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Company Taxation and Merger Incentives in International Oligopoly: on International Policy Coordination with Strategic Trade

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Abstract

We analyse how national taxation of firms is likely to affect merger incentives in international markets. In particular, we ask whether non-coordinated trade policies stimulate cross-border mergers that are overall inefficient, and if this then is an argument for international coordination of such policies? We address this issue in a setting where policy makers use two-part tariffs to tax exporting firms. The analysis reveals that while non-coordinated policies may induce cross-border mergers by allowing the firms in question to play national policy makers out against each other, this can nevertheless be overall welfare enhancing compared to market outcomes under coordinated policy making.

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Notes

  1. There is an upstart theoretical literature on national champions. See for example Lommerud et al. (2005, 2006), Haufler and Nielsen (2008) and Südekum (2009). The wider literature on domestic versus international mergers include Barros and Cabral (1994), Head and Ries (1997), Horn and Persson (2001a, b), Qiou and Zhou (2006) and Neary (2007).

  2. The strategic trade literature is enormous, but the paper closest to us is perhaps Huck and Konrad (2004). These authors find that active strategic trade policy can lead firms to choose national over international mergers, because this in turn triggers higher per unit subsidies from the domestic government. A few papers discuss commitment issues in a strategic trade setting, for example Leahy and Neary (2000).

  3. Kydland and Prescott (1980) can be considered a predecessor to Kehoe. Also Janeba (2000) concerns himself with hold-up problems in a tax competition context. Becker and Fuest (2009), and Norbäck et al. (2009) and Haufler and Schulte (2009) all concern themselves with tax competition and its effects on domestic and international mergers, but the focus is not on international policy coordination and the allievement of hold-up problems.

  4. It should be noted that there are close structural similarities between the model presented here and the relatively large literature on mergers in vertical structures. Examples of this line of work include Horn and Wolinsky (1988), Inderst and Wey (2003) and Lommerud et al. (2005, 2006). The production firms in the model can be seen as ‘downstream’ firms that supply to a market, while the tax authorities will be ‘upstream’ input suppliers (supplying ‘access’ or ‘licence to operate’). The present model adds to this literature on several counts. Firstly, the upstream agents are here regulators that have a broader objective function than profit-maximising input suppliers. Secondly, many of the mentioned articles only study the consequences of downstream mergers—while we look at the possibility of different types of downstream mergers and how such mergers can influence upstream cooperation. Thirdly, we allow upstream agents to use two-part tariffs.

  5. As is standard in the trade literature, we can interpret the third country as an integrated world market.

  6. If consumers lived in countries A or B rather in the unspecified third country, merger could have a detrimental effect on competition at home, and consumers might suffer. The paper is about governments that want mergers to take place but are afraid that too heavy profit taxation might block this. With consumers ‘at home’ the starting premise that mergers are wanted might no longer hold.

  7. Transportation costs are assumed to be included in the cost function \( C\left( \cdot \right) \).

  8. Many other examples can be found where government requirements indeed inflict a lump-sum tax that firms must meet before they can gain a ‘license to operate’ in a given market. For example, broadcasters and telecom firms find that entry allowances sell at enormous prices, perhaps decided through auctions.

  9. Technically, we can do this by attaching a weight α < 1 to profits in the welfare function and then evaluate the optimal solution at α→1. This is a simplification that does not affect the main results of the paper.

  10. If the lump-sum part is literally interpreted as a one-off licence fee, the appropriate assumption might in some cases be that a committed decision on taxes was made before the merger decision was undertaken. Naturally, this would significantly change our model.

  11. The tax non-deductible small cost of contemplating a merger could for example be the time and effort of entrepreneurs and owners of the firms that do not show up as costs in the books of these. Of course, this might also hold for other types of investments than mergers, for example greenfield FDI. Lommerud et al. (2009) go some way towards studying an international oligopoly where both domestic and cross-border mergers, as well as greenfield FDI, are possible.

