Production location of multinational firms under transfer pricing: the impact of the arm’s length principle

Abstract

When multinational enterprises (MNEs) separate the geographical location of affiliates, they can shift profits between the affiliates by manipulating intra-firm prices of inputs. We show that if the international tax difference between the parent and the host countries is large, MNEs choose to separately locate their affiliates in the two countries. We also investigate the impact of the arm’s length principle (ALP) on the location choice, which requires that the intra-firm price of inputs should be set equal to the price of similar inputs for the independent downstream firms. The ALP may change the location choice of MNEs, bringing smaller tax revenues to the host country, but greater revenues globally.

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Fig. 1
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Notes

  1. 1.

    For comprehensive surveys, see Markusen (2004), Navaretti and Venables (2004); and Blonigen (2005).

  2. 2.

    Hebous et al. (2011) show that lower corporate tax induces inflows of foreign capital irrespective of the type of investment, such as greenfield foreign direct investment and cross-border mergers and acquisitions. Voget (2011) finds that one percentage point decline in foreign effective tax rate augments the likelihood of headquarters’ relocation by 0.22 percentage point. Karkinsky and Riedel (2012) and Griffith et al. (2014) investigate the link between corporate taxation and patent location.

  3. 3.

    Bernard et al. (2010) show that over 46% of US imports were composed of intra-firm transactions in 2000. Lanz and Miroudot (2011) report that US imports of intermediate products scored around 50% in 2009. See also Slaughter (2000) and Hanson et al. (2005) for the importance of intra-firm trade.

  4. 4.

    For (in)direct evidence on transfer pricing, see Swenson (2001), Bartelsman and Beetsma (2003), Clausing (2003), Bernard et al. (2006), Cristea and Nguyen (2016), Gumpert et al. (2016), Guvenen et al. (2017), and Davies et al. (2018).

  5. 5.

    The project is called “Base Erosion and Profit Shifting.” Further details can be found at https://www.oecd.org/g20/topics/taxation/beps.htm, accessed on 17 March 2017.

  6. 6.

    See http://www.oecd.org/ctp/oecd-presents-outputs-of-oecd-g20-beps-project-for-discussion-at-g20-finance-ministers-meeting.htm, accessed on 17 March 2017.

  7. 7.

    The CUP method is applied to tangible assets. The corresponding method for intangible assets is called the comparable uncontrolled transaction (CUT) method. There are other methods such as cost-plus method, resale price method, and profit split method. See OECD (2017, ch.2) for details.

  8. 8.

    The uncontrolled transaction includes both a transaction of an MNE with an independent firm (“internal comparables”) and a transaction between other independent firms (“external comparables”). Our framework captures the internal comparable transaction.

  9. 9.

    In our setting, the arm’s length price is the price that the upstream affiliate charged to the local downstream firm. As MNEs are usually not price takers, the arm’s length price in an internal comparable transaction is more or less an MNE’s choice variable and thus is subject to manipulation ( Cristea and Nguyen (2016)). Although tax authorities recognize this possibility of manipulation (see e.g., IRS\(\S \)1.482–1(d)(4)(iii)), they have to refer to internal comparable transactions in some cases due to limited information available. One recent example of such case is the transfer pricing case of Medtronic, a medical device company based in the USA, v. the Internal Revenue Service (IRS) (see for details Global Tax Alert (News from Transfer Pricing), 21 June 2016: http://www.ey.com/gl/en/services/tax/international-tax/alert--us-tax-court-imposes-a-proper-arms-length-allocation-method-for-transfer-pricing, accessed on 2 June 2018). Medtronic US gave license to its Puerto Rican affiliate for production. The affiliate purchased components from Medtronic US, manufactured finished medical devices, and sold them to the Puerto Rican market. Whereas the IRS accused Medtronic US of profit shifting for the years at issue, 2005–2006, Medtronic US argued that the royalty rates charged to the Puerto Rican affiliate, which are a sort of transfer price of inputs, were the arm’s length royalty rates in light of the CUT method. The arm’s length royalty rates calculated by Medtronic US came from several internal comparable transactions, including a license agreement between Medtronic US and Siemens (German conglomerate company). In 2016, the US Tax Court accepted the royalty rates proposed by Medtronic US with small adjustments. See Avi-Yonah (2007) for other applications of the CUP/CUT method.

  10. 10.

    Earlier contributions include Copithorne (1971), Horst (1971), Samuelson (1982), and Kant (1988). In addition to the profit-shifting motive of transfer pricing mentioned in the text, studies such as Elitzur and Mintz (1996), Schjelderup and Sørgard (1997), and Zhao (2000) point out a strategic motive. The strategic motive comes from MNEs’ incentive to make their downstream affiliates competitive against rival firms. See Sect. 4.4. for more on this point.

  11. 11.

    In a related context, Choi et al. (2018) find a possibility of dual sourcing where an MNE buys inputs from both independent suppliers and related subsidiaries.

  12. 12.

    The role of the ALP on transfer prices is also studied by Gresik and Osmundsen (2008), Bauer and Langenmayr (2013), Choe and Matsushima (2013), and Keuschnigg and Devereux (2013). However, they do not consider the location choice of MNEs.

  13. 13.

    See Keen and Konrad (2013) for a comprehensive survey.

  14. 14.

    For subsequent development in the literature on bidding for a firm, see, e.g., Bjorvatn and Eckel (2006), Haufler and Wooton (2006), Ferrett and Wooton (2010), and Furusawa et al. (2015).

  15. 15.

    We consider a decentralized decision structure where the MNE leaves quantity choice to the downstream affiliate.

  16. 16.

    If \(t \ge T\), the upstream affiliate is always located in the low-tax parent country (separate location) in both the benchmark and ALP cases. Thus, our focus is on the range of \(t < T\), where the imposition of the ALP may change the location pattern.

  17. 17.

    It is common in the literature to assume exogenous profits or profits independent of transfer price (Schjelderup and Sørgard 1997; Nielsen et al. 2003, 2008; Haufler and Mardan 2014). In these studies, the tax-manipulation effect, which we will define shortly, is so strong that the price-cost margin (and thus profits) can be negative as in our analysis. To isolate the tax-manipulation effect as clearly as possible, we follow the convention of the literature. In Appendix 8, we endogenize it by introducing a local downstream firm in the parent country.

  18. 18.

    More precisely, \(q^S > 0\) requires \(t > t^a\), while \(p^S > 0\) does \(t > t^b\).

  19. 19.

    Clausing (2003) empirically supports this result: she finds that MNEs in the USA tend to set lower export prices, as tax rates in the trading partners are lower.

  20. 20.

    These figures are derived using the following parameter values: \(c=0.3\); \({\bar{\pi }}=3\); (a)\(T=0.35\); (b)\(T=0.2\). In this numerical example, \(\underline{t}=0\) holds. We note that the qualitative results stated in Proposition 1 do not depend on these particular parameter values.

  21. 21.

    We assume that the ALP applies to both cross-border transactions (i.e., separate location) and domestic transactions (i.e., co-location). Article Nine and the OECD guidelines are fully or partly applicable to domestic transfer pricing in some member countries of the OECD such as the UK, Norway and Canada (Wittendorff 2012).

  22. 22.

    To see this formally, we calculate the difference between the coefficient of \(t-T\) in \({\tilde{g}}^S\) and that in \(g^S\):

    $$\begin{aligned} \frac{\partial {\tilde{g}}^S}{\partial (t-T)} - \frac{\partial g^S}{\partial (t-T)}&= \frac{2(1-c)}{3(t-4T +3)}- \frac{1-c}{2(t -2T +1)} \\&= -\frac{(t -8T +7)(1-c)}{12(t-4T +3)(t -2T +1)} < 0. \end{aligned}$$
  23. 23.

    The parameter values are the same as those in Fig. 1a: \(c=0.3\); \(\bar{\pi }=3\); \(T=0.35\). We note that the qualitative results stated in Proposition 1 do not depend on these particular parameter values.

  24. 24.

    For \(t^*\) [defined in Eq. (9)] to be positive, we assume a sufficiently high T such that \(T>{\overline{T}}=1/4\).

  25. 25.

