The effects of merger have usually been examined in the context of homogeneous goods, and are unambiguously established. This paper deals with merger in vertically differentiated industries, presenting two models, one with two firms, and one with three firms. Results depend on the number of previous firms in the industry, and on the qualities produced by the merging firms. However, some results about the welfare effects of merger differ from the standard ones, which is mainly due to the nature of competition in a vertical differentiation set.Merger, vertical differentiation.

Cristina Barbot

English

Research Papers in Economics

FACULDADE DE ECONOMIA
UNIVERSIDADE DO PORTO
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WORKING PAPERS
HORIZONTAL MERGER AND 
VERTICAL DIFFERENTIATION
Cristina Barbot
Investigação - Trabalhos em curso - nº 108, Junho de 2001
www.fep.up.ptHORIZONTAL MERGER AND VERTICAL DIFFERENTIATION 
CRISTINA BARBOT* 
CETE**, Faculdade de Economia do Porto 
Rua Dr. Roberto Frias 
4200-464 PORTO 
PORTUGAL 
email: cbarbot@fep.up.pt 
 
 
 
 
ABSTRACT 
The effects of merger have usually been examined in the context of homogeneous 
goods, and are unambiguously established. This paper deals with merger in vertically 
differentiated industries, presenting two models, one with two firms, and one with three 
firms. Results depend on the number of previous firms in the industry, and on the 
qualities produced by the merging firms. However, some results about the welfare 
effects of merger differ from the standard ones, which is mainly due to the nature of 
competition in a vertical differentiation set. 
Keywords: Merger, vertical differentiation. 
 
RESUMO 
Os efeitos das fusões têm sido normalmente analisados no contexto de bens 
homogéneos, e estão estabelecidos de forma não ambígua. Este artigo debruça-se sobre 
fusões em indústrias com diferenciação vertical, apresentando dois modelos, um com 
duas empresas, e um outro, com três empresas. Neste contexto, alguns resultados sobre 
os efeitos a nível do bem estar diferem dos habituais, o que se deve fundamentalmente à 
natureza da concorrência em diferenciação vertical. 
Palavras chave: Fusões, diferenciação vertical 
 
 
 
 
 * I thank Massimo Motta for his helpful comments on an earlier version of this paper. 
** Research Centre financed by Fundação para a Ciência e a Tecnologia, Portugal.   3
HORIZONTAL MERGER AND VERTICAL 
DIFFERENTIATION 
 
1. INTRODUCTORY NOTE 
Theoretical concerns with horizontal merger have often been addressed to its welfare 
effects. They usually bring out two fundamental issues, which are an increase in market 
power, by the reduction of the number of firms, and the possibility of efficiency gains, 
due to lower unity costs, mainly provided by economies of scale and by some 
rationalisation of the production process.  
These expected results of merger have generally been established for industries with 
homogeneous or horizontally differentiated goods. But, as far as I know, the case of 
merger in a vertical differentiation context has never been examined. 
In industries with homogeneous goods, market power is an obvious result. Efficiency 
gains, by means of economies of scale are also more likely to happen is this kind of 
industries, provided that the mergers aren’t operating in an upwards sloping zone of 
their unitary cost curves. 
If goods are horizontally differentiated, and if they are close substitutes, market power 
will certainly be a result of merger. Here, efficiency gains may be a result of economies 
of scale, now also provided by lower unit sunk costs (as the costs of product 
engineering, or of introductory advertisement), as some previously rival products, which 
are quite similar, may be eliminated. Economies of scope, by the joint production of old 
and new goods after the merger, may also appear, and cause efficiency gains. Though 
this is not the concern of this paper, the case of merger in a horizontal differentiation 
environment arises interesting questions. 
Following Kuhn and Motta (1999)’s model, unilateral effects of horizontal mergers can 
be established in five lemmas, which are, and in the authors’ words: 
- A merger increases prices and decreases consumer surplus; 
- A merger always benefits the merging firm; 
- A merger increases outsiders’ profits; 
- A merger increases producer surplus; 
- A merger reduces net welfare.   4
This paper examines if these results hold in an industry with vertically differentiated 
goods, in the context of two very simple models. The first model, presented in Section 
2, includes only two goods and two firms, with positive cost functions. In this case, 
merger leads to a monopoly situation, and the issues here become the comparison of 
welfare between a duopoly and a monopoly, as well as the possibility of efficiency 
gains. 
Section 3 deals with the second model, much similar to the first one, in what concerns 
demands and costs. The difference is that here there are three goods and three firms, and 
the idea is to take account of the effects both for the merging firm and for the outsider. 
In fact, the presence of an outsider adds some interest to the issues presented in the two 
firms’ model.  
In both models, some results differ from Khun and Motta (1999)’s ones, which is 
mainly due to the nature of competition in vertically differentiated markets. In 
particular, welfare effects are, in one type of merger, substantially different from those 
established by these authors.  
Finally, in section 4, I draw some conclusions, summarising the results of this work. 
2. THE MODEL WITH TWO FIRMS 
In this section, I consider first an industry composed by two firms, producing two 
vertically differentiated goods, with qualities q and r, with r>q, and prices, respectively, 
p e s. The model I use was purposed by Motta (1993)
1. Utility function is U = vqk - pk, 
where qk represents the utility of consuming one unit of the good with quality qk, pk its 
price, and v the marginal valuation of utility. The parameter v is uniformly distributed 
in the interval [0,1], as in Scarpa (1998)
2.  
Firms bear quality costs, which are assumed to be fixed and growing with the quality of 
each good. So, cost function is Ck = qk
2 / 2.  
Y1 is the quantity of the good with quality q, and Y2 the quantity of the good with 
quality r. These quantities are determined in the usual way. Consumers indifferent 
                                            
