A birth–death model of advertising and pricing

Abstract

This paper employs the methods currently used to solve many queuing control models in order to investigate the behavior of a firm's optimal advertising and pricing strategies over time. Given that a firm's market position expands or deteriorates in a probabilistic way which depends upon the current position, the rate of advertising, and the price the firm charges, we present conditions which ensure that the optimal level of advertising is a monotonic function of the firm's market position, and we discuss the economic meaning of these conditions. Furthermore, although the primary focus is upon a non-competitive environment, we develop the above model as a non-zero sum, two-person stochastic game and show that an equilibrium strategy exists which is simple to compute.