THE EUROPEAN CONSOLIDATION BOARD


                                      European Consolidation Board for Foreign Industry (ECBFI)

A SCIENTIFIC APPRoACH AND FormULAE FOr CONSOLIDATION

THE FORmULAE TO A SUCCESSFUL EUROPEAN CONSOLIDATION

• Reduce competition – Increase market power • cost savings – Economies of scale and scope

Why allow companies to consolidate in Europe? • 

Merger without cost savings

  • Before merger: an n-firm oligopoly

  • After a merger of two firms: an (n – 1)-firm oligopoly

  • Before merger: Each of the merging firms had a market share of 1/n, totalling 2/n

  • After merger: the merged firm has a market share of 1/(n – 1).

  • The price may have increased from the merger, not enough to compensate for a loss in market share.

    So why merge? Why not just expand?

  • There is a factor of production whose total supply is fixed in the industry.

  • If you want to expand, then you need access to more of this factor, which you can only obtain from other firms in the industry.

  • Example: human capital, knowledge on operations.
    A merger combines productive resources that are not available

    outside the industry.
    A firm owning a fraction k of that capital stock and producing

output in quantity x has costs C(x, k). Total costs: C(x,k)= c x2

∂C c 2k Marginal costs: ∂x = k x

  • The more k you have, the lower are your marginal costs.

  • A larger firm is able to make better use of its larger amount of the fixed-supply factor.

  • When two firms merge, the merged entity now has higher

    k then the two separate firms, and therefore lower costs.

    Now, the merged firm obtains a market share in excess of 1/(n – 1) because of its cost benefit. For sufficiently high c, this makes a merger profitable.

Merger policy

  • In general, welfare analyses of mergers are complex – even within rather simple models.

  • An alternative: a sufficient condition for a merger to be welfare improving

  • The Farrell-Shapiro criterion

    A merger affects
    • the merging firms
    • the non-merging firms • consumers

    When a merger is proposed, then – presumably – it is profitable for the merging firms when looking for a sufficient condition for a welfare- improvement -

    → the external effect of a merger

Cournot competition

X – total output in the industry
xi – firm i’s output
yi – all other firms’ output: yi= X – xi

Firm i’s costs: ci(xi) Inverse demand: p(X)

Firm i’s first-order condition:

p(X) + xip’(X) - cix(xi) = 0. ⇒

p(xi + yi) + xip’(xi + yi) - cix(xi) = 0 ⇒

Firm i’s response to a change in other firms’ output: Total differentiation wrt xi and yi:

dxi =Ri =− p'+xip" dy 2p'+x p"−ci

i ixx

 Firm i’s response to a change in total output:

