IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/hal-03587415.html
   My bibliography  Save this paper

Doubling Back on Double Marginalization

Author

Listed:
  • Laurent Linnemer

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique)

Abstract

"Double marginalization" and "Elimination of Double marginalization" are catch-phrases commonly used in the IO literature. In this note, I trace back the origin of the idea to Chapter IX, on complementary goods monopolies, of Cournot (1838). Through the years Cournot's contribution remained a reference but ended being viewed as a special case of the bilateral monopoly model. Yet, it is worth wondering why the most cited paper on this issue is nowadays Spengler (1950) which contains only an informal treatment of the question. In addition to retracing the origin of the idea, I emphasize the elegant proof of Cournot for the simultaneous game and extend it to the sequential game. I also show that prices are usually higher in the sequential game but that they could be lower if demand is very convex.

Suggested Citation

  • Laurent Linnemer, 2022. "Doubling Back on Double Marginalization," Working Papers hal-03587415, HAL.
    • Handle: RePEc:hal:wpaper:hal-03587415
    Note: View the original document on HAL open archive server: https://hal.science/hal-03587415
    as

    Download full text from publisher

    File URL: https://hal.science/hal-03587415/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Claude d'Aspremont & Rodolphe Dos Santos Ferreira & Louis-André Gérard-Varet, 2007. "Competition For Market Share Or For Market Size: Oligopolistic Equilibria With Varying Competitive Toughness," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(3), pages 761-784, August.
    2. Patrick Rey & Jean Tirole, 2019. "Price Caps as Welfare-Enhancing Coopetition," Journal of Political Economy, University of Chicago Press, vol. 127(6), pages 3018-3069.
    3. Bittlingmayer, George, 1983. "A Model of Vertical Restriction and Equilibrium in Retailing," The Journal of Business, University of Chicago Press, vol. 56(4), pages 477-496, October.
    4. Abiru, Masahiro, 1988. "Vertical Integration, Variable Proportions and Successive Oligopolies," Journal of Industrial Economics, Wiley Blackwell, vol. 36(3), pages 315-325, March.
    5. Vernon, John M & Graham, Daniel A, 1971. "Profitability of Monopolization by Vertical Integration," Journal of Political Economy, University of Chicago Press, vol. 79(4), pages 924-925, July-Aug..
    6. Salinger, Michael A, 1991. "Vertical Mergers in Multi-product Industries and Edgeworth's Paradox of Taxation," Journal of Industrial Economics, Wiley Blackwell, vol. 39(5), pages 545-556, September.
    7. Walter Adams, 1953. "Competition, Monopoly and Countervailing Power," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 67(4), pages 469-492.
    8. Gabszewicz, Jean & Sonnac, Nathalie & Wauthy, Xavier, 2001. "On price competition with complementary goods," Economics Letters, Elsevier, vol. 70(3), pages 431-437, March.
    9. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, December.
    10. Carl Shapiro, 2001. "Navigating the Patent Thicket: Cross Licenses, Patent Pools, and Standard Setting," NBER Chapters, in: Innovation Policy and the Economy, Volume 1, pages 119-150, National Bureau of Economic Research, Inc.
    11. McGee, John S & Bassett, Lowell R, 1976. "Vertical Integration Revisited," Journal of Law and Economics, University of Chicago Press, vol. 19(1), pages 17-38, April.
    12. Robert B. Ekelund Jr & Robert F. Hébert, 2002. "Retrospectives: The Origins of Neoclassical Microeconomics," Journal of Economic Perspectives, American Economic Association, vol. 16(3), pages 197-215, Summer.
    13. Joseph J. Spengler, 1950. "Vertical Integration and Antitrust Policy," Journal of Political Economy, University of Chicago Press, vol. 58, pages 347-347.
    14. Choné, Philippe & Linnemer, Laurent, 2020. "Linear demand systems for differentiated goods: Overview and user’s guide," International Journal of Industrial Organization, Elsevier, vol. 73(C).
    15. Irving Fisher, 1898. "Cournot and Mathematical Economics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 12(2), pages 119-138.
    16. Economides, Nicholas, 1989. "Desirability of Compatibility in the Absence of Network Externalities," American Economic Review, American Economic Association, vol. 79(5), pages 1165-1181, December.
    17. Feinberg, Yossi & Kamien, Morton I., 2001. "Highway robbery: complementary monopoly and the hold-up problem," International Journal of Industrial Organization, Elsevier, vol. 19(10), pages 1603-1621, December.
    18. Karni, Edi & Chakrabarti, Subir K., 1997. "Political structure, taxes, and trade," Journal of Public Economics, Elsevier, vol. 64(2), pages 241-258, May.
    19. William Fellner, 1947. "Prices and Wages under Bilateral Monopoly," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 61(4), pages 503-532.