  12. The main mechanisms of the model, and thus our main results, does not particularly depend on the source of merger synergies. Fixed cost savings are thus chosen for analytical simplicity.

  13. Notice that, with fixed cost merger synergies, a non-infinitesimal merger cost would just be equivalent to a reduction in the net cost savings from a merger. This would reduce both private and social merger incentives, but it would not affect the choice between domestic and cross-border merger, nor would it qualitatively affect the welfare trade-off involved in the decision to coordinate tax policies.

  14. Due to the nature of our model, similar results would be obtained in any plausible model of endogenous mergers. Since the decentralised market structure implies zero profits in equilibrium, a merger can never harm non-participating firms. This implies that there are no incentives for ‘pre-emptive mergers’ in our model.

  15. See Horn and Persson (2001a) for a formal definition of decisive owners.

  16. See, e.g., Brander and Spencer (1985).

  17. Although the incentives for strategic trade policy are quantitatively affected, the main thrust of the analysis does not depend on a particular sharing rule.

  18. Explicit expressions for the mobility constraints in the different market structures are presented in the Appendix.

  19. We use equivalent notation under coordinated and non-coordinated policies to denote the different threshold values of K, but where the case of coordinated policies is distinguished by using a star.

  20. Notice that, due to the timing of the game, the merger cost is sunk at the time when policy makers set taxes. Therefore, the merger cost does not enter in the participation constraints of the optimal tax setting problem.

  21. Outside the model presented here, there might of course be other available options for the firms to escape confiscatory taxation even if the two policy makers coordinate their policies. For example, policy coordination between two countries could lead domestic firms to search for merger partners in a third country. If such mergers come about as a consequence of policy coordination, this will presumably reduce the downside of bilateral policy coordination, since some merger synergies can be realised elsewhere. However, the upside is also lower if policy coordination does not include all producing countries.

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Acknowledgement

We thank four anonymous referees for very valuable comments and suggestions.

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Correspondence to Odd Rune Straume.

Appendices

Appendix A: Mobility constraints in M C and M CC

A.1 Non-coordinated policies

In M C , for given tax policies (w A ,T A ) and (w B ,T B ), the internationally merged firm earn a profit of

$$ \pi _{1+3}=\frac{2c\left( c+4\right) \left( c+1\right) ^{2}\eta }{2c\left( 7c+c^{2}+8\right) ^{2}}-K-T_{A}-T_{B}\allowbreak , \label{A1} $$
(41)

where

$$ \begin{array}{lll} \eta &:&=32\left( w_{A}-w_{B}\right) ^{2}+\allowbreak c\left( 37c+10c^{2}+c^{3}+58\right) \left( w_{A}^{2}+w_{B}^{2}\right) \\ &&\kern10pt-4cw_{A}w_{B}\left( 14c+2c^{2}+27\right) -2c\left( c+4\right) \left( c+1\right) ^{2}\left( w_{A}+w_{B}\right) \end{array} $$

if exporting from both countries. However, by relocating all production to country A, the firm can obtain a profit of

$$ \widehat{\pi }_{1+3}\left( A\right) =\frac{\left( c+2\right) \left( 1\allowbreak +c-2w_{A}+w_{B}-cw_{A}\right) ^{2}}{2\left( c+1\right) ^{2}\left( c+4\right) ^{2}}-K-T_{A}. \label{A2} $$
(42)

