IDEAS home Printed from
MyIDEAS: Login to save this article or follow this journal

Existence of equilibrium in the Helpman–Krugman model of international trade with imperfect competition

  • Lutz Arnold


Helpman and Krugman (Market structure and foreign trade. Increasing returns, imperfect competition, and the international economy. MIT Press, Cambridge, 1985 ) provide a synthesis of the traditional factor proportions theory of international trade and the theory of international trade due to the exploitation of scale economies in imperfectly competitive markets. They derive illuminating results about trade patterns and gains from trade, among other things, leaving unanswered the question of existence of equilibrium, however. The central significance of their characterization of properties of free trade equilibria with inter-industry and intra-industry trade calls for an analysis of existence of equilibrium. This is the object of the present paper. We prove the existence of equilibrium for the integrated multi-sector multi-factor Helpman–Krugman economy without national borders. Well-known conditions ensure that the world economy under free trade reproduces this equilibrium and thus establishes existence of a free trade equilibrium. Since an equilibrium of the integrated economy is not necessarily unique, the same holds true for a free trade equilibrium. Copyright Springer-Verlag 2013

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: Access to full text is restricted to subscribers.

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Springer in its journal Economic Theory.

Volume (Year): 52 (2013)
Issue (Month): 1 (January)
Pages: 237-270

in new window

Handle: RePEc:spr:joecth:v:52:y:2013:i:1:p:237-270
Contact details of provider: Web page:

Order Information: Web:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. John Roberts & Hugo Sonnenschein, 1976. "On the Foundations of the Theory of Monopolistic Competition," Discussion Papers 169, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Harris, Richard, 1984. "Applied General Equilibrium Analysis of Small Open Economies with Scale Economies and Imperfect Competition," American Economic Review, American Economic Association, vol. 74(5), pages 1016-32, December.
  3. Krugman, Paul, 1995. "Increasing returns, imperfect competition and the positive theory of international trade," Handbook of International Economics, in: G. M. Grossman & K. Rogoff (ed.), Handbook of International Economics, edition 1, volume 3, chapter 24, pages 1243-1277 Elsevier.
  4. Lutz Arnold, 2007. "A generalized multi-country endogenous growth model," International Economics and Economic Policy, Springer, vol. 4(1), pages 61-100, April.
  5. Kemp, Murray C. & Wan, Henry Jr., 1976. "An elementary proposition concerning the formation of customs unions," Journal of International Economics, Elsevier, vol. 6(1), pages 95-97, February.
  6. Helpman, Elhanan, 1981. "International trade in the presence of product differentiation, economies of scale and monopolistic competition : A Chamberlin-Heckscher-Ohlin approach," Journal of International Economics, Elsevier, vol. 11(3), pages 305-340, August.
  7. JASKOLD GABSZEWICZ, Jean & VIAL, Jean-Philippe, . "Oligopoly "Ã la Cournot" in a general equilibrium analysis," CORE Discussion Papers RP 106, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. Krugman, Paul R., 1979. "Increasing returns, monopolistic competition, and international trade," Journal of International Economics, Elsevier, vol. 9(4), pages 469-479, November.
  9. Yves Balasko & Mich Tvede, 2010. "General equilibrium without utility functions: how far to go?," Economic Theory, Springer, vol. 45(1), pages 201-225, October.
  10. Egbert Dierker & Hildegard Dierker & Birgit Grodal, 2003. "Cournot-Nash Competition in a General Equilibrium Model of International Trade," Discussion Papers 03-28, University of Copenhagen. Department of Economics.
  11. Paul Krugman, 1990. "Increasing Returns and Economic Geography," NBER Working Papers 3275, National Bureau of Economic Research, Inc.
  12. Ethier, Wilfred J, 1982. "National and International Returns to Scale in the Modern Theory of International Trade," American Economic Review, American Economic Association, vol. 72(3), pages 389-405, June.
  13. Fernando Alvarez & Robert E. Lucas, 2005. "General Equilibrium Analysis of the Eaton-Kortum Model of International Trade," NBER Working Papers 11764, National Bureau of Economic Research, Inc.
  14. Simon J. Evenett & Wolfgang Keller, 2002. "On Theories Explaining the Success of the Gravity Equation," Journal of Political Economy, University of Chicago Press, vol. 110(2), pages 281-316, April.
  15. Kiminiori Matsuyama, 1994. "Complementaries and Cumulative Processes In Models of Monopolistic Competition," Discussion Papers 1106, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  16. Kehoe, Timothy J. & Whalley, John, 1985. "Uniqueness of equilibrium in large-scale numerical general equilibrium models," Journal of Public Economics, Elsevier, vol. 28(2), pages 247-254, November.
  17. Oliver D. Hart, 1985. "Monopolistic Competition in the Spirit of Chamberlin: A General Model," Review of Economic Studies, Oxford University Press, vol. 52(4), pages 529-546.
  18. Timothy J. Kehoe, 1991. "Computation and multiplicity of equilibria," Working Papers 460, Federal Reserve Bank of Minneapolis.
  19. Krugman, Paul, 1980. "Scale Economies, Product Differentiation, and the Pattern of Trade," American Economic Review, American Economic Association, vol. 70(5), pages 950-59, December.
  20. Earl L. Grinols & Peri Silva, 2008. "Rules of Origin and Gains from Trade," Development Working Papers 249, Centro Studi Luca d\'Agliano, University of Milano.
  21. Camelia Bejan, 2008. "The objective of a privately owned firm under imperfect competition," Economic Theory, Springer, vol. 37(1), pages 99-118, October.
  22. Helpman, Elhanan, 1976. "Solutions of General Equilibrium Problems for a Trading World," Econometrica, Econometric Society, vol. 44(3), pages 547-59, May.
  23. Timothy J. Kehoe, 1985. "Multiplicity of Equilibria and Comparative Statics," The Quarterly Journal of Economics, Oxford University Press, vol. 100(1), pages 119-147.
  24. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, July.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:spr:joecth:v:52:y:2013:i:1:p:237-270. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla)

or (Christopher F Baum)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.