Transcript Document

Section 2: Mergers
EC 171: Topics in Industrial Organization
Introduction
• Merger mania is everywhere
– each week brings new announcements of mega-mergers
• AOL/Time-Warner
• Pfizer/Warner-Lambert
• Vodafone/Mannesman
– each year seems to break the record of the year before
• Reasons for merger are many
–
–
–
–
need to become “global”
response to other mergers
search for synergies in operations
to achieve significant cost savings
EC 171: Topics in Industrial Organization
Questions
• Why do mergers occur?
– many reasons have been suggested relating to costs and market
power
• Are mergers beneficial or is there a need for regulation?
– the US government is particularly concerned with these questions
– anti-trust website
– mergers might not be beneficial: they operate like legal cartels
• Are all mergers the same or are there different types?
– distinguish mergers that are
• horizontal
• complementary
• vertical
EC 171: Topics in Industrial Organization
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
EC 171: Topics in Industrial Organization
An Example
 Assume 3 identical firms; market demand P = 140 - Q; each firm with
marginal costs of $20. The firms act as Cournot competitors.
 Applying the Cournot equations we know that:
each firm produces output q(3) = (140 - 20)/(3 + 1) = 30 units
the product price is P(3) = 140 - 3x30 = $50
profit of each firm is p(3) = (50 - 20)x30 = $900
 Now suppose that two of these firms merge
then there are two independent firms so output of each changes to:
q(2) = (140 - 20)/3 = 40 units; price is P(2) = 140 - 2x40 = $60
profit of each firm is p(2) = (60 - 20)x40 = $1,600
 But prior to the merger the two firms had aggregate profit of $1,800
This merger is unprofitable and should not occur
EC 171: Topics in Industrial Organization
Example (cont.)
 Now suppose that all three firms merge.
 This creates a monopoly so that we have:
output = (140 - 20)/2 = 60 units
price = (140 - 60) = $80
profit = p(1) = (80 - 20)x60 = $3,600
 Prior to this merger aggregate profit was 3x$900 = $2,700
Merger to monopoly is always profitable
EC 171: Topics in Industrial Organization
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 that the profit of each firm is:
pCi
(A - c)2
B(N + 1)2
The ordering of the firms
does not matter
=
 Now suppose that firms 1, 2,… M merge. This gives a market in which
there are now N - M + 1 independent firms.
EC 171: Topics in Industrial Organization
Generalization (cont.)
 The newly merged firm chooses output qm to maximize profit, given by
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
EC 171: Topics in Industrial Organization
Generalization (cont.)
 The profit of each of the merged and non-merged firms is then:
pCm
=
pCnm
(A - c)2
=
B(N - M + 2)2
Profit of each surviving firm
increases with M
 The aggregate profit of the merging firms pre-merger is:
M.pCi
M.(A - c)2
=
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
M > 0.8N for this inequality to be satisfied
EC 171: Topics in Industrial Organization
The Merger Paradox
• Why is this happening?
–
–
–
–
the 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
• product differentiation
• Bertrand competition
– give the merged firms some additional market power
• perhaps they can exercise market leadership
EC 171: Topics in Industrial Organization
Horizontal Merger and Leadership
• Suppose that when two firms merge they become
Stackelberg leaders
– how does this affect merger profitability?
– what is the impact on consumers?
EC 171: Topics in Industrial Organization
Merger and leadership: an example
 Suppose that there are N identical Cournot firms in the market
 Market demand is P = 140 - Q and marginal cost is $20
 Prior to the merger the Cournot equilibrium has:
