Enforcement and Deterrence in Merger Control: The Case of Merger Remedies

Andreea Cosnita-Langlais; Lars Sørgard

doi:10.1515/rle-2015-0014

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Enforcement and Deterrence in Merger Control: The Case of Merger Remedies

Andreea Cosnita-Langlais und Lars Sørgard

Veröffentlicht/Copyright: 1. September 2017

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Aus der Zeitschrift Review of Law & Economics Band 14 Heft 3

Abstract

This paper deals with the enforcement of merger control in the presence of remedies, and studies how merger remedies affect the deterrence accomplished by controlling mergers. We determine the optimal frequency of investigations launched by the agency, and find that when conditional approvals are possible, it may be harder to deter the most welfare-detrimental mergers, and the agency might have to investigate mergers more often. Furthermore, we find that remedies may very well decrease welfare. Finally, we show that our theoretical results help to understand some of the empirical findings in the literature.

Keywords: merger control; merger remedies; enforcement; deterrence

JEL Classification: K21; L41

Acknowledgements

We are indebted for their helpful comments to the participants of ASSET 2013-Bilbao, EARIE 2014-Milan, and EALE 2014-Aix-en-Provence conferences, as well as the CRED-University Paris 2 seminar. Sø rgard thanks the Norwegian Research Council for support through the project ’Improving Competition Policy’ at SNF. The usual disclaimer applies.

Appendix

Proof of Proposition 1

Recall that gS=g+γh.

Thus ERΠ(y)−ESΠ(y)=ΠM(y)1−p+pg(y)+ΠR(y)ph(y)−C−ΠM(y)1−p+pg(y)+pΠM(y)γh(y)−C=ph(y)ΠR(y)−γΠM(y). Therefore ERΠ(y)>ESΠ(y) iff ΠR(y)ΠM(y)>γ.

Proof of Proposition 2

Under the remedy regime, the worst mergers will be deterred if ∂ERΠ(y)∂y<0⇔∂ΠM∂y1−p+pg+ΠM(y)p∂g(y)∂y+∂ΠR∂yph+ΠR(y)p∂h(y)∂y<0. Equivalently,

ΠM(y)1−p+pg∂ΠM∂yΠM(y)+p∂g(y)∂y1−p+pg+ΠR(y)ph∂ΠR∂yΠR(y)+∂h(y)∂yh<0, where ∂g(y)∂y<0 and ∂h(y)∂y<0 as well.

Proof of Lemma 1

Recall that γ≷ΠRΠM⇔y∗∗(p)≶y∗(p) for a given p, and in this case ∫0y∗∗(p)WM(y)(1−p+pg(y))dy≶∫0y∗(p)WM(y)1−p+pg(y)dy. Then in order for ERW≶ESW, it is enough to have ∫0y∗∗(p)WR(y)ph(y)dy≶∫0y∗(p)WM(y)γph(y)dy , and for this a sufficient condition is γ≷WRWM.

Proof of Lemma 2

Merger profitability is decreasing in p, so from the expected profit function ERΠ(y) one can easily derive that the “right” deterrence, i.e. ∂ERΠ(y)∂y<0, implies dy∗∗dp<0. Rewriting eq. (6) as ∫0y∗∗(p)g(y)−1WM(y)+h(y)WR(y)dy⏟ enforcement effect=−dy∗∗dp⏟>0WM(y∗∗)1−p+pg(y∗∗)+ph(y∗∗)WR(y∗∗) indicates that in equilibrium

sign( enforcement effect)=sign1−p+pg(y∗∗)WM(y∗∗)+ph(y∗∗)WR(y∗∗). A sufficient condition for signing the enforcement effect in equilibrium, and thereby the deterrence effect as well, is that signWM(y∗∗)=signWR(y∗∗).

Proof of Proposition 3

In order to compare the two FOCs when y∗≠y∗∗, one may use their monotonicity and consider evaluating one of them at the optimal activity level corresponding to the other regime, since we focus on the case of a unique interior optimum. For instance, if ∂ESW∂pp∗∗≷0, then p∗∗≶p∗.