1 As I use Motta (1993)’s model, the explanation is very brief. The main difference I introduce is in the 
calculation of the solutions. Readers may get better acquainted with the model by consulting its original 
presentation. 
2 Motta (1993) has introduced this model for two firms, and his v lies between a superior limit, v, and an 
inferior one, v. Scarpa (1998) uses the same model for three firms, v lying between zero and the unit.   8
This result was expected, because of monopoly power. And, obviously, the sum of 
profits should be higher, as this is also the collusion solution. To check more properly 
changes in welfare, it is interesting to compute consumer surplus (CS) and total welfare 
(TW) in both situations. CS is calculated as in Motta (1993)
3. 
CS pre merger = 0.0432       CS merger = 0.0313 
TW pre merger = 0.0692        TW merger = 0.0625  
Proposition 3: Consumer surplus is larger in the pre merger situation, so it 
decreases with  monopoly, and total welfare decreases too. These results are 
according to the general results for merger, as enunciated by Khun and Motta 
(1999).  
Proposition 4: The merger brings some efficiency gains. Indeed, costs are 
reduced in 6%, by the elimination of the costs with the worse quality, and the 
reduction of the costs with the best quality. Then, though firms benefit of cost 
reductions, society is also benefited, as a smaller amount of resources is used in 
this industry. 
The reader should notice, however, that, in a vertical differentiation context, efficiency 
gains have a different source. As stated above, in the case of horizontal merger without 
product differentiation, economies of scale are evident, whenever the cost function 
allows for them. Horizontal differentiation may enable the merger to eliminate goods 
that are much alike. Here, there is no point for economies of scale, as products are 
different, and, as we have seen, the whole amount of production is smaller after the 
merger. In fact, there aren’t properly efficiency gains, but resource savings on sunk 
quality costs, which, anyway, make society better off.   
Finally, it is interesting to mention that these results are quite similar to those of Mussa 
and Rosen (1978). These authors compare pure competition and monopoly solutions in 
a market with a vertically differentiated good. It is true that they use quite different tools 
(as their paper came to day a little before the core of vertical differentiation theory was 
published), and that they examine pure competition and not duopoly as a starting point. 
                                            