An equivalent expression characterises the profits that can be obtained by relocating all production to country B. The profit gains of relocating all production to one or the other country translate into the following mobility constraints:

$$ T_{A}\leq \overline{T}_{A}:=\frac{\left( c+c^{2}-4w_{A}+4w_{B}-4cw_{A}+3cw_{B}-c^{2}w_{A}\right) \lambda _{A}}{ 2c\left( c+1\right) ^{2}\left( c+4\right) ^{2}\left( 7c+c^{2}+8\right) ^{2}} \label{A3} $$
(43)

and

$$ T_{B}\leq \overline{T}_{B}:=\frac{\left( \allowbreak c+4w_{A}-4w_{B}+3cw_{A}-4cw_{B}-c^{2}w_{B}+c^{2}\right) \lambda _{B}}{ 2c\left( c+1\right) ^{2}\left( c+4\right) ^{2}\left( 7c+c^{2}+8\right) ^{2}}, \label{A4} $$
(44)

where

$$ \begin{array}{lll} \lambda _{A} &:&=64c-128w_{A}+128w_{B}-392cw_{A}+328cw_{B}-496c^{2}w_{A} \\ &&\kern10pt+330c^{2}w_{B}-314c^{3}w_{A}+159c^{3}w_{B}-101c^{4}w_{A}+36c^{4}w_{B}+c^{6} \\ &&\kern10pt-16c^{5}w_{A}+3c^{5}w_{B}-c^{6}w_{A}+166c^{2}+155c^{3}+65c^{4}+13c^{5} \end{array} $$

and

$$ \begin{array}{lll} \lambda _{B} &:&=64c+128w_{A}-128w_{B}+328cw_{A}-392cw_{B}+\allowbreak 330c^{2}w_{A} \\ &&\kern10pt-496c^{2}w_{B}+159c^{3}w_{A}-314c^{3}w_{B}+\allowbreak 36c^{4}w_{A}-101c^{4}w_{B}+c^{6} \\ &&\kern10pt+3c^{5}w_{A}-16c^{5}w_{B}-c^{6}w_{B}+\allowbreak 166c^{2}+155c^{3}+65c^{4}+13c^{5}. \end{array} $$

In M CC , for given tax policies (w A ,T A ) and (w B ,T B ), an internationally merged firm earn a profit of

$$ \pi _{1+3}=\frac{2c\left( c+4\right) -2c\left( w_{A}+w_{B}\right) \left( c+4\right) -4w_{A}w_{B}\left( 2c+9\right) +\mu }{2c\left( c+6\right) ^{2}} \allowbreak -K-T_{A}-T_{B}, \label{A5} $$
(45)

where \(\mu :=\left( w_{A}^{2}+w_{B}^{2}\right) \left( 8c+c^{2}+18\right) \), if exporting from both countries. By relocating all production to country A, the firm can obtain a profit of

$$ \widehat{\pi }_{1+3}\left( A\right) =\frac{\left( c+2\right) \left( 2+\allowbreak c-3w_{A}+w_{B}-cw_{A}\right) ^{2}}{2\left( 6c+c^{2}+6\right) ^{2}}-K-T_{A}. \label{A6} $$
(46)

An equivalent expression characterises the profits that can be obtained by relocating all production to country B. Due to symmetry, these profit expressions apply to both of the internationally merged firms. The profit gains of relocating all production to one or the other country translate into the following mobility constraints:

$$ T_{A}\leq \overline{T}_{A}:=\allowbreak \frac{\left( \allowbreak c-3w_{A}+3w_{B}-cw_{A}\right) \varphi _{A}}{2c\left( c+6\right) ^{2}\left( 6c+c^{2}+6\right) ^{2}} \label{A7} $$
(47)

and

$$ T_{B}\leq \overline{T}_{B}:=\allowbreak \frac{\left( c+3w_{A}-3w_{B}-cw_{B}\right) \varphi _{B}}{2c\left( c+6\right) ^{2}\left( 6c+c^{2}+6\right) ^{2}}, \label{A8} $$
(48)

where

$$ \begin{array}{lll} \varphi _{A} &:&=120c-216w_{A}+216w_{B}-432cw_{A}+312cw_{B} \\ &&\kern10pt-\allowbreak 328c^{2}w_{A}-\allowbreak 17c^{4}w_{A}+3c^{4}w_{B}+168c^{2}w_{B}+c^{5} \\ &&\kern10pt-110c^{3}w_{A}+38c^{3}w_{B}-c^{5}w_{A}+160c^{2}+72c^{3}+14\allowbreak c^{4} \end{array} $$

