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On the microeconomic foundations of linear demand for differentiated products

Author

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  • Amir, Rabah
  • Erickson, Philip
  • Jin, Jim

Abstract

This paper provides a thorough exploration of the microeconomic foundations for the multi-variate linear demand function for differentiated products, which is widely used in industrial organization. The setting is the standard representative consumer with a quasi-linear utility function. A key finding is that strict concavity of the quadratic utility function is critical for the demand system to be well defined. Otherwise, the true demand function may be quite complex: Multi-valued, non-linear and income-dependent. We uncover failures of duality relationships between substitute products and complementary products, as well as the incompatibility between high levels of complementarity and concavity. The two-good case emerges as a special case with strong but non-robust properties. A key implication is that all conclusions derived in applied economic models via the use of linear demand that does not satisfy the Law of Demand ought to be regarded with some suspicion.

Suggested Citation

  • Amir, Rabah & Erickson, Philip & Jin, Jim, 2017. "On the microeconomic foundations of linear demand for differentiated products," Journal of Economic Theory, Elsevier, vol. 169(C), pages 641-665.
    • Handle: RePEc:eee:jetheo:v:169:y:2017:i:c:p:641-665
    DOI: 10.1016/j.jet.2017.03.005
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    References listed on IDEAS

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    1. Deneckere, R., 1983. "Duopoly supergames with product differentiation," Economics Letters, Elsevier, vol. 11(1-2), pages 37-42.
    2. Choné, Philippe & Linnemer, Laurent, 2008. "Assessing horizontal mergers under uncertain efficiency gains," International Journal of Industrial Organization, Elsevier, vol. 26(4), pages 913-929, July.
    3. Rabah Amir, 2005. "Supermodularity and Complementarity in Economics: An Elementary Survey," Southern Economic Journal, John Wiley & Sons, vol. 71(3), pages 636-660, January.
    4. Avinash Dixit, 1979. "A Model of Duopoly Suggesting a Theory of Entry Barriers," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 20-32, Spring.
    5. Rabah Amir, 2005. "Supermodularity and Complementarity in Economics: An Elementary Survey," Southern Economic Journal, John Wiley & Sons, vol. 71(3), pages 636-660, January.
    6. Armstrong, Mark & Vickers, John, 2015. "Which demand systems can be generated by discrete choice?," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 293-307.
    7. Lionel McKenzie, 1957. "Demand Theory Without a Utility Index," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 24(3), pages 185-189.
    8. Nirvikar Singh & Xavier Vives, 1984. "Price and Quantity Competition in a Differentiated Duopoly," RAND Journal of Economics, The RAND Corporation, vol. 15(4), pages 546-554, Winter.
    9. Okuguchi, Koji, 1987. "Equilibrium prices in the Bertrand and Cournot oligopolies," Journal of Economic Theory, Elsevier, vol. 42(1), pages 128-139, June.
    10. Amir, Rabah & Jin, Jim Y., 2001. "Cournot and Bertrand equilibria compared: substitutability, complementarity and concavity," International Journal of Industrial Organization, Elsevier, vol. 19(3-4), pages 303-317, March.
    11. Hackner, Jonas, 2000. "A Note on Price and Quantity Competition in Differentiated Oligopolies," Journal of Economic Theory, Elsevier, vol. 93(2), pages 233-239, August.
    12. Nocke, Volker & Schutz, Nicolas, 2017. "Quasi-linear integrability," Journal of Economic Theory, Elsevier, vol. 169(C), pages 603-628.
    13. Amir, Rabah & Halmenschlager, Christine & Jin, Jim, 2011. "R&D-induced industry polarization and shake-outs," International Journal of Industrial Organization, Elsevier, vol. 29(4), pages 386-398, July.
    14. Francis Bloch, 1995. "Endogenous Structures of Association in Oligopolies," RAND Journal of Economics, The RAND Corporation, vol. 26(3), pages 537-556, Autumn.
    15. Judy Hsu & X. Wang, 2005. "On Welfare under Cournot and Bertrand Competition in Differentiated Oligopolies," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 27(2), pages 185-191, September.
    16. Bresnahan, Timothy F, 1987. "Competition and Collusion in the American Automobile Industry: The 1955 Price War," Journal of Industrial Economics, Wiley Blackwell, vol. 35(4), pages 457-482, June.
    17. Xavier Vives, 1987. "Small Income Effects: A Marshallian Theory of Consumer Surplus and Downward Sloping Demand," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(1), pages 87-103.
    18. LaFrance, Jeffrey T., 1985. "Linear demand functions in theory and practice," Journal of Economic Theory, Elsevier, vol. 37(1), pages 147-166, October.
    19. Vives, Xavier, 1985. "On the efficiency of Bertrand and Cournot equilibria with product differentation," Journal of Economic Theory, Elsevier, vol. 36(1), pages 166-175, June.
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    More about this item

    Keywords

    Linear demand; Gross substitutes; Gross complements; Edgeworth complements; Representative consumer; Law of Demand;
    All these keywords.

    JEL classification:

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

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