Horizontal mergers and competitive intensity

Horizontal mergers and competitive intensity Marc Escrihuela-Villar Universitat de les Illes Balears November, 2010 Abstract We use the conjectural variations solution, first introduced by Bowley (1924), to analyze the profitability of horizontal mergers as a function of the degree of competition. We prove that any merger can be profitable if the environment is relatively competitive since in industries that are already cooperating a merger loses attractiveness as an anti-competitive device. We also derive two welfare results: (i) mergers are socially beneficial if the competition is intense enough and (ii) any welfare enhancing merger is also profitable if the proportion of firms involved in the merger is relatively large. Finally, we obtain that the presence of free entry raises merger profitability only when the degree of competition is low enough. JEL Classification: L13; L40; L41. Keywords: Horizontal mergers; Conjectural variations; Free entry Mailing address: Departamento Economia Aplicada. Edificio Jovellanos Ctra. Valldemossa km.7.5. 07122 Palma de Mallorca Baleares - España. Tel. +34 971173242. Fax: +34 971172389. Email: marc.escrihuela@uib.es 1

1 Introduction In a symmetric linear Cournot oligopoly setting with homogenous goods, Salant, Switzer and Reynolds (1983) (henceforth, SSR) showed that horizontal mergers are generally not profitable since the minimum profitable merger involves at least 80 percent of the firms in theindustry. Mergerstypicallyarenotprofitable for insiders, but are profitable for nonmerging firms (outsiders). Unprofitability comes from the fact that non-merging firms react to the merger by increasing their output. This result is often known as the merger paradox and makes it hard to explain how merger activity gets started, since a firm would always prefer to remain an outsider. This approach leaves out the competitive intensity and assumes Cournot behavior. To the best of our knowledge, only few papers address related aspects of mergers in a competitive environment. For instance, Escrihuela-Villar (2008) analyzes the price effects of horizontal mergers in a collusive environment by using an infinitely repeated game and in Rodrigues (2001) numerical examples are provided to illustrate the determinants of merger occurrence showing that the equilibrium market concentration is increasing (among other factors) in the expected competitive intensity. However, except from the papers mentioned before, most of the literature on merger profitability do not consider the competitive intensity. The main purpose of this paper is to study to what extent the competitive intensity is a crucial determinant of merger profitability. We analyze the conjectural variations oligopoly solution model, first introduced by Bowley (1924), with homogeneous and quantity-setting firms in which first, a merger among firms may occur and second, firms produce. Our main result is that any merger is profitable if the competition is intense enough. The intuition is that in industries that are already cooperating, mergers add less to the profits that firms are otherwise achieving. Our analysis also suggests that mergers are likely to be welfare enhancing in a sufficiently competitive market. Using our model, we also study the profitability of mergers when the number of active firms in the industry is not fixed exogenously. Earlier work investigates also horizontal mergers in a model where free entry and exit shapes the long-run industry structure. For instance, David- 2

son and Mukherjee (2007) obtain that with free entry there is no free rider problem and Spector (2003) examines the price effects of horizontal mergers with free entry. Such models,however,leaveouttheeffects of the degree of competition on merger profitability. We find that when we allow for free entry merger profitability decreases only when competition is low enough since, in this case, the entry of new firms is such that the resultant industry size is sufficiently large for any merger to be unprofitable. The rest of the paper is structured as follows. In section 2, we present the model and in two subsections we analyze merger profitability and the welfare effects of mergers respectively. Section 3 analyses merger profitability in the presence of free entry. We conclude in section 4. All proofs are grouped together in the appendix. 2 Model and results We consider an industry with N 2 firms, indexed by i =1,..., N. Eachfirm produces a quantity of a homogeneous product and compete in quantities with a linear cost function c(q i )=cq i,whereq i istheoutputproducedbyfirm i. The industry inverse demand is given by the piecewise linear function p(q) =max(0,a Q) where Q = P N i=1 q i is the industry output, p is the output price and a>0 with a>c.eachfirm faces also a fixed cost of F 0 whichweassumeisidenticalforallfirms. We analyze the conjectural variations oligopoly solution by assuming that each firm expects a one-unit change in its quantity to lead to a change of 1+λ in total output. In other words, each firm conjectures that a one-unit change in its output leads to a variation of λ in the other firms output. By varying the value of λ between 1 and N 1 one obtains different solutions, from the most competitive to the most collusive one respectively. 1 We also assume for simplicity that this conjecture is identical for all firms 1 To be rigorous, since we are going to analyze mergers of M +1 firms, assuming perfectly collusive expectations is equivalent to assuming λ = N 1 before the merger but λ = N M 1 after the merger. However, as we will see in the following subsections, we focus on relatively competitive rather than collusive markets. 3

