Horizontal Mergers
Chapter 11: Horizontal Mergers
1
Introduction
• Merger mania of 1990s disappeared after 9/11/2001
• But now appears to be returning
– Oracle/PeopleSoft
– AT&T/Cingular
– Bank of America/Fleet
• Reasons for merger
– cost savings
– search for synergies in operations
– more efficient pricing and/or improved service to customers
Chapter 11: Horizontal Mergers
2
Questions
• Are mergers beneficial or is there a need for regulation?
– cost reduction is potentially beneficial
– but mergers can “look like” legal cartels
• and so may be detrimental
• US government is particularly concerned with these
questions
– Antitrust Division Merger Guidelines
• seek to balance harm to competition with avoiding unnecessary
interference
• Explore these issues in next two chapters
– distinguish mergers that are
• horizontal: Bank of America/Fleet
• vertical: Disney/ABC
• conglomerate: Gillette/Duracell; Quaker Oats/Snapple
Chapter 11: Horizontal Mergers
3
Horizontal mergers
• Merger between firms that compete in the same product
market
– some bank mergers
– hospitals
– oil companies
• Begin with a surprising result: the merger paradox
– take the standard Cournot model
– merger that is not merger to monopoly is unlikely to be profitable
• unless “sufficiently many” of the firms merge
• with linear demand and costs, at least 80% of the firms
• but this type of merger is unlikely to be allowed
Chapter 11: Horizontal Mergers
4
An Example
 Assume 3 identical firms; market demand P = 150 - Q; each firm
with marginal costs of $30. The firms act as Cournot competitors.
 Applying the Cournot equations we know that:
each firm produces output q(3) = (150 - 30)/(3 + 1) = 30 units
the product price is P(3) = 150 - 3x30 = $60
profit of each firm is p(3) = (60 - 30)x30 = $900
 Now suppose that two of these firms merge, then
there are two independent firms so output of each changes to:
q(2) = (150 - 30)/3 = 40 units; price is P(2) = 150 - 2x40 = $70
profit of each firm is p(2) = (70 - 30)x40 = $1,600
 But prior to the merger the two firms had total profit of $1,800
This merger is unprofitable and should not occur
Chapter 11: Horizontal Mergers
5
A Generalization
 Take a Cournot market with N identical firms.
 Suppose that market demand is P = A - B.Q and that marginal
costs of each firm are c.
 From standard Cournot analysis we know the profit of each firm is:
(A - c)2
The ordering of the firms
C
p i=
does not matter
B(N + 1)2
 Now suppose that firms 1, 2,… M merge. This gives a market in
which there are now N - M + 1 independent firms.
Chapter 11: Horizontal Mergers
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Generalization 2
 The newly merged firm chooses output qm to maximize profit:
pm(qm, Q-m) = qm(A - B(qm + Q-m) - c)
where Q-m = qm+1 + qm+2 + …. + qN is the aggregate output of the
N - M firms that have not merged
 Each non-merged firm chooses output qi to maximize profit:
pi(qi, Q-i) = qi(A - B(qi + Q-i) - c)
where Q-i = is the aggregate output of the N - M firms excluding
firm i plus the output of the merged firm qm
 Comparing the profit equations then tells us:
the merged firm becomes just like any other firm in the market
all of the N - M + 1 post-merger firms are identical and so must
produce the same output and make the same profits
Chapter 11: Horizontal Mergers
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Generalization 3
 The profit of each of the merged and non-merged firms is then:
(A - c)2
Profit of each surviving firm
C
C
p m = p nm =
increases with M
B(N - M + 2)2
 The aggregate profit of the merging firms pre-merger is:
M(A - c)2
C
Mp i =
B(N + 1)2
 So for the merger to be profitable we need:
(A - c)2
M(A - c)2
>
this simplifies to:
2
2
B(N - M + 2)
B(N + 1)
(N + 1)2 > M(N - M + 2)2
Chapter 11: Horizontal Mergers
8
The Merger Paradox
 Substitute M = aN to give the equation
(N + 1)2 > aN(N – aN + 2)2
Solving this for a > a(N) tells us that a merger is profitable for
the merged firms if and only if:
a > a(N) = 3  2 N  5  4 N
2N
Typical examples of a(N) are:
N
5
10
15
20
25
a(N)
80%
81.5% 83.1% 84.5% 85.5%
M
4
9
13
17
22
Chapter 11: Horizontal Mergers
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The Merger Paradox 2
• Why is this happening?
– merged firm cannot commit to its potentially greater size
• the merged firm is just like any other firm in the market
• thus the merger causes the merged firm to lose market share
• the merger effectively closes down part of the merged firm’s
operations
– this appears somewhat unreasonable
• Can this be resolved?
– need to alter the model somehow
• asymmetric costs
• timing: perhaps the merged firms act like market leaders
• product differentiation
Chapter 11: Horizontal Mergers
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Merger and Cost Synergies
• Suppose that firms in the market
– may have different variable costs
– incur fixed costs
• Merger might be profitable if it creates cost savings
• An example
– three Cournot firms with market demand P = 150
–Q
– two firms have marginal costs of 30 and fixed
costs of f
– total costs are:
– C(q1) = f + 30q1; C(q2) = f + 30q2
– third firms has potentially higher marginal costs
– C(q3) = f + 30bq3, where b > 1
Chapter 11: Horizontal Mergers
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Case A: Merger Reduces Fixed Costs
• Suppose that b = 1
– all firms have the same marginal costsMerger
of 30 is likely to be profitable
– but the merged firms has fixed costs af
withfixed
1 < costs
a < 2are “high” and
when
the merger gives “significant”
• We know from the previous example
that:
savings in fixed costs
– pre-merger profit of each firm are 900 – f
– post-merger
• the non-merged firm has profit 1,600 - f
• the merged firm has profit 1,600 – af
• The merger is profitable for the merged firm if:
– 1,600 – af > 1,800 – 2f
– which requires that a < 2 – 200/f
Chapter 11: Horizontal Mergers
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Case A: 2
• Also, the non-merged firm always gains
– and gains more than the merged firms
• So the merger paradox remains in one form
– why merge?
– why not wait for other firms to merge?
Chapter 11: Horizontal Mergers
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Case B: Merger Reduces Variable Costs
• Suppose that merger reduces variable costs
–
–
–
–
–
assume that b > 1 and that f = 0
firms 2 and 3 merge
so production is rationalized by shutting down high-cost operations
pre-merger:
210  90b
C
C 90  3b C
outputs are:
q1  q2 
; q3 
– profits are:
4
4
2
2




