Optimal Pricing of a Product Diffusing in Rich and Poor Populations

R.F. Hartl, A.J. Novak, A.G. Rao and Suresh Sethi
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R.F. Hartl: University of Vienna
A.J. Novak: University of Vienna
A.G. Rao: Washington University

Journal of Optimization Theory and Applications, 2003, vol. 117, issue 2, No 6, 349-375

Abstract: 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 (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1023/A:1023635807884

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