Salant et al. (1983) showed in a Cournot setting that horizontal mergers are unprofitable because outsiders react by increasing their output. We show that this negative effect may be compensated by the positive effect that horizontal mergers have on the buyer power of merging firms in input markets.buyer power; mergers; input markets.

Lluís Bru Martínez

Ramón Faulí-Oller

English

Research Papers in Economics

 
 
 
 
 
 
 
HORIZONTAL MERGERS FOR BUYER POWER* 
 
Lluís Bru and Ramón Faulí-Oller** 
 
WP-AD 2003-32 
 
 
 
 
 
 
 
Corresponding author: Ramón Faulí-Oller, Universidad de Alicante, Departamento de Fundamentos de 
Análisis Económico, Campus de San Vicente del Raspeig, 03071 Alicante, Spain. Phone 34 965 90 34 00 
(ext. 3226), Fax 34 965 90 38 98, E-mail: fauli@merlin.fae.ua.es. 
 
Editor: Instituto Valenciano de Investigaciones Económicas, S.A. 
Primera Edición Septiembre 2003 
Depósito Legal: V-4052-2003 
  
IVIE working papers offer in advance the results of economic research under way in order to 
encourage a discussion process before sending them to scientific journals for their final 
publication. 
 
 
 
 
 
                                                 
* Bru acknowledges partial financial support from the Spanish Ministry of Education project PB98-1402 
and Faulí-Oller from project BEC2001-0535 and from the IVIE.  
 
** L. Bru: Universitat de les Illes Balears; R. Faulí-Oller: Universidad de Alicante.   2
HORIZONTAL MERGERS FOR BUYER POWER 
 
Lluís Bru and Ramon Faulí-Oller 
 
 
 
 
 
 
 
 
ABSTRACT 
 
Salant et al. (1983) showed in a Cournot setting that horizontal mergers are 
unprofitable because outsiders react by increasing their output. We show that this 
negative effect may be compensated by the positive effect that horizontal mergers have 
on the buyer power of merging firms in input markets. 
JEL classification: L11, L20 
Keywords: buyer power; mergers; input markets.   3
1. Introduction 
There has been a long debate on merger profitability in Cournot settings since 
the seminal paper by Salant et al. (1983). They show in a symmetric linear Cournot 
model that mergers that do not include 80% of the active firms are unprofitable. They 
explain their result by pointing out that mergers have the negative strategic effect of 
increasing production of non-participating firms. 
Several extensions have tried to increase merger profitability by reducing the 
extent of the reaction of outsiders to a merger. This can be obtained by allowing either 
more convex demands (Faulí-Oller (1997)) or more convex costs (Perry and Porter 
(1985)).  
Here we take another approach. We consider that firms not only sell the final 
good, but must also buy an input in an imperfectly competitive market. Therefore firms 
not only care about market profits, but also about how these rents are shared with input 
suppliers. We show that mergers increase the share of profits that downstream firms can 
appropriate. This positive effect on firms’ profits of mergers must be evaluated against 
the negative strategic effect of increasing production of non-participating firms. 
We obtain that mergers are profitable when the positive effect is important 
enough. This is the case when the monopolistic power of upstream firms is so high that 
they are able to extract most of the rents of the vertical relationship. In this case, 
downstream firms strongly need to create buyer power from mergers.  
2. The  model 
There is an upstream firm U that produces an intermediate input at marginal cost 
0 ≥ c . There exists also a competitive supply of the input at marginal cost  c c > . In the 
downstream sector there are n firms that transform one unit of input into one unit of 
final product without additional costs of production. The final product is homogeneous 
and its demand is given by  Q Q P − =α ) ( .   4
Upstream and downstream firms set vertical contracts that establish the terms 
under which inputs are transferred. We model this vertical relationship following the 
framework in Rey and Tirole (forthcoming), where contracts are secret (or 
unobservable) and firms have passive conjectures. After contracts are set, competition 
downstream is à la Cournot. 
We want to address how mergers of downstream firms affect the process 
discussed above. Mergers change both the buyer power of downstream firms in the 
intermediate market and their market power in the final market. Salant et al (1983) 
showed that mergers solely to increase market power are seldom profitable. We will see 
that, when achieving buyer power is very important to increase profits, because 
competition upstream is very low (high c), the results on merger profitability are 
reversed. 
More specifically the situation is modelled according to the following timing: 
Stage 1: The efficient upstream firm secretly offers each downstream firm i a 
two-part supply contract  i i i i i F q w q T + = ) ( ; each downstream accepts or refuses the deal. 
If he refuses, he may use the alternative supply. If he accepts, he orders a quantity of 
input and pays accordingly. 
Stage 2: Downstream firms transform input into final product and compete in the 
final market à la Cournot. 
We are going to study the Perfect Bayesian Equilibrium of this game. We have 
multiplicity of equilibria if no restriction is imposed on the off-the-equilibium beliefs of 
firms about the contracts received by competitors. As in Rey and Tirole (forthcoming) 
we restrict attention to the case where those beliefs are unaffected by the off-the-
equilibrium contract a firm receives. Then firms are said to have passive conjectures.  
The upstream firm offers to each downstream firm i  the supply contract he 
would offer to a monopolist downstream facing (residual) demand  i
c
i q Q − − − α , where 
c
i Q−  is the output sold by competitors in equilibrium. Then the variable part of the 
supply tariff is set equal to marginal cost,  c wi =
* , whereas the fixed fee will be set to 
extract all the rents from firm i, except the amount he can obtain using the competitive 
supply of the input.     5
Hence, the fixed fee is given by () {} i i
c
i
q
c
i
i q c q Q Max
c Q
F
i
− − − − 






