International Tariffs in a Mixed Oligopoly with Research Spillovers

Shoji Haruna; Rajeev K. Goel

doi:10.1515/peps-2016-0007

Article

International Tariffs in a Mixed Oligopoly with Research Spillovers

Shoji Haruna and Rajeev K. Goel

Published/Copyright: June 20, 2016

Published by

Become an author with De Gruyter Brill

Submit Manuscript Author Information Explore this Subject

From the journal Peace Economics, Peace Science and Public Policy Volume 22 Issue 3

Abstract

This paper merges three strands of the literature – industrial organization, international trade, and economics of technical change – to examine the effect of tariffs on international mixed oligopolies which conduct research and development (R&D) that is prone to spillovers. Mixed oligopolies are prevalent in the defense sector, among other sectors. Using a two-stage sequential game with R&D in the first stage and production in the second stage, results show that higher tariffs reduce outputs of both the domestic public firm and foreign private firms, and private R&D. Effects on domestic R&D and welfare, and profits of foreign private firms depend upon spillovers. Within a large range of research spillovers, higher tariffs can in fact lower welfare. Some of these findings are different from traditional oligopolies and from models that ignore research spillovers. Policy implications are discussed.

Keywords: mixed oligopoly; R&D; spillovers; cost reduction; import tariffs; defense sector

JEL: O33; L22; F19

Acknowledgments

We would like to thank Raul Caruso and a referee for comments, and Shabana Tabassum for research assistance. Goel thanks CESifo for hospitality during a research stay that facilitated work on revising this paper. Haruna gratefully acknowledges financial support by the Japan Society for the Promotion of Science under the Grant-in-Aid for Scientific Research (C), No. 22638030206.

Appendix

A. Derivation of R&D and outputs

The first-order conditions for maximization regarding output in the second stage are:

(A1)dπf1dqf1=a−c−t+xf1+β(xf2+xd)−3qf1−qf2−qd=0 (A1)

(A2)dπf2dqf2=a−c−t+xf2+β(xf1+xd)−qf1−3qf2−qd=0 (A2)

(A3)dWdqd=a−c+xd+β(xf1+xf2)−2qd=0. (A3)

Solving these conditions for output yields

(A4)qf1=a−c−2t+(3−2β)xf1+(2β−1)(xf2+xd)8 (A4)

(A5)qf2=a−c−2t+(3−2β)xf2+(2β−1)(xf1+xd)8 (A5)

(A6)qd=a−c+xd+β(xf1+xf2)2. (A6)

The first-order conditions for maximization regarding R&D in the first stage are:

(A7)dπf1dxf1=3(3−2β)(a−c)−6(3−2β)t+[3(3−2β)2−64]xf1+3(3−2β)(2β−1)(xf2+xd)64=0 (A7)

(A8)dπf2dxf2=3(3−2β)(a−c)−6(3−2β)t+[3(3−2β)2−64]xf2+3(3−2β)(2β−1)(xf1+xd)64=0 (A8)

(A9)dWdxd=(7+2β)(a−c)+2(2β−1)t+(−7−4β+4β2)xd+(−1+10β)(xf1+xf2)16=0. (A9)

It follows from (A7), (A8), and (A9) that

xi∗=(4032β+5952β2−9216β3+2304β4)(a−c)−12(3−2β)(3+4β−4β2)(28+60β−24β2)tD

i=f1, f2

xd∗=(8512+28544β+12096β2−14592β3+2304β4)(a−c)−32(49+301β+126β2−708β3+216β4)tD,

where D=8512+32128β+4544β²–44928β³+26880β⁴–4608β⁵. Furthermore, by substituting R&D into (A4), (A5), and (A6), we have optimal outputs:

qi∗=(3584β+7680β2−3072β3)(a−c)−(2688+9344β+1792β2−10752β3+3072β4)tD

i=f1, f2

qd∗=(8512+30336β+12352β2−23808β3+5376β4)(a−c)−(784+7840β+10512β2−16320β3−9984β4+11520β5−2304β6)tD.

