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Doubling Back on Double Marginalization

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  • Laurent Linnemer

    (CREST, ENSAE, Institut Polytechnique de Paris)

Abstract

“Double marginalization” and “Elimination of Double marginalization” are catch-phrases commonly used in the IO literature. In this article, I trace back the origin of the idea to Cournot (1838, Ch. IX) on complementary goods monopolies. 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 in J Polit Econ 58(4):347–352, 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," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 61(1), pages 1-19, August.
  • Handle: RePEc:kap:revind:v:61:y:2022:i:1:d:10.1007_s11151-022-09872-z
    DOI: 10.1007/s11151-022-09872-z
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    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, April.
    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(4), 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(2), 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(2), 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(4), 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(2), 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.
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    Cited by:

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    2. Nicolas Pasquier, 2024. "Decentralization and Consumer Welfare with Substitutes or Complements," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 64(3), pages 449-469, May.

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    More about this item

    Keywords

    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

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