Journal of Economics

, Volume 126, Issue 1, pp 75–93 | Cite as

Comparing welfare and profit in quantity and price competition within Stackelberg mixed duopolies

  • Kosuke Hirose
  • Toshihiro Matsumura


We compare welfare and profits under price and quantity competition in Stackelberg mixed duopolies. Under public leadership, price competition always yields greater profits and welfare than quantity competition. By contrast, under private leadership, the result depends on the nationality of the private firm. When the private firm is domestic (foreign), welfare is greater under quantity (price) competition. However, private firms always earn more under price competition. Introducing the nonnegative profit constraint affects welfare ranking but not profit ranking. These results indicate that profit ranking is fairly robust to the time structure in Stackelberg mixed duopolies, but welfare ranking is not.


Public leadership Private leadership Mixed markets Cournot–Bertrand comparison 

JEL Classification

H42 H44 L13 L32 



We are grateful to Ming Hsin Lin, Noriaki Matsushima, Masaki Nakabayashi, Yoshihiro Tomaru, and the participants of seminars at The University of Tokyo for their helpful comments. We are indebted to two anonymous referees for their valuable and constructive suggestions. We acknowledge financial support from JSPS KAKENHI Grant Numbers (15K03347, 16J04589) and the Zengin Foundation for Studies on Economics and Finance. Needless to say, we are responsible for any remaining errors.


