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Multiproduct Pricing Made Simple

Listed author(s):
  • Armstrong, Mark
  • Vickers, John

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.

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File URL: https://mpra.ub.uni-muenchen.de/68717/1/MPRA_paper_68717.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 68717.

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Date of creation: 08 Jan 2016
Handle: RePEc:pra:mprapa:68717
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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. Ricardo Alonso & Niko Matouschek, 2008. "Optimal Delegation," Review of Economic Studies, Oxford University Press, vol. 75(1), pages 259-293.
  4. De Fraja, Giovanni, 1996. "Product line competition in vertically differentiated markets," International Journal of Industrial Organization, Elsevier, vol. 14(3), pages 389-414, May.
  5. 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.
  6. Armstrong, Mark & Vickers, John, 2001. "Competitive Price Discrimination," RAND Journal of Economics, The RAND Corporation, vol. 32(4), pages 579-605, Winter.
  7. 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.
  8. Nocke, Volker & Schutz, Nicolas, 2016. "Multiproduct-Firm Oligopoly: An Aggregative Games Approach," CEPR Discussion Papers 11539, C.E.P.R. Discussion Papers.
  9. Slade, Margaret E, 1994. "What Does an Oligopoly Maximize?," Journal of Industrial Economics, Wiley Blackwell, vol. 42(1), pages 45-61, March.
  10. Bergstrom, Theodore C. & Varian, Hal R., 1985. "Two remarks on Cournot equilibria," Economics Letters, Elsevier, vol. 19(1), pages 5-8.
  11. 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.
  12. 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.
  13. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
  14. 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.
  15. Mirrlees, J. A., 1976. "Optimal tax theory : A synthesis," Journal of Public Economics, Elsevier, vol. 6(4), pages 327-358, November.
  16. 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, 06.
  17. Ricardo Alonso & Niko Matouschek, 2008. "Optimal delegation," LSE Research Online Documents on Economics 58665, London School of Economics and Political Science, LSE Library.
  18. 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.
  19. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
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