90

3
b
210

90
b
pC  pC 
; pC 
1
2
16
3
16
– post-merger profits are $1,600 for both the merged and nonmerged firms
Chapter 11: Horizontal Mergers
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Case B: 2
• Is this a profitable merger?
• For the merged firm’s profit to increase requires:
 90  3b 2 210  90b 2 Merger of a high-cost and low0
1,600  

 cost firm is profitable if cost
16
16

 disadvantage of the high-cost
• This simplifies to: 25(7 – 3b)(15b – 9)/2 >firm
0 is “great enough”
• first term must be positive for firm 3 to have non-negative output
pre-merger
• so the merger is profitable if the second term is positive
• which requires b > 19/15
Chapter 11: Horizontal Mergers
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Summary
• Mergers can be profitable if cost savings are great enough
– but there is no guarantee that consumers gain
– in both our examples consumers lose from the merger
• Farrell and Shapiro (1990)
– cost savings necessary to benefit consumers are much greater than
cost savings that make a merger profitable
– so should be skeptical of “cost savings” justifications of mergers
– and the paradox remains
• non-merged firms benefit more from merger than merged firms
Chapter 11: Horizontal Mergers
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The Merger Paradox Again
• The merger paradox arises because despite
merging, merged firms are symmetric with nonmerged firms?
• What kind of asymmetries might arise?
– merged firms become Stackelberg leaders post-merger
– By committing to merger, merged firms may induce
others to merge
– Can these alterations remedy the merger paradox?
Chapter 11: Horizontal Mergers
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A Leadership Game
• Suppose that there has been a set of two-firm
mergers
–
–
–
–
market has L leaders and F followers = N = F+L total
assume linear demand P = A – BQ
each firm has constant marginal cost of c
two-stage game:
• stage 1: each leader firm chooses its output ql independently
• gives aggregate output QL
• stage 2: each follower firm chooses its output qf independently,
but in response to the aggregate output of the leader firms
• gives aggregate follower output QF
• clearly, leader firms correctly anticipate QF
Chapter 11: Horizontal Mergers
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Leadership Game 2
• Recall that
–
–
–
–
if the inverse demand function is P = a – bQ
there are n identical Cournot firms
and all firms have marginal costs c
then each firm’s Cournot equilibrium output is:
ac
q 
n  1b
C
i
• In our example
– if the leaders produce QL then inverse demand for the followers is
P = (A – BQL) – bQF
– there are N - L identical Cournot follower firms
– so that a = (A – BQL), b = B and n = N – L
Chapter 11: Horizontal Mergers
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Leadership Game 3
• So the Cournot equilibrium output of each follower firm is:
A  BQ L  c
QL
Ac
q 


