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Export Restraints in a Model of Trade with Capital Accumulation

  • G. Calzolari
  • L. Lambertini

This paper examines the impact of voluntary export restraints (VERs) in an international duopoly modelled as a differential game. We employ two well known capital accumulation dynamics for firms, due to Herlove and Arrow and to Ramsey, respectively. First we investigate Cournot behavour, showing that, in both models, a VERs cannot ne “voluntarily” employed by the foreign firms. Our analysis therefore suggests that the empirical observation of VERs corresponds to their use either as coordinating or as quasi-collusive devices in markets where firms are price setters and sales are not capacity-constrained. This is confirmed by our analysis of price competition. The Bertrand steady state of the Solow-Nerlove-Arrow model coincides with the Cournot equilibrium, and therefore the foreign firm cannot be expected to voluntarily adopt an export restraint. However, the opposite holds in the case of price behavior in the ramsey setting, where the adoption of anexport restraint may increase the profits of both firms.

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Paper provided by Dipartimento Scienze Economiche, Universita' di Bologna in its series Working Papers with number 420.

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Date of creation: 2001
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Handle: RePEc:bol:bodewp:420
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  1. Engelbert J. Dockner & Alfred A. Haug, 1991. "The Closed-Loop Motive for Voluntary Export Restraints," Canadian Journal of Economics, Canadian Economics Association, vol. 24(3), pages 679-85, August.
  2. Fershtman, C. & Kamien, M.I., 1988. "Turnpike Properties In A Finite Horizon Differential Game: Dynamic Duopoly With Sticky Prices," Papers 4-88, Tel Aviv.
  3. Kemp, Murray C. & Van Long, Ngo & Shimomura, Koji, 2001. "A differential game model of tariff war," Japan and the World Economy, Elsevier, vol. 13(3), pages 279-298, August.
  4. R. Cellini & L. Lambertini, 2001. "Differential Oligopoly Games where the Closed-Loop Memoryless and Open-Loop Equilibria Coincide," Working Papers 402, Dipartimento Scienze Economiche, Universita' di Bologna.
  5. Driskill, Robert A. & McCafferty, Stephen, 1989. "Dynamic duopoly with adjustment costs: A differential game approach," Journal of Economic Theory, Elsevier, vol. 49(2), pages 324-338, December.
  6. Krishna, Kala, 1989. "Trade restrictions as facilitating practices," Journal of International Economics, Elsevier, vol. 26(3-4), pages 251-270, May.
  7. Brander, James A., 1995. "Strategic trade policy," Handbook of International Economics, in: G. M. Grossman & K. Rogoff (ed.), Handbook of International Economics, edition 1, volume 3, chapter 27, pages 1395-1455 Elsevier.
  8. Pomfret, Richard, 1989. " The Economics of Voluntary Export Restraint Agreements," Journal of Economic Surveys, Wiley Blackwell, vol. 3(3), pages 199-211.
  9. R. Cellini & L. Lambertini, 2000. "Non-Linear Market Demand and Capital Accumulation in A Differential Oligopoly Game," Working Papers 372, Dipartimento Scienze Economiche, Universita' di Bologna.
  10. James Levinsohn & Steven Berry & Ariel Pakes, 1999. "Voluntary Export Restraints on Automobiles: Evaluating a Trade Policy," American Economic Review, American Economic Association, vol. 89(3), pages 400-430, June.
  11. Herguera, Inigo & Kujal, Praveen & Petrakis, Emmanuel, 2000. "Quantity restrictions and endogenous quality choice," International Journal of Industrial Organization, Elsevier, vol. 18(8), pages 1259-1277, December.
  12. Kotaro Suzumura & Jota Ishikawa, 1993. "Voluntary Trade Restraints and Economic Welfare," Discussion Paper Series a272, Institute of Economic Research, Hitotsubashi University.
  13. David M. Kreps & Jose A. Scheinkman, 1983. "Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 326-337, Autumn.
  14. Richard Harris, 1984. "Why Voluntary Export Restraints are 'Voluntary'," Working Papers 559, Queen's University, Department of Economics.
  15. Miravete, E.J., 1997. "Time-Consistent Protection With Learning by Doing," UFAE and IAE Working Papers 395.97, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  16. Dockner, Engelbert J. & Haug, Alfred A., 1990. "Tariffs and quotas under dynamic duopolistic competition," Journal of International Economics, Elsevier, vol. 29(1-2), pages 147-159, August.
  17. Cellini, Roberto & Lambertini, Luca, 1998. "A Dynamic Model of Differentiated Oligopoly with Capital Accumulation," Journal of Economic Theory, Elsevier, vol. 83(1), pages 145-155, November.
  18. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, December.
  19. Cheng, Leonard K, 1987. "Optimal Trade and Technology Policies: Dynamic Linkages," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(3), pages 757-76, October.
  20. Robert Driskill & Stephen McCafferty, 1989. "Dynamic Duopoly with Output Adjustment Costs in International Markets: Taking the Conjecture out of Conjectural Variations," NBER Chapters, in: Trade Policies for International Competitiveness, pages 125-144 National Bureau of Economic Research, Inc.
  21. Tsutsui, Shunichi & Mino, Kazuo, 1990. "Nonlinear strategies in dynamic duopolistic competition with sticky prices," Journal of Economic Theory, Elsevier, vol. 52(1), pages 136-161, October.
  22. Reynolds, Stanley S, 1987. "Capacity Investment, Preemption and Commitment in an Infinite Horizon Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(1), pages 69-88, February.
  23. Fershtman, Chaim & Kamien, Morton I, 1987. "Dynamic Duopolistic Competition with Sticky Prices," Econometrica, Econometric Society, vol. 55(5), pages 1151-64, September.
  24. A. Michael Spence, 1979. "Investment Strategy and Growth in a New Market," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 1-19, Spring.
  25. Chaim Fershtman & Eitan Muller, 1983. "Capital Accumulation Games of Infinite Duration," Discussion Papers 553, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  26. Nirvikar Singh & Xavier Vives, 1984. "Price and Quantity Competition in a Differentiated Duopoly," RAND Journal of Economics, The RAND Corporation, vol. 15(4), pages 546-554, Winter.
  27. Chao-Cheng Mai & Hong Hwang, 1988. "Why Voluntary Export Restraints Are Voluntary: An Extension," Canadian Journal of Economics, Canadian Economics Association, vol. 21(4), pages 877-82, November.
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