output of each firm: 120/(N + 1); price: PC = (140 + 20N)/(N + 1)
profit of each firm: pC = 14,400/(N + 1)2
 Now suppose that 2 firms merge and become market leaders
 Since a merger is a legal cartel we can use the Selten analysis of the
previous chapter to get the effect of this merger
 The merged firm will produce the Stackelberg output:
QL = (140 - 20)/2 = 60 units
EC 171: Topics in Industrial Organization
The leadership example (cont.)
 There are N - 2 non-merged firms that act as followers. So they each
produce output:
qF =
140 - 20
60
=
2(N - 1)
(N - 1)
 Total output is: QT = 60 +
 Price is: PL = 140 - QT =
60(N - 2)
60(2N - 3)
=
(N - 1)
(N - 1)
40 + 20N
(N - 1)
and the price-cost margin is PL - 20 =
60
(N - 1)
EC 171: Topics in Industrial Organization
The leadership example (cont.)
 Profit of the merged (lead) firm is:
pL = (PL - 20)QL = 3,600/(N - 1)
 Profit of each non-merged (follower) firm is:
pF = (PL - 20)qF = 3,600/(N - 1)2
The merged firm is always more profitable than each non-merged firm
 Is the merger profitable for the merged firms?
Profit pre-merger was: 2pC = 28,800/(N + 1)2
3,600
28,800
>
which requires:
so pL > 2pC requires:
2
(N - 1)
(N + 1)
(N + 1)2 > 8(N - 1)
This is always true for N > 3
EC 171: Topics in Industrial Organization
The leadership example (cont.)
 What about the effect of the merger on the non-merged firms and on
consumers?
 Profit pre-merger was: pC = 14,400/(N + 1)2
3,600
14,400
>
which requires:
so pF > pC requires:
2
2
(N - 1)
(N + 1)
(N + 1)2 > 4(N - 1)2
This is only true for N < 3
 The pre-merger price-cost margin is: PC - 20 = 120/(N + 1)
 The post-merger price-cost margin is: PL - 20 = 60/(N - 1)
the merger reduces price if:
60
<
N-1
120
or 60N + 60 > 120N - 120
N+1
This is true if N > 3
EC 171: Topics in Industrial Organization
Mergers and Market Leadership
• A two-firm merger that creates a market leader is profitable
for the merged firms if there are three or more firms in the
market
• Moreover, such a merger
– increases the market share of the merged firms
– reduces profit and market share for each non-merged firm
– benefits consumers by reducing price
•
•
•
•
So why worry about mergers?
What might the non-merged firms do?
Will they also seek merger partners?
If so, what then happens to price and consumer welfare?
EC 171: Topics in Industrial Organization
Mergers and leadership (cont.)
• The “leadership” merger reduces profits of the non-merged
firms
• Won’t these firms also seek merger partners?
– certainly consistent with casual evidence
• So, consider more than one two-firm merger
– creates a series of merged firms
– and a series of non-merged firms
• How does “leadership” work here?
– (Daughety) merged firms compete against each other
– but as a group act as leaders relative to the non-merged firms
– another variant on the Cournot model
EC 171: Topics in Industrial Organization
Mergers and leadership (cont.)
• Need to distinguish output decisions of the group of
leaders (L) and the group of followers (F)
– stage game
• stage 1: leaders each choose their output levels in competition with
the other lead firms
• stage 2: followers see output decisions of the lead firms then choose
their outputs with respect to residual demand in competition with
other follower (non-merged) firms
• Stick with the Cournot model we have used
– market demand P = 140 - Q; marginal cost $20; N firms
– the firms are in two groups
• L leaders or merged firms
• N - L followers or non-merged firms
– solve this game “backwards”
EC 171: Topics in Industrial Organization
Mergers and leadership (cont.)
 Suppose that the aggregate output of the lead firms is QL
 Residual demand for the non-merged firms is then:
P = 140 - QL - QF
where Q = QL + QF and QF is output of the non-merged firms
