Optimal Pricing of a Product Diffusing in Rich and Poor Populations
Journal of Optimization Theory and Applications, Vol. 117, No. 2, pp. 349–375, May 2003
Posted: 21 Jun 2009
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 nonlinear 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 price increasing and then decreasing in the other.
Keywords: Optimal control, marketing, pricing, market diffusion, aspirational group
JEL Classification: M30, D4, C61
Suggested Citation: Suggested Citation