 dxi = Ridyi ⇒ dxi(1 Ri) Ri(dxi + dyi) =RidX

dxi Ri =p'(X)+xip"(X)=−λ<0 dX 1+ R ci(x )− p'(X i

i xx i


• Before merger: Each of the merging firms had a market 
share of 1/n, totalling 2/n
• Before merger: an n-firm oligopoly
• After a merger of two firms: an (n – 1)-firm oligopoly
• Before merger: Each of the merging firms had a market 
share of 1/n, totalling 2/n 
• After merger: the merged firm has a market share of
1/(n – 1). 
• Before merger: an n-firm oligopoly
• After a merger of two firms: an (n – 1)-firm oligopoly
• Before merger: Each of the merging firms had a market 
share of 1/n, totalling 2/n 
• After merger: the merged firm has a market share of
1/(n – 1). 
Why merge? 
• reduce competition – increase market power 
• cost savings – economies of scale and scope 
Why allow mergers? 
• cost savings 
ƒ Oliver Williamson: the efficiency defense 
Merger without cost savings
• Before merger: an n-firm oligopoly
• After a merger of two firms: an (n – 1)-firm oligopoly
• Before merger: Each of the merging firms had a market 
share of 1/n, totalling 2/n 
• After merger: the merged firm has a market share of
1/(n – 1). 
• The price may have increased somewhat from the 
merger, but hardly enough to compensate for a loss in 
market share. 
So why merge? Why not just expand? 
Tore Nilssen – Strategic Competition – Lecture 12 – Slide 1The Perry-Porter model
• There is a factor of production whose total supply is fixed 
in the industry. 
• If you want to expand, then you need access to more of 
this factor, which you can only obtain from other firms in 
the industry. 
• Example: human capital, knowledge on operations. 
A merger combines productive resources that are not available 
outside the industry. 
A firm owning a fraction k of that capital stock and producing 
output in quantity x has costs C(x, k). 
Total costs: ( ) 2
,
2
c
C x k x
k
=
Marginal costs: C c
x
x k
=
• The more k you have, the lower are your marginal costs. 
• A larger firm is able to make better use of its larger 
amount of the fixed-supply factor. 
• When two firms merge, the merged entity now has higher 
k then the two separate firms, and therefore lower costs. 
Now, the merged firm obtains a market share in excess of 
1/(n – 1) because of its cost benefit. For sufficiently high c, 
this makes a merger profitable. 
Tore Nilssen – Strategic Competition – Lecture 12 – Slide 2Merger policy
• In general, welfare analyses of mergers are complex – 
even within rather simple models. 
• An alternative: a sufficient condition for a merger to be 
welfare improving 
• The Farrell-Shapiro criterion 
A merger affects 
• the merging firms 
• the non-merging firms 
• consumers 
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 welfareimprovement - 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 to a large extent only the merging parties. 
So focusing on the external effect, we do not need to assess 
vague statements about cost savings from a merger. 
If the merger leads to a higher price, then non-merging firms 
benefit, and consumers suffer. But what is the total external 
effect? 
Tore Nilssen – Strategic Competition – Lecture 12 – Slide 3Cournot competition
X – total output in the industry 
xi
 – firm i’s output 
yi
 – all other firms’ output: yi
= X – xi
Firm i’s costs: c
i
(xi
Inverse demand: p(X) 
Firm i’s first-order condition: 
p(X) + xi
p’(X) - c
i
x(xi
) = 0. 
p(xi
 + yi
) + xi
p’(xi
 + yi
) - c
i
x(xi
) = 0 
Firm i’s response to a change in other firms’ output: Total 
differentiation wrt xi
 and yi
' "
2 ' "
i i
i i
i i
dx p x p
R
dy p x p c
+
= = −
+ − xx
From which we find firm i’s response to a change in total 
output: 
dxi
 = Ri
dyi
⇒ dxi
(1 + Ri
) = Ri
(dxi
 + dyi
) = Ri
dX
( ) ( )
( ) ( )
' "
0
1 '
i i i
i i
i xx i
dx R p X x p X
dX R c x p X
λ
+
= = = −
+ −
<
Tore Nilssen – Strategic Competition – Lecture 12 – Slide 4Welfare effects of a merger
Two sets of firms: 
I – insiders 
O – outsiders 
An infinitesimal merger 