BN  L  1 BN  L  1 N  L  1

f
• Aggregate output of the follower firms is then:
QF 
N  L A  c  N  LQL
BN  L  1 N  L  1
• Substituting this into the market inverse demand gives the inverse
demand for the leader firms:
A  N  L c
B
P

QL
N  L  1 N  L  1
• in this case a = (A + (N – L)c/(N – L + 1); b = B/(N – L +1) and n = L
Chapter 11: Horizontal Mergers
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Leadership Game 4
• So the Cournot equilibrium output of each leader firm is:
Ac
q 
BL  1

l
• Note that when L = 1 this is just the standard Stackelberg output for
the lead firm.
• Substitute into the follower firm’s equilibrium and simplifying gives
the output of each follower firm:
Ac
q 
BL  1N  L  1
*
f
• Clearly, each leader has greater output than each follower
• merger to join the leader group has an advantage
Chapter 11: Horizontal Mergers
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Leadership Game 5
• Substituting the equilibrium outputs into the inverse demand gives the
equilibrium price-cost margin and profits for each type of firm:
Ac
Pc 
L  1N  L  1
2
2


A  c
A  c
p L N , L  
; p F N , L  
2
2
2
BL  1 N  L  1
BL  1 N  L  1
• The leaders are more profitable than the non-merged followers
• Is one more merger profitable for the merging firms?
• Such a merger leads to there being L + 1 leaders, F – 2 followers and
N – 1 firms in all
Chapter 11: Horizontal Mergers
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Leadership Game 6
• So for an additional merger to be profitable for the merging firms we
need pL(N – 1, L + 1) > 2pF(N, L)
• This requires that (L + 1)2(N – L + 1)2 – 2(L + 2)2(N – L – 1) > 0
• Note that this does not depend on any demand parameters A, B or c
• It is possible to show that this condition is always satisfied
• No matter how many leaders and followers there are an additional two
follower firms will always want to merge
– this squeezes profits of the non-merged firms
– so resolves the merger paradox
Chapter 11: Horizontal Mergers
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Leadership Game 7
• What about consumers?
• For an additional merger to benefit consumers N – 3(L + 1) > 0
• An additional merger benefits consumers only if the current group of
leaders contains fewer than one-third of the total number of firms in
the market.
• Admittedly this model is stylized
– how to attain leadership?
– distinction between leaders and followers not necessarily sharp
• But it is suggestive of actual events and so qualitatively useful
Chapter 11: Horizontal Mergers
24
Sequential Mergers
• It is possible to think of the merger paradox as a
coordination problem. What does this mean?
• It may be the case that if enough firms complete mergers
each merger will be profitable but that for small group to
merge by itself is not profitable
• Consider a market with potential merger pairs:
– Merger Pair 1 (Firm A and Firm B)
– Merger Pair 2 (Firm A’ and B’)
• The game may have two Nash Equilibria, one where both
pairs merge and one where neither merges
Chapter 11: Horizontal Mergers
25
Sequential Mergers 2
Ideally, the merger pairs would like to coordinate their decisions and
arrive at the Both Merge equilibrium. However, with simultaneous
play, it is not clear how such coordination will happen.
This is also a Nash
This is a Nash
Merger Pair 2 Equilibrium in
Equilibrium in
simultaneous play
simultaneous play
Don’t Merge
Merge
Don’t Merge
($772, $772)
$772)
($772,
($1063, $752)
Merger Pair 1
Merge
($752, $1063) ($1100,
($1100,$1100)
$1100)
Chapter 11: Horizontal Mergers
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Sequential Mergers 3
Sequential play with Merger Pair 1 going first solves the
coordination problem. Merger Pair 2 will realize that if they
merge, Merger Pair 2 will do the same
This will make Merger Pair 1’s merger profitable
This is a Nash
Equilibrium in
sequential play
Merger Pair 2
Don’t Merge
Don’t Merge
($772, $772)
Merge
($1063, $752)
Merger Pair 1
Merge
($752, $1063) ($1100,
($1100,$1100)
$1100)
Chapter 11: Horizontal Mergers
27
Sequential Mergers 4
• The sequential merger analysis may solve the merger
paradox if the source of that paradox is a coordination
problem
• The analysis has an advantage over the Stackelberg leader
model because it is explicitly sequential, i.e., mergers
happen in chronological sequence. In the leader model,
every firm wants to become a leader simultaneously
• Cost breakthroughs or changes in transportation and trade
barriers can create the setting for the sequential merger
analysis
• Such events can therefore lead to merger waves
Chapter 11: Horizontal Mergers
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Horizontal Mergers and Product Differentiation
• Assumption thus far is that firms offer identical products
• But we clearly observe considerable product differentiation
• Does this affect the profitability of merger?
– affects commitment
• need not remove products post-merger
– affects the nature of competition
• quantities are strategic substitutes
– passive move by merged firms met by aggressive response of nonmerged firms
• prices are strategic complements
– passive move by merged firms induces passive response by non-merged
firms
Chapter 11: Horizontal Mergers
29
Merger with Price Competition
• Mergers with price competition and product differentiation
are profitable
• Why?
– prices are strategic complements
– merged firms can strategically commit to producing a range of
products
– with homogeneous products there is no such ability to commit
• unless the merged firms can somehow become market leaders
Chapter 11: Horizontal Mergers
30
Merger with Price Competition 2
• Suppose there are N firms with linear demand
1 N 

