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Optimal Pricing of a Product Diffusing in Rich and Poor Populations

Author

Listed:
  • R.F. Hartl

    (University of Vienna)

  • A.J. Novak

    (University of Vienna)

  • A.G. Rao

    (Washington University)

  • S.P. Sethi

    (University of Texas at Dallas)

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.

Suggested Citation

  • R.F. Hartl & A.J. Novak & A.G. Rao & S.P. Sethi, 2003. "Optimal Pricing of a Product Diffusing in Rich and Poor Populations," Journal of Optimization Theory and Applications, Springer, vol. 117(2), pages 349-375, May.
    • Handle: RePEc:spr:joptap:v:117:y:2003:i:2:d:10.1023_a:1023635807884
    DOI: 10.1023/A:1023635807884
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    References listed on IDEAS

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    1. Gustav Feichtinger & Richard F. Hartl & Suresh P. Sethi, 1994. "Dynamic Optimal Control Models in Advertising: Recent Developments," Management Science, INFORMS, vol. 40(2), pages 195-226, February.
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