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
6
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
7
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
9
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
10
Introduction
• General Electric and Honeywell proposed to merge in
2000
– GE supplies jet engines for commercial aircraft
– Honeywell produced various electrical and other control systems
for jet aircraft
• Deal was approved in the US
• But was blocked by the EU Competition Directorate
– this was a merger of complementary firms
– it is “like” a vertical merger
– so can potentially remove inefficiencies in pricing
• benefiting the merged firms and consumers
– so why block the merger?
Chapter 12: Vertical and
Conglomerate Mergers
11
Introduction 2
• Vertical mergers can be detrimental
– if they facilitate market foreclosure by the merged firms
• refuse to supply non-merged rivals
• But they can also be beneficial
– if they remove market inefficiencies
• Regulators need to look for the balance these two forces in
considering any proposed merger
Chapter 12: Vertical and
Conglomerate Mergers
12
Complementary Mergers
• Consider first a merger between firms that supply
complementary products
• A simple example:
–
–
–
–
–
–
final production requires two inputs in fixed proportions
one unit of each input is needed to make one unit of output
input producers are monopolists
final product producer is a monopolist
demand for the final product is P = 140 - Q
marginal costs of upstream producers and final producer (other
than for the two inputs) normalized to zero.
• What is the effect of merger between the two upstream
producers?
Chapter 12: Vertical and
Conglomerate Mergers
13
Complementary mergers 2
Supplier 1
Supplier 2
price v2
price v1
Final Producer
price P
Consumers
Chapter 12: Vertical and
Conglomerate Mergers
14
Complementary producers
 Consider the profit of the final producer: this is
pf = (P - v1 - v2)Q = (140 - v1 - v2 - Q)Q
 Maximize this with respect to Q
Solve this for Q
pf/Q = 140 - (v1 + v2) - 2Q = 0
 Q = 70 - (v1 + v2)/2
 This gives us the demand for each input
Q1 = Q2 = 70 - (v1 + v2)/2
 So the profit of supplier 1 is then:
p1 = v1Q1 = v1(70 - v1/2 - v2/2)
 Maximize this with respect to v1
Chapter 12: Vertical and
Conglomerate Mergers
15
The price charged by
We need to solve
each supplier is a
function of theComplementary
other
producers these
2 two pricing
equations
supplier’s
price
1
Solve this for v
p = v1Q1 = v1(70 - v1/2 - v2/2)
1
 Maximize this with respect to v1
p1/v1 = 70 - v1 - v2/2 = 0
v1 = 70 - v2/2
 We can do exactly the same for v2 v2
140
v2 = 70 - v1/2
R1
v1 = 70 - (70 - v1/2)/2 = 35 + v1/4
so 3v1/4 = 35, i.e., v1 = $46.67
and v2 = $46.67
70
46.67
R2
46.67 70
Chapter 12: Vertical and
Conglomerate Mergers
140
v1
16
Complementary products 3
 Recall that Q = Q1 = Q2 = 70 - (v1 + v2)/2
so Q = Q1 = Q2 = 23.33 units
 The final product price is P = 140 - Q = $116.67
 Profits of the three firms are then:
supplier 1 and supplier 2: p1 = p2 = 46.67 x 23.33 = $1,088.81
final producer: pf = (116.67 - 46.67 - 46.67) x 23.33 = $544.29
Chapter 12: Vertical and
Conglomerate Mergers
17
Complementary products 4
Supplier 1
Now suppose that the
two suppliers merge Supplier 2
23.33 units @
$46.67 each
23.33 units @
$46.67 each
Final Producer
23.33 units @ $116.67 each
Consumers
Chapter 12: Vertical and
Conglomerate Mergers
18
Complementary mergers 5
Supplier 1
Supplier 2
price v
The merger allows the
two firms to coordinate
their prices
Final Producer
price P
Consumers
Chapter 12: Vertical and
Conglomerate Mergers
19
Complementary mergers 6
 Consider the profit of the final producer: this is
pf = (P - v)Q = (140 - v - Q)Q
 Maximize this with respect to Q
pf/Q = 140 - v - 2Q = 0
 Q = 70 - v/2
 This gives us the demand for each input
Q1 = Q2 = Qm = 70 - v/2
 So the profit of the merged supplier is:
pm = vQm = v(70 - v/2)
Solve this for
Q
 Maximize this with respect to v
Chapter 12: Vertical and
Conglomerate Mergers
20
Complementary
mergers 7
This is the cost of the combined
pm = vQm = v(70 - v/2)
The has
merger
has reduced
input: the merger
reduced
the final
product price:
costs to the final
producer
 Differentiate with respect to v
consumers gain
pm/v = 70 - v = 0
so v = $70
 Recall that Qm = Q = 70 - v/2 so Qm = Q = 35 units
 This gives the final product price P = 140 - Q = $105
This is greater
 What about profits? For the merged upstream
firm: than the
combined pre-merger
profit
pm = vQm = 70 x 35 = $2,480
 For the final producer:
pf = (105 - 70) x 35 = $1,225
This is greater than the
pre-merger profit
Chapter 12: Vertical and
Conglomerate Mergers
21
Complementary mergers 8
• A merger of complementary producers has
– increased profits of the merged firms
– increased profit of the final producer
– reduced the price charged to consumers
Everybody gains from this merger: a Pareto improvement! Why?
• This merger corrects a market failure
– prior to the merger the upstream suppliers do not take full
account of their interdependence
– cut in price by one of them reduces downstream costs, increases
downstream output and benefits the other upstream firm
– but this is an externality and so is ignored
• Merger internalizes the externality
Chapter 12: Vertical and
Conglomerate Mergers
22
Vertical Mergers
• The same result arises when we consider vertical mergers:
mergers of upstream and downstream firms
• If the merging firms have market power
– lack of co-ordination in their independent decisions
– double marginalization
– merger can lead to a general improvement
• Illustrate with a simple model
– one upstream and one downstream monopolist
–
–
–
–
• manufacturer and retailer
upstream firm has marginal costs c
sells product to the retailer at price r per unit
no other retail costs: one unit of input gives one unit of output
retail demand is P = A – BQ
Chapter 12: Vertical and
Conglomerate Mergers
23
Vertical merger 2
Marginal
costs c
Manufacturer
wholesale price r
Price P
Consumer Demand: P = A - BQ
Chapter 12: Vertical and
Conglomerate Mergers
24
Vertical merger 3
• Consider the retailer’s decision
– identify profit-maximizing output
– set the profit maximizing price
Price
A
Demand

