IDEAS home Printed from https://ideas.repec.org/p/bol/bodewp/wp1044.html
   My bibliography  Save this paper

Beyond the Uniform Distribution: Equilibrium Prices and Qualities in a Vertically Differentiated Duopoly

Author

Listed:
  • C. Benassi
  • A. Chirco
  • C. Colombo

Abstract

The paper proves the existence of a subgame perfect Nash equilibrium in a vertically differentiated duopoly with uncovered market, for a large set of symmetric and asymmetric distributions of consumers, including, among others, all logconcave distributions. The proof relies on the income share elasticity representation of the consumers density function, which ensures the analytical tractability of the firms optimality conditions at a high level of generality. Some illustrative examples of the solution are offered, in order to assess the impact of distributive shocks on the equilibrium market configuration.

Suggested Citation

  • C. Benassi & A. Chirco & C. Colombo, 2015. "Beyond the Uniform Distribution: Equilibrium Prices and Qualities in a Vertically Differentiated Duopoly," Working Papers wp1044, Dipartimento Scienze Economiche, Universita' di Bologna.
    • Handle: RePEc:bol:bodewp:wp1044
    as

    Download full text from publisher

    File URL: http://amsacta.unibo.it/4424/1/WP1044.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Osharin, Alexander & Thisse, Jacques-François & Ushchev, Philip & Verbus, Valery, 2014. "Monopolistic competition and income dispersion," Economics Letters, Elsevier, vol. 122(2), pages 348-352.
    2. Yurko, Anna V., 2011. "How does income inequality affect market outcomes in vertically differentiated markets?," International Journal of Industrial Organization, Elsevier, vol. 29(4), pages 493-503, July.
    3. Dixit, Avinash K & Stiglitz, Joseph E, 1977. "Monopolistic Competition and Optimum Product Diversity," American Economic Review, American Economic Association, vol. 67(3), pages 297-308, June.
    4. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, April.
    5. Jean‐Marc Bonnisseau & Rim Lahmandi‐Ayed, 2007. "Vertical differentiation with non‐uniform consumers' distribution," International Journal of Economic Theory, The International Society for Economic Theory, vol. 3(3), pages 179-190, September.
    6. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    7. An, Mark Yuying, 1998. "Logconcavity versus Logconvexity: A Complete Characterization," Journal of Economic Theory, Elsevier, vol. 80(2), pages 350-369, June.
    8. Corrado Benassi & Alessandra Chirco & Caterina Colombo, 2005. "A Model Of Monopolistic Competition With Personal Income Dispersion," Metroeconomica, Wiley Blackwell, vol. 56(3), pages 305-317, July.
    9. Avner Shaked & John Sutton, 1982. "Relaxing Price Competition Through Product Differentiation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(1), pages 3-13.
    10. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    11. Corrado Benassi & Alessandra Chirco & Caterina Colombo, 2006. "Vertical Differentiation And The Distribution Of Income," Bulletin of Economic Research, Wiley Blackwell, vol. 58(4), pages 345-367, October.
    12. Corrado Benassi & Alessandra Chirco & Marcella Scrimitore, 2002. "Income concentration and market demand," Oxford Economic Papers, Oxford University Press, vol. 54(4), pages 584-596, October.
    13. Jaskold Gabszewicz, J. & Thisse, J. -F., 1979. "Price competition, quality and income disparities," Journal of Economic Theory, Elsevier, vol. 20(3), pages 340-359, June.
    14. Anderson, Simon P. & Goeree, Jacob K. & Ramer, Roald, 1997. "Location, Location, Location," Journal of Economic Theory, Elsevier, vol. 77(1), pages 102-127, November.
    15. Esteban, Joan M, 1986. "Income-Share Elasticity and the Size Distribution of Income," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(2), pages 439-444, June.
    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. Barigozzi, Francesca & Ma, Ching-to Albert, 2018. "Product differentiation with multiple qualities," International Journal of Industrial Organization, Elsevier, vol. 61(C), pages 380-412.