Total industry output is

Q∗=(8512+37504β+27712β2−29952β3+5376β4)(a−c)−(6160+26528β+14096β2−37824β3−3840β4+11520β5−2304β6)tD.

B. Effects of changes in tariffs on profits and domestic welfare

B1. The effect of an increase in tariffs on industry output is

dQ∗dt=−(6160+26528β+14096β2−37824β3−3840β4+11520β5−2304β6)D<0.

B2. Differentiating the profit function of ith foreign private firm with respect to tariff yields

dπi∗dt=3qi∗dqi∗dt−xi∗dxi∗dt=1D2[(−16708608β−110143488β2−207209472β3+5197824β4+263245824β5+1769472β6−122535936β7+47775744β8−5308416β9)(a−c)+(12531456+99316224β+248841984β2+93167616β3−409841664β4−259375104β5+353378304β6+88473600β7−16630368β8+53084160β9−5308416β10)t].

Given the assumption a–c>t, we have A(a–c)+Bt≤(A+B)t for A≤0. When A+B<0, we have A(a–c)+Bt<0. Now A+B<0 for 0.8661≤β≤1, where A=–16708608β–110143488β²–207209472β³+5197824β⁴+263245824β⁵+1769472β⁶– 122535936β⁷+47775744β⁸–5308416β⁹<0, and B=12531456+99316224β+248841984β²+ 93167616β³–409841664β⁴–259375104β⁵+353378304β⁶+88473600β⁷–16630368β⁸+53084160β⁹–5308416β¹⁰, while A+B>0 for 0≤β≤0.8660. Thus the sign of dπi∗/dt becomes negative for 0.8661≤β≤1, but it is of either sign for other spillovers. In particular, evaluating the effect at t=0, we have (dπi∗/dt)t=0=A(a−c)/D2≤0 for any spillovers.

B3. Differentiating the profit function of the public firm with respect to the tariff yields

dπd∗dt=(qd∗−2qf1∗)dqd∗dt−(2qd∗dqf1∗dt+xd∗dxd∗dt)=1D2[(52433920+364005376β+723296256β2−22800384β3−1018848256β4+502087685+408514560β6−41553100β7+299188224β8−102629376β9+12386304β10)(a−c)+(−5356288−71099392β−228304384β2−94041088β3+409960704β4+190900224β5−362803200β6−6561792β7+357654528β8−395476992β9+207028224β10−53084160β11+5308416β12)t],

where πd∗=(qd∗)2/2−2qd∗qf1∗−(xd∗)2/2 and qf1∗=qf2∗. It follows from the assumption a–c>t that E(a–c)+Ft>(E+F)t for E>0. Thus, if E+F>0, then E(a–c)+Ft>0 holds. Now we get E+F>0, where E=52433920+364005376β+723296256β²–22800384β³– 1018848256β⁴+50208768β⁵+408514560β⁶–41553100β⁷+299188224β⁸–102629376β⁹+12386304β¹⁰>0 and F=–5356288–71099392β–228304384β²–94041088β³+ 409960704β⁴+190900224β⁵–362803200β⁶–6561792β⁷+357654528β⁸–395476992β⁹+207028224β¹⁰ –53084160β¹¹+5308416β¹². Then E(a−c)+Ft>0 holds, so that we obtain dπd*/dt>0.

B4. Arranging the function of domestic welfare, we have W=[2(q_d)²+4(q_f1)²–(x_d)²+4tq_f1]/2, where q_f1=q_f2. Differentiating the welfare with respect to the tariff yields

dW∗dt=2qd∗dqd∗dt+(4qf1∗+2t)dqf1∗dt−xd∗dxd∗dt+2qf1∗=1D2[(−520882432β−4842925568β2−6519696640β3+9713931264β4+6875197440β5−7396110336β6+697946112β7+728727552β8−233570304β9+2477260810)(a−c)+(5996032+44613632β+147421184β2+247539712β3−104795648β4−894775296β5+24502272β6+1311031296β7−687882240β8−309657600β9+357433344β10−106168320β11+10616832β12)t].

