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On the Foundation of Monopoly in Bilateral Exchange

Author

Listed:
  • Francesca Busetto
  • Giulio Codognato
  • Sayantan Ghosal
  • Damiano Turchet
Abstract
We address the problem of monopoly in general equilibrium in a mixed version of a monopolistic two-commodity exchange economy where the monopolist, represented as an atom, is endowed with one commodity and "small traders," represented by an atomless part, are endowed only with the other. We provide a theoretical foundation of the monopoly solution in this bilateral framework through a formalization of an explicit trading process inspired by Pareto (1896) for an exchange economy with a finite number of commodities. Then, we provide a game theoretical foundation of our monopoly solution through a two-stage reformulation of our model. This allows us to prove that the set of the allocations corresponding to a monopoly equilibrium and the set of the allocations corresponding to a subgame perfect equilibrium of the two-stage game coincide. Finally, we give the conditions under which our monopoly solution coincides with that defined by Kats (1974) and those, more restrictive, under which it has the geometric characterization proposed by Schydlowsky and Siamwalla (1966). Moreover, we establish the formal relationships between our concept of a monopoly equilibrium and that proposed by Pareto (1896), by redefining the latter in terms of our bilateral exchange setting.

Suggested Citation

  • Francesca Busetto & Giulio Codognato & Sayantan Ghosal & Damiano Turchet, 2021. "On the Foundation of Monopoly in Bilateral Exchange," Working Papers 2021_04, Business School - Economics, University of Glasgow.
    • Handle: RePEc:gla:glaewp:2021_04
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    References listed on IDEAS

    as
    1. Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan, 2008. "Cournot-Walras Equilibrium as a Subgame Perfect Equilibrium," The Warwick Economics Research Paper Series (TWERPS) 837, University of Warwick, Department of Economics.
    2. Francesca Busetto & Giulio Codognato & Sayantan Ghosal & Ludovic Julien & Simone Tonin, 2020. "Existence and optimality of Cournot–Nash equilibria in a bilateral oligopoly with atoms and an atomless part," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 933-951, December.
    3. Amoz Kats, 1974. "Monopolistic trading economies: A case of governmental control," Public Choice, Springer, vol. 20(1), pages 17-32, December.
    4. Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan, 2011. "Noncooperative oligopoly in markets with a continuum of traders," Games and Economic Behavior, Elsevier, vol. 72(1), pages 38-45, May.
    5. Dreze, Jacques H. & Gabszewicz, Jean Jaskold & Postlewaite, Andrew, 1977. "Disadvantageous monopolies and disadvantageous endowments," Journal of Economic Theory, Elsevier, vol. 16(1), pages 116-121, October.
    6. Okuno, Masahiro & Postlewaite, Andrew & Roberts, John, 1980. "Oligopoly and Competition in Large Markets," American Economic Review, American Economic Association, vol. 70(1), pages 22-31, March.
    7. Codognato, Giulio & Ghosal, Sayantan, 2000. "Cournot-Nash equilibria in limit exchange economies with complete markets and consistent prices," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 39-53, August.
    8. Gavin C. Reid, 1979. "Forchheimer on Partial Monopoly," History of Political Economy, Duke University Press, vol. 11(2), pages 303-308, Summer.
    9. Daniel M. Schydlowsky & Ammar Siamwalla, 1966. "Monopoly Under General Equilibrium: A Geometric Exercise," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 80(1), pages 147-153.
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    11. David M. Kreps, 2012. "Microeconomic Foundations I: Choice and Competitive Markets," Economics Books, Princeton University Press, edition 1, volume 1, number 9890.
    12. Greenberg, J. & Shitovitz, B., 1977. "Advantageous monopolies," Journal of Economic Theory, Elsevier, vol. 16(2), pages 394-402, December.
    13. Sahi, Siddhartha & Yao, Shuntian, 1989. "The non-cooperative equilibria of a trading economy with complete markets and consistent prices," Journal of Mathematical Economics, Elsevier, vol. 18(4), pages 325-346, September.
    14. Edgeworth, Francis Ysidro, 1881. "Mathematical Psychics," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number edgeworth1881.
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    More about this item

    JEL classification:

    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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