4820–13
Mergers
Geir B.
Asheim
Mergers
Introduction
Efficiency
defense
4820–13
FarrellShapiro
criterion
Geir B. Asheim
Department of Economics, University of Oslo
ECON4820
Spring 2010
Last modified: 2010.05.04
Why merge?
Why allow mergers?
4820–13
Mergers
Geir B.
Asheim
Firms merge to
Introduction
Outline
Efficiency
defense
reduce competition — increase market power
reap cost savings — economics of scale and scope
FarrellShapiro
criterion
Firms should be allowed to merge if
cost savings are greater than the efficiency loss
Oliver Williamson’s efficiency defense
Outline
4820–13
Mergers
Geir B.
Asheim
Introduction
Outline
Efficiency
defense
FarrellShapiro
criterion
Evaluation of the efficiency defense
Static effects of mergers
The Farrell-Shapiro criterion:
A sufficient condition under Cournot competition
Evaluation of the efficiency defense
4820–13
Mergers
Geir B.
Asheim
Introduction
Efficiency
defense
FarrellShapiro
criterion
Williamson’s point: It may not take a hugh cost saving to
dominate the deadweight loss from a merger. But what if . . .
. . . the pre-competitive price is not competitive?
. . . cost-savings don’t accrue to the non-merging firms?
Product reshuffling: More of the production in the industry
will be made by the low-cost merging firm — an additional
source of cost savings in the industry
. . . maximization of aggregate surplus is not the appropriate
welfare standard?
. . . dynamic effects are important?
R&D, capacity investment, new products, etc.
Static effects of mergers
4820–13
Mergers
Geir B.
Asheim
Introduction
Efficiency
defense
FarrellShapiro
criterion
External
effect
A merger
model
Welfare
analysis
What is λi ?
Discussion
In general, the welfare analysis of mergers are complex, even
within rather simple models. An alternative: A sufficient
condition for a merger to be welfare improving.
This is what the Farrell-Shapiro criterion provides, assuming that
firm engage in Cournot competition. A merger affects
the merging firms
price
costs
the non-merging firms
price
consumers
price
Positive external effect is sufficient
4820–13
Mergers
Geir B.
Asheim
Introduction
Efficiency
defense
FarrellShapiro
criterion
External
effect
A merger
model
Welfare
analysis
What is λi ?
Discussion
When a merger is proposed, then presumably
it is profitable for the merging firms
So the competition authority when
looking for a sufficient condition for a welfare-improvement
can limit the analysis to the merger’s effect on
(i) non-merging firms, and
(ii) consumers
→ the external effect of a merger
Cost savings affect mainly the merging parties.
So focusing on the external effect, we need not access
vague statements from the firms on their cost savings.
If the merger leads to a higher price,
then non-merging firms benefit and consumers suffer.
But what is the total effect?
A merger model with Cournot competition
4820–13
Mergers
Geir B.
Asheim
Introduction
Efficiency
defense
FarrellShapiro
criterion
External
effect
A merger
model
Welfare
analysis
What is λi ?
Discussion
X:
C:
xi :
ci
I:
O:
XI
X−i
total output in the industry
total cost in the industry
output of firm i
= ci (xi ): cost of firm i
Insiders (merging firms)
Outsiders (non-merging firms)
= i∈I xi : total output in the merging firms, etc.
= j=i xj : total output of all firms but i
dxi
: Firm i’s output increase in a response to
λi = − dX
a unit decrease of total output
P(X ): Inverse demand function
Firm i’s FOC under Cournot competition:
0 = P(X ) + xi P (X ) − ci (xi )
Welfare effects of a merger
4820–13
Mergers
Geir B.
Asheim
Introduction
Efficiency
defense
FarrellShapiro
criterion
External
effect
A merger
model
Welfare
analysis
What is λi ?
Discussion
dW = pdX − dC
= pdXI − dCI + pdXO − dCO
= (pdXI + XI dp − dCI ) −XI dp +
dπI
= dπI − XI P (X )dX +
i∈O
[P(X ) − ci (xi )]dxi
i∈O
xi P (X )λi dX
xi
XP (X )dX +
λi X
XP (X )dX
i∈O
λi si − sI XP (X )dX
= dπI +
= dπI −
XI
X
i∈O
Farrell-Shapiro criterion: Assume that dX < 0. Then
λi si − sI XP (X )dX > 0
dW − dπI =
if and only if
i∈O
i∈O λi si
> sI .
But what is λi ?
(Firm i’s response to a change in total output)
4820–13
Mergers
Let P (X ) + P (X )X < 0 & ci (xi ) > P (X ), ∀X , ∀i, ∀xi ≤ X
Geir B.
Asheim
0 = P(xi + X−i ) + xi P (xi + X−i ) − ci (xi )
Introduction
0 = (2P + xi P − ci )dxi + (P + xi P )dX−i
Efficiency
defense
FarrellShapiro
criterion
External
effect
A merger
model
Welfare
analysis
What is λi ?
Discussion
dxi
dX−i
iP
= Ri (X−i ) = − 2P P +x+x
i P −c
i
dxi = Ri dX−i ⇒ dxi (1 + Ri ) = Ri [dxi + dX−i ] = Ri dX
R
dxi
λi = − dX
= − 1+Ri =
i
P (X )+xi P (X )
P (X )−ci (xi )
>0
Example: Constant MC (ci = 0) and linear demand (P = 0),
so that λi = 1. All firms have equal cost and, thus, is of equal
size before merger. The external effect is positive if the number
of merging firms is less than half the number of all firms:
sI < i∈O si ⇔ m < n2
Discussion
4820–13
Mergers
Geir B.
Asheim
Introduction
Efficiency
defense
FarrellShapiro
criterion
External
effect
A merger
model
Welfare
analysis
What is λi ?
Discussion
Criticism of the Farrell-Shapiro approach
The merger might not be privately profitable
Empire building
Tax motivated mergers
Preemption (or encouragement) of other mergers
A merger’s effects on collusion
What effect does a merger have in an industry where firms
collude? — On balance: unclear.
The merging firms now earn more and have reduced incentives to cheat on the collusive agreement after the merger
(Especially) the non-merging firms now earn more without
collusion and therefore have increased incentives for breaking
out of the collusive agreement after the merger
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