and does not vary over time. Therefore, profit maximization implies that the equilibrium quantities and firms profits depend on λ. It is then straightforward to show that, in equilibrium q i = a c N + λ +1. This expression leads to the following equilibrium profits obtained by firm i (λ +1)(a c)2 Π i (N,λ) = F. (1) (N + λ +1) 2 We study the incentives of firms to merge. 2 Letusexaminethefollowingsimpletwostage game: first, a merger among M +1 firms may occur if it is beneficial to the merging parties; second, firms produce. In absence of synergies in the marginal cost of production, once M +1firms have merged there will be N M firms in the market. 3 We assume, further, that the merger has no impact on firms conjectural variations but it implies a fixed cost economy in such a way the fixed cost of the merged firm equals (M+1) F where (σ+1) 0 <σ M. Therefore, the post-merger equilibrium quantities will be characterized by identical production for each of the firms and post-merger profit will be given by the following expression: Π m (λ +1)(a c)2 (M +1) i (N, M, λ,σ) = F. (2) (N M + λ +1) 2 (σ +1) 2.1 Profitable mergers In this subsection we provide an analysis of the impact of mergers on industry structure. A merger is considered to be profitable if the profits of merging firms increase after merger which implies that Π m i (N,M,λ,σ) (M +1)Π i (N,λ) > 0. (3) 2 We do not consider here the process of endogenous merger formation. Its consideration probably requires a set-up in which the merger formation game is in a sequential fashion similar to Prokop s (1999) sequential cartel formation process. Otherwise, we would always have trivial Nash equilibria in which no firm would merge. This is an issue not raised here and left for future research. 3 We avoid integer problems following the standard approach in the literature on oligopolistic interaction which consists of treating the number of firmsasacontinuousvariable. 4

In this set-up, two motives could lead firms to merge: market power through a price increase and efficiency. It is well known that the price increase does not guarantee by itself the profitability of a merger. For example, in a Cournot setting (as in SSR) although mergers increase price, they are (generally) not profitable because non-merging firms react to the merger by expanding their output. 4 Obviously,amergeramongasubsetoffirms in the industry is profitableifitallowsforenoughfixed cost economies. It is easy to verify that there exists a σ(n,m,λ) such that when σ σ the merger of M +1 firmsisprofitable and 0 σ M for a certain range of the parameters N,M and λ. Intuitively, if fixed cost economies are sufficiently important any merger will be profitable. This, however, is not the approach that we take. In what follows, to assess the impact of the competitive intensity on merger profitability we focus on λ. Proposition 1 Regardless of the value of the fixedcosteconomyandtheindustrysize,a merger of M +1 firms is always profitable if the competition is intense enough. Proposition 1 indicates that the competitive intensity is a crucial determinant of merger profitability. This implies that when the competitive intensity of the industry is large enough any merger is profitable even for negligible fixed cost economies and for any industry size. Therefore, given that the present model encompasses the Cournot case if λ =0, Proposition 1 confirms that the results by SSR are sensitive to the assumption of pre-merger Cournot competition. The intuition behind Proposition 1 is as follows. When firms merge we have two different effects. First, the number of firmsisreducedand consequently price increases. This effect helps merger profitability. Second, non-merging firms react to the merger by increasing their output which reduces the incentives to merge. Proposition 1 comes from the fact that the first effect dominates the second one when the 4 SSR show that the minimum profitable merger under Cournot oligopoly involves at least 80 percent of the firms in the industry. This paradoxical result is valid only in Cournot environments, and generally fails to hold in differentiated Bertrand models. This is an issue not raised here and left for future research. It would also be interesting to see an extension to a wider range of demand functions (see Cheung (1992) and Faulí-Oller (1997)). 5