Recall that ∂ESW∂p=∫0y∗(p)((g(y)−1)WM(y)+γh(y)WM(y))dy+(WM(y∗)(1−p + pg(y∗))+WM(y∗)pγh(y∗))dy∗dp and that p∗∗ is such that∂ERW∂p=∫0y∗∗(p)g(y)−1WM(y)+h(y)WR(y)dy+WM(y∗∗)1−p+pg(y∗∗)+ph(y∗∗)WR(y∗∗)dy∗∗dp=0.

Therefore ∂ESW∂pp∗∗=∫0y∗(p∗∗)g(y)−1WM(y)dy+∫0y∗(p∗∗)γh(y)WM(y)dy

+dy∗dpp∗∗WM(y∗)1−p∗∗+p∗∗g(y∗)+dy∗dpp∗∗p∗∗h(y∗)γWM(y∗). (i) let γ<ΠRΠM (i.e. y∗∗>y∗) and γ<WRWM

Then ∫0y∗(p∗∗)g(y)−1WM(y)dy+∫0y∗(p∗∗)γh(y)WM(y)dy

<∫0y∗∗(p∗∗)g(y)−1WM(y)+h(y)WR(y)dy=−WM(y∗∗)1−p∗∗+p∗∗g(y∗∗)+p∗∗h(y∗∗)WR(y∗∗)dy∗∗dp therefore ∂ESW∂pp∗∗<dy∗dpp∗∗WM(y∗)1−p∗∗+p∗∗g(y∗)+p∗∗h(y∗)WR(y∗)

−dy∗∗dpp∗∗WM(y∗∗)1−p∗∗+p∗∗g(y∗∗)+p∗∗h(y∗∗)WR(y∗∗)dy∗∗dpp∗∗<(1−p∗∗)+p∗∗(g(y∗∗)+γh(y∗∗))WM(y∗)dy∗dpp∗∗−WR(y∗)γdy∗∗dpp∗∗, thanks to γ<WRWM,dy∗dpp∗∗<0, −dy∗∗dpp∗∗>0, and the monotonicity of WM,WR,g, and h.

In order for ∂ESW∂pp∗∗<0, leading to p∗∗>p∗, it is enough to have WM(y∗)dy∗dpp∗∗−WR(y∗)γdy∗∗dpp∗∗<0⇔dy∗dpp∗∗dy∗∗dpp∗∗<WR(y∗)γWM(y∗), and since γ<WRWM, a sufficient condition for this is dy∗dpp∗∗dy∗∗dpp∗∗<1.

(ii) let γ>ΠRΠM and γ>WRWM

Thanks to γ>ΠRΠM, i.e. y∗∗<y∗,dy∗dpp∗∗<0, −dy∗∗dpp∗∗>0, and the monotonicity of WM,WR,g, and h, one has that:

∂ESW∂pp∗∗>dy∗dpp∗∗(WM(y∗)1−p∗∗+p∗∗g(y∗)+p∗∗h(y∗)γWM(y∗))−WM(y∗∗)1−p∗∗+p∗∗g(y∗∗)+p∗∗h(y∗∗)WR(y∗∗)dy∗∗dpp∗∗>dy∗dpp∗∗WM(y∗∗)1−p∗∗+p∗∗g(y∗∗)+p∗∗h(y∗∗)γ−dy∗∗dpp∗∗WR(y∗∗)γ1−p∗∗+p∗∗g(y∗∗)+p∗∗h(y∗∗)γ=1−p∗∗+p∗∗g(y∗∗)+p∗∗h(y∗∗)γdy∗dpp∗∗WM(y∗∗)−dy∗∗dpp∗∗WR(y∗∗)γ. Then ∂ESW∂pp∗∗>0 if dy∗dpp∗∗WM(y∗∗)−dy∗∗dpp∗∗WR(y∗∗)γ>0, and for this a sufficient condition is that dy∗dpp∗∗>dy∗∗dpp∗∗ since γ>WRWM.

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Published Online: 2017-09-01

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merger control; merger remedies; enforcement; deterrence