3 See Motta (1993), in his note 4.   10
The amount of the uncovered market means that about 9% of the consumers don’t buy 
any variety of the vertically differentiated good. It is much smaller than in any of the 
cases of the previous situation, which enhances the importance of another firm in the 
industry for consumer welfare. 
3.2. Merger 
In this model, market changes from three to two firms, so is interesting to examine 
market power and the effects for the outsider. Results depend on the firms that merge. 
Theoretically, it may happen with any pair of the three firms, leaving one firm as the 
outsider. In real world, it is more natural that the neighbouring qualities firms merge. I 
shall develop the model for two possible cases, the merger of firms 1 and 2, and the 
merger of firms 2 and 3. 
3.2.1. Merger of Firms 1 and 2 
First, let’s see the effects of the lower qualities firms merger, being the higher quality 
one left as the outsider. On the demand side, everything remains as before. On the 
supply side, and in the first stage, the merging firm will maximise its joint short run 
profits, there resulting “reaction functions” between their goods, and between these and 
the other one. As before, short run profits are equal to revenues, as quality costs are 
already chosen in this stage. The outsider also maximises his own short run profit. As 
expected, “reaction functions” are all positively sloped, and represented by: 
  p = zq / m (16) 
 z = 0.5 (2p(r-m)) + s (m-q)) / (r-q) (17) 
 s = 0.5z + 0.5(r-m) (18) 
It is useful to recall the expressions of reaction functions for the pre merger case, as 
calculated by Scarpa (1998): 
 p = 0.5zq / m (19) 
 z = 0.5 (p(r-m)) + s (m-q)) / (r-q) (20) 
 s = 0.5z + 0.5(r-m) (21)   13
Notice that maximal differentiation isn’t the best choice for the merger, owing to 
competition from the outsider. 
Again, better qualities drive the worst quality away. By eliminating this latter, the 
merger may sell the intermediate quality at higher prices, though leaving some of his 
previous consumers to the outsider. The best quality firm increases slightly its quantity, 
as it becomes farther apart from the intermediate one. Thus, the outsider is highly 
benefited, as it sells more at a higher price, by means of the worsening of m.  Finally, 
the number of consumers who don’t buy any unit of the good increases.  
With higher prices and smaller quantities, consumers should be worst off. And, then, 
will the rise in profits offset the expected decrease in consumer surplus? It is possible to 
compute consumer surplus (CS) in the pre merger and in the merger situation, using the 
method indicated in the previous section. Then, by adding long run profits, we get total 
welfare (TW). 
CS pre merger =  0.0443         CS merger = 0.0432 
TW pre merger = 0.0691         TW merger = 0.0692 
Proposition 6:  When firms 1 and 2 merge, consumer surplus decrease, but 
total welfare increases. Besides, there are some efficiency gains with the merger.  
Indeed, profits increase in 4.7%, and consumer surplus decreases in 2.5%. Higher 
profits are the result of higher revenues and lower costs. So, there is a point here for 
efficiency gains. The elimination of the worst quality, and the fact that the intermediate 
one becomes worse, mean lower costs for the merger firm, as well as for the two firms 
together, and, so, there result some efficiency gains. Again, these efficiency gains result 
from resource savings.  
However, the interesting point here is that total welfare increases
5, which changes 
general results for horizontal merger, when vertical differentiation is present. Thus, 
society is better off with two firms than with only one. For this, accounts the elimination 
of the worse quality, chosen by the merger. As this latter can manipulate qualities, and 
                                            
5 I checked this result using another method of calculating consumer surplus, by deducing the expense on 
each good to the definite integral of the demand function, and adding for the three goods. Results don’t 
change.   16
price, and, though its neighbouring quality is worse and sold at a lower price, it 
gets to rise profits in such a way. 
As in the previous section, it is easy to compute welfare indicators: 
CS pre merger = 0.0443         CS merger = 0.0351 
TW pre merger = 0.0691         TW merger = 0.0635 
Proposition 8: When the best quality firms merge, consumer surplus decreases, 
and is lower than in the case of firms 1 and 2 merger. Total welfare also 
decreases. As the whole demand diminishes, and two of the prices are higher, 
consumers are worst off.  
Changes in welfare are more drastic than in the previous case. Profits rise is of 15%, not 
offsetting the decrease of 21% in consumer surplus. Indeed, this situation is much worse 
for consumers than the previous one, and, conversely, much better for firms.  
Besides, cost decrease in 5%, mainly due to the intermediate quality costs, and leading 
to efficiency gains. 
4. Concluding Remarks 
Maybe that the most striking result of this essay is the increase in total welfare, in the 
case of three firms, and when the lowest and intermediate quality firms merge. In fact, 
this is the only case that doesn’t match the general results of merger. It is true that the 
reduction in consumer surplus is small, as well as the rise in profits. So, the merger 
doesn’t make too much difference to anyone. However, total welfare is higher. 
As in the general results for merger, it always happens that after the merger consumer 
surplus decrease, profits increase and the outsider is better off. Nevertheless, what really 
changes is how much this latter increases his profits. When the outsider is the lowest 
quality firm, its profits rise in 778%, but if it happens to be the better quality firm, 
profits only get 4% higher.  
Another important conclusion is that, in the context of vertical differentiation, it matters 
who was first. One cannot say that a market with two firms and two qualities has always 
the same solution. Indeed, the same solution is found for one a priori two firms 
situation, and for the merger of firms with the worst and intermediate qualities. But if,   17
instead, the intermediate and better quality firms merge, the market solution is different. 
In this case, the outsider has a much higher quality than if there were a priori two firms, 
though the merger worsens a little its better quality, which means that the quality space 
is significantly narrowed. 
 
REFERENCES 
KUHN and MOTTA, M. (1999), Chapter on Horizontal Mergers. Competition Policy: 
Theory and Practice, in preparation, European University Institute, Florence. 
MOTTA, M. (1993), Endogenous Quality Choice: Price versus Quantity Competition, 
The Journal of Industrial Economics,  XLI, 113-131.  
MUSSA, M. and ROSEN, S. (1978), Monopoly and Product Quality, Journal of Economic 
Theory, 18, 301-317. 
SCARPA, C. (1998), Minimum Quality Standards with More than Two Firms, 
International Journal of Industrial Organisation, 16, 665-676. 

Horizontal Merger and Vertical Differentiation

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