and

$$ \begin{array}{lll} \varphi _{B} &:&=120c+216w_{A}-216w_{B}+312cw_{A}-432cw_{B} \\ &&\kern10pt+\allowbreak 168c^{2}w_{A}-328c^{2}w_{B}+38c^{3}w_{A}-110c^{3}w_{B}+\allowbreak 3c^{4}w_{A} \\ &&\kern10pt-17c^{4}w_{B}-c^{5}w_{B}+160c^{2}+72c^{3}+14\allowbreak c^{4}+c^{5}. \end{array} $$

A.2 Coordinated policies

In M C , for a given tax policy (w,T), the internationally merged firm earn a profit of

$$ \pi _{1+3}\allowbreak =\frac{\allowbreak \left( c+1\right) ^{2}\left( c+4\right) \left( 1-w\right) ^{2}}{\left( 7c+c^{2}+8\right) ^{2}}-K-2T, \label{A9} $$
(49)

while, if relocating all production to one or the other country, it can earn a profit of

$$ \widehat{\pi }_{1+3}=\allowbreak \allowbreak \frac{\left( c+2\right) \left( 1-w\right) ^{2}}{2\left( c+4\right) ^{2}}-K-T, \label{A10} $$
(50)

which translates into the following mobility constraint:

$$ T\leq \overline{T}:=\frac{c\left( 1-w\right) ^{2}\left( 102c+53c^{2}+12c^{3}+c^{4}+64\right) }{2\left( c+4\right) ^{2}\left( 7c+c^{2}+8\right) ^{2}}. \label{A11} $$
(51)

In M CC , for a given tax policy (w,T), the internationally merged firm earn a profit of

$$ \pi _{1+3}\allowbreak =\frac{\left( c+4\right) \left( 1-w\right) ^{2}}{ \left( c+6\right) ^{2}}-K-2T, \label{A12} $$
(52)

while, if relocating all production to one or the other country, it can earn a profit of

$$ \widehat{\pi }_{1+3}=\frac{\left( c+2\right) ^{3}\left( 1-w\right) ^{2}}{ 2\left( 6c+c^{2}+6\right) ^{2}}-K-T\allowbreak , \label{A13} $$
(53)

which translates into the following mobility constraint:

$$ T\leq \overline{T}:=\frac{c\left( 1-w\right) ^{2}\left( 160c+72c^{2}+14c^{3}+c^{4}+120\right) }{2\left( c+6\right) ^{2}\left( 6c+c^{2}+6\right) ^{2}}. \label{A14} $$
(54)

Appendix B: The profitability of a second cross-border merger

B.1 Non-coordinated policies

In M C , equilibrium profits for an outside firm (that does not participate in the merger) are given by

$$ \pi _{o}\left( M_{C}\right) =\allowbreak \frac{\left( 192c+98c^{2}+23c^{3}+2c^{4}+128\right) \left( c+4\right) ^{2}\left( 13c+10c^{2}+2c^{3}+4\right) ^{2}}{2\left( 2208c+3640c^{2}+3007c^{3}+1349c^{4}+330c^{5}+41c^{6}+2c^{7}+512\right) ^{2}} \allowbreak -K \label{B1} $$
(55)

if \(K<\widehat{K}\) (otherwise, outside profits are zero), while in M CC , equilibrium profits of an internationally merged firm are given by

$$ \pi _{m}\left( M_{CC}\right) =\allowbreak \frac{2\left( 102c+52c^{2}+12c^{3}+c^{4}+72\right) \left( c+3\right) ^{2}\left( 6c+c^{2}+6\right) ^{2}}{\left( 1476c+1398c^{2}+676c^{3}+170c^{4}+21c^{5}+c^{6}+648\right) ^{2}}\allowbreak -K. \label{B2} $$
(56)

