On the microeconomic foundations of linear demand for differentiated products

Abstract

This paper provides a thorough exploration of the microeconomic foundations for the multivariate 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.

The Social Value of Information and the Competition Motive: Price vs. Quantity Games

“…Second, the paper extends to a context of imperfect and dispersed information the systematic comparison of price and quantity competition initiated by Singh and Vives (1984) for a differentiated duopoly with linear demand (recent contributions, also under perfect information, are provided by Jin, 2001, andAmir, Erickson andJin, 2017). In the same vein, we observe the development of a literature on the aggregation of private information in oligopolies with either demand or cost uncertainty 6 (Raith, 1996, Vives, 1988, 2011.…”

Effective risk aversion in thin risk‐sharing markets

“…in Amir, Erickson, and Jin (2017). In our model, we adopt linear demand functions from their competitive form, resulting to downward slopes because the variance-covariance matrix is positive definite, and not part of traders' strategic sets.…”

Environmental quality and monopoly pricing

“…The part D p (p, a) < 0 captures the usual law of demand, and D a (p, a) > 0 means that higher quality leads to higher demand. 4 The cost structure reflects constant returns to scale in production for all possible quality levels,…”