 QF can be written qf + QF-f
where QF-f denotes output of the non-merged firms other than firm f
 So the profit of non-merged firm f can be written:
pf = (140 - QL - QF-f - qf - 20)qf = (120 - QL - QF-f - qf)qf
 Differentiate this with respect to qf to give the condition:
pf/ qf = 120 - QL - QF-f - 2qf = 0
Solve this for qf
EC 171: Topics in Industrial Organization
An example of leadership (cont.)
 We have the best response function for firm f:
qf = 60 - QL/2 - QF-f/2
as a response to both the output of the leaders and the other followers
 But all the followers are identical
so in equilibrium they produce the same outputs:
so Q*F-f = (N - L - 1)q*f
so q*f = 60 - QL/2 - (N - L - 1)q*f/2 so (N - L + 1)q*f/2 = 60 - QL/2
120 - QL
q*f =
N-L+1
 Aggregate output of the non-merged firms is then:
(N - L)(120 - QL)
Q*F =
N-L+1
EC 171: Topics in Industrial Organization
An example of leadership (cont.)
 What about a lead (merged) firm in stage 1?
 The same technique can be used. Residual demand for a lead firm is:
P = 140 - QF - QL = 140 - QF - Q-l - ql
where Q-l is output of all the lead firms other than firm l
 The difference between the merged firms and the non-merged firms is
that each merged firm knows what QF is going to be.
 The typical lead firm correctly anticipates the actions of the nonmerged firms and so can use this information
(N - L)(120 - QL)
 Recall that Q*F =
N-L+1
and substitute this into the residual demand equation
EC 171: Topics in Industrial Organization
An example of leadership (cont.)
 This gives the residual demand equation
P = 140 -
(N - L)(120 - QL)
N-L+1
- QL
140 + 20(N - L)
=
+
N-L+1
(N - L)QL
N-L+1
140 + 20(N - L)
=
N-L+1
QL
N-L+1
For the moment we
treat the merged firms
as a group
- QL
 This can now be rewritten:
140 + 20(N - L) - Q-l
ql
P=
N-L+1
N-L+1
EC 171: Topics in Industrial Organization
An example of leadership (cont.)
 Profit of a typical merged firm is: pl = (P - 20)ql
 But we know what P is so we have
140 + 20(N - L) - Q-l
ql
P - 20 =
- 20
N-L+1
N-L+1
=
140 - 20 - Q-l
N-L+1
-
ql
N-L+1
 So profit of a typical merged firm becomes:
pl =
(120 - Q-l - ql)
(N - L + 1)
ql
 Differentiate this with respect to ql to give the profit maximizing
condition.
EC 171: Topics in Industrial Organization
An example of leadership (cont.)
 We have: pl =
(120 - Q-l - ql)
(N - L + 1)
ql
 Differentiating gives the condition:
pl/ ql =
120 - Q-l - 2ql
N-L+1
=0
 So we have the condition: Q*-l + 2q*l = 120
 In solving this we canSince
againQusecontains
a symmetry argument:
-l
in equilibrium all the lead Lfirms
will have the same output
- 1 firms
so Q*-l = (L - 1)q*l which gives: (L + 1)q*l = 120 so q*l = 120/(L + 1)
 Aggregate output of the merged firms is then: Q*L = 120L/(L + 1)
EC 171: Topics in Industrial Organization
An example of leadership (cont.)
 Recall that Q*F =
(N - L)(120 - QL)
N-L+1
 Now substitute for Q*L = 120L/(L + 1). This gives:
Q*F
=
(N - L)120
(N - L + 1)(L + 1)
and
q*F
=
120
(N - L + 1)(L + 1)
 This has been a lot of work!!! But now we can see the effect of a
group of mergers.
 We can easily compare outputs of the different types of firms.
The leader (merged) firms are larger than the follower (nonmerged) firms: as we would expect
EC 171: Topics in Industrial Organization
An example of leadership (cont.)
 What about profits? Is the profit of a leader firm more than twice
that of the profit it would make as a follower?
 To make this comparison we need the equilibrium price.
 Aggregate output is: Q*F + Q*L
so Q*T =
(N - L)120
(N - L + 1)(L + 1)
+
120L
(L + 1)
=
120(N + NL - L2)
(N - L + 1)(L + 1)
 This looks nasty but check that it is greater than the Cournot output
 Stackelberg leaders produce more than Cournot firms. This reduces
output of the followers but not by an offsetting amount.
