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EC 171: Topics in Industrial Organization
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 (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 (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 = (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:
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
The ordering of the firmsdoes not matter
EC 171: Topics in Industrial Organization
Generalization (cont.)
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, given by
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
EC 171: Topics in Industrial Organization
Generalization (cont.) 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
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
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
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:
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: C = 14,400/(N + 1)2
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
2(N - 1)=
Total output is: QT =
60
(N - 1)
60 +60(N - 2)
(N - 1)=
60(2N - 3)
(N - 1)
Price is: PL = 140 - QT =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:
L = (PL - 20)QL = 3,600/(N - 1)
Profit of each non-merged (follower) firm is:
F = (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: 2C = 28,800/(N + 1)2
so L > 2C requires:3,600
(N - 1)>
28,800
(N + 1)2which requires:
(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: C = 14,400/(N + 1)2
so F > C requires:3,600
(N - 1)2>
14,400
(N + 1)2which requires:
(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
N + 1or 60N + 60 > 120N - 120
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
QF can be written qf + QF-f
where QF-f denotes output of the non-merged firms other than firm f
where Q = QL + QF and QF is output of the non-merged firms
So the profit of non-merged firm f can be written:
f = (140 - QL - QF-f - qf - 20)qf = (120 - QL - QF-f - qf)qf
Differentiate this with respect to qf to give the condition:
f/ qf = 120 - QL - QF-f - 2qf = 0Solve this for qf
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
q*f =120 - QL
N - L + 1
Aggregate output of the non-merged firms is then:
Q*F =(N - L)(120 - QL)
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 non-merged firms and so can use this information
Recall that Q*F =(N - L)(120 - QL)
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
For the moment wetreat the merged firms
as a group
For the moment wetreat the merged firms
as a group
=140 + 20(N - L)
N - L + 1+
(N - L)QL
N - L + 1- QL
=140 + 20(N - L)
N - L + 1-
QL
N - L + 1
This can now be rewritten:
P =140 + 20(N - L) - Q-l
N - L + 1-
ql
N - L + 1
EC 171: Topics in Industrial Organization
An example of leadership (cont.) Profit of a typical merged firm is: l = (P - 20)ql
140 + 20(N - L) - Q-l
N - L + 1-
ql
N - L + 1
But we know what P is so we have
P - 20 = - 20
=140 - 20 - Q-l
N - L + 1-
ql
N - L + 1
So profit of a typical merged firm becomes:
l =(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.)
l =(120 - Q-l - ql)
(N - L + 1)ql We have:
Differentiating gives the condition:
l/ ql =120 - Q-l - 2ql
N - L + 1= 0
So we have the condition: Q*-l + 2q*l = 120
In solving this we can again use a symmetry argument:
in equilibrium all the lead firms will have the same output
so Q*-l = (L - 1)q*l
Since Q-l containsL - 1 firms
Since Q-l containsL - 1 firms
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
Recall that Q*F =(N - L)(120 - QL)
N - L + 1
An example of leadership (cont.)
Now substitute for Q*L = 120L/(L + 1). This gives:
Q*F =(N - L)120
(N - L + 1)(L + 1)q*F =
120
(N - L + 1)(L + 1)and
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 (non-merged) firms: as we would expect
EC 171: Topics in Industrial Organization
An example of leadership (cont.)
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
What about profits? Is the profit of a leader firm more than twice that of the profit it would make as a follower?
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 =120(N + NL - L2)
(N - L + 1)(L + 1)140 -
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:
f(N, L) =14,400
(N - L + 1)2(L + 1)2
Profit of a typical leader is:
l(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
QP = 49.52 - 5.48PP + 1.40PC
MCC = $4.96
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 illustrated
Firm 1 Firm 2
Assume that firm 1 setsprice p1 and firm 2 sets
price p2
Price Price
p1
p2
xm
All consumers to theleft of xm buy from
firm 1And all consumers
to the right buy fromfirm 2
What if firm 1 raisesits price?
p’1
x’m
xm moves to theleft: some consumers
switch to firm 2
EC 171: Topics in Industrial Organization
The Spatial Model• Suppose that there are five firms evenly distributed
1
2
34
5
these firms will split the market
r12
r23
r34
r45
r51
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
EC 171: Topics in Industrial Organization
Merger of Differentiated Products
1 2 3 4 5
Price
Main Circle (flattened)
r51 r12 r23 r34 r45 r51
now consider a merger between some of these firms
a merger of non-neighboring firms has no effect
A merger of firms2 and 4 does
nothing
but a merger of neighboring firms changes the equilibrium
A merger of firms2 and 3 doessomething
EC 171: Topics in Industrial Organization
Merger of Differentiated Products
1 2 3 4 5
Price
Main Circle (flattened)
r51 r12 r23 r34 r45 r51
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?
EC 171: Topics in Industrial Organization
Spatial Merger (cont.)