A second cross-border merger is privately profitable if \(\pi _{m}\left( M_{CC}\right) >2\pi _{o}\left( M_{C}\right) \), which is true if

$$ K>\underline{K}:=\frac{\phi }{\left( 1476c+1398c^{2}+676c^{3}+170c^{4}+21c^{5}+c^{6}+648\right) ^{2}\sigma ^{2}} \label{B3} $$
(57)

where

$$ \sigma :=2208c+3640c^{2}+3007c^{3}+1349c^{4}+330c^{5}+41c^{6}+2c^{7}+512 $$

and

$$ \begin{array}{lll} \phi &:&=24\,\allowbreak 206\,376\,960c+157\,\allowbreak 147\,693\,056c^{2}+588\,\allowbreak 783\,845\,376c^{3}+1471\,\allowbreak 273\,684\,992c^{4} \\ &&\kern10pt+2654\,\allowbreak 605\,913\,088c^{5}+3633\,\allowbreak 689\,412\,416c^{6}+3900\,\allowbreak 436\,110\,736c^{7} \\ &&\kern10pt+3359\,\allowbreak 840\,947\,808c^{8}+2360\,\allowbreak 764\,713\,584c^{9}+1368\,\allowbreak 538\,292\,464c^{10} \\ &&\kern10pt+659\,\allowbreak 451\,822\,256c^{11}\kern-.7pt+\kern-.7pt265\,\allowbreak 252\,066\,048c^{12}\kern-.7pt+\kern-.7pt89\,\allowbreak 172\,529\,984c^{13}\kern-.7pt+\kern-.7pt25\,\allowbreak 015\,690\,394c^{14} \\ &&\kern10pt+5829\,489\,804c^{15}+1119\,592\,898c^{16}+175\,100\,967c^{17}+21\,913 \,312c^{18} \\ &&\kern10pt+2138\,971c^{19}+156\,672c^{20}+8088c^{21}+262c^{22}+4c^{23}+1528\,823 \,808. \end{array} $$

B.2 Coordinated policies

In M C , equilibrium profits for an outside firm (that does not participate in the merger) are given by

$$ \pi _{o}\left( M_{C}\right) =\frac{\left( 192c+98c^{2}+23c^{3}+2c^{4}+128\right) \left( 2c+3\right) ^{2}}{2\left( c+4\right) ^{2}\left( 53c+22c^{2}+2c^{3}+36\right) ^{2}}\allowbreak -K\allowbreak \label{B4} $$
(58)

if \(K<\widehat{K}^{\ast }\) (otherwise, outside profits are zero), while in M CC , equilibrium profits of an internationally merged firm are given by

$$ \pi _{m}\left( M_{CC}\right) =\allowbreak \allowbreak \allowbreak \frac{ 2\left( 102c+52c^{2}+12c^{3}+c^{4}+72\right) }{\left( 6c+c^{2}+6\right) ^{2}\left( c+8\right) ^{2}}-K. \label{B5} $$
(59)

A second cross-border merger is privately profitable if \(\pi _{m}\left( M_{CC}\right) >2\pi _{o}\left( M_{C}\right) \), which is true if

$$ K>\underline{K}^{\ast }:=\allowbreak \frac{\phi ^{\ast }}{\left( c+4\right) ^{2}\left( c+8\right) ^{2}\left( 6c+c^{2}+6\right) ^{2}\left( 53c+22c^{2}+2c^{3}+36\right) ^{2}} \label{B6} $$
(60)

where

$$ \begin{array}{lll} \phi ^{\ast } &:&=-1022\,976c-1082\,880c^{2}-188\,160c^{3}+590\,200c^{4}+622\,368c^{5}+313 \,560c^{6} \\ &&\kern11pt+95\,248c^{7}+18\,244c^{8}+2151c^{9}+142c^{10}+4c^{11}-331\,776. \end{array} $$

