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

See all articles by R. F. Hartl

R. F. Hartl

University of Vienna

Andreas J. Novak

University of Vienna - Department of Statistics and Decision Support Systems

Ambar G. Rao

Washington University in St. Louis - John M. Olin Business School

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

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 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

Hartl, R. F. and Novak, Andreas J. and Rao, Ambar G. and Sethi, Suresh, 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, Available at SSRN: https://ssrn.com/abstract=1421503

R. F. Hartl

University of Vienna ( email )

Bruenner Strasse 72
Vienna 1210, Vienna
Austria
+43-1-4277-38091 (Phone)
+43-1-4277-38094 (Fax)

Andreas J. Novak

University of Vienna - Department of Statistics and Decision Support Systems ( email )

Universitaetsstr. 5
Vienna, A-1010
Austria

Ambar G. Rao

Washington University in St. Louis - John M. Olin Business School ( email )

One Brookings Drive
Campus Box 1133
St. Louis, MO 63130-4899
United States
314-935-4515 (Phone)
314-935-6359 (Fax)

Suresh Sethi (Contact Author)

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 W. Campbell Road, SM30
Richardson, TX 75080-3021
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Abstract Views
357
PlumX Metrics