Intertemporal Price Discrimination with Multiple Products
55 Pages Posted: 15 May 2017
Date Written: May 2017
We study the multiproduct monopoly profit maximisation problem for a seller who can commit to a dynamic pricing strategy. We show that if consumers' valuations are not strongly-ordered then optimality for the seller requires intertemporal price discrimination and it can be implemented by dynamic pricing on the cross-sell to the bundle. If consumers are perfectly negatively correlated, reducing the cross-sell price at a single point in time is optimal. For general valuations we show that if the cross-partial derivative of the profit function is negative then dynamic pricing on the cross-sell is more profitable than fixing prices. So we show that the celebrated Stokey (1979) no-discrimination-across-time result does not extend to multiple good sellers when consumers' valuations are drawn from the tilted uniform, the shifted uniform, the exponential, or the normal distribution. We extend our results to welfare, to complementarities in demand, and to the determination of optimal discount schedules.
Keywords: Multidimensional Mechanism Design; Second Degree Price Discrimination; Bundling; Time Discounting; Cross-sell.
JEL Classification: D42, L11
Suggested Citation: Suggested Citation