On the microeconomic foundations of linear demand for differentiated products
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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.
Amir , R , Erickson , P & Jin , J 2017 , ' On the microeconomic foundations of linear demand for differentiated products ' Journal of Economic Theory , vol. 169 , pp. 641-665 . https://doi.org/10.1016/j.jet.2017.03.005
Journal of Economic Theory
© 2017 Elsevier Ltd. All rights reserved. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1016/j.jet.2017.03.005
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