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Multiproduct Pricing Made Simple

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  • Armstrong, Mark
  • Vickers, John

Abstract

We study multiproduct firms in the contexts of unregulated monopoly, regulated monopoly and Cournot oligopoly. Using the concept of consumer surplus as a function of quantities (rather than prices), we present simple formulas for optimal prices and show that Cournot equilibrium exists and corresponds to a Ramsey optimum. We then discuss a tractable class of preferences that involve a generalized form of homotheticity. Profit-maximizing quantities are proportional to efficient quantities. We discuss optimal monopoly regulation when the firm has private information about its cost vector, and find situations where optimal regulation leaves relative price decisions to the firm.

Suggested Citation

  • Armstrong, Mark & Vickers, John, 2016. "Multiproduct Pricing Made Simple," CEPR Discussion Papers 11692, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:11692
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    Cited by:

    1. Mark Armstrong & John Vickers, 2023. "Multiproduct Cost Pass-Through: Edgeworth’s Paradox Revisited," Journal of Political Economy, University of Chicago Press, vol. 131(10), pages 2645-2665.
    2. Thomas Favory, 2020. "Multiproduct Firms and Discrete Choice Models of Demand: Existence and Uniqueness of the Bertrand-Nash Equilibrium," Economics Discussion / Working Papers 20-24, The University of Western Australia, Department of Economics.
    3. Cole, Matthew T. & Eckel, Carsten, 2018. "Tariffs and markups in retailing," Journal of International Economics, Elsevier, vol. 113(C), pages 139-153.
    4. Stahl, Konrad & Legros, Patrick, 2019. "Local Search Markets and External Competition," CEPR Discussion Papers 13764, C.E.P.R. Discussion Papers.
    5. Yongmin Chen & Jianpei Li & Marius Schwartz, 2021. "Competitive differential pricing," RAND Journal of Economics, RAND Corporation, vol. 52(1), pages 100-124, March.
    6. Leal, Mariel & Garcia, Arturo & Lee, Sang-Ho, 2020. "Strategic CSR and merger in multiproduct mixed markets with state-holding corporation," MPRA Paper 102351, University Library of Munich, Germany, revised 10 Aug 2020.
    7. Adachi, Takanori, 2023. "A sufficient statistics approach for welfare analysis of oligopolistic third‐degree price discrimination," International Journal of Industrial Organization, Elsevier, vol. 86(C).
    8. Genakos, C. & Grey, F. & Ritz, R., 2020. "Generalized linear competition: From pass-through to policy," Cambridge Working Papers in Economics 2078, Faculty of Economics, University of Cambridge.
    9. Inderst, Roman & Griem, Fabian & Schaffer, Greg, 2022. "Tying under Double-Marginalization," CEPR Discussion Papers 17314, C.E.P.R. Discussion Papers.
    10. Nocke, Volker & Schutz, Nicolas, 2018. "An Aggregative Games Approach to Merger Analysis in Multiproduct-Firm Oligopoly," CEPR Discussion Papers 12905, C.E.P.R. Discussion Papers.
    11. Aguirre, Iñaki, 2017. "Cournot Oligopoly, Price Discrimination and Total Output," MPRA Paper 80166, University Library of Munich, Germany.
    12. Ratula Chakraborty, 2018. "Do Retailers Manipulate Prices to Favour Private Label over Brands?," Working Paper series, University of East Anglia, Centre for Competition Policy (CCP) 2018-02, Centre for Competition Policy, University of East Anglia, Norwich, UK..
    13. Paolo Bertoletti, 2024. "Ramsey pricing: a simple example of a subordinate commodity," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 23(2), pages 241-247, May.
    14. Justin P. Johnson & Andrew Rhodes, 2021. "Multiproduct mergers and quality competition," RAND Journal of Economics, RAND Corporation, vol. 52(3), pages 633-661, September.
    15. Anna D'Annunzio & Antonio Russo, 2022. "Ad Valorem Taxation in a Multiproduct Monopoly," CESifo Working Paper Series 9881, CESifo.
    16. Stefanie Bossard & Armin Schmutzler, 2021. "Selecting valuation distributions: non-price decisions of multi-product firms," ECON - Working Papers 396, Department of Economics - University of Zurich.
    17. Etro, Federico, 2016. "Research in economics and industrial organization," Research in Economics, Elsevier, vol. 70(4), pages 511-517.
    18. Leal, Mariel & García, Arturo & Lee, Sang-Ho, 2021. "Strategic CSR and merger decisions in multiproduct mixed markets with state-holding corporation," International Review of Economics & Finance, Elsevier, vol. 72(C), pages 319-333.
    19. Paul Belleflamme & Eric Toulemonde, 2016. "Tax Incidence on Competing Two-Sided Platforms: Lucky Break or Double Jeopardy," CESifo Working Paper Series 5882, CESifo.
    20. Takanori ADACHI & Michal Fabinger, 2021. "Pass-Through and the Welfare Effects of Taxation under Imperfect Competition: A General Analysis," Discussion papers e-21-003, Graduate School of Economics , Kyoto University.
    21. Arturo García & Mariel Leal & Sang‐Ho Lee, 2020. "Welfare‐improving cooperation with a consumer‐friendly multiproduct corporation," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 41(7), pages 1144-1155, October.
    22. Garcia, Arturo & Leal, Mariel & Lee, Sang-Ho, 2020. "Merger incentive and strategic CSR by a multiproduct corporation," MPRA Paper 98830, University Library of Munich, Germany.

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    More about this item

    Keywords

    Multiproduct pricing; Homothetic preferences; Cournot oligopoly; Monopoly regulation; Ramsey pricing; Cost passthrough; Multidimensional screening;
    All these keywords.

    JEL classification:

    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • 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
    • L51 - Industrial Organization - - Regulation and Industrial Policy - - - Economics of Regulation

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