 Followers are under pressure: lower output and lower prices.
 Increases the likelihood that followers will merge.
EC 171: Topics in Industrial Organization
An example of leadership (cont.)
 Check the profitability of an additional merger. To do so,we need
profits of followers and leaders.
 This requires that we calculate the price-cost margin.
Price is PL = 140 - Q*T = 140 -
120(N + NL - L2)
(N - L + 1)(L + 1)
and the price-cost margin is PL - 20 which gives:
PL - 20 =
120
(N - L + 1)(L + 1)
 This then gives us the profit equations for each type of firm
EC 171: Topics in Industrial Organization
An example of leadership (cont.)
 Profit of a typical follower is:
pf(N, L) =
14,400
(N - L + 1)2(L + 1)2
 Profit of a typical leader is:
pl(N, L) =
14,400
(N - L + 1)(L + 1)2
 Each leader is more profitable than each follower but this is not the
appropriate comparison
 Compare profits of two followers before they merge with their
profits after they merge.
EC 171: Topics in Industrial Organization
An example of leadership (cont.)
• Starting from any configuration of leaders and followers a
further two firms will always wish to merge.
• Is such a group of two-firm mergers desirable for
consumers?
– firms that join the leader group increase output
– but there are fewer firms in the market
• So will a further two-firm merger increase or decrease
output?
– for this to happen we must have L < N/3 - 1
For price to fall as a result of a merger the leader group
should contain no more than one-third of the total number of
firms in the market
EC 171: Topics in Industrial Organization
Product Differentiation and Merger
• The discussion so far has assumed that products are
identical
• It can be extended to differentiated products:
– suppose demand is of the form:
– q1 = A - Bp1 + C(p2 + p3 +…+ pn)
– and similarly for the other products
• Now a merger allows coordination of the outputs of the
different products
• but the merger does not lead to one of the products being
eliminated
EC 171: Topics in Industrial Organization
An Example of Product
Differentiation
QC = 63.42 - 3.98PC + 2.25PP
MCC = $4.96
QP = 49.52 - 5.48PP + 1.40PC
MCP = $3.96
This example can be generalized to more than two products
EC 171: Topics in Industrial Organization
Product differentiation
• Take a different approach
– spatial model of product differentiation
• The idea is simple
– suppose firms are offering different varieties of a product
– the analogy is that these products have different “locations”
– then merger between some of these firms avoids some of the
problems of the merger paradox
• don’t have to close down particular locations
• but can coordinate prices and, perhaps, locations
• Many mergers “look like” this
– join product lines that compete but do not perfectly overlap
EC 171: Topics in Industrial Organization
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
EC 171: Topics in Industrial Organization
The spatial
model
Assume
that firmillustrated
1 sets
Price
What if firm 1 raises
price p1 and firm 2 sets
Price
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
EC 171: Topics in Industrial Organization
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
EC 171: Topics in Industrial Organization
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)
EC 171: Topics in Industrial Organization
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)
EC 171: Topics in Industrial Organization
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
EC 171: Topics in Industrial Organization
361tL2/7200
49tL2/900
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
EC 171: Topics in Industrial Organization
Price Discrimination
 What happens if the firms can price discriminate?
 This leads to a dramatic change in the price equilibrium
Price