marginal revenue downstream is
MR = A – 2BQ
 retail marginal cost is r

equate MC = MR to give the
quantity Q = (A - r)/2B

identify the price from the demand
curve: P = A - BQ = (A + r)/2

profit to the retailer is (P - r)Q
which is pD = (A - r)2/4B
(A+r)/2
Retail
Profit
r
Man.
c Profit
A-r
2B
MC
MR
A/2B

profit to the manufacturer is (r-c)Q
which is pM = (r - c)(A - r)/2B
A/B Quantity
Chapter 12: Vertical and
Conglomerate Mergers
25
Vertical merger 4

suppose the manufacturer sets a
different price r1
 then the downstream firm’s
output choice changes to the output
Q1 = (A - r1)/2B
Price
A
Demand

r1
r
A - r1
2B
and so on for other input prices
demand for the manufacturer’s
output is just the downstream
marginal revenue curve

MC
Upstream demand
MR
Quantity
A - r A/2B
A/B
2B
Chapter 12: Vertical and
Conglomerate Mergers
26
Vertical merger 5
Price
A
Manufacturer Profit
(3A+c)/4
Demand
(A+c)/2
Upstream demand
c
(A-c)/4B
MRu
MR
A/4B A/2B
the manufacturer’s marginal cost is c
 upstream demand is Q = (A - r)/2B which
is r = A – 2BQ
 upstream marginal revenue is, therefore,
MRu = A – 4BQ
 equate MRu = MC: A – 4BQ = c

Retail Profit
MC
A/B

so Q*=(A-c)/4B the input price is (A+c)/2

while the consumer price is (3A+c)/4

the manufacturer’s profit is (A-c)2/8B

the retailer’s profit is (A-c)2/16B
Quantity
Chapter 12: Vertical and
Conglomerate Mergers
27
Vertical merger 6
• Now suppose that the retailer and manufacturer merge
–
–
–
–
manufacturer takes over the retail outlet
retailer is now a downstream division of an integrated firm
the integrated firm aims to maximize total profit
Suppose the upstream division sets an internal (transfer)
price of r for its product
– Suppose that consumer demand is P = P(Q) The internal transfer
price nets out of the
– Total profit is:
• upstream division: (r - c)Q
• downstream division: (P(Q) - r)Q
• aggregate profit: (P(Q) - c)Q
profit calculations
• Back to the example
Chapter 12: Vertical and
Conglomerate Mergers
28
Vertical merger 7
This merger has
 the integrated demand is P(Q) = A - BQ
benefited the two
This merger has
 marginal revenue is MR = A – 2BQ
Price firms benefited consumers

A
Demand
(A+c)/2
Aggregate
Profit
c
MR
(A-c)/2B
marginal cost is c
 so the profit-maximizing output requires
that A – 2BQ = c
 so Q* = (A – c)/2B
 so the retail price is P = (A + c)/2

aggregate profit of the integrated firm is
(A – c)2/4B
MC
A/B
Quantity
Chapter 12: Vertical and
Conglomerate Mergers
29
Vertical merger 8
• Integration increases profits and consumer surplus
• Why?
– the firms have some degree of market power
– so they price above marginal cost
– so integration corrects a market failure: double marginalization
• What if manufacture were competitive?
– retailer plays off manufacturers against each other
– so obtains input at marginal cost
– gets the integrated profit without integration
• Why worry about vertical integration?
– two possible reasons
• price discrimination
• vertical foreclosure
Chapter 12: Vertical and
Conglomerate Mergers
30