    20. A. C. Hoffman, 1940. "Changing Organization of Agricultural Markets," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 22(1), pages 162-172.
    21. Josh Lerner & Jean Tirole, 2004. "Efficient Patent Pools," American Economic Review, American Economic Association, vol. 94(3), pages 691-711, June.
    22. Mathewson, G F & Winter, R A, 1983. "Vertical Integration by Contractual Restraints in Spatial Markets," The Journal of Business, University of Chicago Press, vol. 56(4), pages 497-517, October.
    23. Robert W. Dimand, 1995. "Cournot, Bertrand, and Cherriman," History of Political Economy, Duke University Press, vol. 27(3), pages 563-578, Fall.
    24. Anderson, Simon P. & Loertscher, Simon & Schneider, Yves, 2010. "The ABC of complementary products mergers," Economics Letters, Elsevier, vol. 106(3), pages 212-215, March.
    25. Economides, Nicholas & Salop, Steven C, 1992. "Competition and Integration among Complements, and Network Market Structure," Journal of Industrial Economics, Wiley Blackwell, vol. 40(1), pages 105-123, March.
    26. Greenhut, M L & Ohta, H, 1976. "Related Market Conditions and Interindustrial Mergers," American Economic Review, American Economic Association, vol. 66(3), pages 267-277, June.
    27. Perry, Martin K., 1989. "Vertical integration: Determinants and effects," Handbook of Industrial Organization, in: R. Schmalensee & R. Willig (ed.), Handbook of Industrial Organization, edition 1, volume 1, chapter 4, pages 183-255, Elsevier.
    28. Henry L. Moore, 1906. "Paradoxes of Competition," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 20(2), pages 211-230.
    29. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    30. G.F. Mathewson & R.A. Winter, 1984. "An Economic Theory of Vertical Restraints," RAND Journal of Economics, The RAND Corporation, vol. 15(1), pages 27-38, Spring.
    31. Katz, Michael L., 1989. "Vertical contractual relations," Handbook of Industrial Organization, in: R. Schmalensee & R. Willig (ed.), Handbook of Industrial Organization, edition 1, volume 1, chapter 11, pages 655-721, Elsevier.
    32. Gerhard Tintner, 1939. "The Problem of Bilateral Monopoly: A Note," Journal of Political Economy, University of Chicago Press, vol. 47, pages 263-263.
    33. Rey, Patrick & Tirole, Jean, 1986. "The Logic of Vertical Restraints," American Economic Review, American Economic Association, vol. 76(5), pages 921-939, December.
    34. Jean Magnan de Bornier, 1992. "The “Cournot-Bertrand Debate”: A Historical Perspective," History of Political Economy, Duke University Press, vol. 24(3), pages 623-656, Fall.
    35. C. D. Calsoyas, 1950. "The Mathematical Theory of Monopoly in 1839: Charles Ellet, Jr," Journal of Political Economy, University of Chicago Press, vol. 58, pages 162-162.
    36. Margaret E. Slade, 2021. "Vertical Mergers: A Survey of Ex Post Evidence and Ex Ante Evaluation Methods," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 58(4), pages 493-511, June.
    37. George J. Stigler, 1940. "Notes on the Theory of Duopoly," Journal of Political Economy, University of Chicago Press, vol. 48, pages 521-521.
    38. Perry, Martin K, 1978. "Related Market Conditions and Interindustrial Mergers: Comment," American Economic Review, American Economic Association, vol. 68(1), pages 221-224, March.
    39. Didier Laussel, 2008. "Buying Back Subcontractors: The Strategic Limits of Backward Integration," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 17(4), pages 895-911, December.
    40. Hugo Sonnenschein, 1968. "The Dual of Duopoly Is Complementary Monopoly: or, Two of Cournot's Theories Are One," Journal of Political Economy, University of Chicago Press, vol. 76, pages 316-316.
    41. Mathewson, G F & Winter, R A, 1983. "The Incentives for Resale Price Maintenance under Imperfect Information," Economic Inquiry, Western Economic Association International, vol. 21(3), pages 337-348, July.
    42. E. H. Chamberlin, 1929. "Duopoly: Value Where Sellers Are Few," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 44(1), pages 63-100.
    43. Gaudet, Gerard & Salant, Stephen W., 1992. "Mergers of producers of perfect complements competing in price," Economics Letters, Elsevier, vol. 39(3), pages 359-364, July.
    44. Daniel F. Spulber, 2017. "Complementary Monopolies and Bargaining," Journal of Law and Economics, University of Chicago Press, vol. 60(1), pages 29-74.
    45. Patrick Bolton & Giacomo Bonanno, 1988. "Vertical Restraints in a Model of Vertical Differentiation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 103(3), pages 555-570.
    46. Henry L. Moore, 1905. "The Personality of Antoine Augustin Cournot," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 19(3), pages 370-399.
    47. A. P. Lerner, 1934. "The Concept of Monopoly and the Measurement of Monopoly Power," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 1(3), pages 157-175.