  1. Bárcena-Ruiz JC (2007) Endogenous timing in a mixed duopoly: price competition. J Econ 91(3):263–272Google Scholar
  2. Bárcena-Ruiz JC, Garzón MB (2005a) Economic integration and privatization under diseconomies of scale. Eur J Polit Econ 21(1):247–267Google Scholar
  3. Bárcena-Ruiz JC, Garzón MB (2005b) International trade and strategic privatization. Revi Dev Econ 9(4):502–513Google Scholar
  4. Boyer M, Moreaux M (1987) On Stackelberg equilibria with differentiated products: the critical role of the strategy space. J Ind Econ 36(2):217–230Google Scholar
  5. Cato S, Matsumura T (2015) Optimal privatization and trade policies with endogenous market structure. Econ Rec 91:309–323Google Scholar
  6. Chen TL (2017) Privatization and efficiency: a mixed oligopoly approach. J Econ 120(3):251–268Google Scholar
  7. Chirco A, Colombo C, Scrimitore M (2014) Organizational structure and the choice of price versus quantity in a mixed duopoly. Jpn Econ Rev 65(4):521–542Google Scholar
  8. Chirco A, Scrimitore M (2013) Choosing price or quantity? The role of delegation and network externalities. Econ Lett 121(3):482–486Google Scholar
  9. Colombo S (2016) Mixed oligopolies and collusion. J Econ 118(2):167–184Google Scholar
  10. Corneo G, Jeanne O (1994) Oligopole mixte dans un marche commun. Annales d’Economie et de Statistique 33:73–90Google Scholar
  11. Dixit AK (1979) A model of duopoly suggesting a theory of entry barriers. Bell J Econ 10(1):20–32Google Scholar
  12. Estrin S, de Meza D (1995) Unnatural monopoly. J Public Econ 57(3):471–488Google Scholar
  13. Fjell K, Pal D (1996) A mixed oligopoly in the presence of foreign private firms. Can J Econ 29(3):737–743Google Scholar
  14. Fridman A (2017) Partial privatization in an exhaustible resource industry. J Econ.
  15. Gelves JA, Heywood JS (2013) Privatizing by merger: the case of an inefficient public leader. Int Rev Econ Finance 27:69–79Google Scholar
  16. Ghosh A, Mitra M (2010) Comparing Bertrand and Cournot in mixed markets. Econ Lett 109(2):72–74Google Scholar
  17. Han L, Ogawa H (2008) Economic integration and strategic privatization in an international mixed oligopoly. FinanzArchiv 64(3):352–363Google Scholar
  18. Haraguchi J, Matsumura T (2014) Price versus quantity in a mixed duopoly with foreign penetration. Res Econ 68(4):338–353Google Scholar
  19. Haraguchi J, Matsumura T (2016) Cournot-Bertrand comparison in a mixed oligopoly. J Econ 117(2):117–136Google Scholar
  20. Haraguchi J, Matsumura T (2018) Government-leading welfare-improving collusion. forthcoming. Int Rev Econo Finance.
  21. Horiuchi A, Sui QY (1993) Influence of the Japan Development Bank loans on corporate investment behavior. J Jpn Int Econ 7(4):441–465Google Scholar
  22. Ino H, Matsumura T (2010) What role should public enterprises play in free-entry markets? J Econ 101(3):213–230Google Scholar
  23. Ishida J, Matsushima N (2009) Should civil servants be restricted in wage bargaining? A mixed-duopoly approach. J Pub Econ 93(3–4):634–646Google Scholar
  24. Lee SH, Matsumura T, Sato S (2018) An analysis of entry-then-privatization model: welfare and policy implications. J Econ 123(1):71–88Google Scholar
  25. Lin MH, Matsumura T (2012) Presence of foreign investors in privatized firms and privatization policy. J Econ 107(1):71–80Google Scholar
  26. Matsumura T (1998) Partial privatization in mixed duopoly. J Pub Econ 70(3):473–483Google Scholar
  27. Matsumura T (2003a) Endogenous role in mixed markets: a two-production period model. South Econ J 70(2):403–413Google Scholar
  28. Matsumura T (2003b) Stackelberg mixed duopoly with a foreign competitor. Bull Econ Res 55(3):275–287Google Scholar
  29. Matsumura T, Ogawa A (2010) On the robustness of private leadership in mixed duopoly. Aust Econ Pap 49(2):149–160Google Scholar
  30. Matsumura T, Ogawa A (2012) Price versus quantity in a mixed duopoly. Econ Lett 116(2):174–177Google Scholar
  31. Matsumura T, Ogawa A (2017) Inefficient but robust public leadership. J Ind Compet Trade 17(4):387–398Google Scholar
  32. Matsumura T, Okamura M (2015) Competition and privatization policies revisited: The payoff interdependence approach. J Econ 116(2):137–150Google Scholar
  33. Matsumura T, Sunada T (2013) Advertising competition in a mixed oligopoly. Econ Lett 119(2):183–185Google Scholar
  34. Merrill W, Schneider N (1966) Government firms in oligopoly industries: a short-run analysis. Quart J Econ 80(3):400–412Google Scholar
  35. Pal D (1998) Endogenous timing in a mixed oligopoly. Econ Lett 61(2):181–185Google Scholar
  36. Scrimitore M (2013) Price or quantity?: the strategic choice of subsidized firms in a mixed duopoly. Econ Lett 118(2):337–341Google Scholar
  37. Scrimitore M (2014) Profitability under commitment in Cournot and Bertrand mixed markets. J Inst Theor Econ 170(4):684–703Google Scholar
  38. Shubik M, Levitan R (1980) Market structure and behavior. Harvard University Press, CambridgeGoogle Scholar
  39. Singh N, Vives X (1984) Price and quantity competition in a differentiated duopoly. RAND J Econ 15(4):546–554Google Scholar
  40. Vives X (1985) On the efficiency of Bertrand and Cournot equilibria with product differentiation. J Econ Theory 36:166–175Google Scholar
  41. Wang LFS, Lee JY (2013) Foreign penetration and undesirable competition. Econ Model 30(1):729–732Google Scholar
  42. Wang LFS, Mukherjee A (2012) Undesirable competition. Econ Lett 114(2):175–177Google Scholar
  43. Wang LFS, Tomaru Y (2015) The feasibility of privatization and foreign penetration. Int Rev Econ Finance 39:36–46Google Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Graduate School of EconomicsThe University of TokyoTokyoJapan
  2. 2.Institute of Social ScienceThe University of TokyoTokyoJapan

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