    To see this formally, we have

    $$\begin{aligned} q^S + q_*^S - 2{\tilde{q}}&= [2{\tilde{g}} -(g^S +g_*^S)]/2 > 0, \\&\rightarrow t < (4T +1)/5 \equiv t^q. \end{aligned}$$

    There exists t satisfying the above inequality because it holds that \(t^a< t^q < t^*\) and \(t > \underline{t} \equiv \max \{ 0, t^a, t^b \}\) from (A1): \(t>\underline{t}\).

  26. 26.

    Noting that \(g^S < g_*^S\) and \({\tilde{g}} > g_*^S\), we have

    $$\begin{aligned} {\tilde{q}} - q_*^S = (g_*^S -{\tilde{g}})/2> (g_*^S - g)/2 > 0. \end{aligned}$$

    Combining this result with \(q^S +q_*^S > 2{\tilde{q}}\) gives \({\tilde{q}} < q^S\). This also implies that the price-cost margin is smaller in the ALP case than in the benchmark case: \({\tilde{q}} = {\tilde{p}}-{\tilde{g}} < p^S - g^S = q^S\).

  27. 27.

    Similar results can be found in Yao (2013) in a different setting mentioned in the Introduction.

  28. 28.

    We do not distinguish the notation of variables between the unconstrained problem in the text and the constrained problem here.

  29. 29.

    It always holds that \(t' < T\). \(t'\) is decreasing in N if N is not sufficiently large, implying \(t' > \underline{t}\) for not sufficiently large N.

  30. 30.

    \(\delta \) is bounded above by \(\overline{\delta } \equiv \min \{ {\hat{\delta }}, \hat{{\hat{\delta }}} \}\), where \({\hat{\delta }} \equiv \text {sup} \{ \delta : t^{**}>0 \}\) and \(\hat{{\hat{\delta }}} \equiv \min \{ \text {sup} \{ \delta : \Pi> 0 \}, \ \text {sup} \{\delta : \Pi ^S > 0 \} \}\).

  31. 31.

    The parameter values are the same as those in Fig. 1: \(c=0.3\); (a)\(T=0.35\); (b)\(T=0.2\). In this numerical example, \(\underline{t}=0\) holds.

  32. 32.

    The parameter values are the same as those in Fig. 1: \(c=0.3\); (a)\(T=0.35\); (b)\(T=0.2\).

References

  1. Avi-Yonah, R. S. (2007). The rise and fall of arm’s length: A study in the evolution of US international taxation. Law & Economics Working Papers. University of Michigan Law School

  2. Bartelsman, E. J., & Beetsma, R. M. (2003). Why pay more? Corporate tax avoidance through transfer pricing in OECD countries. Journal of Public Economics, 87(9), 2225–2252.

    Article  Google Scholar 

  3. Bauer, C. J., & Langenmayr, D. (2013). Sorting into outsourcing: Are profits taxed at a gorilla’s arm’s length? Journal of International Economics, 90(2), 326–336.

    Article  Google Scholar 

  4. Bernard, A. B, Jensen, J. B, & Schott, P. K. (2006). Transfer pricing by US-based multinational firms. NBER Working Paper, 12493

  5. Bernard, A. B., Jensen, J. B., Redding, S. J., & Schott, P. K. (2010). Intra-firm trade and product contractibility (long version). NBER Working Paper, 15881

  6. Bjorvatn, K., & Eckel, C. (2006). Policy competition for foreign direct investment between asymmetric countries. European Economic Review, 50(7), 1891–1907.

    Article  Google Scholar 

  7. Blonigen, B. A. (2005). A review of the empirical literature on FDI determinants. Atlantic Economic Journal, 33(4), 383–403.

    Article  Google Scholar 

  8. Choe, C., & Matsushima, N. (2013). The arm’s length principle and tacit collusion. International Journal of Industrial Organization, 31(1), 119–130.

    Article  Google Scholar 

  9. Choi, J. P., Furusawa, T., & Ishikawa, J. (2018). Transfer pricing and the arm’s length principle under imperfect competition. Discussion Paper Series HIAS-E-73. Hitotsubashi Institute for Advanced Study, Hitotsubashi University.

  10. Clausing, K. A. (2003). Tax-motivated transfer pricing and US intrafirm trade prices. Journal of Public Economics, 87(9), 2207–2223.

    Article  Google Scholar 

  11. Copithorne, L. W. (1971). International corporate transfer prices and government policy. Canadian Journal of Economics, 4(3), 324–341.

    Article  Google Scholar 

  12. Cristea, A. D., & Nguyen, D. X. (2016). Transfer pricing by multinational firms: New evidence from foreign firm ownerships. American Economic Journal: Economic Policy, 8(3), 170–202.

    Google Scholar 

  13. Davies, R. B., Martin, J., Parenti, M., & Toubal, F. (2018). Knocking on tax haven’s door: Multinational firms and transfer pricing. Review of Economics and Statistics, 100(1), 120–134.

    Article  Google Scholar 

  14. Egger, P., & Seidel, T. (2013). Corporate taxes and intra-firm trade. European Economic Review, 63, 225–242.

    Article  Google Scholar 

  15. Elitzur, R., & Mintz, J. (1996). Transfer pricing rules and corporate tax competition. Journal of Public Economics, 60(3), 401–422.

    Article  Google Scholar 

  16. Ferrett, B., & Wooton, I. (2010). Competing for a duopoly: International trade and tax competition. Canadian Journal of Economics, 43(3), 776–794.

    Article  Google Scholar 

  17. Furusawa, T., Hori, K., & Wooton, I. (2015). A race beyond the bottom: The nature of bidding for a firm. International Tax and Public Finance, 22(3), 452–475.

    Article  Google Scholar 

  18. Gresik, T. A., & Osmundsen, P. (2008). Transfer pricing in vertically integrated industries. International Tax and Public Finance, 15(3), 231–255.

    Article  Google Scholar 

  19. Griffith, R., Miller, H., & O’Connell, M. (2014). Ownership of intellectual property and corporate taxation. Journal of Public Economics, 112, 12–23.

    Article  Google Scholar 

  20. Gumpert, A., Hines, J. R, Jr., & Schnitzer, M. (2016). Multinational firms and tax havens. Review of Economics and Statistics, 98(4), 713–727.

    Article  Google Scholar 

  21. Guvenen, F., Mataloni, Jr R. J., Rassier, D. G., & Ruhl, K. J. (2017). Offshore profit shifting and domestic productivity measurement. NBER Working Paper, 23324

  22. Hanson, G. H., Mataloni, R. J, Jr., & Slaughter, M. J. (2005). Vertical production networks in multinational firms. Review of Economics and Statistics, 87(4), 664–678.

    Article  Google Scholar 

  23. Haufler, A., & Mardan, M. (2014). Cross-border loss offset can fuel tax competition. Journal of Economic Behavior & Organization, 106, 42–61.

    Article  Google Scholar 

  24. Haufler, A., & Wooton, I. (1999). Country size and tax competition for foreign direct investment. Journal of Public Economics, 71(1), 121–139.

    Article  Google Scholar 

  25. Haufler, A., & Wooton, I. (2006). The effects of regional tax and subsidy coordination on foreign direct investment. European Economic Review, 50(2), 285–305.

    Article  Google Scholar 

  26. Hebous, S., Ruf, M., & Weichenrieder, A. J. (2011). The effects of taxation on the location decision of multinational firms: M&A versus greenfield investments. National Tax Journal, 64(3), 817–38.

    Article  Google Scholar 

  27. Horst, T. (1971). The theory of the multinational firm: Optimal behavior under different tariff and tax rates. Journal of Political Economy, 79(5), 1059–1072.

    Article  Google Scholar 

  28. Ishikawa, J., Raimondos, P., & Zhang, X. (2017). Transfer pricing rules under imperfect competition. Mimeo.

  29. Kant, C. (1988). Foreign subsidiary, transfer pricing and tariffs. Southern Economic Journal, 55(1), 162–170.

    Article  Google Scholar 

  30. Karkinsky, T., & Riedel, N. (2012). Corporate taxation and the choice of patent location within multinational firms. Journal of International Economics, 88(1), 176–185.