market is relatively competitive. In other words, when the competition is less intense a merger loses attractiveness as an anti-competitive device. 2.2 Welfare In this subsection, we focus on the effects of the merger on social welfare, which consists of consumers surplus and profits. We have generally two different effects of a merger: i) price increases and consequently consumer surplus decreases and ii) industry profits may increase. 5 The next result shows that when the competitive intensity of the industry is large enough, the second effect dominates the first one. Proposition 2 Regardless of the value of the fixedcosteconomyandtheindustrysize,a merger of M +1 firmsissociallybeneficial if the competition is intense enough. Intuitively, when the degree of competition among firms is large, consumers surplus is highandtheincreaseinpriceismorethancompensatedbytheincreaseinfirms profits due to the merger. The natural question arises of whether the competitive intensity that renders mergers profitableislargerorsmallerthantheonethatmakesthemergersocially beneficial. Proposition 3 All profitable mergers are also socially beneficial when the proportion of firms involved in the merger is below a certain threshold. Conversely, when the proportion of firms involved in the merger exceeds this threshold, profitable mergers are socially beneficial only if the competition is intense enough. The intuition is as follows. It can be easily verified that the degree of competition mentioned in Proposition 1 that is needed for a merger to be profitable is decreasing with M. Therefore, when the merger involves a low percentage of firms, the degree of competition has to be large enough for the merger to be profitable. In this case, 5 To see this note that non-merging firms benefit from the reduced competition whereas, by definition, merging firms obviously only benefit from the merger when it is profitable. Consequently, the impact of a merger on aggregate profits depends on λ. 6

Proposition 2 applies and the merger is also welfare enhancing or equivalently, merger profitability is a sufficient (but not necessary) condition for the merger to increase the social welfare. On the other hand, when the proportion of firmsinvolved inthemerger is relatively large, the price increase caused by the merger increases firms profits and, as a consequence, the decrease in the consumers surplus can only be offset in order for the merger to be welfare enhancing if the competition is intense enough. In other words, merger profitability is a necessary (but not sufficient) condition for the merger to increase the social welfare. 3 Free entry We consider in this section the effects of horizontal mergers in the presence of free entry with complete information and no uncertainty. In addition to the model described in the last section, we assume that in equilibrium the profit of the marginal entrant (net of fixed costs) is equal to 0. 6 Therefore, we consider the following 3-stage game. In stage 1, M +1forward-looking firms enter the market whenever they expect it to be profitable. We assume that this decision is made with the knowledge that they may merge in a later stage and that additional firms may enter afterwards before production takes place. Therefore, these M +1 firms may agree (or not) to merge. 7 In stage 2, additional firms are free to enter, being N the total number of firms in the industry. Finally, in stage 3 firms compete in quantities (à la Cournot). From the previous section we know that the fixed cost economy increases merger profitability which is obviously true with and without free entry. To simplify the analysis thus we assume in this section that σ =0. 6 We assume for simplicity that all firms that enter the market have the same value of the conjectural variation parameter. The assumption is based on the fact that the competitive intensity can also be seen as the degree of coordination between firms which in the literature is often considered as exogenously given (see for instance Verboven (1997), Martin (2006) or Escrihuela-Villar (2008)). 7 We avoid strategic entry assuming that entry occurs sequentially. Otherwise there may be multiple Nash equilibria for the entry game and we could have a coordination problem with respect to the entry. See more on the issue of simultaneous entry decision in Cabral (2004). 7

