Inter-temporal Pricing and Consumer Stockpiling

40 Pages Posted: 31 Aug 2007 Last revised: 8 May 2012

See all articles by Xuanming Su

Xuanming Su

University of Pennsylvania - Operations & Information Management Department

Date Written: June 2009


We study a dynamic pricing problem for a class of products with stable consumption patterns (e.g., household items, staple foods). Consumers may stock up the product at current prices for future consumption, but they incur inventory holding costs. We model this situation as a dynamic game over an infinite time horizon: in each period, the seller sets a price, and each consumer chooses how many units to buy. We develop a solution methodology based on rational expectations. By endowing each player with beliefs, we decouple the dynamic game into individual dynamic programs for each player. We solve for the rational expectations equilibrium, where all players make optimal dynamic decisions given correct beliefs about others' behavior. In equilibrium, the seller may either charge a constant fixed price or offer periodic price promotions at predictable time intervals. We show that promotions are useful when frequent shoppers are willing to pay more than occasional shoppers for the product. We also develop several model extensions to study the impact of consumer stockpiling on the seller's inventory, production, and rationing strategies.

Keywords: dynamic pricing, stockpiling, consumer inventory, promotions, rational expectations, price discrimination

JEL Classification: C61, D10, D42

Suggested Citation

Su, Xuanming, Inter-temporal Pricing and Consumer Stockpiling (June 2009). Available at SSRN: or

Xuanming Su (Contact Author)

University of Pennsylvania - Operations & Information Management Department ( email )

Philadelphia, PA 19104
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Abstract Views
PlumX Metrics