    Article  Google Scholar 

  31. Kato, H., & Okoshi, H. (2017). Production location of multinational firms under transfer pricing: The impact of the arm’s length principle. Keio-IES Discussion Paper Series 2017-016, Institute for Economics Studies, Keio University

  32. Keen, M., & Konrad, K. A. (2013). The theory of international tax competition and coordination. In A. J. Auerbach, R. Chetty, M. Feldstein, & E. Saez (Eds.), Handbook of public economics (Vol. 5, pp. 257–328). Oxford: Elsevier.

    Google Scholar 

  33. Keuschnigg, C., & Devereux, M. P. (2013). The arm’s length principle and distortions to multinational firm organization. Journal of International Economics, 89(2), 432–440.

    Article  Google Scholar 

  34. Kind, H. J., Midelfart, K. H., & Schjelderup, G. (2005). Corporate tax systems, multinational enterprises, and economic integration. Journal of International Economics, 65(2), 507–521.

    Article  Google Scholar 

  35. Lanz, R., & Miroudot, S. (2011). Intra-firm trade. OECD Trade Policy Working Papers, 114

  36. Ma, J., & Raimondos, P. (2015). Competition for FDI and profit shifting. CESifo Working Paper Series, 5153

  37. Markusen, J. R. (2004). Multinational firms and the theory of international trade. Cambridge, MA: MIT Press.

    Google Scholar 

  38. Navaretti, G. B., & Venables, A. (2004). Multinational firms in the world economy. Princeton, NJ: Princeton University Press.

    Google Scholar 

  39. Nielsen, S. B., Raimondos-Møller, P., & Schjelderup, G. (2003). Formula apportionment and transfer pricing under oligopolistic competition. Journal of Public Economic Theory, 5(2), 419–437.

    Article  Google Scholar 

  40. Nielsen, S. B., Raimondos-Møller, P., & Schjelderup, G. (2008). Taxes and decision rights in multinationals. Journal of Public Economic Theory, 10(2), 245–258.

    Article  Google Scholar 

  41. OECD. (2017). OECD transfer pricing guidelines for multinational enterprises and tax administrations 2017. Paris: OECD Publishing.

    Book  Google Scholar 

  42. Samuelson, L. (1982). The multinational firm with arm’s length transfer price limits. Journal of International Economics, 13(3–4), 365–374.

    Article  Google Scholar 

  43. Schjelderup, G., & Sørgard, L. (1997). Transfer pricing as a strategic device for decentralized multinationals. International Tax and Public Finance, 4(3), 277–290.

    Article  Google Scholar 

  44. Slaughter, M. J. (2000). Production transfer within multinational enterprises and American wages. Journal of International Economics, 50(2), 449–472.

    Article  Google Scholar 

  45. Swenson, D. L. (2001). Tax reforms and evidence of transfer pricing. National Tax Journal, 54(1), 7–25.

    Article  Google Scholar 

  46. Voget, J. (2011). Relocation of headquarters and international taxation. Journal of Public Economics, 95(9), 1067–1081.

    Article  Google Scholar 

  47. Wittendorff, J. (2012). Consistency: Domestic vs. international transfer pricing law. Tax Notes International, 1127–1134

  48. Yao, J. T. (2013). The arm’s length principle, transfer pricing, and location choices. Journal of Economics and Business, 65, 1–13.

    Article  Google Scholar 

  49. Zhao, L. (2000). Decentralization and transfer pricing under oligopoly. Southern Economic Journal, 67(2), 414–426.

    Article  Google Scholar 

Download references

Acknowledgements

We wish to acknowledge the valuable comments from two anonymous referees. Thanks are also due to David Agrawal, Jay Pil Choi, Dave Donaldson, Taiji Furusawa, Makoto Hasegawa, Andreas Haufler, Jota Ishikawa, Michael Keen, Kozo Kiyota, Yoshimasa Komoriya, Christopher Ludwig, Yasusada Murata, Ben Lockwood, Yukihiro Nishimura, Hikaru Ogawa, Toshihiro Okubo, Pascalis Raimondos, Yasuhiro Sato, Nicolas Schmitt, Yoichi Sugita, Kimiko Terai, Eiichi Tomiura, and Lorenzo Trimarchi for helpful suggestions. This paper was presented at HITS-MJT (Kanazawa Seiryo U), Hitotsubashi-Sogang Trade Workshop (Hitotsubashi U), Public Economics Workshop (U of Tokyo), Study Group on Spatial Economics (Kyushu Sangyo U), JSIE Kanto Meeting (Nihon U), International Symposium of Urban Economics and Public Economics (Osaka U), Applied Economics Workshop (Keio U), Australasian Trade Workshop (U of Auckland), 17th GEP/CEPR Annual Postgraduate Conference (U of Nottingham), Public Economics Seminar (LMU), and International Institute of Public Finance (U of Tampere). Financial support from the Japan Society for the Promotion of Science (Grant Number: JP16J01228), the MEXT-Supported Program for the Strategic Research Foundation at Private Universities (Grant Number: JPS1391003), the Obayashi Foundation, the Japan Legislatic Society Foundation, and the German Research Foundation through GRK are gratefully acknowledged. All remaining errors are our responsibility.

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Correspondence to Hayato Kato.

Appendix

Appendix

List of key variables

Benchmark Co-location Separate location
Internal price of the input g \(g^S\) (transfer price)
Arm’s length price of the input \(g_*\) \(g_*^S\)
Price of the affiliate’s final good p \(p^S\)
Price of the local firm’s final good \(p_*\) \(p_*^S\)
Quantity of the affiliate’s final good q \(q^S\)
Quantity of the local firm’s final good \(q_*\) \(q_*^S\)
Pre-tax profit of the upstream affiliate \(\pi _u\) \(\pi _u^S\)
Pre-tax profit of the downstream affiliate \(\pi \) \(\pi ^S\)
Pre-tax profit of the local firm \(\pi _*\) \(\pi _*^S\)
Total post-tax profit of the MNE \(\Pi \) \(\Pi ^S\)
Arm’s Length Principle (ALP) Co-location Separate location
Arm’s length price of the input \({\tilde{g}}\) \({\tilde{g}}^S\)
Price of the affiliate’s final good \({\tilde{p}}\) \({\tilde{p}}^S\)
Price of the local firm’s final good \({\tilde{p}}_*\) \({\tilde{p}}_*^S\)
Quantity of the affiliate’s final good \({\tilde{q}}\) \({\tilde{q}}^S\)
Quantity of the local firm’s final good \({\tilde{q}}_*\) \({\tilde{q}}_*^S\)
Pre-tax profit of the upstream affiliate \({\tilde{\pi }}_u\) \({\tilde{\pi }}_u^S\)
Pre-tax profit of the downstream affiliate \({\tilde{\pi }}\) \({\tilde{\pi }}^S\)
Pre-tax profit of the local firm \({\tilde{\pi }}_*\) \({\tilde{\pi }}_*^S\)
Total post-tax profit of the MNE \({\widetilde{\Pi }}\) \({\widetilde{\Pi }}^S\)

We note that (i) in the ALP case, the internal price is equal to the arm’s length price, (ii) the downstream firms produce one unit of final goods using one unit of intermediate inputs, and (iii) the pre-tax profits from the parent country \({\bar{\pi }}\) are always constant.

