Endogenous Merger with Learning

Can Erutku

doi:10.1515/bejeap-2013-0101

Article

Endogenous Merger with Learning

Can Erutku

Published/Copyright: April 18, 2014

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From the journal The B.E. Journal of Economic Analysis & Policy Volume 14 Issue 3

Abstract

We look at a concentrated market structure to determine the more likely merger when firms are initially asymmetric. A feature of the analysis is that a high cost firm participating in a merger can learn from the low cost participant. The determination of the equilibrium ownership structure (EOS) rests on the size of the cost asymmetries and learning abilities. Using an endogenous merger model, we find that the EOS always involves a merger between the two most efficient firms. This result holds whether firms adopt a decentralized or centralized structure post-merger and whether learning abilities are known or uncertain pre-merger. In most cases, welfare increases after the merger.

Keywords: endogenous; merger; asymmetry; learning

JEL Codes: L13; L4

Appendix

Let us denote by πiM=(qiM)2 firm i’s profit in market structure M when it produces output qiM.

Proof for Lemma 1

M^A dom M⁰ via D^0A = {1, 2} for K>4 and θA∈(0,1]. Two cases need to be considered. The difference between π1A+π2A and π10+π20 is written as 5K(K−4)+2(K2−16)+16θA(K−4)+40θA2 which is greater than zero for all K∈(4,KA] with KA=4+θA and θA∈(0,1]. When K>KA and for any θA∈(0,1], π1A+π2A−π10+π20 simplifies as 2K−4+5>0.
M^B dom M⁰ via D^0B = {1, 3} for K>max{4,KB} with KB=8−5θB and θB∈(0,1]. The difference between the post- and pre-merger profits for firms 1 and 3 is simplified as K−8+5θB and is greater than zero for any value of K>KB with KB>4 for all θB∈(0,4/5).
M^C dom M⁰ via D^0C = {2, 3} for K>max{4,KC} with KC=(12−5θC)/2 and θC∈(0,1]. π2C+π3C−π20+π30=2K−12+5θC>0 for any value of K>KC with KC>4 for all θC∈(0,4/5).

Proof for Proposition 1

By Lemma 1, M^A dom M⁰ via D^0A = {1, 2} for K>4 and θA∈(0,1] implying that M⁰ cannot be an EOS.
By Lemma 1, M^A is the EOS for θi∈[0,4/5] with i = A, B, C and K∈(4,KC].
Two cases need to be considered when comparing decisive owners’ profits between M^A and M^C. First, when K∈(4,KA] we have that π1A(π2A) is decreasing (increasing) in θA. In addition, π2C(π3C) is increasing (decreasing) in θC. Replacing θA by 1 (0) in π1A(π2A) and θC by 0 (1) in π2C(π3C), we have π1A+π2A−π2C+π3C>0. This means that for all θA∈(0,1] and θC∈(0,1], M^C cannot be an EOS if K∈(4,KA].
Second, when K>KA, π1A+π2A−π2C+π3C=f2K,θA,θC with f2K,θA,θC=8K+2KθA−4θA+5θA2−2KθC+12θC−5θC2. Remark that ∂f2(K,θA,θC)/∂K>0 for all θA∈(0,1] and θC∈(0,1]. Because f24,θA,θC>0 for all θA∈(0,1] and θC∈(0,1], M^C cannot be an EOS if K>KA.
When comparing decisive owners’ profits under M^B and M^C, π1B+π3B−π2C+π3C, we obtain gK,θB,θC=4K+4KθB−2KθC−32θB+12θC+20θB2−5θC2+8. Remark that ∂h1(K,θA,θB)/∂K=4+2θA−4θB≥0 for all θB∈(0,1], and θC∈(0,1]. Because g4,θB,θC>0 for all θB∈(0,1] and θC∈(0,1], M^C cannot be an EOS for any K>4.
Two cases need to be considered when comparing decisive owners’ profits between M^A and M^B. When K>KA, we have h1K,θA,θB=4K+2KθA−4θA+5θA2−4KθB+32θB−20θB2−8, which represents the difference between π1A+π2A and π1B+π3B. Remark that ∂h1(K,θA,θB)/∂K=4+2θA−4θB≥0 for all θA∈(0,1] and θB∈(0,1]. Because h14,θA,θB>0 for all θA∈(0,1] and θB∈(0,1], M^A is the EOS if K>KA.
When K∈(4,KA], π1A+π2A−π1B+π3B simplifies as 80+32θA(K−4)+80θA2+72θB(K−4)+72KθB+288θB2+28(K−4)+4K2>0 for all θA∈(0,1], θB∈(0,1], and K∈(4,KA] implying that M^A is the EOS.