Appendix C: Equilibrium domestic welfare in M C and M CC

C.1 Non-coordinated policies

$$ W_{j}\left( M_{C}\right) =\left\{ \begin{array}{ccc} \frac{\left( c+4\right) ^{2} \left( 13c+10c^{2}+2c^{3}+4\right) \left( c+2\right) \rho }{2\left( 2208c+3640c^{2}+3007c^{3}+1349c^{4}+330c^{5}+41c^{6}+2c^{7}+512\right) ^{2}}- \frac{3}{2}K & if & K\leq \widehat{K} \\[9pt] \frac{ 2\left( 66c+113c^{2}+104c^{3}+40c^{4}+4c^{5}+24\right) \left( 13c+10c^{2}+2c^{3}+4\right) \left( c+2\right) }{ \left( 172c+147c^{2}+46c^{3}+4c^{4}+64\right) ^{2}\left( c+1\right) ^{2} } -\frac{3}{2}K & if & K>\widehat{K} \end{array} \right. , \label{C1} $$
(61)
$$ W_{j}\left( M_{CC}\right) = \frac{\left( c+3\right) \left( 6c+c^{2}+6\right) ^{2}\omega }{\left( 1476c+1398c^{2}+676c^{3}+170c^{4}+21c^{5}+c^{6}+648\right) ^{2} } -K, \label{C2} $$
(62)

where ρ: = 1440c + 2728c2 + 2881c3 + 1652c4 + 494c5 + 72c6 + 4c7 + 384 and ω: = 828c + 816c2 + 464c3 + 136c4 + 19c5 + c6 + 432 .

C.2 Coordinated policies

$$ W_{j}\left( M_{C}\right) =\frac{ \left( 2c+3\right) ^{2}}{2\left( 53c+22c^{2}+2c^{3}+36\right) } -\frac{3}{2}K, \label{C3} $$
(63)
$$ W_{j}\left( M_{CC}\right) =\frac{1}{\left( c+8\right) }-K . \label{C4} $$
(64)

Appendix D: Welfare effects of policy coordination

If \(K\in \left( \overline{K}^{\ast },\overline{K}\right) \), the equilibrium welfare effect of policy coordination is given by a comparison of (C2) and (C3):

$$ \begin{array}{lll} \Delta W_{j} &=&W_{j}^{coord}\left( M_{C}\right) -W_{j}^{non-coord}\left( M_{CC}\right) \\ &=&\frac{\Phi }{2\left( 53c+22c^{2}+2c^{3}+36\right) \Theta ^{2}} -\frac{1}{2}K, \end{array} $$
(65)

where

$$ \Theta :=1476c+1398c^{2}+676c^{3}+170c^{4}+21c^{5}+c^{6}+648 $$

and

$$ \begin{array}{lll} \Phi &:&=3032\,640c+9389\,520c^{2}+16\,398\,288c^{3}+18\,018\,180c^{4} \\ &&\kern10pt+13\,162\,752c^{5}+6579\,072c^{6}+2276\,508c^{7}+543\,856c^{8} \\ &&\kern10pt+87\,932c^{9}+9179c^{10}+558c^{11}+15c^{12}+419\,904. \end{array} $$

It follows that \(\Delta W_{j}>\left( <\right) 0\) if

$$ K<\left( >\right) \widetilde{K}:=\frac{\Phi }{\left( 53c+22c^{2}+2c^{3}+36\right) \Theta ^{2}}. \label{D2} $$
(66)

It is relatively straightforward to confirm that \(\widetilde{K}<\overline{K} ^{\ast }\) for all c ≥ 0.

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Lommerud, K.E., Olsen, T.E. & Straume, O.R. Company Taxation and Merger Incentives in International Oligopoly: on International Policy Coordination with Strategic Trade. J Ind Compet Trade 10, 161–186 (2010). https://doi.org/10.1007/s10842-009-0060-7

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