DP12034 Intertemporal Price Discrimination with Multiple Products

Author(s): Jean-Charles Rochet, John Thanassoulis
Publication Date: May 2017
Keyword(s): Multidimensional Mechanism Design; Second Degree Price Discrimination; Bundling; Time Discounting; Cross-sell.
JEL(s): D42, L11
Programme Areas: Industrial Organization
Link to this Page: www.cepr.org/active/publications/discussion_papers/dp.php?dpno=12034

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.