Proof of Proposition 3

Tax revenues in the host country Assuming \(T>{\overline{T}}=1/4\), we show that when \(t \in (\underline{t}, t^*)\), tax revenues in the benchmark case, \(TR_H\), are greater than those in the ALP case, \({\widetilde{TR}}_H\). It suffices to check the difference of taxable profits:

$$\begin{aligned} {\widetilde{TR}}_H - TR_H&= t [{\tilde{\pi }}_u + {\tilde{\pi }} + {\tilde{\pi }}_* - (\pi ^S + \pi _*^S)]< 0, \\&\rightarrow {\tilde{\pi }}_u + {\tilde{\pi }} + {\tilde{\pi }}_* - (\pi ^S + \pi _*^S) \equiv \Gamma < 0. \end{aligned}$$

If it is shown that (i) \(\Gamma < 0\) holds at \(t=t^*\) and (ii) \(\Gamma \) is increasing in t, we can conclude that \(\Gamma \) is negative for \(t \in (\underline{t}, t^*)\). First we check (i):

$$\begin{aligned}&\Gamma |_{t = t^*} = -\frac{13(1-c)^2}{72} < 0. \end{aligned}$$

(ii) requires the following condition:

$$\begin{aligned} \frac{\mathrm{d}\Gamma }{\mathrm{d}t} =&-\frac{\partial (\pi ^S + \pi _*^S)}{\partial g^S} \frac{\mathrm{d}g^S}{\mathrm{d}t} > 0, \end{aligned}$$

where

$$\begin{aligned} \frac{\mathrm{d}g^S}{\mathrm{d}t} = \frac{2(1-c)(1-T)}{t -2T +1} > 0, \end{aligned}$$

noting that profits earned in the host under the ALP, \({\tilde{\pi }}_u + {\tilde{\pi }} + {\tilde{\pi }}_*\), are independent of transfer price and thus of tax rates. We only need to check that profits in the host in the benchmark case, \(\pi ^S + \pi _*^S\), are decreasing in transfer price, \(g^S\):

$$\begin{aligned} \frac{\partial (\pi ^S + \pi _*^S)}{\partial g^S}&= \frac{5g^S -4}{8} \\&< \frac{g_*^S -1}{2} < 0, \end{aligned}$$

where we make use of \(g^S < g_*^S\) and \(g_*^S<1\). Both (i) and (ii) are proved to be true, and thus we complete the proof.

Tax revenues in the world We first show \(g^S < c\) for \(t \in (\underline{t}, t^*)\) while assuming \(T>{\overline{T}}=1/4\). \(g^S < c\) requires the following condition:

$$\begin{aligned} g^S - c = \frac{(1-c)(t -T)}{t -2T +1} < 0, \end{aligned}$$

which obviously holds under our assumption.

We then show the following:

$$\begin{aligned} {\widetilde{TR}}_W - TR_W&= -T \pi _u^S + t [{\tilde{\pi }}_u + {\tilde{\pi }} + {\tilde{\pi }}_* - (\pi ^S + \pi _*^S)] \\&= -T \pi _u^S + t \Gamma \equiv \Delta > 0, \end{aligned}$$

where \(TR_W\) and \({\widetilde{TR}}_W\) are world tax revenues in the benchmark and the ALP cases, respectively.

Analogous to the previous case, if it is shown that (i) \(\Delta \) is positive at \(t=t^*\) and (ii) \(\Delta \) is decreasing in t, we can conclude that \(\Delta > 0\) holds for \(t \in (\underline{t}, t^*)\). First we see (i):

$$\begin{aligned} \Delta |_{t=t^*} = \frac{(13-2T)(1-c)^2}{216} > 0. \end{aligned}$$

To prove (ii), it suffices to show

$$\begin{aligned} \frac{\mathrm{d}\Delta }{\mathrm{d}t}&= - T \frac{\mathrm{d}\pi _u^S}{\mathrm{d}t} + \Gamma + t \frac{\mathrm{d}\Gamma }{\mathrm{d}t} \\&< t \left( \frac{\mathrm{d}\Gamma }{\mathrm{d}t} - \frac{\mathrm{d}\pi _u^S}{\mathrm{d}t} \right) + \Gamma \\&= t \frac{\partial (\pi ^S +\pi _*^S -\pi _u^S)}{\partial g^S} \frac{\mathrm{d}g^S}{\mathrm{d}t} + \Gamma < 0, \end{aligned}$$

where from the first to the second line we make use of \(t< t^* < T\). As we have seen \(dg^S/dt>0\) and \(\Gamma <0\), we only need to check

$$\begin{aligned} \frac{\partial (\pi ^S +\pi _*^S -\pi _u^S)}{\partial g^S}&= -\frac{c +2 - 3g^S}{2} \\&< -\frac{c +2 - 3c}{2} \\&= -(1-c) < 0, \end{aligned}$$

noting that \(g^S<c\) from the first to the second line. We complete the proof.

A local firm in the upstream industry

In the text, the upstream affiliate is the only supplier of inputs. One may wonder this setting is crucial for the results, but it is not the case. We see that the upstream affiliate may be located in the high-tax parent country (“separate location”) in the benchmark case (Proposition 1) and the imposition of the ALP may change this location pattern (Proposition 2). We introduce a local upstream firm in the host country. The local upstream firm has the same marginal cost c as the MNE’s upstream affiliate and competes with the affiliate in a Bertrand fashion. The timing proceeds in the same manner as in the text. First, the MNE chooses a location for upstream production. Then the MNE and the local upstream firm set input prices. Finally the downstream affiliate and the local firm source the inputs and produce final goods.

As inputs produced by the two upstream firms are homogeneous, the downstream firms buy inputs from the lowest price supplier. Hence, the dominant strategy for the local upstream is to set its input price equal to the marginal cost c. Considering this strategy of the local upstream, the MNE sets input prices equal or lower than c. We need to modify the MNE’s maximization problem so as to include inequality constraints on input prices.

Benchmark case Let us first look at the separate-location scheme. The maximization problem for the MNE is modified asFootnote 28

$$\begin{aligned}&\max _{g^S, g_*^S} \ \Pi ^S = (1-T)[{\bar{\pi }} + (g^S-c)q^S +(g_*^S-c)q_*^S] +(1-t)(p^S -g^S)q^S, \\&\text {s.t.} \ \ g^S \le c, \ \ g_*^S \le c, \end{aligned}$$

where the final good’s price \(p^S\) and quantities \((q^S, q_*^S)\) are defined in Sect. 3 and we assume that the MNE upstream affiliate takes all the input demand if its prices are equal to the ones of the local upstream.

Letting \(\lambda \) and \(\mu \) be the Lagrange multipliers for the constraints of \(g^S \le c\) and \(g_*^S \le c\), respectively, we solve the above problem to get

$$\begin{aligned}&g^S = c + \dfrac{(1-c)(t-T)}{t -2T +1} < c, \\&\lambda = 0, \\&g_*^S = c, \\&\mu = (1-c)(1-T)/2 > 0, \end{aligned}$$

where we maintain the assumptions (A1): \(t>\underline{t}\) and \(t < T\). As the multipliers are all nonnegative, the equilibrium prices satisfy the Kuhn–Tucker conditions for optimization. \(g^S\) allows a similar interpretation to the one for the unconstrained optimal transfer price defined in Eq. (6). The first term is the base price equal to the arm’s length price. The second term represents the tax-manipulation effect.

The associated post-tax profits are then given by

$$\begin{aligned} \Pi ^S = (1-T)\left[ {\bar{\pi }} + \dfrac{(1-T)(1-c)^2}{4(t -2T +1)} \right] . \end{aligned}$$

Under the co-location scheme in the benchmark case as discussed in Sect. 3, the MNE sets input prices higher than c in the unconstrained maximization problem, i.e., \(g > c\) and \(g_* > c\). Hence, in the constrained problem here, it can be confirmed that the MNE sets input prices equal to c, i.e., \(g=c\) and \(g_*=c\), and obtains the following post-tax profits:

$$\begin{aligned} \Pi = (1-T){\bar{\pi }} + \frac{(1-t)(1-c)^2}{4}. \end{aligned}$$

As easily seen, \(\Pi \) is smaller than \(\Pi ^S\) at \(t \in (\underline{t}, T)\). In other words, the MNE’s optimal choice is that the upstream affiliate is always located in the parent country (separate location). Even when considering the local upstream, our conclusion still holds; the upstream production may be located in the high-tax country for the tax-manipulation purpose.

ALP case In the ALP case, the optimal input prices in the unconstrained problem discussed in Sect. 4 are never below the marginal cost c under the two schemes, i.e., \({\tilde{g}} >c\) and \({\tilde{g}}^S > c\). By the same reasoning as before, it can be confirmed that the constrained problem gives the input prices equal to the marginal cost, i.e., \({\tilde{g}}=c\) and \({\tilde{g}}^S=c\). Hence, the associated profits are identical with the one under the co-location scheme in the benchmark case, i.e., \({\widetilde{\Pi }} = {\widetilde{\Pi }}^S = \Pi \) at \(t \in (\underline{t}, T)\). Unlike the benchmark case, the tax-manipulation effect disappears and the two countries are indifferent as to the location choice. In this generalized setting, we still see that the imposition of the ALP may change the location pattern as argued in the text.