qi p1,...,p N   V  p i  γ  p i   j 1 p j 
N


• With zero marginal cost, each firm’s first order condition is
π i
2γ
γ N
 V  2pi  2γγ i 
pi   p j  0

p
N
N j 1
• Using i symmetry we get
j i
NV
p0 
2N  γ(N  1)
• If firms 1,…M merge, it will have a new first order
condition:
M
 k 1 π k π m M π k


p m
p m k 1 p m
k m
Chapter 11: Horizontal Mergers
31
Merger with Price Competition
• Because of symmetry, the prices on all the products of the
merged firms will be the same and the prices and only the
nonmerged firms will bill be the same. For a not merged
firm and a merged firm we have
N
p
j 1
j i
j
 Mpm  N  M  1 p nm
• Using
p k M  1p m



p
N
k 1
m
M
k m
N
 p  M 1p  N  M p
j
m
nm
j1
jm

Chapter 11: Horizontal Mergers
32
Merger with Price Competition
• Gives first order conditions for the nonmerged firms
p i

 V  2  pnm  Mpm  M 1pnm   0
pnm
N
• And for the merged firm
 p k
M
k1
pm
 V  21 pm 
• Which gives prices

N  M pnm  2Mpm 

N
2 N   2 N  1
N M 
4 N  2 (3N  M  1)   2 
2 N  M  2
 N 
2 N   2 N  M 
V
2 N  M 
4 N  2 (3N  M  1)   
2 N  M  2
 N 
pm  V

p nm
Chapter 11: Horizontal Mergers
33
Merger with Price Competition
• The merged firm set higher prices
– Since prices are strategic complements,
nonmerging firms also have higher prices
• The merger is profitable for the merging firms, but
even more profitable for the nonmerging firms
• The greater the number of merging firms, the
more profitable it is
Chapter 11: Horizontal Mergers
34
A Spatial Approach
• Consider a different approach to product differentiation
–
–
–
–
spatial model of Hotelling
products are differentiated by “location” or characteristics
merger allows coordination of prices
but merged firms can continue to offer the pre-merger product
range
– is merger profitable?
Chapter 11: Horizontal Mergers
35
The Spatial Model
• The model is as follows
–
–
–
–
–
a market called Main Circle of length L
consumers uniformly distributed over this market
supplied by firms located along the street
the firms are competitors: fixed costs F, zero marginal cost
each consumer buys exactly one unit of the good provided that its
full price is less than V
– consumers incur transport costs of t per unit distance in travelling
to a firm
– a consumer buys from the firm offering the lowest full price
• What prices will the firms charge?
• To see what is happening consider two representative firms
Chapter 11: Horizontal Mergers
36
The spatial model illustrated
Price
Assume that firm
1 sets
What
if firm 1 raises Price
price p1 and firm 2 sets
its price?
price p2
p’1
p2
p1
x’
m
Firm 1
xm
All consumers to xthe
Firm 2
m moves to the
left of xm buy left:
fromsome consumers
And all consumers
firm 1
to 2the right buy from
switch to firm
firm 2
Chapter 11: Horizontal Mergers
37
The Spatial Model
• Suppose that there are five firms evenly distributed
1