• dXI
 – a small exogenous change in industry output 
Change in welfare from this merger: 
I i
I x i
i O
dW pdX dc p c dx
= − + ⎡
− ⎤
∑⎣ ⎦
• changes in output assessed at market price p. 
• c
I
 – insiders’ total costs 
• Note: dxi
 = – λi
dXI
 for each outsider firm 
• From an outsider firm’s FOC: p – c
i
x = – xi
p’(X) 
( ) '
( )
I
I I I i i
i O
dW pdX X dp dc X dp p X λ x dX
= + − − +
' ' ( ) ( )
I
I I i
i O
dW dπ λ X p X dX p X x dX
− = − +
∑ i I
' ' ( ) ( ) I
i i I I i i I I
i O i O
dW dπ λ x X p X dX λ s s Xp X dX
∈ ∈
⎡ ⎤ ⎡ ⎤
− = − = − ⎢ ⎥ ⎢ ⎥
⎣ ⎦ ⎣ ⎦
∑ ∑
Here, p’ < 0 and, typically, dXI
 < 0. So the external effect of a 
merger (the accumulation of many infinitesimal mergers) is 
positive if and only if: 
i i I
i O
λs s
∑ > !
→ An upper bound on the merging firms’ joint (pre-merger) 
market share in order for their merger to improve welfare. 
Tore Nilssen – Strategic Competition – Lecture 12 – Slide 5Examples
1. Constant marginal costs, linear demand 
c
i
xx = 0, p” = 0 → λI
 = 1. 
Before merger: all firms of equal size. The external effect is 
positive if the set of merging firms is less than half of all 
firms: 
⇔m < n/2 I
i O
s
<
∑ i
s
• But: will it always be profitable? 
2. The Perry-Porter model, quadratic costs, linear demand 
i
i
i
k
c k
λ =
+
FOC for firm i: 
p + xi
p’ – C’(xi
) = 0 ⇔ 0 i i
i
c
p x x
k
− − = ⇔ i
i
x
p
λ
= ⇔
i i
i
x s
p
λ
ε
= =
The external effect is positive if: 
1 2
I i
i O
s s
ε
<
• The size of the external effect depends on how 
concentrated the non-merging part of the industry is! 
• A merger is more likely to be welfare-enhancing if the 
rest of the industry is concentrated. 
• A merger among small firms leads to the other, big, firms 
to expand, which is good. 
Tore Nilssen – Strategic Competition – Lecture 12 – S
Why merge? 
• reduce competition – increase market power 
• cost savings – economies of scale and scope 
Why allow mergers? 
• cost savings 
ƒ Oliver Williamson: the efficiency defense 
Merger without cost savings
• Before merger: an n-firm oligopoly
• After a merger of two firms: an (n – 1)-firm oligopoly
• Before merger: Each of the merging firms had a market 
share of 1/n, totalling 2/n 
• After merger: the merged firm has a market share of
1/(n – 1). 
• The price may have increased somewhat from the 
merger, but hardly enough to compensate for a loss in 
market share. 
So why merge? Why not just expand? 
Tore Nilssen – Strategic Competition – Lecture 12 – Slide 1The Perry-Porter model
• There is a factor of production whose total supply is fixed 
in the industry. 
• If you want to expand, then you need access to more of 
this factor, which you can only obtain from other firms in 
the industry. 
• Example: human capital, knowledge on operations. 
A merger combines productive resources that are not available 
outside the industry. 
A firm owning a fraction k of that capital stock and producing 
output in quantity x has costs C(x, k). 
Total costs: ( ) 2
,
2
c
C x k x
k
=
Marginal costs: C c
x
x k
=
• The more k you have, the lower are your marginal costs. 
• A larger firm is able to make better use of its larger 
amount of the fixed-supply factor. 
• When two firms merge, the merged entity now has higher 
k then the two separate firms, and therefore lower costs. 
Now, the merged firm obtains a market share in excess of 
1/(n – 1) because of its cost benefit. For sufficiently high c, 
this makes a merger profitable. 
Tore Nilssen – Strategic Competition – Lecture 12 – Slide 2Merger policy
• In general, welfare analyses of mergers are complex – 
even within rather simple models. 
• An alternative: a sufficient condition for a merger to be 
welfare improving 
• The Farrell-Shapiro criterion 
A merger affects 
• the merging firms 
• the non-merging firms 
• consumers 
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 welfareimprovement - 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 to a large extent only the merging parties. 