Proof of Corollary 1

Two cases need to be considered when firms 1 and 2 merge. The difference between the post- and pre-merger total surplus simplifies as 10K+23θA>0 for all θA∈(0,1] when K>KA.
Second, consider the case where K∈(4,KA]. There is an increase in total surplus post-merger only if K is less than (4/7)(16+16θA+39+46θA+37θA2)2. Welfare increases because the latter is greater than KA.
The post-merger total surplus is greater than the pre-merger total surplus when K<(16+23θB)/7=K¯B with KˉB=KB when θB=20/29.

Acknowledgments

I am grateful to the editor and two anonymous referees for their valuable and insightful comments. I also thank Xavier de Vanssay, Vathy Kamulete, and Marc Duhamel for their helpful comments. All errors are mine.

References

Amir, R., E.Diamantoudi, and L.Xue. 2009. “Merger Performance under Uncertainty Efficiency Gains.” International Journal of Industrial Organization27:264–73.10.1016/j.ijindorg.2008.08.006Search in Google Scholar

Banal-Estanol, A., I.Macho-Stadler, and J.Seldeslachts. 2008. “Endogenous Mergers and Endogenous Efficiency Gains: The Efficiency Defence Revisited.” International Journal of Industrial Organization26:69–91.10.1016/j.ijindorg.2006.10.007Search in Google Scholar

Barros, P. P. 1998. “Endogenous Mergers and Size Asymmetry of Merger Participants.” Economics Letters60:113–19.10.1016/S0165-1765(98)00082-2Search in Google Scholar

Farrell, J., and C.Shapiro. 1990. “Horizontal Mergers: An Equilibrium Analysis.” American Economic Review80:107–26.Search in Google Scholar

Horn, H., and L.Persson. 2001. “Endogenous Mergers in Concentrated Markets.” International Journal of Industrial Organization19:1213–44.10.1016/S0167-7187(99)00062-4Search in Google Scholar

Salant, S. W., and G.Shaffer. 1999. “Unequal Treatment of Identical Agents in Cournot Equilibrium.” American Economic Review89:585–604.10.1257/aer.89.3.585Search in Google Scholar

Salant, S. W., S.Switzer, and R. J.Reynolds. 1983. “Losses from Horizontal Merger: The Effects of an Exogenous Change in Industry Structure on Cournot-Nash Equilibrium.” Quarterly Journal of Economics98:185–99.10.2307/1885620Search in Google Scholar

Socorro, M. P. 2004. “Mergers and the Importance of Fitting Well.” Economics Letters84:269–74.10.1016/j.econlet.2003.07.011Search in Google Scholar

Tombak, M. M. 2002. “Mergers to Monopoly.” Journal of Economics & Management Strategy11:513–46.10.1162/105864002320272594Search in Google Scholar

1
The dynamic dimension, i.e. the possibility of observing a sequence of mergers, in Tombak (2002)’s analysis is absent here. Thus, firms do not consider how a merger taking place today can influence a target’s future purchase price.
2
Real-world examples include the defunct Dailmer-Chrysler merger and the Renault-Nissan and Chrysler-Fiat strategic alliances. Tombak (2002) provides case studies of mergers where the operations of the target were kept distinct from those of the acquirer.
3
The assumption that the differences in marginal costs are the same between firms 1 and 2 and firms 2 and 3 simplifies the presentation of the results without restricting the analysis. Barros (1998) makes the same assumption.
4
There is only one round of mergers, and a merger cannot involve more than two firms.
5
There would be no gain and no reason to merge if it were known with certainty that θ_ij = 0.
6
This notation is commonly used in the licensing literature and is quite similar to the one adopted by Barros (1998).
7
Firm 1 does not merge with firm 3 even when asymmetries are small and firm 3’s learning abilities are higher than those of firm 2. This is true, in particular, for the extreme case where θ_A→0, θ_B = 1, and ε = 0.
8
This means that the EOS cannot encompass a merger between firms 2 and 3 since firm 1 is an efficient outsider.
9
Proofs of this section are available from the author upon request.
10
The emptiness of the core arises because of the intransitivity of the dominance relation (see Horn and Persson 2001, 1221): for K∈(12, 28] we have M^A^’dom M^B^’, M^B^’dom M^0’, and M^0’dom M^A^’ (with M^A^’, M^B^’, and M^0’ all dominating M^C^’).
11
The merged firm would produce a combined output equal to (2K + 1 + θ_A)ε/3, if it were to adopt a decentralized structure.
12
Amir, Diamantoudi, and Xue (2009) assume that all firms have the same marginal cost pre-merger.

Published Online: 2014-4-18

Published in Print: 2014-7-1

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Articles in the same Issue

https://doi.org/10.1515/bejeap-2013-0101

Keywords for this article

endogenous; merger; asymmetry; learning