    48. Fernando Luco & Guillermo Marshall, 2020. "The Competitive Impact of Vertical Integration by Multiproduct Firms," American Economic Review, American Economic Association, vol. 110(7), pages 2041-2064, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Van Cayseele Patrick & Reynaerts Jo, 2011. "Complementary Platforms," Review of Network Economics, De Gruyter, vol. 10(1), pages 1-33, March.
    2. Sexton, Richard J., 1991. "Game Theory: A Review With Applications To Vertical Control In Agricultural Markets," Working Papers 225865, University of California, Davis, Department of Agricultural and Resource Economics.
    3. Alexei Alexandrov & Russell Pittman & Olga Ukhaneva, 2018. "Pricing of Complements in the U.S. Freight Railroads: Cournot Versus Coase," EAG Discussions Papers 201801, Department of Justice, Antitrust Division.
    4. Sexton, Richard J., 1993. "Noncooperative Game Theory: A Review with Potential Applications to Agricultural Markets," Research Reports 25183, University of Connecticut, Food Marketing Policy Center.
    5. Spulber, Daniel F., 2016. "Patent licensing and bargaining with innovative complements and substitutes," Research in Economics, Elsevier, vol. 70(4), pages 693-713.
    6. Hattori Keisuke & Lin Ming-Hsin, 2011. "Alliance Partner Choice in Markets with Vertical and Horizontal Externalities," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-27, June.
    7. Dertwinkel-Kalt, Markus & Wey, Christian, 2021. "Multi-Product Pricing and Minimum Resale Price Maintenance," VfS Annual Conference 2021 (Virtual Conference): Climate Economics 242338, Verein für Socialpolitik / German Economic Association.
    8. Matsushima, Noriaki & Mizuno, Tomomichi, 2013. "Vertical separation as a defense against strong suppliers," European Journal of Operational Research, Elsevier, vol. 228(1), pages 208-216.
    9. Drew Fudenberg, 2015. "Tirole's Industrial Regulation and Organization Legacy in Economics," Scandinavian Journal of Economics, Wiley Blackwell, vol. 117(3), pages 771-800, July.
    10. Gupta, Barnali & Heywood, John S. & Pal, Debashis, 1995. "Strategic behavior downstream and the incentive to integrate: A spatial model with delivered pricing," International Journal of Industrial Organization, Elsevier, vol. 13(3), pages 327-334, September.
    11. Alexandrov, Alexei & Pittman, Russell & Ukhaneva, Olga, 2017. "Royalty stacking in the U.S. freight railroads: Cournot vs. Coase," MPRA Paper 78249, University Library of Munich, Germany.
    12. Fronmueller, M. P. & Reed, R., 1996. "The competitive advantage potential of vertical integration," Omega, Elsevier, vol. 24(6), pages 715-726, December.
    13. Dertwinkel-Kalt, Markus & Wey, Christian, 2023. "Resale price maintenance in a successive monopoly model," DICE Discussion Papers 395, Heinrich Heine University Düsseldorf, Düsseldorf Institute for Competition Economics (DICE).
    14. Barick Chung & Eric Rasmusen, 2008. "Price Discrimination between Retailers with and without Market Power," Working Papers 2008-14, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy.
    15. Michael A. Salinger, 2021. "The New Vertical Merger Guidelines: Muddying the Waters," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 59(2), pages 161-176, September.
    16. Donna, Javier D. & Pereira, Pedro & Trindade, Andre & Yoshida, Renan C., 2020. "Direct-to-Consumer Sales by Manufacturers and Bargaining," MPRA Paper 105773, University Library of Munich, Germany.
    17. Didier Laussel & Joana Resende, 2020. "Complementary Monopolies with asymmetric information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 943-981, November.
    18. Giorgio Zanarone, 2009. "Vertical Restraints and the Law: Evidence from Automobile Franchising," Journal of Law and Economics, University of Chicago Press, vol. 52(4), pages 691-700, November.
    19. Schuett, Florian, 2012. "Field-of-use restrictions in licensing agreements," International Journal of Industrial Organization, Elsevier, vol. 30(5), pages 403-416.
    20. Sofia Berto Villas-Boas, 2007. "Vertical Relationships between Manufacturers and Retailers: Inference with Limited Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(2), pages 625-652.

    More about this item

    Keywords

    JEL codes: B160; B210; K210; L120; L13; L420; Cournot; Complements; Successive monopolies;
    All these keywords.

    JEL classification:

    • B16 - Schools of Economic Thought and Methodology - - History of Economic Thought through 1925 - - - Quantitative and Mathematical
    • B21 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Microeconomics
    • K21 - Law and Economics - - Regulation and Business Law - - - Antitrust Law
    • L12 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Monopoly; Monopolization Strategies
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • L42 - Industrial Organization - - Antitrust Issues and Policies - - - Vertical Restraints; Resale Price Maintenance; Quantity Discounts

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:hal-03587415. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.