r12
r51
5
2
r45
r23
4
3
these firms will split the
market
 we can then calculate the
Nash equilibrium prices each
firm will charge
 each firm will charge a price
of p* = tL/5
 profit of each firm is then
tL2/25 - F
r34
Chapter 11: Horizontal Mergers
38
Merger of Differentiated Products

now consider a
merger between some
of these firms
 a merger of nonneighboring firms has
no effect
AAmerger
mergerofoffirms
firms
22and
and43does
does
nothing
something
Price

but a merger of
neighboring firms
changes the equilibrium
r51
1
r12
2 r23 3
r34
4 r45 5
r51
Main Circle (flattened)
Chapter 11: Horizontal Mergers
39
Merger of Differentiated Products

merger of 2 and 3
induces them to raise
their prices
 so the other firms also
increase their prices
 the merged firms lose
some market share
 what happens to
profits?
Price
r51
1
r12
2 r23 3
r34
4 r45 5
r51
Main Circle (flattened)
Chapter 11: Horizontal Mergers
40
Spatial Merger (cont.)
 The impact of the merger on prices and profits is as follows
Pre-Merger
Price
Profit
1
tL/5
tL2/25
2
tL/5
3
Post-Merger
Price
Profit
1
14tL/60
49tL2/900
tL2/25
2
19tL/60 361tL2/7200
tL/5
tL2/25
3
19tL/60
4
tL/5
tL2/25
4
14tL/60
5
tL/5
tL2/25
5
13tL/60 169tL2/3600
Chapter 11: Horizontal Mergers
361tL2/7200
49tL2/900
41
Spatial Merger (cont.)
• This merger is profitable for the merged firms
• And it is not the best that they can do
– change the locations of the merged firms
• expect them to move “outwards”, retaining captive consumers
– perhaps change the number of firms: or products on offer
• expect some increase in variety
• But consumers lose out from this type of merger
– all prices have increased
• For consumers to derive any benefits either
– increased product variety so that consumers are “closer”
– there are cost synergies not available to the non-merged firms
• e.g. if there are economies of scope
• Profitability comes from credible commitment
Chapter 11: Horizontal Mergers
42
Price Discrimination
 What happens if the firms can price discriminate?
 This leads to a dramatic change in the price equilibrium
Price