Many local firms in the downstream industry

As in Appendix 3, we see here that our main conclusions are maintained in a more generalized setting than in the text. Consider N local firms in the downstream industry. The local firms are assumed to be symmetric and have the same marginal cost c. If N is set to be unity, all the following results reduce to the corresponding results in the text.

The demand functions for the downstream affiliate and the local firm j are, respectively, given by

$$\begin{aligned} p&= 1 - q, \\ p_{*j}&= 1 -q_{*j}. \end{aligned}$$

The following procedure is the same as in the text and we solve the problem backward. Considering the above demand schedules, the downstream firms choose quantities to maximize their own profits:

$$\begin{aligned} q&= \frac{1-g}{2}, \\ q_{*j}&= \frac{1-g_{*j}}{2}. \end{aligned}$$

Benchmark case Given the optimal quantities the downstream firms choose, the MNE sets input prices to maximize its post-tax profits. In the co-location scheme, the equilibrium input prices are given by

$$\begin{aligned} g&= c, \\ g_*&= \frac{1+c}{2}, \end{aligned}$$

where \(g_{*j}=g_*\) holds for all j and the SOCs trivially hold.

The total post-tax profits in equilibrium are calculated as

$$\begin{aligned} \Pi = (1-T){\bar{\pi }} + \frac{(1-t)(1-c)^2(2+N)}{8}. \end{aligned}$$

The equilibrium input prices in the separate-location scheme are given by

$$\begin{aligned} g^S&= c + \frac{(1-c)(t-T)}{t -2T +1}, \\ g_*^S&= \frac{1+c}{2}, \end{aligned}$$

where \(t -2T +1>0\) and the SOCs hold under (A1): \(t>\underline{t}\). Note also \(g_{*j}^S=g_*^S\) for all j. Under \(t < T\), the second term of \(g^S\) is negative so that the tax-manipulation effect works in the same way as in Eq. (6).

The total post-tax profits in equilibrium are calculated as

$$\begin{aligned} \Pi ^S = (1-T)\left[ {\bar{\pi }} + \frac{(1-c)^2\{Nt -2(1+N)T +2 +N\}}{8(t -2T +1)} \right] . \end{aligned}$$

Taking difference between the post-tax profits in the two schemes gives

$$\begin{aligned} \Pi - \Pi ^S = \frac{\Theta ' (1-c)^2 (T-t)}{16(t -2T +1)}, \end{aligned}$$

where

$$\begin{aligned} \Theta ' \equiv 2(2 +N)t +4(1+N)T +2N. \end{aligned}$$

The profit difference becomes zero at \(t=T\) and \(t=t'\) where \(t'\) is the solution of \(\Theta '=0\). It can be confirmed that \(t'\) is in between \((\underline{t}, 1]\) if N is not sufficiently large.Footnote 29 In this case, we have \(\Pi -\Pi ^S < 0\) for \(t \in (\underline{t}, t')\) and \(\Pi - \Pi ^S \ge 0\) for \(t \in [t', T)\). We can conclude that the MNE chooses the separate location if the tax difference is large as in Proposition 1.

ALP case Analogous to the benchmark case, the equilibrium input price under the co-location scheme becomes

$$\begin{aligned} {\tilde{g}} = \frac{c+N+cN}{1+2N}, \end{aligned}$$

where the SOC trivially holds. It can be confirmed that \(g< {\tilde{g}} < g_*\) holds as in the text. The total post-tax profits are given by

$$\begin{aligned} {\widetilde{\Pi }} = (1-T){\bar{\pi }} + \frac{(1-t)(1-c)^2(1+N)^2}{4(1+2N)}. \end{aligned}$$

Turning to the separate-location scheme, the equilibrium input price becomes

$$\begin{aligned} {\tilde{g}}^S = \underbrace{\frac{c+N+cN}{1+2N}}_{={\tilde{g}}} + \frac{(1-c)(1+N)(t-T)}{(1+2N)[t -2(1+N)T +1 +2N]}. \end{aligned}$$

We can check that as long as N is not sufficiently large, \(g^S< \tilde{g}^S < g_*^S\) holds as in the text.

The total post-tax profits under the separate-location scheme are given by

$$\begin{aligned} {\widetilde{\Pi }}^S = (1-T)\left[ {\bar{\pi }} + \frac{(1-T)(1-c)^2(1+N)^2}{4\{ t -2(1+N)T +1 +2N\}} \right] , \end{aligned}$$

where the SOC requires

$$\begin{aligned} t -2(1+N)T +1+2N> 0. \end{aligned}$$

The profit difference then becomes

$$\begin{aligned} {\widetilde{\Pi }} - {\widetilde{\Pi }}^S = \frac{(T-t)(1-c)^2(1+N)^2 [t -(1+2N)T +2N]}{4(1+2N)[ t -2(1+N)T +1+2N]}, \end{aligned}$$

which is positive as long as the SOC holds. This implies that in the ALP case the MNE always chooses the co-location scheme as in Proposition 2.

Trade costs

We introduce here trade costs for inputs. If the upstream affiliate is located in the parent country, the downstream firms pay an extra unit trade cost \(\tau > 0\) when importing inputs (Kind et al. 2005). If it is located in the host country, trade costs play no role and the analysis is the same as in the text. Thus, we present only the results in the separate-location scheme in the following.

Benchmark case The maximization problems of the downstream firms are modified as

$$\begin{aligned} \max _{q} \, \pi ^S&= (p^S-g^S-\tau )q^S, \\ \max _{q_*} \, \pi _*^S&= (p_*^S-g_*^S-\tau )q_*^S. \end{aligned}$$

Solving these gives

$$\begin{aligned} q^S&= \frac{1-g^S-\tau }{2}, \\ q_*^S&= \frac{1-g_*^S-\tau }{2}. \end{aligned}$$

The total post-tax profit of the MNE is also modified accordingly:

$$\begin{aligned} \Pi ^S = (1-T)[\bar{\pi } + (g^S-c)q^S +(g_*^S -c)q_*^S] + (1-t) (p^S -g^S -\tau )q^S. \end{aligned}$$

The equilibrium input prices to maximize it are given by

$$\begin{aligned} g^S&\,= c + \frac{(1-c -\tau )(t-T)}{t -2T +1}, \\ g_*^S&\,= \frac{1+c -\tau }{2}. \end{aligned}$$

We impose an assumption of \(\tau < 1-c\) to ensure positive outputs. The equilibrium total post-tax profit is calculated as

$$\begin{aligned} \Pi ^S = (1-T)\left[ {\bar{\pi }} + \frac{(1-c-\tau )^2(t-4T+3)}{8(t -2T +1)} \right] . \end{aligned}$$

Taking difference between the post-tax profits in the two schemes gives

$$\begin{aligned} \Pi - \Pi ^S = \frac{F(t)}{16(t -2T +1)}, \end{aligned}$$

where

$$\begin{aligned} F(t) \equiv&-3(1-c)^2 t^2 +[\tau \{2(1-c)-\tau \} +(1-c)^2(7T-1)]t \\&+\tau [2(1-c)-\tau ](1-T)(3-4T)+T(4T-1)(1-c)^2. \end{aligned}$$

We check (i) whether \(F(t)=0\) has two real roots and (ii) whether at least either of them falls into \((\underline{t}, T)\).

