Horizontal Mergers, Firm Heterogeneity, and R&D Investments

Noriaki Matsushima; Yasuhiro Sato; Kazuhiro Yamamoto

doi:10.1515/bejeap-2012-0058

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Horizontal Mergers, Firm Heterogeneity, and R&D Investments

Noriaki Matsushima , Yasuhiro Sato und Kazuhiro Yamamoto

Veröffentlicht/Copyright: 24. August 2013

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Aus der Zeitschrift The B.E. Journal of Economic Analysis & Policy Band 13 Heft 2

Abstract

We investigate the incentive and welfare implications of a merger when heterogeneous oligopolists compete both in process R&D and on the product market. We examine how a merger affects the output, investment, and profits of firms. In addition, we examine whether firms have merger incentives, and, if so, whether such mergers are desirable from the viewpoint of social welfare. If R&D is not expensive and if large cost differences between efficient and inefficient firms exist, a merger between homogeneous firms tends to occur even though it harms welfare.

Keywords: mergers; oligopoly; R&D; heterogeneity

JEL Classification: L41; L13; O32

Appendix A: derivations of the effects of mergers

From eqs [3] and [4], we obtain

A larger value of makes these tendencies weak, because

Moreover, the differences between the efficient and inefficient firms in their reactions to a particular type of merger are given by

These differences are smaller for a larger value of , because

Appendix B: profitability and desirability of a pairwise merger in the case of homogeneous firms

Let denote the profit of a merged firm. We can show that the difference between and the joint profit of firms involved in the merger is given as follows:

[9]

Therefore, is positive, if and only if

For a given number of firms, N (), the firms supply goods as long as . Therefore, the lower bound of the relevant interval of is . Evaluating at this lower bound, we have

Regarding the desirability, by plugging eqs [1], [4], and [3] under into eq. [8], we have

This is positive, if and only if

Evaluating at this lower bound, we have

for .

Appendix C: profitability and desirability of a pairwise merger in the case of heterogeneous firms

A Type (I) pairwise merger (i.e. a merger of efficient firms) is profitable, if .

A Type (II) pairwise merger (i.e. a merger of heterogeneous firms) is profitable, if .

A Type (III) pairwise merger (i.e. a merger of inefficient firms) is profitable, if .

The upper bound of the relevant interval of is , given in eq. [5], and the lower bound of the relevant interval of is , given in eq. [6]. Evaluating gains from a merger at these bounds, we obtain

We thus see that when is sufficiently large and is sufficiently small, a pairwise merger of Type (I) is profitable if

Similarly, a pairwise merger of Type (II) is profitable, if

The desirability of a merger comes from the following results:

This implies that a merger is desirable, if

Acknowledgments

We would like to thank two anonymous referees for their many constructive and helpful comments. We would also like to thank seminar participants at Nagoya University for their helpful comments. We would like to thank Emi Kurimune for her research assistance. Our research has been financially supported by the Grand-in-Aid for Scientific Research.

1
Capron (1999) pointed out the significant risk of damaging acquisition performance when the divested assets and redeployed resources are those of the target.
2
Perry and Porter (1985) investigated the impact of a horizontal merger that causes a cost reduction through aggregating the capital of the merging firms. Fumagalli and Vasconcelos (2009) extended this to the discussion of international mergers. Those articles cannot investigate how a horizontal merger changes the strategic interaction of efforts on cost-reducing activities. Farrell and Shapiro (1990) comprehensively investigated the effect of the change in the output through a horizontal merger. One of our main concerns is how firms execute horizontal mergers under Cournot competition with R&D although the properties in Farrell and Shapiro (1990) are shared with those in our article.
3
Ziss (1994) discussed a merger under a duopoly case in which two firms engage in R&D with spillover. Kabiraj and Mukherjee (2000) considered the case in which two firms with the same ex ante marginal cost engage in R&D and then decide whether to merge given the outcome of R&D is determined. Mukherjee (2006) discussed the effect of cross-border mergers on R&D and welfare. Jost and van der Velden (2008) also discussed the effect of horizontal mergers when firms engage in R&D investments for a patent race with spillover.
4
Friberg, Norbäck, and Persson (2012) and Phillips and Zhdanov (2013) captured the bidding behavior of firms in an acquisition process after firms engage in R&D. These articles mainly focus on the strategic aspect of premerger R&D. We discuss the relationship between those articles and ours in Section 4.
5
Sinha (2006) also discussed the effect of horizontal mergers when the outcome of R&D can be private information. Atallah (2005) analyzed merger profitability in the case of cost-reducing R&D. In his numerical example, however, R&D investment does not provide incentives for mergers in most cases.
6
This type of cost heterogeneity is also used in Barros and Nilssen (1999) and Ishida, Matsumura, and Matsushima (2011).
7
We do not consider heterogeneity of R&D investment costs; that is, is common to all firms. Although incorporating this matter would be important, it complicates the analysis in this article. Moreover, we guess that this type of heterogeneity would have a similar effect on the incentive to merge as ex ante cost heterogeneity.
8
Throughout the article, we study the pairwise mergers, which means that mergers consist of two firms.
9
This criterion is consistent with the equilibrium concept of the core (see Horn and Persson 2000, 2001). In fact, when the firms are homogeneous, an allocation involving a merger that satisfies this criterion is in the core under the restriction of a pairwise merger. In the next section, where we introduce firm heterogeneity, we use the core as an equilibrium concept and provide an analysis of the equilibrium.
10
A change in the market share due to a pairwise merger is given by
which is greater for a smaller number of firms.
11
See Davidson and Ferrett (2007), Lommerud, Straume, and Sørgard (2006), and Qiu and Zhou (2006) for recent examples.
12
See Horn and Persson (2001) for a detailed discussion on these points.
13
Incorporating convex cost functions into quantity competition models, Heywood and McGinty (2007, 2008) reconsidered the problem of the “merger paradox.”
14
Although the discussion is not reported in this article, the result is available upon request.
15
They show that the strategic trade policy induces the domestic firms’ merger, because a domestic merger induces government to give subsidies to the merged domestic firm.

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Schlagwörter für diesen Artikel

mergers; oligopoly; R&D; heterogeneity