p1 i
p1i+1
p2 i
p*i(s)
t
i
t
s
and firm i+1
these consumers
i+1
take two neighboring firms
 consider a consumer located at s
 suppose firm i sets price p1i
 i+1 can undercut with price p1i+1
 i can undercut with price p2i
 and so on
 i wins this competition by “just”
undercutting i+1’s cost of supplying s
 the same thing happens at every
consumer location
 equilibrium prices are illustrated by
the bold lines
Chapter 11: Horizontal Mergers
43
Merger with price discrimination
This is much better
 Start with a no-merger equilibrium
for consumers than no
price discrimination
1
2
Price for
equilibrium
Profit
each firm
pre-merger
is the
given
is given by
byshaded
the bold
lines
areas
3
Chapter 11: Horizontal Mergers
4
44
Merger with price discrimination
This is beneficial for the
 Now suppose that firms 2 and 3 merge
merged firms but harms
Prices
theprice
captive
 They no longer compete in prices
sotothe
equilibrium
consumerschanges
consumers between
2 and 3 increase
Profits to the
merged firms
increase
1
2
3
Chapter 11: Horizontal Mergers
4
45
Public Policy and Horizontal Mergers
• Antitrust authorities consider the unilateral effects
discussed above and coordinate effects
– A merger may make collusion easier
• Consider
– Number of firms
– Cost structures across firms
– Entry barriers
Chapter 11: Horizontal Mergers
46
Public Policy and Surplus
• Focus is generally on Consumer surplus
– Ignores profits to merging firms
– And to their competitors
• Most economic theory favors a measure of total
surplus, but..
– Distributional concerns favor consumer surplus
– Firms may exaggerate cost savings, and consumers are not
represented at proceedings
• Also, firms may have a choice among mergers
– Having a criteria of consumer surplus will push them towards
ones with higher total surplus since they favor ones with higher
producer surplus
Chapter 11: Horizontal Mergers
47
Empirical Application: Merger Simulation
• Antitrust evaluation of a proposed merger requires some
prediction of prices and outputs in the post-merger market
• One way to make such a prediction is to build a
mathematical model of the post-merger market and to
simulate its workings on a computer
• Merger simulation is a combination of economic modeling
and econometric estimation
– Economic modeling reflects standard maximizing behavior in the
context of strategic interaction to characterize the post-merger
equilibrium
– Econometric estimation is required to obtain realistic values for the
key parameters of the economic model
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Merger Simulation 2
• Consider a product-differentiated market before any
• First-order condition for each firm i is:
pi  ci 1

0
pi
ii
• Here ii the (negative of the) elasticity of the firm’s demand with
respect to its own price.
• Defining the price-cost margin as ii and the firm’s market
share as sii this may be rewritten as
si iii  si  0
• Note: Market share and price are observable and relatively easy
to measure. Cost is difficult to know. But if we have an estimate of
the elasticity, then cost can be inferred from the above relationship.
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Merger Simulation 3
• If two firms, say firms 1 and 2, merge and if they continue to
market both products, they will now coordinate the pricing of
each good to maximize the combined profits
• The two first order conditions now are:
s1111  s1  s2  2 21  0
s2  2 22  s2  s1112  0
• Assuming market shares do not change “too much”, it is easy to
see how the knowledge of the relevant own- and cross-price
elasticities, along with the estimates of marginal cost from the
pre-merger data can be used to work out the price-cost margins
and therefore the prices in the post-merger world
• What is key is getting estimates of all the relevant elasticities
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50
Merger Simulation 4
• Estimating all the relevant elasticities though is a tall order
– Need to specify a demand system
– Need to link demand parameters to elasticities
• Usual to specify an almost ideal demand system (AIDS). If
there are four pre-merger firms this system is:
s1  a1  b11 ln p1  b12 ln p 2  b13 ln p3  b14 ln p 4
s 2  a 2  b21 ln p1  b22 ln p 2  b23 ln p3  b24 ln p 4
s3  a3  b31 ln p1  b32 ln p 2  b33 ln p3  b34 ln p 4
s 4  a 4  b41 ln p1  b42 ln p 2  b43 ln p3  b44 ln p 4
•
It is easy to show how the bij coefficients may be translated into
corresponding ij elasticities. Still it is clear that even ignoring
the aij intercept term, estimating the relevant elasticities for an n
firm market requires obtaining estimates for n2 parameters.
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Merger Simulation 4
• Estimating n2 parameters with precision is difficult
• So, the typical estimation procedure usually imposes
additional structure on the market model.
• For example, Proportionally Calibrated AIDS assumes that
the sales loss by a firm when it raises its price is translated to
rivals in proportion to their market shares.
• This removes the need to estimate the cross-elasticities
• However, such structural restrictions are not without
consequences.
• Depending on the precise demand specification and crosselasticity restrictions, Slade (2008) find differences in postmerger predictions as high as 40 percent
• MORAL: Merger simulation is as much art as science and
requires great care in implementation & interpretation
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Merger Simulation 5
• Even if agreement can be reached on simulation technique,
different techniques are available for estimating the needed
elasticities and these two can lead to great variation in
post-merger outcomes
• Staples-Office Depot Merger is a good example
– Are the relevant competitors to a retail office supply store all
the other suppliers in a standard metropolitan area, or;
– Does the strength of competition decline as the rival firm is
located farther from the store under consideration?
• Producing clear, statistical evidence that non-economists
and the courts can easily assess is very difficult
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53