In the previous section case, with a fixed number of firms, it is easy to show that for a given competitive intensity and for any given number of participants in the merger, there is always an industry size N sufficiently large for the merger to be unprofitable. However, a more dynamic analysis might show that the entry of firms into the industry could increase if mergers are allowed or, in other words, entry might affect merger profitability. At first glance, it may appear that the existence of free entry might decrease the incentives to merge by increasing the industry size. Nevertheless, it is important to keep in mind that the number of firmsthatenterthemarketalsodependonthedegreeofcompetition. Firstofall, itcanbeeasilyverified that, without free entry (with N fixed), the sufficient 5+4(N+λ) condition for the merger to be profitable is that M 1/2 +N + λ which 2 is less binding if the degree of competition increases. On the other hand, with free entry the sufficient condition on M can be obtained by setting Π i (N M, λ) (as defined in (1)) equal to zero, solving for N and afterwards substituting in (3) before solving for M. Consequently, when M (a c)2 (1+λ) 2 (a c) 2 F (1+λ) mergers are profitable with free F entry. 8 We are now in the position to analyze how the existence of free entry affects industry structure when firms have the possibility to merge. Proposition 4 The existence of free entry decreases merger profitability only when competition is low enough. The intuition behind this result is that a low degree of competition among firms attracts entry of new firms such that the resultant industry size is sufficiently large for any merger to be unprofitable. On the contrary, when the competition is intense enough the prospect of achieving low profits attracts a small number of firms such that a merger of M +1 firmsisprofitable. In other words, eliminating entry barriers might render mergers profitable if the market is already competitive. 8 It is also easy to check that the number of firms that will enter the market depend positively on λ, which means that when competition is less intense this causes more firms to enter the market. 8

4 Concluding comments We have developed a theoretical framework to study merger profitability and the effects of horizontal mergers in social welfare in an imperfectly competitive environment, a problem that, to the best of our knowledge, has not been extensively considered. We prove that the results by SSR are sensitive to the assumption of pre-merger Cournot competition. We show that the competitive intensity is a crucial determinant of profitability and welfare effects of mergers in such a way that if the market is competitive enough any merger is profitable and may also be welfare enhancing. Interestingly, these results hold in the absence of synergies or fixed cost economies. Our results provide also the interpretation that the effects of the well-known merger paradox on merger profitability might vanish when we consider the degree of competition. We also analyze the incentives to merge in the presence of free entry. We prove that when the number of firmsthatenterthemarket depend on the degree of competition only if competition is low enough the existence of free entry diminishes the incentives to merge. The framework we have worked with is, admittedly, a particular one. To analyze real-world cases of mergers, firms capacities, cost asymmetries or variable cost synergies should also be considered. We believe that those are subjects for future research. Acknowledgements I am grateful to Ramon Faulí-Oller for his advice and encouragement and to Antonio Jiménez, Michael Margolis, Joel Sandonís, Luís Corchón, Pedro Barros, Javier López- Cunyat and Inés Macho for their helpful comments. The current version of the paper has benefited from helpful comments of the seminar participants at the European Network on Industrial Policy (EUNIP) 2010 International Conference. Financial support by the Ministerio de Educación y Ciencia through its project Políticas de salud y bienestar: incentivos y regulación (Ref: ECO2008-04321/ECON) is gratefully acknowledged. Any remaining errors are my own. 9

