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On the microeconomic foundations of linear demand for diferentiated products

Author

Listed:
  • Rabah Amir

    () (University of Iowa)

  • Philip Ericksonz

    () (University of Iowa)

  • Jim Jin

    () (University of St Andrews)

Abstract

This paper provides a thorough exploration of the microeconomic foundations for the multi- variate linear demand function for di¤erentiated products that is widely used in industrial or- ganization. A key ?nding is that strict concavity of the quadratic utility function is critical for the demand system to be well de?ned. Otherwise, the true demand function may be quite com- plex: Multi-valued, non-linear and income-dependent. The solution of the ?rst order conditions for the consumer problem, which we call a local demand function, may have quite pathological properties. We uncover failures of duality relationships between substitute products and com- plementary 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 via the use of linear demand that does not satisfy the law of Demand ought to be regarded with some suspiscion.

Suggested Citation

  • Rabah Amir & Philip Ericksonz & Jim Jin, 2015. "On the microeconomic foundations of linear demand for diferentiated products," Discussion Paper Series, Department of Economics 201507, Department of Economics, University of St. Andrews.
  • Handle: RePEc:san:wpecon:1507
    as

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    File URL: http://www.st-andrews.ac.uk/~wwwecon/repecfiles/4/1507.pdf
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    References listed on IDEAS

    as
    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, Southern Economic Association, 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. 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.
    6. Lionel McKenzie, 1957. "Demand Theory Without a Utility Index," Review of Economic Studies, Oxford University Press, vol. 24(3), pages 185-189.
    7. 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.
    8. Okuguchi, Koji, 1987. "Equilibrium prices in the Bertrand and Cournot oligopolies," Journal of Economic Theory, Elsevier, vol. 42(1), pages 128-139, June.
    9. 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.
    10. 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.
    11. repec:eee:jetheo:v:169:y:2017:i:c:p:603-628 is not listed on IDEAS
    12. 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.
    13. Francis Bloch, 1995. "Endogenous Structures of Association in Oligopolies," RAND Journal of Economics, The RAND Corporation, vol. 26(3), pages 537-556, Autumn.
    14. 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.
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    17. LaFrance, Jeffrey T., 1985. "Linear demand functions in theory and practice," Journal of Economic Theory, Elsevier, vol. 37(1), pages 147-166, October.
    18. Nocke, Volker & Schutz, Nicolas, 2017. "Quasi-linear integrability," Journal of Economic Theory, Elsevier, vol. 169(C), pages 603-628.
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    Citations

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    Cited by:

    1. Camille Cornand & Rodolphe Dos Santos Ferreira, 2017. "The social value of information and the competition motive: Price vs. quantity games," Working Papers halshs-01614815, HAL.
    2. Amir, Rabah & Evstigneev, Igor V., 2018. "A new look at the classical Bertrand duopoly," Games and Economic Behavior, Elsevier, vol. 109(C), pages 99-103.
    3. repec:eee:jetheo:v:169:y:2017:i:c:p:603-628 is not listed on IDEAS
    4. repec:eee:jetheo:v:175:y:2018:i:c:p:58-87 is not listed on IDEAS
    5. Maria Rosa, Battaggion & Vittoria, Cerasi, 2018. "Endogenous interlocking directorates," Working Papers 380, University of Milano-Bicocca, Department of Economics, revised 01 May 2018.
    6. repec:eee:energy:v:150:y:2018:i:c:p:1006-1017 is not listed on IDEAS
    7. Nocke, Volker & Schutz, Nicolas, 2017. "Quasi-linear integrability," Journal of Economic Theory, Elsevier, vol. 169(C), pages 603-628.

    More about this item

    Keywords

    linear demand; substitutes; complements; representative consumer; Law of Demand;

    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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