Optimal Pricing of a Product Which Diffuses in Rich and Poor Populations Richard F. Hartl Department of Business Studies, University of Vienna Andreas J. Novak Department of Statistics and Decision Support Systems, University of Vienna Ambar G. Rao John M. Olin School of Business, Washington University in St. Louis Suresh P. Sethi School of Management, University of Texas at Dallas 6. Mai 2002 Abstract We consider a market consisting of two populations, termed rich and poor for convenience. If a product is priced such that it is very expensive for the poor, but affordable to the rich, then it becomes a status symbol for the poor and this makes it more desirable for the poor. At a lower price the product is affordable by both populations. However, as more of the poor buy the product, it ceases to be a status symbol, and becomes less appealing to the rich. We present a two-state non- linear optimal control problem that aims to obtain profit-maximizing prices over time in this environment. We find that there are three categories of optimal price paths. One is status symbol pricing with high initial price, declining over time. The other two are mass market pricing, with price declining in one, and increasing and then decreasing in the other. Key Words Optimal control, marketing, pricing, market diffusion, aspirational group