chapter 11: horizontal mergers1 mergers. chapter 11: horizontal mergers2 introduction merger mania...
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Chapter 11: Horizontal Mergers 1
Mergers
Chapter 11: Horizontal Mergers 2
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 3
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 4
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 5
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 unitsthe product price is P(3) = 150 - 3x30 = $60profit of each firm is (3) = (60 - 30)x30 = $900
Now suppose that two of these firms merge, thenthere 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 (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 6
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:
Ci =
(A - c)2
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.
The ordering of the firmsdoes not matter
Chapter 11: Horizontal Mergers 7
Generalization 2
Each non-merged firm chooses output qi to maximize profit:
i(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
The newly merged firm chooses output qm to maximize profit:
m(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
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 8
Generalization 3 The profit of each of the merged and non-merged firms is then:
Cm = C
nm =(A - c)2
B(N - M + 2)2
The aggregate profit of the merging firms pre-merger is:
Profit of each surviving firmincreases with M
Ci =
M(A - c)2
B(N + 1)2
So for the merger to be profitable we need:
(A - c)2
B(N - M + 2)2>
M(A - c)2
B(N + 1)2this simplifies to:
(N + 1)2 > M(N - M + 2)2
Chapter 11: Horizontal Mergers 9
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) = N
NN
2
4523
Typical examples of a(N) are:
N 5 10 15 20 25a(N) 80% 81.5% 83.1% 84.5% 85.5%
M 4 9 13 17 22
Chapter 11: Horizontal Mergers 10
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 12: Vertical and Conglomerate Mergers
11
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
12
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
13
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
14
Complementary mergers 2
Supplier 1 Supplier 2
price v1price v2
price P
Final Producer
Consumers
Chapter 12: Vertical and Conglomerate Mergers
15
Complementary producers Consider the profit of the final producer: this is
f = (P - v1 - v2)Q = (140 - v1 - v2 - Q)Q
Maximize this with respect to Q
f/Q = 140 - (v1 + v2) - 2Q = 0
Solve this for Q
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:
1 = v1Q1 = v1(70 - v1/2 - v2/2) Maximize this with respect to v1
Chapter 12: Vertical and Conglomerate Mergers
16
Complementary producers 2
Maximize this with respect to v1
1 = v1Q1 = v1(70 - v1/2 - v2/2)
1/v1 = 70 - v1 - v2/2 = 0
Solve this for v1
v1 = 70 - v2/2 We can do exactly the same for v2
v2 = 70 - v1/2
The price charged byeach supplier is a
function of the othersupplier’s price
We need to solvethese two pricing
equations
v2
v1
140
70
R1
70
140
R2
v1 = 70 - (70 - v1/2)/2 = 35 + v1/4so 3v1/4 = 35, i.e., v1 = $46.67
46.67
and v2 = $46.6746.67
Chapter 12: Vertical and Conglomerate Mergers
17
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: 1 = 2 = 46.67 x 23.33 = $1,088.81
final producer: f = (116.67 - 46.67 - 46.67) x 23.33 = $544.29
Chapter 12: Vertical and Conglomerate Mergers
18
Complementary products 4
Supplier 1 Supplier 2
23.33 units @ $46.67 each
23.33 units @ $116.67 each
Final Producer
Consumers
23.33 units @ $46.67 each
Now suppose that thetwo suppliers merge
Chapter 12: Vertical and Conglomerate Mergers
19
Complementary mergers 5
Supplier 1 Supplier 2
price v
price P
Final Producer
Consumers
The merger allows thetwo firms to coordinate
their prices
Chapter 12: Vertical and Conglomerate Mergers
20
Complementary mergers 6 Consider the profit of the final producer: this is
f = (P - v)Q = (140 - v - Q)Q
Maximize this with respect to Q
f/Q = 140- v - 2Q = 0
Solve this for Q
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:
m = vQm = v(70 - v/2)
Maximize this with respect to v
Chapter 12: Vertical and Conglomerate Mergers
21
Complementary mergers 7m = vQm = v(70 - v/2)
Differentiate with respect to v
m/v = 70 - v = 0so v = $70
This is the cost of the combinedinput: the merger has reduced
costs to the final producer
Recall that Qm = Q = 70 - v/2 so Qm = Q = 35 units
This gives the final product price P = 140 - Q = $105
The merger has reducedthe final product price:
consumers gain
What about profits? For the merged upstream firm:m = vQm = 70 x 35 = $2,480
This is greater than thecombined pre-merger
profit For the final producer:
f = (105 - 70) x 35 = $1,225 This is greater than the
pre-merger profit
Chapter 12: Vertical and Conglomerate Mergers
22
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
23
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
24
Vertical merger 2
ManufacturerMarginal costs c
wholesale price r
Price P
Consumer Demand: P = A - BQ
Chapter 12: Vertical and Conglomerate Mergers
25
Vertical merger 3
• Consider the retailer’s decision– identify profit-maximizing output
– set the profit maximizing pricePrice
Quantity
DemandA
A/B
marginal revenue downstream is MR = A – 2BQ
MRA/2B
retail marginal cost is r
MCr
equate MC = MR to give the quantity Q = (A - r)/2B
A - r2B
identify the price from the demand curve: P = A - BQ = (A + r)/2
(A+r)/2 profit to the retailer is (P - r)Q which is D = (A - r)2/4B
profit to the manufacturer is (r-c)Q which is M = (r - c)(A - r)/2B
Retail
Profit
c
Man. Profit
Chapter 12: Vertical and Conglomerate Mergers
26
Vertical merger 4
Price
Quantity
DemandA
A/B
MR
A/2B
MCr
suppose the manufacturer sets a different price r1
r1
A - r2B
then the downstream firm’s output choice changes to the output Q1 = (A - r1)/2B
A - r1
2B
and so on for other input prices
demand for the manufacturer’s output is just the downstream marginal revenue curve
Upstream demand
Chapter 12: Vertical and Conglomerate Mergers
27
Vertical merger 5
Price
Quantity
Demand
A
A/B
MR
A/2B
the manufacturer’s marginal cost is c
Upstream demand
c MC
upstream demand is Q = (A - r)/2B which is r = A – 2BQupstream marginal revenue is, therefore, MRu = A – 4BQ
A/4B
equate MRu = MC: A – 4BQ = c
so Q*=(A-c)/4B
(A-c)/4B
the input price is (A+c)/2 (A+c)/2
while the consumer price is (3A+c)/4
(3A+c)/4
the manufacturer’s profit is (A-c)2/8B
the retailer’s profit is (A-c)2/16BMRu
Manufacturer Profit
Retail Profit
Chapter 12: Vertical and Conglomerate Mergers
28
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)– Total profit is:
• upstream division: (r - c)Q• downstream division: (P(Q) - r)Q• aggregate profit: (P(Q) - c)Q
The internal transferprice nets out of theprofit calculations
• Back to the example
Chapter 12: Vertical and Conglomerate Mergers
29
Vertical merger 7
Price
Quantity
Demand
A
A/B
MR
the integrated demand is P(Q) = A - BQ
c MC
marginal revenue is MR = A – 2BQ
marginal cost is cso the profit-maximizing output requires that A – 2BQ = cso Q* = (A – c)/2B
(A-c)/2B
so the retail price is P = (A + c)/2(A+c)/2
This merger has benefited consumers
aggregate profit of the integrated firm is (A – c)2/4B
This merger has benefited the two
firms
Aggregate Profit
Chapter 12: Vertical and Conglomerate Mergers
30
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