So focusing on the external effect, we do not need to assess 
vague statements about cost savings from a merger. 
If the merger leads to a higher price, then non-merging firms 
benefit, and consumers suffer. But what is the total external 
effect? 
Tore Nilssen – Strategic Competition – Lecture 12 – Slide 3Cournot competition
X – total output in the industry 
xi
 – firm i’s output 
yi
 – all other firms’ output: yi
= X – xi
Firm i’s costs: c
i
(xi
Inverse demand: p(X) 
Firm i’s first-order condition: 
p(X) + xi
p’(X) - c
i
x(xi
) = 0. 
p(xi
 + yi
) + xi
p’(xi
 + yi
) - c
i
x(xi
) = 0 
Firm i’s response to a change in other firms’ output: Total 
differentiation wrt xi
 and yi
' "
2 ' "
i i
i i
i i
dx p x p
R
dy p x p c
+
= = −
+ − xx
From which we find firm i’s response to a change in total 
output: 
dxi
 = Ri
dyi
⇒ dxi
(1 + Ri
) = Ri
(dxi
 + dyi
) = Ri
dX
( ) ( )
( ) ( )
' "
0
1 '
i i i
i i
i xx i
dx R p X x p X
dX R c x p X
λ
+
= = = −
+ −
<
Tore Nilssen – Strategic Competition – Lecture 12 – Slide 4Welfare effects of a merger
Two sets of firms: 
I – insiders 
O – outsiders 
An infinitesimal merger 
• dXI
 – a small exogenous change in industry output 
Change in welfare from this merger: 
I i
I x i
i O
dW pdX dc p c dx
= − + ⎡
− ⎤
∑⎣ ⎦
• changes in output assessed at market price p. 
• c
I
 – insiders’ total costs 
• Note: dxi
 = – λi
dXI
 for each outsider firm 
• From an outsider firm’s FOC: p – c
i
x = – xi
p’(X) 
( ) '
( )
I
I I I i i
i O
dW pdX X dp dc X dp p X λ x dX
= + − − +
' ' ( ) ( )
I
I I i
i O
dW dπ λ X p X dX p X x dX
− = − +
∑ i I
' ' ( ) ( ) I
i i I I i i I I
i O i O
dW dπ λ x X p X dX λ s s Xp X dX
∈ ∈
⎡ ⎤ ⎡ ⎤
− = − = − ⎢ ⎥ ⎢ ⎥
⎣ ⎦ ⎣ ⎦
∑ ∑
Here, p’ < 0 and, typically, dXI
 < 0. So the external effect of a 
merger (the accumulation of many infinitesimal mergers) is 
positive if and only if: 
i i I
i O
λs s
∑ > !
→ An upper bound on the merging firms’ joint (pre-merger) 
market share in order for their merger to improve welfare. 
Tore Nilssen – Strategic Competition – Lecture 12 – Slide 5Examples
1. Constant marginal costs, linear demand 
c
i
xx = 0, p” = 0 → λI
 = 1. 
Before merger: all firms of equal size. The external effect is 
positive if the set of merging firms is less than half of all 
firms: 
⇔m < n/2 I
i O
s
<
∑ i
s
• But: will it always be profitable? 
2. The Perry-Porter model, quadratic costs, linear demand 
i
i
i
k
c k
λ =
+
FOC for firm i: 
p + xi
p’ – C’(xi
) = 0 ⇔ 0 i i
i
c
p x x
k
− − = ⇔ i
i
x
p
λ
= ⇔
i i
i
x s
p
λ
ε
= =
The external effect is positive if: 
1 2
I i
i O
s s
ε
<
• The size of the external effect depends on how 
concentrated the non-merging part of the industry is! 
• A merger is more likely to be welfare-enhancing if the 
rest of the industry is concentrated. 
• A merger among small firms leads to the other, big, firms 
to expand, which is good. 
Tore Nilssen – Strategic Competition – Lecture 12 – S
Why merge? 
• reduce competition – increase market power 
• cost savings – economies of scale and scope 
Why allow mergers? 
• cost savings 
ƒ Oliver Williamson: the efficiency defense 
Merger without cost savings
• Before merger: an n-firm oligopoly
• After a merger of two firms: an (n – 1)-firm oligopoly
• Before merger: Each of the merging firms had a market 
share of 1/n, totalling 2/n 
• After merger: the merged firm has a market share of
1/(n – 1). 
• The price may have increased somewhat from the 
merger, but hardly enough to compensate for a loss in 
market share. 
So why merge? Why not just expand? 
Tore Nilssen – Strategic Competition – Lecture 12 – Slide 1The Perry-Porter model
• There is a factor of production whose total supply is fixed 
in the industry. 
• If you want to expand, then you need access to more of 
this factor, which you can only obtain from other firms in 
the industry. 
• Example: human capital, knowledge on operations. 
A merger combines productive resources that are not available 
outside the industry. 
A firm owning a fraction k of that capital stock and producing 
