Correspondence: Leo MacDonald, Department of Economics, Finance and Quantitative Analysis, Coles College of Business, Kennesaw State University, 1000 Chastain Road, Kennesaw, Georgia 30144, USA. E-mail: lmacdon4@kennesaw.edu

¹is an assistant professor in the Department of Economics, Finance and Quantitative Analysis at the Coles College of Business, Kennesaw State University. His primary research interests are in Revenue Management and Pricing/Inventory policies. Professor MacDonald's industry experience includes several years as a professional engineer, including consulting, project management and research/product development.

²was formerly Professor Emeritus in the Department of Applied Mathematics, University of Western Ontario. His academic career spanned over three decades and included more than 90 refereed publications in modeling and applied numerical analysis.

^†Dedicated to the memory of Henning Rasmussen, mentor, colleague and friend.

Received 14 July 2009; Revised 14 July 2009; Published online 30 October 2009.

Abstract

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.