On the microeconomic foundations of linear demand for diferentiated products

Rabah Amir, Philip Ericksonz, Jim Yongtao Jin

    Research output: Working paperDiscussion paper


    This paper provides a thorough exploration of the microeconomic foundations for the multivariate linear demand function for di¤erentiated products that is widely used in industrial organization. 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. The solution of the first 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 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 via the use of linear demand that does not satisfy the law of Demand ought to be regarded with some suspiscion.
    Original languageEnglish
    Place of PublicationSt Andrews
    PublisherUniversity of St Andrews
    Publication statusPublished - 9 Jul 2015

    Publication series

    NameSchool of Economics & Finance Discussion Paper
    PublisherUniversity of St Andrews
    ISSN (Print)0962-4031
    ISSN (Electronic)2055-303X


    • Linear demand
    • Substitutes
    • Complements
    • Representative consumer
    • Law of Demand


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