Components of optimal price under logit demand

Amiya Basu, Tridib Mazumdar, S. P. Raj

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

Demand for durables can be modeled using a logit framework in which a customer chooses one brand from several alternatives, or buys nothing at all. In this framework, optimal prices for competing brands can be expressed as a system of non-linear equations, which, however, do not have closed form solutions. Although the optimal price can be determined by numerical search, the solution offers limited understanding of its components. In this article, we develop a linear approximation of the Nash equilibrium optimal price of a brand as its marginal cost plus a weighted sum of: (1) the inverse of the price sensitivity of the market, (2) the average value added by all brands in the market, and (3) the value advantage (or disadvantage) of the brand. The weights depend primarily upon the number of competing brands, with price insensitivity having the strongest impact, followed by value advantage of the brand, and average value added by all brands. This approximation for optimal price is found to be robust under a wide range of conditions. Additionally, we demonstrate that using the approximation results in only marginal deviation of profits from the theoretical Nash optimal.

Original languageEnglish (US)
Pages (from-to)1084-1106
Number of pages23
JournalEuropean Journal of Operational Research
Volume182
Issue number3
DOIs
StatePublished - Nov 1 2007

Keywords

  • