Revenue management with dynamic pricing and advertising

In this article, we analyze the temporal pricing and advertising strategy of a monopolist with a fixed inventory to sell over a finite horizon. The arrival of the customers is modeled by a Poisson process where the arrival rate is given by an increasing convex function of the advertising expenditure, and the willingness of a customer to pay is modeled by a decreasing function of the price. For specific functions for the arrival rate and willingness-to-pay, we derive and solve a system of ordinary differential equations for the optimal pricing and advertising strategy. We show that this optimal strategy is very close to a fixed optimal strategy.