Price Trends and Dynamic Pricing in Perishable Product Market Consisting of Superior and Inferior Firms

Abstract

We consider the problem of a firm that sells perishable products with a dynamic pricing scheme in the presence of a firm offering a superior product. We provide a probabilistic characterization of the optimal price process under the existence of such a firm for an aggregate demand model and for a multinomial logit demand model. Our results demonstrate that if the seller takes the price of the other firm into account in their optimal policy, then the optimal price process tends to increase over time before the inventory level falls to one, after which it decreases. Otherwise, the price process decreases and then increases (this path is called a J-shaped curve) before the inventory level falls to one if the price of the other firm is relatively low and the customer's valuation remains unchanged over time early in the sales period. We also demonstrate numerically that when the firm uses a monopolistic policy and the difference in service quality between the two firms is large, the switching time between the downward and upward trends takes place in the early stage of the sales period and in particular this J-shaped phenomenon is strongly observed.