guidelines public enables firms to make better decisions about the
future costs of a merger.
Page 14
Market Definition
I Economic definition typically based on price co
elations and cross price
elasticities. Products that are close substitutes are in the same market.
I Antitrust definition is based on the Hypothetical Monopolist test:
“A market is defined as a product or group of products and a geographic area in
which it is sold that a hypothetical, profit-maximizing firm, not subject to price
egulation, that was the only present and future seller of those products in that
area would impose a small but significant and non-transitory increase in price
(SSNIP) above prevailing or likely future levels.”
Idea: A “market” should contain products which compete with each other and be
small enough such that consumers can choose not to participate. But how to
define what a market is?
Big Question: Is there a simple, yet effective way (i.e., a “sufficient statistic”) of
to identify a market as well as use the cu
ent equili
ium to forecast a future one?
Page 15
The Herfindahl-Hirschman Index (HHI)
I Herfindahl-Hirschman Index (HHI) is given by
HHI =
N∑
i=1
(100si )
2
Range of the index is from 10,000/N (equal- sharing) to 10,000.
Page 16
Properties of HHI
a. HHI decreases with number of firms.
. HHI increases with the variance of the distribution of firm sizes.
c. Recall from the Cournot model that in equili
ium, each firm i’s output satisfies
the first order condition
(P? − ci )/P? = si/η(Y ?)
Multiplying by 10000si and summing over all i yields
N∑
i=1
10000si ((P
? − ci )/P? = (HHI )/η(Y ?)
In other words, HHI is proportional to a weighted average of the firms’ percentage
markups of price over cost. It is a summary statistic of market power.
I A market with a higher HHI has a higher average markup.
I Useful, since markups are not observable.
Page 17
Challenge Criteria - HHI
The DOJ says it will not challenge a merger if post-merger HHI is
I Less than 1000
I Between 1000 and 1800, and ∆HHI < 100;
I > 1800 and ∆HHI < 50.
Remark: Post-merger HHI is calculated on the basis of pre-merger shares. Theory
suggests that this is not a reasonable assumption.
Page 18
An Example
I The soft drink industry consists of firms with the following market shares.
Company si
Coca-Cola 26%
Pepsi 24%
Sprite 14%
Seven-Up 13%
Snapple 10%
Others 13%
I Suppose Seven-Up makes an offer to acquire Snapple.
I Calculate the pre-merger HHI of industry concentration, the post-merger HHI, and the
change in the HHI. For simplicity, let’s treat “others” as one firm.
The pre-merger HHI is
XXXXXXXXXX XXXXXXXXXX = 1, 886
The post-merger HHI is
XXXXXXXXXX XXXXXXXXXX = 2, 146
I The ∆HHI is 260.
I The DOJ would look into the merger. They may still approve it but the investigation will be
expensive and time-consuming.
Page 19
Another Sufficient Statistic - Diversion Ratios
I Relevant to industries where firms produce horizontally-differentiated goods.
I Consider the discrete choice framework we discussed earlier (i.e., multinomial
logit) where a consumer buys one of J + 1 products.
I A diversion ratio, which measures the fraction of consumers that switch from
one product to an alternative after a price increase, is a central calculation of
interest to antitrust authorities for analyzing horizontal mergers.
I Mathematically, define (qj , qk) as demand for products j and k