Employing the assumption a–c>t, we have G(a–c)+Ht≤(G+H)t for G≤0. As G=–520882432β–4842925568β²–6519696640β³+9713931264β⁴+687519744 0β⁵ –736110336β⁶+697946112β⁷+728727552β⁸–233570304β⁹+24772608¹⁰≤0 and H=5996032+44613632β+147421184β²+247539712β³–104795648β⁴–894775296β⁵+ 24502272β⁶+1311031296β⁷–678882240β⁸–309657600β⁹+357433344β¹⁰–106168320β¹¹+10616832β¹², it follows that G+H>0 for 0≤β≤0.0113 and G+H<0 for 0.0114≤β≤1. Then the sign of dW^*/dt becomes negative for 0.0114≤β≤1, while it is of either sign for 0≤β≤0.0113; but we have (dWi∗/dt)t=0=G(a−c)/D2≤0 when evaluating at t=0.

References

Bárcena-Ruiz, J.C., Garzón, M.B., (2009), Relocation and Public Ownership of Firms, Journal of the Japanese and International Economies, vol. 23, no. 1, pp. 71–85.10.1016/j.jjie.2009.01.002Search in Google Scholar

Bárcena-Ruiz, J.C., Garzón, M.B., (2010), Endogenous Timing in a Mixed Oligopoly with Semipublic Firms, Portuguese Economic Journal, vol. 9, no. 2, pp. 97–113.10.1007/s10258-010-0054-8Search in Google Scholar

Brander, J.A., Spencer, B.J., (1984), Trade Warfare: Tariffs and Cartels, Journal of International Economics, vol. 16, no. 3–4, pp. 227–242.10.3386/w1193Search in Google Scholar

Carlson, J., (2008), Cooperative R&D and Strategic Trade Policy with Bertrand Competition, Review of International Economics, vol. 16, no. 2, pp. 355–367.10.1111/j.1467-9396.2008.00738.xSearch in Google Scholar

Caruso, R., Locatelli, A., (2013), Company Survey Series II: Finmeccanica amid International and State Control: A Survey of Italian Defence Industry, Defence and Peace Economics, vol. 24, no. 1, pp. 89–104.10.1080/10242694.2011.635952Search in Google Scholar

Coe, D.T., Helpman, E., (1995), International R&D Spillovers, European Economic Review, vol. 39, no. 5, pp. 859–887.10.3386/w4444Search in Google Scholar

Colombo, S., (2016), Mixed Oligopolies and Collusion, Journal of Economics, forthcoming. DOI 10.1007/s00712-015-0467-z (in press).Search in Google Scholar

d’Aspremont, C., Jacquemin, A., (1988), Cooperative and Noncooperative R&D in Duopoly with Spillovers, American Economic Review, vol. 78, no. 5, pp. 1133–1137.Search in Google Scholar

Dawn, (2015), Pakistan is Producing State of the Art Defence Products, says President Mamnoon, Dawn.com, December 2. http://www.dawn.com/news/1223744.Search in Google Scholar

De Fraja, G., Delbono, F., (1990), Game Theoretic Models of Mixed Oligopoly, Journal of Economic Surveys, vol. 4, no. 1, pp. 1–17.10.1111/j.1467-6419.1990.tb00077.xSearch in Google Scholar

Dixit, A.K., (1984), International Trade Policy for Oligopolistic Industries, Economic Journal, vol. 94, Supplement, pp. 1–16.10.2307/2232651Search in Google Scholar

Fjell, K., Pal, D., (1996), A Mixed Oligopoly in the Presence of Foreign Private Firms, Canadian Journal of Economics, vol. 29, no. 3, pp. 737–743.10.2307/136260Search in Google Scholar

Gangadharan, S., (2014), Searching for the Ideal FDI in Defence Production, The Hindu, July 24, http://www.thehindu.com/opinion/op-ed/searching-for-the-ideal-fdi-in-defence-production/article6242496.ece?ref=relatedNews.Search in Google Scholar