output in quantity x has costs C(x, k). 
Total costs: ( ) 2
,
2
c
C x k x
k
=
Marginal costs: C c
x
x k
=
• The more k you have, the lower are your marginal costs. 
• A larger firm is able to make better use of its larger 
amount of the fixed-supply factor. 
• When two firms merge, the merged entity now has higher 
k then the two separate firms, and therefore lower costs. 
Now, the merged firm obtains a market share in excess of 
1/(n – 1) because of its cost benefit. For sufficiently high c, 
this makes a merger profitable. 
Tore Nilssen – Strategic Competition – Lecture 12 – Slide 2Merger policy
• In general, welfare analyses of mergers are complex – 
even within rather simple models. 
• An alternative: a sufficient condition for a merger to be 
welfare improving 
• The Farrell-Shapiro criterion 
A merger affects 
• the merging firms 
• the non-merging firms 
• consumers 
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 welfareimprovement - 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 to a large extent only the merging parties. 
So focusing on the external effect, we do not need to assess 
vague statements about cost savings from a merger. 
If the merger leads to a higher price, then non-merging firms 
benefit, and consumers suffer. But what is the total external 
effect? 
Tore Nilssen – Strategic Competition – Lecture 12 – Slide 3Cournot competition
X – total output in the industry 
xi
 – firm i’s output 
yi
 – all other firms’ output: yi
= X – xi
Firm i’s costs: c
i
(xi
Inverse demand: p(X) 
Firm i’s first-order condition: 
p(X) + xi
p’(X) - c
i
x(xi
) = 0. 
p(xi
 + yi
) + xi
p’(xi
 + yi
) - c
i
x(xi
) = 0 
Firm i’s response to a change in other firms’ output: Total 
differentiation wrt xi
 and yi
' "
2 ' "
i i
i i
i i
dx p x p
R
dy p x p c
+
= = −
+ − xx
From which we find firm i’s response to a change in total 
output: 
dxi
 = Ri
dyi
⇒ dxi
(1 + Ri
) = Ri
(dxi
 + dyi
) = Ri
dX
( ) ( )
( ) ( )
' "
0
1 '
i i i
i i
i xx i
dx R p X x p X
dX R c x p X
λ
+
= = = −
+ −
<
Tore Nilssen – Strategic Competition – Lecture 12 – Slide 4Welfare effects of a merger
Two sets of firms: 
I – insiders 
O – outsiders 
An infinitesimal merger 
• dXI
 – a small exogenous change in industry output 
Change in welfare from this merger: 
I i
I x i
i O
dW pdX dc p c dx
= − + ⎡
− ⎤
∑⎣ ⎦
• changes in output assessed at market price p. 
• c
I
 – insiders’ total costs 
• Note: dxi
 = – λi
dXI
 for each outsider firm 
• From an outsider firm’s FOC: p – c
i
x = – xi
p’(X) 
( ) '
( )
I
I I I i i
i O
dW pdX X dp dc X dp p X λ x dX
= + − − +
' ' ( ) ( )
I
I I i
i O
dW dπ λ X p X dX p X x dX
− = − +
∑ i I
' ' ( ) ( ) I
i i I I i i I I
i O i O
dW dπ λ x X p X dX λ s s Xp X dX
∈ ∈
⎡ ⎤ ⎡ ⎤
− = − = − ⎢ ⎥ ⎢ ⎥
⎣ ⎦ ⎣ ⎦
∑ ∑
Here, p’ < 0 and, typically, dXI
 < 0. So the external effect of a 
merger (the accumulation of many infinitesimal mergers) is 
positive if and only if: 
i i I
i O
λs s
∑ > !
→ An upper bound on the merging firms’ joint (pre-merger) 
market share in order for their merger to improve welfare. 
Tore Nilssen – Strategic Competition – Lecture 12 – Slide 5Examples
1. Constant marginal costs, linear demand 
c
i
xx = 0, p” = 0 → λI
 = 1. 
Before merger: all firms of equal size. The external effect is 
positive if the set of merging firms is less than half of all 
firms: 
⇔m < n/2 I
i O
s
<
∑ i
s
• But: will it always be profitable? 
2. The Perry-Porter model, quadratic costs, linear demand 
i
i
i
k
c k
λ =
+
FOC for firm i: 
p + xi
p’ – C’(xi
) = 0 ⇔ 0 i i
i
c
p x x
k
− − = ⇔ i
i
x
p
λ
= ⇔
i i
i
x s
p
λ
ε
= =
The external effect is positive if: 
1 2
I i
i O
s s
ε
<
• The size of the external effect depends on how 
concentrated the non-merging part of the industry is! 
• A merger is more likely to be welfare-enhancing if the 
rest of the industry is concentrated. 
• A merger among small firms leads to the other, big, firms 
to expand, which is good. 
Tore Nilssen – Strategic Competition – Lecture 12 – S