Appendix Proof of Proposition 1. Rearranging (2) and (1) we have that merger profitability is given by the following expression Π m i (N,M,λ,σ) (M +1)Π i (N,λ) =F (1 + M)(1 1 (λ+1)(a c)2 )+ (λ+1)(m+1)(a c)2. It is easy to see that for σ>0, (1 1 ) 0 and σ+1 (N M+λ+1) 2 (N+λ+1) 2 σ+1 therefore all terms of this expression are positive except for the last one. The last two terms, however, tend to zero as λ tends to 1. Consequently, for every σ > 0, there exists a λ close to 1 such that Π m i (N,M,λ,σ) (M +1)Π i (N,λ) > 0. Proof of Proposition 2. We use the standard definition of social welfare as the sum of consumers surplus and firms profits. Standard calculations show that the social welfare is given by the following expression W (N,M,λ) = F ((1+M)σ N(1+σ)) 1+σ + (a c)(n M)(1+N M+λ+2(a c)(1+λ)) 2(1+N M+λ) 2. Therefore, W(N,M,λ) M = Fσ (a c)(1+λ)(1+n M+λ+2(a c)(1+m N+λ)) 1+σ 2(1+N M+λ) 3, which for each possible value of σ is always positive when λ 2(a c)(n M 1) (N M+1) 2(a c)+1. Proof of Proposition 3. Using the expression for the merger profitability given in the proof of Proposition 1, we have that (Πm i (N,M,λ,σ) (M+1)Π i(n,λ)) σ = F (1+M) (1+σ) 2 > 0 which means that, as expected, merger profitability increases with the fixed cost economies. Therefore, a sufficient condition for a merger to be profitable can be obtained for the case of σ =0. In this case, Π m i (N,M,λ,0) (M +1)Π i (N,λ) 0 if λ M + 2 1+M N. Now we can compare the last constraint about λ with the one obtained in the proof of Proposition 3 (λ 2(a c)(n M 1) (N M+1) ). We obtain that whenever M M 2(a c)+1 1 4a(3a+1)+4c+12c(2a c)+32an(a 2c)+32c 2 N+( 1 2(a c)) 2 (1 6(a c)) 2 +64(a c) 2 N, the λ needed for 32(a c) 2 the merger to be welfare enhancing is smaller than the one needed for the merger to be profitable. The reverse is true if M<M. Consequently, the result holds. Proof of Proposition 4. provided in the third section. We only have to compare the sufficient conditions on M It is immediate to check that the number of merging firms required for the merger to be profitable is larger with free entry than with N fixed only when λ 2h4 2F 2 (1 + N)+Fh 2 (5 + 2N)+ p F 2 h 2 (h 2 4N(F h 2 )) where 2(F h 2 ) 2 h a c. We note that this is the only valid root whenever F < F (a c)2 (1+λ) (1+N+λ) 10

where F is the maximal fixed cost in order for the pre-merger equilibrium to be an interior equilibrium. In other words, for a particular industry size (N) andfixed cost (F )ifλ is small enough M 2 >M 1 where M 1 5+4(N+λ) 1/2 +N + λ and M 2 2 (a c) 2 (1+λ) 2 (a c) 2 F (1+λ). F References -Bowley, A., (1924). The mathematical groundwork of economics. Oxford University Press, Oxford. -Cabral, L., (2004). Simultaneous entry and welfare. European Economic Review 48, 943 957. -Cheung, F. K. (1992). Two remarks on the equilibrium analysis of horizontal merger. Economics Letters 40, 119-123. -Davidson, C., Mukherjee,A. (2007). Horizontal mergers with free entry. International Journal of Industrial Organization 25 (2007) 157-172 -Escrihuela-Villar, M. (2008). Partial coordination and mergers among quantitysetting firms. International Journal of Industrial Organization 26, 803 810. -Faulí-Oller, R. (1997). On merger profitability in a Cournot setting. Economic letters 54, 75-79. -Martin, S. (2006). Competition policy, collusion, and tacit collusion. International Journal of Industrial Organization 24 (6), 1299-1332. -Prokop, J. (1999). Process of dominant-cartel formation. International Journal of Industrial Organization 17, 241-257. -Rodrigues, V. (2001). Endogenous mergers and market structure. International Journal of Industrial Organization 19, 1245-1261. -Salant, S., Switzer, S., Reynolds, R. (1983). The Effects of an Exogenous Change in Industry Structure on Cournot-Nash Equilibrium. Quarterly Journal of Economics 98(2), 185-99. -Spector, D. (2003). Horizontal mergers, entry, and efficiency defences. Interna- 11

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