Gil-Moltó, M.J., Poyago-Theotoky, J., Zikos, V., (2011), R&D Subsidies, Spillovers, and Privatizations in Mixed Markets, Southern Economic Journal, vol. 78, no. 1, pp. 233–255.10.4284/0038-4038-78.1.233Search in Google Scholar

Goel, R.K., (1990), The Substitutability of Capital, Labor, and R&D in U.S. Manufacturing, Bulletin of Economic Research, vol. 42, no. 3, pp. 211–227.10.1111/j.1467-8586.1990.tb00671.xSearch in Google Scholar

Goel, R.K., Haruna, S., (2011), Cost-Reducing R&D with Spillovers and Trade, Journal of Institutional and Theoretical Economics, vol. 167, no. 2, pp. 314–326.10.1628/093245611796589997Search in Google Scholar

Goel, R.K., Payne, J.E., Ram, R., (2008), R&D Expenditures and U.S. Economic Growth: A Disaggregated Approach, Journal of Policy Modeling, vol. 30, no. 2, pp. 237–250.10.1016/j.jpolmod.2007.04.008Search in Google Scholar

Gold, D., (1994), The Internationalization of Military Production, Peace Economics, Peace Science and Public Policy, vol. 1, no. 3, pp. 3–13.Search in Google Scholar

Griliches, Z., (1992), The Search for R&D Spillovers, Scandinavian Journal of Economics, vol. 94, Supplement, pp. S29–S47.10.3386/w3768Search in Google Scholar

Han, L., (2012), Strategic Privatization and Trade Policies in International Mixed Oligopoly, The Manchester School, vol. 80, no. 5, pp. 580–602.10.1111/j.1467-9957.2011.02245.xSearch in Google Scholar

Hartley, K., (2006), Defence Industrial Policy in a Military Alliance, Journal of Peace Research, vol. 43, no. 4, pp. 473–489.10.1177/0022343306064976Search in Google Scholar

Hartley, K., Sandler, T. (eds.), (1995), Handbook of Defense Economics, North-Holland, Amsterdam.Search in Google Scholar

Haruna, S., Goel, R.K., (2015), R&D Strategy in International Mixed Duopoly with Research Spillovers, Australian Economic Papers, vol. 54, no. 2, pp. 88–103.10.1111/1467-8454.12042Search in Google Scholar

Haruna, S., Goel, R.K., (2016), Output Subsidies in Mixed Oligopoly with Research Spillovers, Journal of Economics and Finance, forthcoming. DOI 10.1007/s12197-015-9346-2 (in press).Search in Google Scholar

Ishibashi, I., Matsumura, T., (2006), R&D Competition between Public and Private Sectors, European Economic Review, vol. 50, no. 6, pp. 1347–1366.10.1016/j.euroecorev.2005.04.002Search in Google Scholar

Jinji, N., Zhang, X., Haruna, S., (2015), Trade Patterns and International Technology Spillovers: Evidence from Patent Citations, Review of World Economics, vol. 151, no. 4, pp. 635–658.10.1007/s10290-015-0223-zSearch in Google Scholar

Katrak, H., (1996), Trade Policies, Enterprise Characteristics and Technological Effort in Developing Countries, Journal of International Development, vol. 8, no. 1, pp. 39–51.10.1002/(SICI)1099-1328(199601)8:1<39::AID-JID262>3.0.CO;2-OSearch in Google Scholar

Kesavayuth, D., Zikos, V., (2013), R&D versus Output Subsidies in Mixed Markets, Economics Letters, vol. 118, no. 2, pp. 293–296.10.1016/j.econlet.2012.11.017Search in Google Scholar

Luckraz, S., (2011), R&D Games in a Cournot Duopoly with Isoelastic Demand Functions: A Comment, Economic Modelling, vol. 28, no. 6, pp. 2873–2876.10.1016/j.econmod.2011.07.019Search in Google Scholar

Matsumura, T., (1998), Partial Privatization in Mixed Duopoly, Journal of Public Economics, vol. 70, no. 3, pp. 473–483.10.1016/S0047-2727(98)00051-6Search in Google Scholar