\(F(t)=0\) has two real roots if its determinant D is positive:

$$\begin{aligned} D(\tau )&\equiv (1-T)^2[\tau ^4 -4(1-c)\tau ^3 -30(1-c)^2 \tau ^2 -68(1-c)^3 \tau \\&\quad +(1-c)^4] > 0, \ \ \text {for} \ \tau \in [0, 1-c). \end{aligned}$$

We can verify this inequality by noting the following relations:

$$\begin{aligned}&D(\tau =0) = (1-T)^2(1-c)^4> 0, \\&D(\tau =1-c) =36 (1-T)^2(1-c)^4> 0, \\&D'(\tau ) = -4(1-T)^2(1-c-\tau )[\tau ^2 -2(1-c)\tau -17(1-c)^2] > 0. \end{aligned}$$

Let \(t_1\) and \(t_2\) be, respectively, the smaller and the larger root of \(F(t)=0\). From the facts that F(t) has a negative coefficient of the quadratic term and that \(\partial F(t; \tau )/\partial \tau = 2(1-T)(1-c-\tau )(t-4T+3) > 0\) holds, we see \(t_1\) is decreasing in \(\tau \) while \(t_2\) is increasing in \(\tau \). At \(\tau =0\), \(t_1\) is reduced to \(t^*=(4T-1)/3\) and \(t_2\) to T.

If \(T>3/4\) holds, \(t_1\) lies in (0, T) regardless of \(\tau \) so that the separate-location scheme is chosen for \(t \in (0, t_1)\). If \(T \le 3/4\) holds, \(t_1\) may become negative at sufficiently high trade costs. The maximum level of trade costs that allows for the separate-location scheme is given by

$$\begin{aligned} \overline{\tau } = (1-c)\sqrt{ 1 - \frac{8T^2 -8T +3}{(1-T)(3-4T)} }. \end{aligned}$$

Even if \(T \le 3/4\), we observe the separate-location scheme for \(t \in (0, t_1]\) as long as \(\tau < \overline{\tau }\).

In sum, as in Proposition 1, assuming the parent’s tax rate is high enough (\(T>3/4\)), the MNE locates the upstream affiliate in the high-tax parent country if the host’s tax rate is low enough (\(t \in (\underline{t}, t_1]\)) and otherwise locates it in the low-tax host country. Higher trade costs reduce the range of tax rates where the separate-location scheme is chosen, i.e., \(dt_1/d\tau <0\).

ALP case Analogously, the equilibrium input price to maximize the total post-tax profit is given by

$$\begin{aligned} {\tilde{g}}^S = \frac{1+2c-\tau }{3} + \frac{2(1-c -\tau )(t-T)}{3(t -4T +3)}. \end{aligned}$$

The associated total post-tax profit becomes

$$\begin{aligned} {\widetilde{\Pi }}^S = (1-T) \left[ \overline{\pi } + \frac{(1-c -\tau )^2(1-T)}{t -4T +3} \right] . \end{aligned}$$

The profit difference is given by

$$\begin{aligned} {\widetilde{\Pi }} - {\widetilde{\Pi }}^S = \frac{(1-c)^2 (t -3T +2)(T-t) +3\tau [2(1-c)-\tau ](1-T)^2 }{3(t -4T +3)} > 0, \end{aligned}$$

where we note that \(\tau< 1-c < 2(1-c)\). This implies that with the ALP the MNE always chooses the co-location scheme as in Proposition 2.

Costs of transfer pricing

Some studies in the literature assume that MNEs are subject to an extra concealment cost of transfer pricing (e.g., Nielsen et al. 2003, 2008; Kind et al. 2005). We formulate here the concealment cost as a quadratic function of the difference between the transfer price and the arm’s length price, i.e., \(C(g, g_*)=\delta (g-g_*)^2/2\) with \(\delta \ge 0\). Following the above-mentioned studies, we assume that the upstream affiliate bears this cost. Thus, the concealment cost does not affect the optimal choices by the downstream firms, which are the same as those given in the text.

Benchmark case In the co-location scheme, the total post-tax profit is modified as

$$\begin{aligned} \Pi = (1-T)\bar{\pi } + (1-t)[(g-c)q +(g_*-c)q_* - C(g, g_*) + (p-g)q], \end{aligned}$$

where

$$\begin{aligned} C(g, g_*) = \delta (g-g_*)^2/2, \, \, \, \,\delta \ge 0, \end{aligned}$$

noting that the optimal outputs \((q, q_*)\) chosen by the downstream firms are the same as those in the text: \(q=(1-g)/2\); \(q_*=(1-g_*)/2\). The equilibrium input prices to maximize it are given by

$$\begin{aligned} g&=\, \frac{\delta + c(1 +2\delta )}{1+3\delta }, \\ g_*&=\, \frac{1+2\delta +c(1+4\delta )}{2(1+3\delta )}. \end{aligned}$$

The equilibrium total post-tax profit then becomes

$$\begin{aligned} \Pi = (1-T)\bar{\pi } + \frac{(1-t)(1-c)^2(3+8\delta )}{8(1+3\delta )}. \end{aligned}$$

In the separate-location scheme, we can analogously define the total post-tax profit and compute the equilibrium input prices as follows:

$$\begin{aligned} g^S&=\, c + \frac{(1-c)[t-T +\delta (t-2T+1)]}{t -2T +1 + \delta (t-4T+3)}, \\ g_*^S&=\, \frac{(t-2T+1)(1+c+2\delta ) +4c\delta (1-T)}{2[t -2T +1 + \delta (t-4T+3)]}. \end{aligned}$$

The equilibrium total post-tax profit is calculated as

$$\begin{aligned} \Pi ^S = (1-T)\left[ \bar{\pi } + \frac{(1-c)^2\{ t-4T+3 +8\delta (1-T)\} }{8\{ t -2T +1 + \delta (t-4T+3)\}} \right] . \end{aligned}$$

Taking difference between the post-tax profits in the two schemes gives

$$\begin{aligned} \Pi - \Pi ^S = \frac{G(t) (1-c)^2 (T-t)}{8(1+3\delta )[t -2T +1 + \delta (t-4T+3)]}, \end{aligned}$$

where

$$\begin{aligned} G(t) \equiv (1+\delta )(3+8\delta ) t - 8(3T-2)\delta ^2 -(20T-9)\delta +1-4T, \end{aligned}$$

noting that its sign only depends on G(t). \(G(t)=0\) holds at \(t^{**}\), which is defined by

$$\begin{aligned} t^{**} = \frac{4T-1}{3} - \frac{8\delta (2+5\delta )(1-T)}{3(1+\delta )(3+8\delta )}. \end{aligned}$$

Without the concealment cost, \(t^{**}\) is reduced to \(t^*\) defined in Eq. (9). When \(T>{\overline{T}}=1/4\) holds as in the text and \(\delta \) is not too high, \(t^{**}\) becomes positive.Footnote 30 In this case, as in Proposition 1, we observe the separate-location scheme for \(t \in (\underline{t}, t^{**}]\) and the co-location scheme for \(t \in (t^{**}, T)\). The more difficult concealment is, the less likely we are to observe the separate-location scheme, i.e., \(dt^{**}/d\delta < 0\).

ALP case As the transfer price must be equal to the arm’s length price, the concealment cost plays no role. The results in both schemes are the same as those in the text.

Differentiated inputs

In the text, the downstream affiliate and the local firm purchase the same input from the upstream affiliate. We consider here the situation where the two downstream firms need a different type of inputs. The upstream affiliate produces the two different inputs using different technology. That is, the marginal cost of input for the downstream affiliate is \(c \in [0, 1)\), while that for the local firm is \(c_* \in [0, 1)\).

As the input for the downstream firm is not perfectly comparable to that for the local firm, tax authorities cannot require that the prices of the two inputs must be the same. Instead, they allow for a certain range of arm’s length price. This arm’s length range gives the MNE room for price differentiation even under the ALP. The partial comparability of the two inputs implies that they are produced using more or less the same technology. We thus assume the difference of marginal cost is not too large: \(|c_*-c| < 1-c\).

