Dynamic Pricing of Di¤erentiated Products

We examine the dynamic pricing decision of a …rm facing random demand while selling a …xed stock of two di¤erentiated products over an in…nite horizon. Prices in each period depend on the available stock of both products (varieties). In addition to the standard tradeo¤ between a higher revenue and the probability of selling the product, a higher price for one product also a¤ects the probability of a sale for the other product. We characterize the optimal price paths of the two varieties and …nd that the market may be optimally ‘covered’ or ‘not covered’. With a positive stock of only one variety, the price path is nondecreasing. The same holds for the price paths with two varieties, with respect to the own stock level and as long as the probability of no sale is positive. When this probability equals one, the price of a given variety is decreasing in its own stock and increasing in the stock of the other variety. The optimal paths re‡ect the property that the stream of expected future pro…ts is higher when the inventory levels of the two products tend to be closer to each other. Kotseva: Department of Economics, Athens University of Economics and Business, Patision 76, Athens, 10434, Greece; [email protected]. Vettas (corresponding author): Department of Economics, Athens University of Economics and Business, Patision 76, Athens, 10434, Greece and CEPR, UK; [email protected]. Financial support from the European Commission and the Greek Ministry of Education (“Herakleitos”program) is gratefully acknowledged.