Monopolist Pricing with Dynamic Demand and Production Cost

Abstract

This paper deals with pricing of a new product over time by a monopolist who maximizes the discounted profit stream. The interdependency of cost and demand on cumulative production makes the problem inherently dynamic. Cost is assumed to be declining with cumulative production (learning curve effect), while demand is a function of price and cumulative sales, representing word-of-mouth and saturation effects. The paper addresses this problem in a general framework that includes several previous results as special cases, and provides new insights in other situations. While the learning curve and word-of-mouth effect cause prices to be lower than the price that maximizes immediate revenues, the saturation factor has the opposite effect. The price path over time is affected by these factors and the interest rate. We characterize the price path under several different situations and interpret the results for policy guidelines.pricing, dynamic pricing, learning curve, diffusion of innovations

Dynamic Pricing in Management Science

“…But word-of-mouth can also be negative. This is what happens when buyers discover that the product does not suit them (Kalish, 1983).…”

“…Each new sale reduces the future market. As total sales increase, there is less and less unsatisfied demand, which reduces future sales (Bass, 1969;Kalish, 1983).…”

“…In management science, there are two main questions about pricing (Kalish, 1983). The first is to know what the optimal dynamic price level is, relative to the myopic price.…”

“…In addition, such models do not characterize the price dynamics and sales of a product during its life cycle (Jorgensen et al, 2007). To address these shortcomings, several models have been developed in management science to explicitly include the dynamic or intertemporal element in the study of pricing policies (Kalish, 1983;Dockner et al, 2000).…”

“…Robinson and Lakhani (1975) studied dynamic pricing numerically, integrating diffusion effects. Kalish (1983) characterizes analytically the different pricing policies for different types of dynamic effects. Dockner and al.…”