Benchmark case In the co-location scheme, the total post-tax profit is

$$\begin{aligned} \Pi = (1-T)\bar{\pi } + (1-t)[(g-c)q +(g_*-c_*)q_* + (p-g)q], \end{aligned}$$

where the optimal outputs \((q, q_*)\) chosen by the downstream firms are the same as those in the text: \(q=(1-g)/2\); \(q_*=(1-g_*)/2\). The equilibrium input prices to maximize it are

$$\begin{aligned} g&= \,c, \\ g_*&=\, \frac{1+c_*}{2}, \end{aligned}$$

where we note \(g < g_*\). The equilibrium total post-tax profit then becomes

$$\begin{aligned} \Pi = (1-T)\bar{\pi } + (1-t)\left[ \frac{(1-c)^2}{4} + \frac{(1-c_*)^2}{8} \right] . \end{aligned}$$

In the separate-location scheme, the total post-tax profit is modified as follows:

$$\begin{aligned} \Pi ^S = (1-T)[\bar{\pi } + (g^S-c)q^S +(g_*^S-c_*)q_*^S] + (1-t)(p^S-g^S)q^S. \end{aligned}$$

The equilibrium input prices are

$$\begin{aligned} g^S&= c + \frac{(1-c)(t-T)}{t -2T +1}, \\ g_*^S&= \frac{1+c_*}{2}, \end{aligned}$$

where we note \(g^S < g_*^S\). The equilibrium total post-tax profit is calculated as

$$\begin{aligned} \Pi ^S = (1-T) \left[ \bar{\pi } + \frac{(1-c_*)^2}{8} + \frac{(1-T)(1-c)^2}{4(t -2T +1)} \right] . \end{aligned}$$

The MNE prefers the co-location scheme if

$$\begin{aligned} \Pi - \Pi ^S&= \frac{(T-t)[t\{3-2c(2-c)-c_*(2-c_*)\} -2T\{(1-c)^2+(1-c_*)^2\} + (1-c_*)^2 ]}{8(t-2T+3)}> 0, \\&\rightarrow t > t^* \equiv \frac{2T[(1-c)^2+(1-c_*)^2] - (1-c_*)^2}{3-2c(2-c)-c_*(2-c_*)}. \end{aligned}$$

where we can confirm \(t^* \in (0, T)\) if T is sufficiently large:

$$\begin{aligned} T > \overline{T} \equiv \max \left\{ \frac{1}{4}, \ \frac{(1-c_*)^2}{2[(1-c)^2+(1-c_*)^2]} \right\} . \end{aligned}$$

The co-location scheme is chosen if the host’s tax rate is close to the parent’s (\(t \in (t^*, T)\)) and the separate-location scheme is chosen otherwise (\(t \in (0, t^*]\)) as in Proposition 1.

ALP case In the co-location scheme, the transfer price \({\tilde{g}}\) must be within the range of \([{\tilde{g}}_*-e, {\tilde{g}}_*+e]\) with \(e>0\). We assume e is not too large, otherwise the situation is reduced to the benchmark case. The MNE sets the price \({\tilde{g}}_*\) to the local firm and \({\tilde{g}}={\tilde{g}}_*+ {\tilde{e}}\) to the downstream affiliate, where \({\tilde{e}} \in [-e, e]\). It chooses \({\tilde{g}}_*\) and \({\tilde{e}}\) to maximize the total post-tax profit:

$$\begin{aligned} \max _{{\tilde{g}}_*, {\tilde{e}}} \ {\widetilde{\Pi }} = (1-T)\bar{\pi } + (1-t)[({\tilde{g}}_*+{\tilde{e}}-c){\tilde{q}} + ({\tilde{g}}_* -c_*){\tilde{q}}_* + ({\tilde{p}}-{\tilde{g}}_*-{\tilde{e}}){\tilde{q}}], \end{aligned}$$

noting that the optimal outputs \(({\tilde{q}}, {\tilde{q}}_*)\) chosen by the downstream firms are the same as those in the text.

As the fact that \(g < g_*\) holds in the benchmark case suggests, the MNE tries to set \({\tilde{g}}\) lower than \({\tilde{g}}_*\) and thus chooses \({\tilde{e}}=-e\). The equilibrium input prices are

$$\begin{aligned} {\tilde{g}}_*&= \frac{1 +c +c_* +e}{3}, \\ {\tilde{g}}&= {\tilde{g}}_* - e = \frac{1+c+c_*-2e}{3}. \end{aligned}$$

The total post-tax profit can then be rewritten as

$$\begin{aligned} {\widetilde{\Pi }} = (1-T)\bar{\pi } + (1-t) \left[ \frac{(2-c-c_*)^2}{12} - \frac{e(1-2c+c_*+e)}{6} \right] . \end{aligned}$$

In the separate-location scheme, we can analogously define the total post-tax profit and compute the equilibrium input prices as follows:

$$\begin{aligned} {\tilde{g}}_*^S&= \frac{1 +c +c_* +e}{3} + \frac{(2-c-c_* +2e)(t-T)}{3(t-4T+3)}, \\ {\tilde{g}}^S&= {\tilde{g}}_*^S - e = \frac{1 +c +c_* -2e}{3} + \frac{(2-c-c_*+2e)(t-T)}{3(t-4T+3)}, \end{aligned}$$

where the MNE sets \({\tilde{e}}=-e\) as implied by \(g^S<g_*^S\). The equilibrium total post-tax profit is calculated as

$$\begin{aligned} {\widetilde{\Pi }}^S = (1-T)\left[ \bar{\pi } + \frac{(1-T)(2-c-c_*)^2 -2e\{ e(t-2T+1) +\kappa \} }{4(t-4T+3)} \right] , \end{aligned}$$

where

$$\begin{aligned} \kappa \equiv (1-c)(1-t) -(c-c_*)(t-2T+1). \end{aligned}$$

Taking difference between the post-tax profits in the two schemes gives

$$\begin{aligned} {\widetilde{\Pi }} - {\widetilde{\Pi }}^S = \frac{H(e) (T-t)}{12(t-4T+3)}, \end{aligned}$$

where

$$\begin{aligned} H(e) \equiv&-2(t-6T+5)e^2 +2[1-t +2c(t-3T+2) -c_*(t-6T+5)]e \\&+(2-c-c_*)^2(t-3T+2). \end{aligned}$$

Since \(T-t>0\) and \(t-4T+3>0\) hold, the inequality is positive if \(H(e)>0\) holds. Noting that \(t-6T+5>0\) and \(t-3T+2>0\) hold because of (A1): \(t>\underline{t}\), we see that H(e) has a negative coefficient of the quadratic term and that \(H(0)>0\). These observations imply that \(H(e)>0\) holds if \(e \in (0, e_2)\), where \(e_2\) is the larger root of \(H(e)=0\). In other words, if the degree of input differentiation is so low that the arm’s length range is narrow enough, the MNE always chooses the co-location scheme as in Proposition 2.

Endogenous profits in the parent market

In the text, we assume that the MNE earns exogenous profits \(\bar{\pi }\) from different business in the parent country. Here we endogenize it by introducing a local downstream firm in the parent. The local firm is the monopolist facing the demand curve of \(P_* = 1 - Q_*\). It sources the same type of inputs as do the downstream firms in the host, from the upstream affiliate at the price of \(G_*\). As the parent’s and the host’s markets are segmented, the presence of the local firm does not affect the equilibrium outputs and input prices for the downstream firms in the host. It only affects the location choice of the MNE, as we shall see below.

Benchmark case In the co-location scheme, the total post-tax profit is modified as

$$\begin{aligned} \Pi = (1-t)[(g-c)q +(g_*-c)q_* + (G_*-c)Q_* + (p-g)q], \end{aligned}$$

where the optimal outputs \((q, q_*)\) chosen by the downstream firms are the same as those in the text: \(q=(1-g)/2\); \(q_*=(1-g_*)/2\). We also note \(Q_* = (1 -G_*)/2\). The equilibrium input prices to maximize it are given by

$$\begin{aligned} g =&c, \\ g_* =&G_* = \frac{1+c}{2}. \end{aligned}$$

The equilibrium total post-tax profit then becomes

$$\begin{aligned} \Pi = \frac{(1-t)(1-c)^2}{2}. \end{aligned}$$

In the separate-location scheme, the total post-tax profit is modified as follows:

$$\begin{aligned} \Pi ^S = (1-T)[(g^S-c)q^S +(g_*^S-c)q_*^S + (G_*^S-c)Q_*^S] + (1-t)(p^S-g^S)q^S. \end{aligned}$$

The equilibrium input prices are

$$\begin{aligned} g^S =&c + \frac{(1-c)(t-T)}{t -2T +1}, \\ g_*^S =&G_*^S = \frac{1+c}{2}. \end{aligned}$$

The equilibrium total post-tax profit is calculated as

$$\begin{aligned} \Pi ^S = \frac{(1-T)(1-c)^2(t-3T+2)}{4(t -2T +1)}. \end{aligned}$$

The profit difference takes a complex form and is hard to characterize analytically. We thus rely on numerical simulations. Fig. 4 draws the total post-tax profits in the two schemes for different levels of the host’s tax rate.Footnote 31 In Fig. 4a, where the parent’s tax rate is high (\(T=0.35\)), the separate-location scheme is chosen for \(t \in (0, t^*)\) and the co-location scheme for \(t \in [t^*, T)\). In Fig. 4b, where the parent’s tax rate is low (\(T=0.2\)), the co-location scheme is chosen for the entire range \(t \in (0, T)\). We have experimented various parameter values and confirmed the qualitatively same results as in Proposition 1. That is, the higher the parent’s tax rate is, the more likely we are to observe the separate-location scheme as Fig. 4a shows.