    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. Corrado Benassi & Alessandra Chirco & Caterina Colombo, 2019. "Vertical differentiation beyond the uniform distribution," Journal of Economics, Springer, vol. 126(3), pages 221-248, April.
    2. Benassi, Corrado & Castellani, Massimiliano & Mussoni, Maurizio, 2016. "Price equilibrium and willingness to pay in a vertically differentiated mixed duopoly," Journal of Economic Behavior & Organization, Elsevier, vol. 125(C), pages 86-96.
    3. Liu, Ting & Albert Ma, Ching-to & Mak, Henry Y., 2018. "Incentives for motivated experts in a partnership," Journal of Economic Behavior & Organization, Elsevier, vol. 152(C), pages 296-313.
    4. Laine, Liisa T. & Ma, Ching-to Albert, 2017. "Quality and competition between public and private firms," Journal of Economic Behavior & Organization, Elsevier, vol. 140(C), pages 336-353.
    5. Corrado Benassi & Marcella Scrimitore, 2017. "Income Distribution in Network Markets," Journal of Industry, Competition and Trade, Springer, vol. 17(3), pages 251-271, September.
    6. Ngo Van Long & Zhuang Miao, 2020. "Multiple‐quality Cournot oligopoly and the role of market size," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 29(4), pages 932-952, October.
    7. Barigozzi, Francesca & Ma, Ching-to Albert, 2018. "Product differentiation with multiple qualities," International Journal of Industrial Organization, Elsevier, vol. 61(C), pages 380-412.
    8. Janko Hernández Cortés & Paolo Morganti, 2022. "Existence and uniqueness of price equilibria in location-based models of differentiation with full coverage," Journal of Economics, Springer, vol. 136(2), pages 115-148, July.
    9. Dieter Pennerstorfer & Nora Schindler & Christoph Weiss & Biliana Yontcheva, 2020. "Income Inequality and Product Variety: Empirical Evidence," Economics working papers 2020-17, Department of Economics, Johannes Kepler University Linz, Austria.
    10. Auer, Raphael A. & Sauré, Philip, 2017. "Dynamic entry in vertically differentiated markets," Journal of Economic Theory, Elsevier, vol. 167(C), pages 177-205.
    11. Belleflamme,Paul & Peitz,Martin, 2015. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9781107687899.
    12. Corrado Benassi & Alessandra Chirco & Caterina Colombo, 2006. "Vertical Differentiation And The Distribution Of Income," Bulletin of Economic Research, Wiley Blackwell, vol. 58(4), pages 345-367, October.
    13. Constantatos, Christos & Perrakis, Stylianos, 1995. "Différenciation verticale et structure du marché," L'Actualité Economique, Société Canadienne de Science Economique, vol. 71(1), pages 71-98, mars.
    14. Francesco Angelini & Corrado Benassi & Massimiliano Castellani, 2021. "Platform competition and willingness to pay in a vertical differentiated two-sided market," Economics Bulletin, AccessEcon, vol. 41(2), pages 772-780.
    15. Alventosa, Adriana & Pacheco Pires, Cesaltina & Ferreira Jorge, Sílvia & Pinho, Joana & Catalão-Lopes, Margarida, 2023. "How does firms’ cost structure affect their quality–price mix? An experimental analysis," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 107(C).
    16. Namrata Gulati & Prabal Roy Chowdhury, 2010. "Income inequality, neighbourhood effects and product quality," Discussion Papers 10-06, Indian Statistical Institute, Delhi.
    17. Bos, Iwan & Marini, Marco A., 2019. "Cartel stability under quality differentiation," Economics Letters, Elsevier, vol. 174(C), pages 70-73.
    18. Cédric Argenton, 2010. "Exclusive Quality," Journal of Industrial Economics, Wiley Blackwell, vol. 58(3), pages 690-716, September.
    19. Fullerton, Don & Metcalf, Gilbert E., 2002. "Tax incidence," Handbook of Public Economics, in: A. J. Auerbach & M. Feldstein (ed.), Handbook of Public Economics, edition 1, volume 4, chapter 26, pages 1787-1872, Elsevier.
    20. Ying He & Huaxia Rui, 2022. "Probabilistic selling in vertically differentiated markets: The role of substitution," Production and Operations Management, Production and Operations Management Society, vol. 31(11), pages 4191-4204, November.

    More about this item

    JEL classification:

    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    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:bol:bodewp:wp1044. 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: Dipartimento Scienze Economiche, Universita' di Bologna (email available below). General contact details of provider: https://edirc.repec.org/data/sebolit.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.