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Intertemporal Price Discrimination with Multiple Products

55 Pages Posted: 15 May 2017  

Jean-Charles Rochet

University of Zurich - Swiss Banking Institute (ISB); University of Toulouse I - Institut d'Economie Industrielle (IDEI); Swiss Finance Institute

John E. Thanassoulis

University of Warwick - Warwick Business School; Oxford-Man Institute, University of Oxford; Nuffield College, University of Oxford

Multiple version iconThere are 2 versions of this paper

Date Written: May 2017

Abstract

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

Rochet, Jean-Charles and Thanassoulis, John E., Intertemporal Price Discrimination with Multiple Products (May 2017). CEPR Discussion Paper No. DP12034. Available at SSRN: https://ssrn.com/abstract=2968375

Jean-Charles Rochet (Contact Author)

University of Zurich - Swiss Banking Institute (ISB) ( email )

Plattenstrasse 14
CH-8032 Zurich, Zurich 8032
Switzerland

University of Toulouse I - Institut d'Economie Industrielle (IDEI) ( email )

Manufacture des Tabacs
21 Allee de Brienne bat. F
Toulouse Cedex, F-31000
France
+33 5 6112 8641 (Phone)
+33 5 6112 8637 (Fax)

Swiss Finance Institute ( email )

c/o University of Geneve
40, Bd du Pont-d'Arve
1211 Geneva, CH-6900
Switzerland

John Thanassoulis

University of Warwick - Warwick Business School ( email )

Coventry CV4 7AL
United Kingdom

HOME PAGE: http://https://sites.google.com/site/thanassoulis/

Oxford-Man Institute, University of Oxford ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

Nuffield College, University of Oxford ( email )

New Road
Oxford, OX1 1NF
United Kingdom

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