 − −
= −
− α
α
2
*
2
. As 
all firms operate in equilibrium at marginal cost c , each firm produces 
1
) (
+
−
=
n
c
n q
c α . 
Then the net profits of a downstream firm will amount to 
( ) { } i i
c
q
q c q n q n Max
i
− − − − ) ( ) 1 ( α . If we define 
c
c c
−
−
≡
α
θ , profits of downstream firms can 
be written as: 
()




 



+
< 




 −
+
−
=
otherwise
n
if
n
c
n
0
1
2
2 1
1
) , (
2
2 θ
θ
α
θ π  
θ  parametrizes the monopolistic power of the upstream firm and will play an 
important role in our analysis. Observe that θ  is increasing in c  and decreasing in c . 
The smaller the cost gap, the higher the competition faced by the upstream firm and 
lower the value of θ . Correspondingly, profits of downstream firms are decreasing in θ . 
We then have that, at one extreme, when θ  = 0 there is perfect competition upstream, 
and we are back to the standard Cournot model. At the other extreme, when 
1
2
+
≥
n
θ , 
the upstream supplier is de facto a monopolist because the competitive supply is so 
inefficient that does not constitute a valid alternative; as a consequence downstream 
firms obtain zero profits and all the rents are appropriated by the upstream firm. The 
“monopolistic” nature of the input supply, however, depends not only on the level of 
production costs but also on the number of firms n that compete downstream. We will 
concentrate below our analysis to the case where  


 

+
∈
1
2
, 0
n
θ , and the results we obtain 
will allow us to address straightforwardly what happens when 
1
2
+
≥
n
θ . 
Profits from a horizontal merger of k+1 downstream firms is defined
1 as the 
difference between post-merger and pre-merger profits of participating firms: 
                                                 
1 Vertical mergers are addressed in the original paper of Rey and Tirole (forthcoming).    6
) , ( ) 1 ( ) , ( θ π θ π n k k n + − −           ( 1 )  
A merger is said to be profitable if (1) is non-negative. It is useful to rewrite the 
profitability of mergers condition the following way: 
1
) , (
) , (
+ ≥
−
k
n
k n
θ π
θ π
         ( 2 )  
We can identify the effect of θ  on profitability through the effect of changes of θ  
on the left hand side of (2), which is strictly increasing in θ . This analysis yields to the 
following result: 
Proposition 1 A merger of k+1 firms is profitable for  () {} 


 

+
∈
1
2
, , , 0
n
n k max θ θ , 
where  ()
k n
k k n
n
n k
− +
+ − −
+
≡
1
1
1
2
, θ . 
Salant et al. (1983) obtained in a Cournot setting that mergers are profitable only if the 
number of participating firms is high enough.
2 In proposition 1, we show that mergers 
of any size are profitable, provided that θ  is high enough.
3 
The intuition of the result is interesting but not straightforward. A graphical 
illustration is useful to explain it. Figure 1 illustrates the situation in the standard 
Cournot setting ( 0 = θ ). Figure 1.a plots the pre-merger residual demand of a firm, and 
figure 1.b the post-merger residual demand. The reduction in rivalry moves the residual 
demand to the right, even though in equilibrium non-participating firms expand their 
production. Salant et al. (1983) show that, unless k is high enough, the profits obtained 
after the merger (area B) are lower than k+1 times the profits obtained before the 
merger (area A). 
                                                 