p1i
p1i+1
p2i
p*i(s)
t
i
t
s
i+1
Firm i suppliesand firm i+1
these consumers
these consumers
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
EC 171: Topics in Industrial Organization
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
EC 171: Topics in Industrial Organization
4
Merger with price discrimination
This is beneficial for the
 Now suppose that firms 2 and 3 merge
merged firms but harms
 They no longer compete in prices
sotothe
equilibrium
Prices
theprice
captive
consumerschanges
consumers between
Profits
to the
2 and
3 increase
merged firms
increase
1
2
3
4
EC 171: Topics in Industrial Organization
Vertical Mergers
• Now consider very different types of mergers
– between firms at different stages in the production chain
– also applies to suppliers of complementary products
• These mergers turn out, in general, to be beneficial for
everyone.
EC 171: Topics in Industrial Organization
Complementary Mergers
• Take 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?
EC 171: Topics in Industrial Organization
Complementary mergers (cont.)
Supplier 1
Supplier 2
price v2
price v1
Final Producer
price P
Consumers
EC 171: Topics in Industrial Organization
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
EC 171: Topics in Industrial Organization
Complementary producers (cont.)
The price charged by
= v1Q1 = v1(70 - v1/2 - v2/2)each supplier is a
We
need
to solve
function
of the
other
Solve
this
for
v
1
 Maximize this with respect to v1
supplier’sthese
pricetwo pricing
equations
p1/v1 = 70 - v1 - v2/2 = 0
p1
v1 = 70 - v2/2
 We can do exactly the same for v2
v2 = 70 - v1/2
v1 = 70 - (70 - v1/2)/2 = 35 + v1/4
so 3v1/4 = 35 so v1 = $46.67
v2
140
R1
70
46.67
R2
and v2 = $46.67
46.67 70
EC 171: Topics in Industrial Organization
140
v1
Complementary products (cont.)
 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
EC 171: Topics in Industrial Organization
Complementary products (cont)
Supplier 1
23.33 units @
$46.67 each
Now suppose that the
two suppliers merge Supplier 2
23.33 units @
$46.67 each
Final Producer
23.33 units @ $116.67 each
Consumers
EC 171: Topics in Industrial Organization
Complementary mergers (cont.)
Supplier 1
Supplier 2
price v
The merger allows the
two firms to coordinate
their prices
Final Producer
price P
Consumers
EC 171: Topics in Industrial Organization
Complementary merger (cont.)
 Consider the profit of the final producer: this is
pf = (P - v)Q = (140 - v - Q)Q
 Maximize this with respect to Q
Solve this for 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)
 Maximize this with respect to v
EC 171: Topics in Industrial Organization
Complementary merger (cont.)
This is the cost of the combined
input so the merger has reduced
costs to the
The
final
merger
producer
has reduced
 Differentiate with respect to v
the final product price:
m
p /v = 70 - v = 0 so v = $70
consumers gain
 Recall that Qm = Q = 70 - v/2 so Qm = Q = 35 units
This is greater than the
combined
 This gives the final product price
P = 140pre-merger
- Q = $105
profit
 What about profits? For the merged upstream firm:
This is greater than the
m
p = vQm = 70 x 35 = $2,480 pre-merger profit
 For the final producer:
pm = vQm = v(70 - v/2)
pf = (105 - 70) x 35 = $1,225
EC 171: Topics in Industrial Organization
Complementary mergers (cont.)
• 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
– reduction 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
EC 171: Topics in Industrial Organization
Vertical Mergers
• The same kinds of result arise 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 $20
sells product to the retailer at price r per unit
retailer has no other costs: one unit of input gives one unit of output
retail demand is P = 140 - Q
EC 171: Topics in Industrial Organization
Vertical merger (cont.)
Marginal
costs $20
Manufacturer
wholesale price r
Price P
Consumer Demand: P = 140 - Q
EC 171: Topics in Industrial Organization
Vertical merger (cont.)
• Consider the retailer’s decision
– identify profit-maximizing output
– set the profit maximizing price
Price
140
Demand