 

Welfare effects of a merger

Two sets of firms: – insiders

– outsiders
An infinitesimal merger

• dXI – a small exogenous change in industry output Change in welfare from this merger:

dW=pdX −dcI + I⎣⎦

∑ i∈O

⎡p−ci⎤dx xi

• changes in output assessed at market price p.
• cI – insiders’ total costs
• Note: dxi = – λidXI for each outsider firm
• From an outsider firm’s FOC: – cix = – xip’(X)

⇒()∑()

dW= pdX +Xdp−dcI −Xdp+ p' X λxdX

ii

iiI
dW−dπI =⎡∑λx −X ⎤p'(X)dX =⎡∑λs −s⎤Xp'(X)dX

III

i∈O p'(X)λxdX

∑ i∈O

Here, p’ < 0 and, typically, dXI < 0. So the external effect of a merger (the accumulation of many infinitesimal mergers) is positive if and only if:

∑λisi >sI i∈O

→ An upper bound on the merging firms’ joint (pre-merger) market share in order for their merger to improve welfare.

dW−dπI =−X p'(X)dX II

⎢iiI⎥I⎢iiI⎥I ⎣ i∈O ⎦ ⎣ i∈O 

 

 1. Constant marginal costs, linear demand cixx =0,p”=0→λI =1.

Before merger: all firms of equal size. The external effect is positive if the set of merging firms is less than half of all firms: ∑ sI< si⇔m<n/2 i∈O

• But: will it always be profitable?
2. The Perry-Porter model, quadratic costs, linear demand

λi = ki c+ki

FOC for firm i:
p+xip’–C’(xi)=0⇔ p−xi
c xi =0 ⇔ p= xi

λi = xi = si

  • The external effect is positive if:

    concentrated the non-merging part of the industry.

    • A merger is more likely to be welfare-enhancing if the

      rest of the industry is concentrated.

    • A merger among small firms leads to the other, big,firms

      to expand, which is good.

      More Information on the Scientific Aproach can be found in the System Integration Bible from the ECBFI. science@ecbfi.co.uk