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Multiproduct Pricing Made Simple

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  • Armstrong, Mark
  • Vickers, John

Abstract

We study pricing by multiproduct firms in the context 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 present a tractable class of demand systems that involve a generalized form of homothetic preferences. As well as standard homothetic preferences, this class includes linear and logit demand. Within the class, profit-maximizing quantities are proportional to efficient quantities. We discuss cost-passthrough, including cases where optimal prices do not depend on other products' costs. Finally, we discuss optimal monopoly regulation when the firm has private information about its vector of marginal costs, and show that if the probability distribution over costs satisfies an independence property, then optimal regulation leaves relative price decisions to the firm.

Suggested Citation

  • Armstrong, Mark & Vickers, John, 2016. "Multiproduct Pricing Made Simple," MPRA Paper 68717, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:68717
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    References listed on IDEAS

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    1. Bliss, Christopher, 1988. "A Theory of Retail Pricing," Journal of Industrial Economics, Wiley Blackwell, vol. 36(4), pages 375-391, June.
    2. David Sappington, 1983. "Optimal Regulation of a Multiproduct Monopoly with Unknown Technological Capabilities," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 453-463, Autumn.
    3. De Fraja, Giovanni, 1996. "Product line competition in vertically differentiated markets," International Journal of Industrial Organization, Elsevier, vol. 14(3), pages 389-414, May.
    4. Jeremy Bulow & Paul Klemperer, 2012. "Regulated Prices, Rent Seeking, and Consumer Surplus," Journal of Political Economy, University of Chicago Press, vol. 120(1), pages 160-186.
    5. Bergstrom, Theodore C. & Varian, Hal R., 1985. "Two remarks on Cournot equilibria," Economics Letters, Elsevier, vol. 19(1), pages 5-8.
    6. Baumol, William J & Bradford, David F, 1970. "Optimal Departures from Marginal Cost Pricing," American Economic Review, American Economic Association, vol. 60(3), pages 265-283, June.
    7. Ricardo Alonso & Niko Matouschek, 2008. "Optimal Delegation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(1), pages 259-293.
    8. Rabah Amir & Jim Y. Jin & Gerald Pech & Michael Tröge, 2016. "Prices and Deadweight Loss in Multiproduct Monopoly," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 18(3), pages 346-362, June.
    9. Anderson, Simon P. & de Palma, Andre & Thisse, Jacques-Francois, 1988. "The CES and the logit : Two related models of heterogeneity," Regional Science and Urban Economics, Elsevier, vol. 18(1), pages 155-164, February.
    10. Loeb, Martin & Magat, Wesley A, 1979. "A Decentralized Method for Utility Regulation," Journal of Law and Economics, University of Chicago Press, vol. 22(2), pages 399-404, October.
    11. Walter Y. Oi, 1971. "A Disneyland Dilemma: Two-Part Tariffs for a Mickey Mouse Monopoly," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 85(1), pages 77-96.
    12. Slade, Margaret E, 1994. "What Does an Oligopoly Maximize?," Journal of Industrial Economics, Wiley Blackwell, vol. 42(1), pages 45-61, March.
    13. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    14. Johnson, Justin P. & Myatt, David P., 2015. "The properties of product line prices," International Journal of Industrial Organization, Elsevier, vol. 43(C), pages 182-188.
    15. Armstrong, Mark & Vickers, John, 2001. "Competitive Price Discrimination," RAND Journal of Economics, The RAND Corporation, vol. 32(4), pages 579-605, Winter.
    16. Volker Nocke & Nicolas Schutz, 2018. "Multiproduct‐Firm Oligopoly: An Aggregative Games Approach," Econometrica, Econometric Society, vol. 86(2), pages 523-557, March.
    17. Sridhar Moorthy, 2005. "A General Theory of Pass-Through in Channels with Category Management and Retail Competition," Marketing Science, INFORMS, vol. 24(1), pages 110-122, August.
    18. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
    19. Jean-Jacques Laffont & Jean Tirole, 1993. "A Theory of Incentives in Procurement and Regulation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262121743, December.
    20. Mirrlees, J. A., 1976. "Optimal tax theory : A synthesis," Journal of Public Economics, Elsevier, vol. 6(4), pages 327-358, November.
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    Keywords

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    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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