marginal revenue downstream is
MR = 140 - 2Q
 marginal cost is r

equate MC = MR to give the
quantity Q = (140 - r)/2

identify the price from the demand
curve: P = 140 - Q = (140 + r)/2

profit to the retailer is (P - r)Q
which is pD = (140 - r)2/4
(140+r)/2
r

profit to the manufacturer is (r-c)Q
which is pM = (r - c)(140 - r)/2
MC
140 - r
2
MR
70
140
Quantity
EC 171: Topics in Industrial Organization
Vertical merger (cont.)

suppose the manufacturer sets a
different price r1
 then the downstream firm’s
output choice changes to the output
Q1 = (140 - r1)/2
Price
140
Demand

r1
and so on for other input prices
demand for the manufacturer’s
output is just the downstream
marginal revenue curve

r
140 - r
140 - r1
MC
Upstream demand
MR
Quantity
70
140
2
2
EC 171: Topics in Industrial Organization
Vertical merger (cont.)
the manufacturer’s marginal cost is $20
 upstream demand is Q = (140 - r)/2
which is r = 140 - 2Q
 upstream marginal revenue is, therefore,
MRu = 140 - 4Q
 equate MRu = MC: 140 - 4Q = 20

Price
140
110
Demand
80
Upstream demand
20
MRu
30
35
MR
70
MC
140

so Q* = 30 and the input price is $80

while the consumer price is $110

the manufacturer’s profit is $1800

the retailer’s profit is $900
Quantity
EC 171: Topics in Industrial Organization
Vertical merger (cont.)
• 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
– Total profit is:
price nets out of the
• upstream division: (r - c)Q
profit calculations
• downstream division: (P(Q) - r)Q
• aggregate profit: (P(Q) - c)Q
• Back to the example
EC 171: Topics in Industrial Organization
Vertical merger (cont.)
Price
140
Thismerger
mergerhas
has  the integrated demand is P(Q) = 140 - Q
This
benefited
the two  marginal revenue is MR = 140 - 2Q
benefited
consumers
 marginal cost is $20
firms

so the profit-maximizing output requires
that 140 - 2Q = 20
 so Q* = 60
 so the retail price is P = $80
Demand
80

aggregate profit of the integrated firm is
(80 - 20)x60 = $3,600
20
MR
60 70
MC
140
Quantity
EC 171: Topics in Industrial Organization
Vertical merger (cont.)
• 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
EC 171: Topics in Industrial Organization
Price discrimination
• Upstream firm selling to two downstream markets
– different demands in the two markets

v1
the seller wants to price
discriminate between these
markets
 set v1 < v2
v2

va
Market 1
P
Market 2
P
D1
D2
Q
Q
but suppose that buyers
can arbitrage
 then buyer 2 offers to buy
from buyer 1 at a price va
such that v1 < va < v2
 arbitrage prevents price
discrimination
 if the seller integrates
into market 1 arbitrage is
prevented
EC 171: Topics in Industrial Organization
Vertical foreclosure
• Vertically integrated firm refuses to supply other firms
– so integration can eliminate competitors

suppose that the seller is supplying
three firms with an essential input

the seller integrates with one buyer

if the seller refuses to supply the other
buyers they are driven out of business

is this a sensible thing to do?
EC 171: Topics in Industrial Organization
Vertical foreclosure
integrated
will
 Suppose that there are some integratedThe
firms
and somefirm
independent
upstream and downstream producersnot source on the independent
market
 Profit of an integrated firm is:
The integrated firm will
pI = (PD - cU - cD)qDi
not sell on the independent
market
 Profit of an independent upstream firm is:
pU = (PU - cU)qUn
 Profit of an independent downstream firm is:
pD = (PD - PU - cD)qDn
EC 171: Topics in Industrial Organization
Vertical foreclosure
 For the independent upstream firms to survive requires PU - cU > 0
 The downstream unit of an integrated firm obtains input at cost cU
 Buying from an independent firm costs PU > cU
so the downstream divisions will not source externally
 Now suppose that an upstream division of an integrated firm is
selling to independent downstream firms it earns PU - cBut
each
U onthis
is unit
true:sold
so
diverting
output from
 Divert one unit to its downstream
division: this leaves
the downstream
from selling
Profit fromProfit
selling
the external market
price unchanged: it earns PDexternally
- cU - cD on this unit diverted
internally
increases profits
PD - PU - cD > 0 for independent downstream firms to survive
PD - cU - cD > PU - cU requires: PD - PU - cD > 0
so the upstream divisions will not sell externally
EC 171: Topics in Industrial Organization
Vertical foreclosure (cont.)
• Foreclosure happens
– but is not necessarily harmful to consumers
• reduces number of buyers in the upstream market
• increases prices charged by independent sellers to non-integrated
downstream firms
• but integrated downstream divisions obtain inputs at cost
• puts pressure on non-integrated downstream firms
– provided there are “enough” independent upstream firms the anticompetitive effects of foreclosure will be offset by the cost
advantages of vertical integration
• There are also strategic effects that might prevent
foreclosure
– to avoid non-integrated firms from integrating
EC 171: Topics in Industrial Organization
EC 171: Topics in Industrial Organization