IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/68717.html
   My bibliography  Save this paper

Multiproduct Pricing Made Simple

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/68717/1/MPRA_paper_68717.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Bliss, Christopher, 1988. "A Theory of Retail Pricing," Journal of Industrial Economics, Wiley Blackwell, vol. 36(4), pages 375-391, June.
    2. 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.
    3. Volker Nocke & Nicolas Schutz, 2018. "Multiproduct‐Firm Oligopoly: An Aggregative Games Approach," Econometrica, Econometric Society, vol. 86(2), pages 523-557, March.
    4. 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.
    5. Mirrlees, J. A., 1976. "Optimal tax theory : A synthesis," Journal of Public Economics, Elsevier, vol. 6(4), pages 327-358, November.
    6. 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.
    7. De Fraja, Giovanni, 1996. "Product line competition in vertically differentiated markets," International Journal of Industrial Organization, Elsevier, vol. 14(3), pages 389-414, May.
    8. 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.
    9. Bergstrom, Theodore C. & Varian, Hal R., 1985. "Two remarks on Cournot equilibria," Economics Letters, Elsevier, vol. 19(1), pages 5-8.
    10. 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.
    11. Ricardo Alonso & Niko Matouschek, 2008. "Optimal Delegation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(1), pages 259-293.
    12. 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.
    13. 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.
    14. 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.
    15. Slade, Margaret E, 1994. "What Does an Oligopoly Maximize?," Journal of Industrial Economics, Wiley Blackwell, vol. 42(1), pages 45-61, March.
    16. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    17. 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.
    18. Armstrong, Mark & Vickers, John, 2001. "Competitive Price Discrimination," RAND Journal of Economics, The RAND Corporation, vol. 32(4), pages 579-605, Winter.
    19. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
    20. 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, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Stahl, Konrad & Legros, Patrick, 2019. "Local Search Markets and External Competition," CEPR Discussion Papers 13764, C.E.P.R. Discussion Papers.
    3. Yongmin Chen & Jianpei Li & Marius Schwartz, 2021. "Competitive differential pricing," RAND Journal of Economics, RAND Corporation, vol. 52(1), pages 100-124, March.
    4. 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.
    5. 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.
    6. Inderst, Roman & Griem, Fabian & Schaffer, Greg, 2022. "Tying under Double-Marginalization," CEPR Discussion Papers 17314, C.E.P.R. Discussion Papers.
    7. 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.
    8. Aguirre, Iñaki, 2017. "Cournot Oligopoly, Price Discrimination and Total Output," MPRA Paper 80166, University Library of Munich, Germany.
    9. 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.
    10. Justin P. Johnson & Andrew Rhodes, 2021. "Multiproduct mergers and quality competition," RAND Journal of Economics, RAND Corporation, vol. 52(3), pages 633-661, September.
    11. Anna D'Annunzio & Antonio Russo, 2022. "Ad Valorem Taxation in a Multiproduct Monopoly," CESifo Working Paper Series 9881, CESifo.
    12. 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.
    13. Etro, Federico, 2016. "Research in economics and industrial organization," Research in Economics, Elsevier, vol. 70(4), pages 511-517.
    14. Paul Belleflamme & Eric Toulemonde, 2016. "Tax Incidence on Competing Two-Sided Platforms: Lucky Break or Double Jeopardy," CESifo Working Paper Series 5882, CESifo.
    15. 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.
    16. 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.
    17. 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.
    18. Cole, Matthew T. & Eckel, Carsten, 2018. "Tariffs and markups in retailing," Journal of International Economics, Elsevier, vol. 113(C), pages 139-153.
    19. 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).
    20. 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..
    21. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mark Armstrong & John Vickers, 2015. "Multiproduct Monopoly Made Simple," Economics Series Working Papers 754, University of Oxford, Department of Economics.