Fig. 4
figure4

Production location choice in the benchmark case: a high T and b low T

ALP case Analogous to the benchmark case, the equilibrium input price in the co-location scheme is derived as follows:

$$\begin{aligned} {\tilde{g}} = {\tilde{g}}_* = {\tilde{G}}_* = \frac{1+2c}{3}. \end{aligned}$$

The associated total post-tax profit becomes

$$\begin{aligned} {\widetilde{\Pi }} = \frac{(1-t)(1-c)(5-8c)}{9}. \end{aligned}$$

To make \({\widetilde{\Pi }}\) positive, we assume \(c<5/8\).

In the separate-location scheme, the equilibrium input prices and the resulting total post-tax profit are

$$\begin{aligned} {\tilde{g}}^S = {\tilde{g}}_*^S = {\tilde{G}}_*^S = \frac{1+2c}{3} + \frac{2(1-c)(t-T)}{3(t -4T +3)}. \end{aligned}$$

The associated total post-tax profit becomes

$$\begin{aligned} {\widetilde{\Pi }}^S = \frac{2(1-T)^2(1-c)^2(t-3T+2)}{(t -4T +3)^2}. \end{aligned}$$

Because the profit difference is difficult to characterize analytically, we again use numerical simulations. Fig. 5 illustrates the total post-tax profits in the two schemes for different levels of the host’s tax rate.Footnote 32 Unlike the benchmark case, the co-location scheme is chosen for the entire range even when the parent’s tax rate is high. We have conducted many simulations and confirmed that the ALP prevents the MNE from choosing the separate-location scheme as in Proposition 2.

Fig. 5
figure5

Production location choice in the ALP case: a high T and b low T

Welfare analysis

We confirm here that the results on tax revenues stated in Proposition 3 carry over to social welfare. That is, the location change induced by the ALP decreases the host country welfare, while increases global welfare.

Host country welfare Assuming \(T>1/4\), we show that when \(t \in (\underline{t}, t^*)\), the social welfare of the host country in the benchmark case, \(W_H\), are greater than that in the ALP case, \({\widetilde{W}}_H\). \(W_H\) and \({\widetilde{W}}_H\) are defined as follows:

$$\begin{aligned} W_H&= \underbrace{\frac{(q^S)^2}{2} + \frac{(q_*^S)^2}{2}}_{\text {Consumer surplus}} + \underbrace{(1-t)(\pi ^S + \pi _*^{S})}_{\text {Producer surplus}} + \underbrace{t(\pi ^S + \pi _*^S)}_{\text {Tax revenues}}, \\ {\widetilde{W}}_H&= \underbrace{2 \times \frac{{\tilde{q}}^2}{2}}_{\text {Consumer surplus}} + \underbrace{(1-t) ( {\tilde{\pi }}_u + 2{\tilde{\pi }})}_{\text {Producer surplus}} + \underbrace{t ( {\tilde{\pi }}_u + 2{\tilde{\pi }})}_{\text {Tax revenues}}, \end{aligned}$$

where we note \({\tilde{q}}={\tilde{q}}_*\) and \({\tilde{\pi }}={\tilde{\pi }}_*\).

Taking the difference of these two gives

$$\begin{aligned} {\widetilde{W}}_H - W_H&= \left[ {\tilde{q}}^2 - \frac{(q^S)^2 +(q_*^S)^2}{2} \right] + \underbrace{[{\tilde{\pi }}_u + 2{\tilde{\pi }} - (\pi ^S + \pi _*^S)]}_{(-)}. \end{aligned}$$

As we know from Proposition 3 that the second square bracket term is negative, it suffices to check the first square bracket term is negative:

$$\begin{aligned} {\tilde{q}}^2 - \frac{(q^S)^2 +(q_*^S)^2}{2} = \frac{(1-c)^2 f(t)}{288(t-2T+1)^2}, \end{aligned}$$

where

$$\begin{aligned} f(t) \equiv 23t^2 +46(1-2T)t +56T^2 -20T -13. \end{aligned}$$

This is negative if \(f(t)<0\). We can confirm \(f(t)<0\) by noting that (i) f(t) is monotonically increasing in t for \(t \in (\underline{t}, t^*)\) and (ii) f(t) takes a negative value at the two endpoints of \(\underline{t}\) and \(t^*\). The host country attains a higher consumer surplus under no regulation than under the ALP. Without the ALP, the lower transfer price helps the downstream affiliate reduce its price, benefiting the host’s consumers more.

We can thus conclude that the location change triggered by the ALP reduces the host country welfare.

Global welfare We show that global welfare under no regulation is higher than that under the ALP for \(t \in (\underline{t}, {\hat{t}})\), where \({\hat{t}}\) is smaller than \(t^*\). Let \(W_P\) (or \({\widetilde{W}}_P\)) be the social welfare of the parent country under the regulation (or under the ALP), which are given by

$$\begin{aligned} W_P&= \underbrace{T (\bar{\pi } + \pi _u^S)}_{\text {Producer surplus}} + \underbrace{(1-T)(\bar{\pi } + \pi _u^S)}_{\text {Tax revenues}}, \\ {\widetilde{W}}_P&= \underbrace{T \bar{\pi }}_{\text {Producer surplus}} + \underbrace{(1-T)\bar{\pi }}_{\text {Tax revenues}}. \end{aligned}$$

Global welfare is defined as the sum of the host’s and parent’s social welfare. Comparing the global welfare under the ALP with that under no regulation yields

$$\begin{aligned} {\widetilde{W}}_P +{\widetilde{W}}_H -(W_P + W_H)&= \bar{\pi } + {\tilde{q}}^2 + {\tilde{\pi }}_u + 2{\tilde{\pi }} \\&\quad - \left[ \bar{\pi } + \frac{(q^S)^2 +(q_*^S)^2}{2} + \pi _u^S + \pi ^S + \pi _*^S \right] \\&= \frac{(1-c)^2 h(t)}{288(t-2T+1)^2}, \end{aligned}$$

where

$$\begin{aligned} h(t) \equiv 97t^2 +2(25-122T)t +136T^2 -28T -11. \end{aligned}$$

This is positive if \(h(t)>0\). We can confirm \(h(t)=0\) at \(t = {\hat{t}} \in (\underline{t}, t^*)\) by noting that (i) h(t) is monotonically decreasing in t for \(t \in (\underline{t}, t^*)\), (ii) \(h(\underline{t})>0\), and (iii) \(h(t^*)<0\).

We can thus conclude that if the international tax difference is sufficiently large (\(t \in (\underline{t}, {\hat{t}})\)), the location change induced by the ALP increases global welfare, i.e., \({\widetilde{W}}_P +{\widetilde{W}}_H -(W_P + W_H)>0\).

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Kato, H., Okoshi, H. Production location of multinational firms under transfer pricing: the impact of the arm’s length principle. Int Tax Public Finance 26, 835–871 (2019). https://doi.org/10.1007/s10797-018-9523-2

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Keywords

  • Multinational enterprises (MNEs)
  • Transfer pricing
  • Production location choice
  • Intra-firm trade
  • Arm’s length principle (ALP)

JEL Classification

  • F12
  • F23
  • H25
  • H26