The impact of the merger on prices and profits is as follows
Pre-Merger Post-Merger
Price Profit Price Profit
1
2
3
4
5
tL/5 tL2/25
tL/5 tL2/25
tL/5 tL2/25
tL/5 tL2/25
tL/5 tL2/25
1
2
3
4
5
14tL/60 49tL2/900
19tL/60 361tL2/7200
19tL/60 361tL2/7200
14tL/60 49tL2/900
13tL/60 169tL2/3600
EC 171: Topics in Industrial Organization
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
t t
i i+1
take two neighboring firms
s
consider a consumer located at s
Pricep1
i
suppose firm i sets price p1i
i+1 can undercut with price p1i+1
p1i+1
i can undercut with price p2i
p2i
and so oni wins this competition by “just” undercutting i+1’s cost of supplying s
p*i(s)
the same thing happens at every consumer locationequilibrium prices are illustrated by the bold linesFirm i supplies
these consumers
Firm i suppliesthese consumers
and firm i+1these consumers
and firm i+1these consumers
EC 171: Topics in Industrial Organization
Merger with price discrimination Start with a no-merger equilibrium
1 2 3 4
Price equilibriumpre-merger is given
by the bold lines
Profit for each firmis given by theshaded areas
This is much betterfor consumers than no price discrimination
EC 171: Topics in Industrial Organization
Merger with price discrimination Now suppose that firms 2 and 3 merge
1 2 3 4
They no longer compete in prices so the price equilibrium changes Prices to the captiveconsumers between
2 and 3 increase
Prices to the captiveconsumers between
2 and 3 increaseProfits to themerged firms
increase
Profits to themerged firms
increase
This is beneficial for the merged firms but harms
consumers
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 v1price v2
price P
Final Producer
Consumers
EC 171: Topics in Industrial Organization
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 QSolve 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
EC 171: Topics in Industrial Organization
Complementary producers (cont.)
Maximize this with respect to v1
1 = v1Q1 = v1(70 - v1/2 - v2/2)
1/v1 =
70 - v1 - v2/2 = 0
Solve this for v1Solve 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 + v1/4
so 3v1/4 = 35 so v1 = $46.67
46.67
and v2 = $46.6746.67
EC 171: Topics in Industrial Organization
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: 1 = 2 = 46.67 x 23.33 = $1,088.81
final producer: f = (116.67 - 46.67 - 46.67) x 23.33 = $544.29
EC 171: Topics in Industrial Organization
Complementary products (cont)
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
EC 171: Topics in Industrial Organization
Complementary mergers (cont.)
Supplier 1 Supplier 2
price v
price P
Final Producer
Consumers
The merger allows thetwo firms to coordinate
their prices
EC 171: Topics in Industrial Organization
Complementary merger (cont.) 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 QSolve 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
EC 171: Topics in Industrial Organization
Complementary merger (cont.)
m = vQm = v(70 - v/2)
Differentiate with respect to v
m/v = 70 - v = 0 so v = $70
This is the cost of the combinedinput so the merger has reduced
costs to the final producer
This is the cost of the combinedinput so 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
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
This is greater than thecombined pre-merger
profit
For the final producer:
f = (105 - 70) x 35 = $1,225
This is greater than thepre-merger profit
This is greater than thepre-merger profit
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.)
ManufacturerMarginal costs $20
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 pricePrice
Quantity
Demand140
140
marginal revenue downstream is MR = 140 - 2Q
MR
70
marginal cost is r
MCr
equate MC = MR to give the quantity Q = (140 - r)/2
140 - r
2
identify the price from the demand curve: P = 140 - Q = (140 + r)/2
(140+r)/2 profit to the retailer is (P - r)Q which is D = (140 - r)2/4
profit to the manufacturer is (r-c)Q which is M = (r - c)(140 - r)/2
EC 171: Topics in Industrial Organization
Vertical merger (cont.)
Price
Quantity
Demand140
140
MR
70
MCr
suppose the manufacturer sets a different price r1
r1
140 - r
2
then the downstream firm’s output choice changes to the output Q1 = (140 - r1)/2
140 - r1
2
and so on for other input prices
demand for the manufacturer’s output is just the downstream marginal revenue curve
Upstream demand
EC 171: Topics in Industrial Organization
Vertical merger (cont.)
Price
Quantity
Demand
140
140
MR
70
the manufacturer’s marginal cost is $20
Upstream demand
20 MC
upstream demand is Q = (140 - r)/2 which is r = 140 - 2Qupstream marginal revenue is, therefore, MRu = 140 - 4Q
35
equate MRu = MC: 140 - 4Q = 20
so Q* = 30
30
and the input price is $80 80
while the consumer price is $110
110
the manufacturer’s profit is $1800
the retailer’s profit is $900MRu
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)
– 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
The internal transferprice nets out of theprofit calculations
• Back to the example
EC 171: Topics in Industrial Organization
Vertical merger (cont.)
Price
Quantity
Demand
140
140
MR
70
the integrated demand is P(Q) = 140 - Q
20 MC
marginal revenue is MR = 140 - 2Q
marginal cost is $20so the profit-maximizing output requires that 140 - 2Q = 20so Q* = 60
60
so the retail price is P = $8080
This merger has benefited consumers
aggregate profit of the integrated firm is (80 - 20)x60 = $3,600
This merger has benefited the two
firms
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
Market 1 Market 2P
Q
P
Q
D1 D2
the seller wants to price discriminate between these marketsv1 v2
set v1 < v2
but suppose that buyers can arbitragethen buyer 2 offers to buy from buyer 1 at a price va such that v1 < va < v2
va
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 Suppose that there are some integrated firms and some independent upstream and downstream producers
Profit of an integrated firm is:
I = (PD - cU - cD)qDi
Profit of an independent upstream firm is:
U = (PU - cU)qUn
Profit of an independent downstream firm is:
D = (PD - PU - cD)qDn
The integrated firm willnot source on the independent
market
The integrated firm willnot sell on the independent
market
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 - cU on each unit sold
Divert one unit to its downstream division: this leaves the downstream price unchanged: it earns PD - cU - cD on this unit diverted
PD - PU - cD > 0 for independent downstream firms to survive
PD - cU - cD PD - PU - cD > 0
But this is true: sodiverting output fromthe external market
increases profits
But this is true: sodiverting output fromthe external market
increases profits
so the upstream divisions will not sell externally
> PU - cU requires:
Profit from sellinginternally
Profit from sellinginternally
Profit from sellingexternally
Profit from sellingexternally
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 anti-competitive 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