    2. Andersson, Tommy, 2004. "Essays on Nonlinear Pricing and Welfare," MPRA Paper 59446, University Library of Munich, Germany.
    3. Simon P. Anderson & Régis Renault, 2011. "Price Discrimination," Chapters, in: André de Palma & Robin Lindsey & Emile Quinet & Roger Vickerman (ed.), A Handbook of Transport Economics, chapter 22, Edward Elgar Publishing.
    4. Henrik Jacobsen Kleven & Claus Thustrup Kreiner & Emmanuel Saez, 2007. "The Optimal Income Taxation of Couples as a Multi-Dimensional Screening Problem," CESifo Working Paper Series 2092, CESifo.
    5. Ingo Vogelsang, 2006. "Electricity Transmission Pricing and Performance-based Regulation," The Energy Journal, International Association for Energy Economics, vol. 0(Number 4), pages 97-126.
    6. Carmona, Miguel, 2010. "The regulatory function in public-private partnerships for the provision of transport infrastructure," Research in Transportation Economics, Elsevier, vol. 30(1), pages 110-125.
    7. María Angeles García Valiñas, 2004. "Eficiencia y equidad en el diseño de precios óptimos para bienes y servicios públicos," Hacienda Pública Española / Review of Public Economics, IEF, vol. 168(1), pages 95-119, march.
    8. Carlier, Guillaume & Zhang, Kelvin Shuangjian, 2020. "Existence of solutions to principal–agent problems with adverse selection under minimal assumptions," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 64-71.
    9. Jensen, S., 2000. "Price Discrimination and Three Part Tariffs in a Duopoly," Papers 3/2000, Norwegian School of Economics and Business Administration-.
    10. Mark Armstrong, 2016. "Nonlinear Pricing," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 583-614, October.
    11. Committee, Nobel Prize, 2007. "Leonid Hurwicz, Eric S. Maskin and Roger B. Myerson: Mechanism Design Theory," Nobel Prize in Economics documents 2007-2, Nobel Prize Committee.
    12. Armstrong, Mark & Sappington, David E.M., 2007. "Recent Developments in the Theory of Regulation," Handbook of Industrial Organization, in: Mark Armstrong & Robert Porter (ed.), Handbook of Industrial Organization, edition 1, volume 3, chapter 27, pages 1557-1700, Elsevier.
    13. Stole, Lars A., 2007. "Price Discrimination and Competition," Handbook of Industrial Organization, in: Mark Armstrong & Robert Porter (ed.), Handbook of Industrial Organization, edition 1, volume 3, chapter 34, pages 2221-2299, Elsevier.
    14. Miao, Chun-Hui, 2022. "The pricing of ancillary goods when selling on a platform," International Journal of Industrial Organization, Elsevier, vol. 83(C).
    15. Mark L. Burkey & Alexandra Kurepa, 2016. "Spatial Nonlinear Pricing with Per-Trip versus Per-Unit Transportation Costs," The Review of Regional Studies, Southern Regional Science Association, vol. 46(3), pages 237-255, Winter.
    16. Ismail Saglam, 2024. "The Bayesian approach to monopoly regulation after 40 years," Journal of Regulatory Economics, Springer, vol. 65(1), pages 108-136, June.
    17. Anderson, Simon P. & Celik, Levent, 2015. "Product line design," Journal of Economic Theory, Elsevier, vol. 157(C), pages 517-526.
    18. Federico Boffa & John Panzar, 2012. "Bottleneck co-ownership as a regulatory alternative," Journal of Regulatory Economics, Springer, vol. 41(2), pages 201-215, April.
    19. Jensen, Sissel, 2008. "Two-part tariffs with quality degradation," International Journal of Industrial Organization, Elsevier, vol. 26(2), pages 473-489, March.
    20. Murray Fulton & James Vercammen, 2014. "Optimal NGO Financing of a Resource Management Certification Scheme," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 58(4), pages 605-626, August.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:68717. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.