2 They consider  0 = θ . Then, a merger is profitable only if  () n k, θ  is negative. This amounts to 
n k k > + + 1 , which only holds if k is high enough. 
3 Observe that  ()
1
2
,
+
<
n
n k θ , and therefore the interval in proposition 1 is non-empty. For θ  in the 
interior of this interval, the merger is strictly profitable.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
P
 
P=α -(n-k-1)q
c(n-k)-qi
 
P
P=α -(n-1)q
c(n)-qi 
2.b 2.a 
Figure 2
A’ 
c   c
B’
c
P
 
P=α -(n-k-1)q
c(n-k)-qi
qi 
P
P=α -(n-1)q
c(n)-qi 
A  B
1.b 1.a 
qi 
 
 
 
c c =  
 
c c =
 
c  
 
qi q i 
Figure 1   8
Figure 2 considers what happens when c  increases while c  stays constant
4. In 
equilibrium, downstream firms will still be supplied by the efficient upstream firm at 
marginal cost. Therefore the sales of firms do not change. This implies that the pre-
merger (post-merger) residual demand in Figure 2a (2b) is like the one in Figure 1a 
(1b). However, the profits downstream firms obtain change because they depend on the 
possibility to use the competitive supply: as it has become less efficient they will 
obviously obtain less profits (A>A' and B>B'). But the main point is that a firm is more 
affected in its profits by an (absolute) increase in costs, the lower its (residual) demand. 
In graphical terms, the ratio between post-merger and pre-merger profits has increased 
(
A
B
 is lower than 
'
'
A
B
). Therefore it is more likely that a merger is profitable, the higher 
the value of c (and hence ofθ ). 
Salant et al. (1983) showed that (given n) mergers larger that a certain minimal 
size were profitable. In our model, the same result is obtained for any θ . The existence 
of the minimal size comes from the fact that the left hand side of (2) is increasing and 
convex in k. Furthermore, the minimal size is decreasing in θ . It comes from the fact 
that the left hand side of (2) is increasing in θ . This highlights the positive effect θ  has 
on merger profitability.  
Combining the existence of a minimal profitable merger size and Proposition 1, 
we can obtain the values of θ  for which mergers of any size are profitable. Consider a 
merger of two firms (i.e. a merger for which k = 1); Proposition 1 tells us that it is 
profitable for  () 


 

+
∈
1
2
}, , 1 , 0 max{
n
n θ θ . If a two-firm merger is profitable then mergers 
of larger size are also profitable, because a minimal profitable merger size exists. 
Hence, all mergers are profitable in this interval. When θ  is high enough, the increase in 
the residual demand (through a merger) is the only way to obtain significant profits. 
Imagine that in figure 2.a we had set c slightly below the intercept of demand. Then 
pre-merger profits would be so close to zero that mergers would be profitable. If any 
merger is profitable although firms are obtaining positive (even if small) profits before 
the merger, it is obvious that mergers will also be profitable when firms do not obtain 
profits at all, i.e. when 
1
2
+
≥
n
θ . 
                                                 
4 It is the change that increases θ that can be represented more easily.    9
3. Concluding  Remarks 
Rey and Tirole (forthcoming) showed that vertical mergers are profitable when 
supply contracts are secret. In the same setting, we have shown that horizontal mergers 
are also profitable. Therefore, in future work, it would be interesting to study the 
interaction between both types of mergers.  
We have considered secret contracts. We are going to devote future research to 
see if the main intuitions still hold when one assumes instead that contracts are 
observable.  
 
 
   10
References 
Faulí-Oller, R, 1997, "On merger profitability in a Cournot setting", Economics Letters 54, 75-
79.  
Perry, M. and R. Porter, 1985, "Oligopoly and the incentives for horizontal merger" American 
Economic Review 75, 219-227.  
Rey, P. and J. Tirole, "A Primer on Foreclosure", in M. Armstrong and R.H. Porter, eds, 
Handbook of Industrial Organization, 3. New York: North-Holland, forthcoming. 
Salant, S.W., S. Switzer and R.J. Reynolds, 1983, "Losses from horizontal mergers: The effects 
of an exogenous change in industry structure on a Cournot-Nash Equilibrium". The 
Quarterly Journal of Economics, 98 (2), 185-199.  
 

Losses from horizontal mergers: The effects of an exogenous change in industry structure on a Cournot-Nash Equilibrium&quot;.

Oligopoly and the incentives for horizontal merger&quot;

On merger profitability in a Cournot setting&quot;,

HORIZONTAL MERGERS FOR BUYER POWER

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HORIZONTAL MERGERS FOR BUYER POWER

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