On the microeconomic foundations of linear demand for differentiated products

Rabah Amir, Philip Erickson, Jim Jin

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    53 Citations (Scopus)
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    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.
    Original languageEnglish
    Pages (from-to)641-665
    JournalJournal of Economic Theory
    Volume169
    Early online date27 Mar 2017
    DOIs
    Publication statusPublished - May 2017

    Keywords

    • Linear demand
    • Gross substitutes
    • Gross complements
    • Edgeworth complements
    • Representative consumer
    • Law of Demand

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