Matsumura, T., Ogawa, A., (2012), Price versus Quantity in a Mixed Duopoly, Economics Letters, vol. 116, no. 2, pp. 174–177.10.1016/j.econlet.2012.02.012Search in Google Scholar

Nakamura, T., (2001), International Knowledge Spillovers and Technology Imports: Evidence from Japanese Chemical and Electrical Equipment Industries, Journal of the Japanese and International Economies, vol. 15, no. 3, pp. 271–297.10.1006/jjie.2001.0470Search in Google Scholar

Pal, D., White, M.D., (1998), Mixed Oligopoly, Privatization and Strategic Trade Policy, Southern Economic Journal, vol. 65, no. 2, pp. 264–281.10.1002/j.2325-8012.1998.tb00149.xSearch in Google Scholar

Reinganum, J.F., (1984), Practical Implications of Game Theoretic Models of R&D, American Economic Review Papers and Proceedings, vol. 74, no. 2, pp. 61–66.Search in Google Scholar

Reitzes, J.D., (1991), The Impact of Quotas and Tariffs on Strategic R&D Behavior, International Economic Review, vol. 32, no. 4, pp. 985–1007.10.2307/2527047Search in Google Scholar

Reuveny, R., (2000), The Trade and Conflict Debate: A Survey of Theory, Evidence and Future Research, Peace Economics, Peace Science and Public Policy, vol. 6, no. 1, DOI 10.2202/1554-8597.1030.Search in Google Scholar

Santos-Paulino, A.U., Squicciarini, M., Fan, P., (2014), Foreign Direct Investment, R&D Mobility and the New Economic Geography: A Survey, The World Economy, vol. 37, no. 12, pp. 1692–1715.10.1111/twec.12208Search in Google Scholar

Shin, R.W., (1998), Implementation of Science and Technology Policies for Global Competition: Korea’s Electronics and Telecommunications Industries, Journal of International Development, vol. 10, no. 6, pp. 715–731.10.1002/(SICI)1099-1328(1998090)10:6<715::AID-JID529>3.0.CO;2-RSearch in Google Scholar

Sriram, J., (2015), A Cannon yet to Fire – Not a Single Big Ticket Proposal, The Hindu, December 13, http://www.thehindu.com/business/Economy/defence-manufacturing-in-india-after-relaxing-fdi-norms/article7983617.ece.Search in Google Scholar

Stewart, F., (1991), A Note on ‘Strategic’ Trade Theory and the South, Journal of International Development, vol. 3, no. 5, pp. 467–484.10.1057/9780230375949_5Search in Google Scholar

Tomaru, Y., Saito, M., (2010), Mixed Oligopoly, Privatization and Subsidization in an Endogenous Timing Framework, The Manchester School, vol. 78, no. 1, pp. 41–59.10.1111/j.1467-9957.2009.02127.xSearch in Google Scholar

White, M.D., (1996), Mixed Oligopoly, Privatization and Subsidization, Economics Letters, vol. 53, no. 2, pp. 189–195.10.1016/S0165-1765(96)00916-0Search in Google Scholar

Yap, Y.J., Luckraz, S., Tey, S.K., (2014), Long-Term Research and Development Incentives in a Dynamic Cournot Duopoly, Economic Modelling, vol. 39, pp. 8–18.10.1016/j.econmod.2014.02.020Search in Google Scholar

Zhu, L., Jeon, B.N., (2007), International R&D Spillovers: Trade, FDI, and Information Technology as Spillover Channels, Review of International Economics, vol. 15, no. 5, pp. 955–976.10.1111/j.1467-9396.2007.00691.xSearch in Google Scholar

Published Online: 2016-6-20

Published in Print: 2016-8-1

You are currently not able to access this content.

Articles in the same Issue

https://doi.org/10.1515/peps-2016-0007

Keywords for this article

mixed oligopoly; R&D; spillovers; cost reduction; import tariffs; defense sector