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Existence and uniqueness of price equilibria in location-based models of differentiation with full coverage

Author

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  • Janko Hernández Cortés

    (Departament of Business Administration. ITAM.)

  • Paolo Morganti

    (Universidad Panamericana Facultad de Ciencias Económicas y Empresariales.)

Abstract

In location-based models of price competition, traditional sufficient conditions for existence and uniqueness of an equilibrium (Caplin and Nalebuff in Econometrica 59(1):25–59) are not robust for the firm that serves the right-tail of the consumers’ distribution. Interestingly, as we relax these conditions, we observe only two new alternative cases. Moreover, we identify a novel, easily testable condition for uniqueness that is weaker than log-concavity and that can also apply to Mechanism Design. Thanks to this general framework, we can solve the equilibrium of general vertical differentiation models numerically and show that inequality has a U-shaped effect on profits and prices of a high-quality firm. Moreover, we prove that extreme levels of concentration can dissolve natural monopolies and restore competition, contrary to the Uniform case.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:jeczfn:v:136:y:2022:i:2:d:10.1007_s00712-021-00770-8
    DOI: 10.1007/s00712-021-00770-8
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    References listed on IDEAS

    as
    1. Song Lin, 2017. "Add-on Policies Under Vertical Differentiation: Why Do Luxury Hotels Charge for Internet While Economy Hotels Do Not?," Marketing Science, INFORMS, vol. 36(4), pages 610-625, July.
    2. 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.
    3. Champsaur, Paul & Rochet, Jean-Charles, 1989. "Multiproduct Duopolists," Econometrica, Econometric Society, vol. 57(3), pages 533-557, May.
    4. Bruce McWilliams, 2012. "Money-Back Guarantees: Helping the Low-Quality Retailer," Management Science, INFORMS, vol. 58(8), pages 1521-1524, August.
    5. 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.
    6. Bonanno, Giacomo & Haworth, Barry, 1998. "Intensity of competition and the choice between product and process innovation," International Journal of Industrial Organization, Elsevier, vol. 16(4), pages 495-510, July.
    7. Corrado Benassi & Alessandra Chirco & Caterina Colombo, 2019. "Vertical differentiation beyond the uniform distribution," Journal of Economics, Springer, vol. 126(3), pages 221-248, April.
    8. Lahmandi-Ayed, Rim, 2000. "Natural Oligopolies: A Vertical Differentiation Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 971-987, November.
    9. Milgrom, Paul & Roberts, John, 1994. "Comparing Equilibria," American Economic Review, American Economic Association, vol. 84(3), pages 441-459, June.
    10. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 1-26.
    11. 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.
    12. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    13. d'Aspremont, C & Gabszewicz, Jean Jaskold & Thisse, J-F, 1979. "On Hotelling's "Stability in Competition"," Econometrica, Econometric Society, vol. 47(5), pages 1145-1150, September.
    14. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 27-41.
    15. Rim Lahmandi-Ayed, 2004. "Finiteness property in vertically differentiated markets: a note on locally increasing and decreasing returns," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(2), pages 371-382, January.
    16. Justin P. Johnson & David P. Myatt, 2006. "On the Simple Economics of Advertising, Marketing, and Product Design," American Economic Review, American Economic Association, vol. 96(3), pages 756-784, June.
    17. Jaskold Gabszewicz, J. & Thisse, J. -F., 1980. "Entry (and exit) in a differentiated industry," Journal of Economic Theory, Elsevier, vol. 22(2), pages 327-338, April.
    18. Rim Lahmandi-Ayed, 2007. "Finiteness property with vertical and horizontal differentiation: does it really matter?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(3), pages 531-548, December.
    19. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January.
    20. 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.
    21. 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.
    22. Cremer, Helmuth & Thisse, Jacques-Francois, 1991. "Location Models of Horizontal Differentiation: A Special Case of Vertical Differentiation Models," Journal of Industrial Economics, Wiley Blackwell, vol. 39(4), pages 383-390, June.
    23. Tamás L. Balogh & Christian Ewerhart, 2015. "On the origin of r-concavity and related concepts," ECON - Working Papers 187, Department of Economics - University of Zurich.
    24. Gal-or, Esther, 1982. "Hotelling's spatial competition as a model of sales," Economics Letters, Elsevier, vol. 9(1), pages 1-6.
    25. Simon P. Anderson & André De Palma, 1988. "Spatial Price Discrimination with Heterogeneous Products," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 55(4), pages 573-592.
    26. X. Henry Wang, 2003. "A Note on the High–quality Advantage in Vertical Differentiation Models," Bulletin of Economic Research, Wiley Blackwell, vol. 55(1), pages 91-99, January.
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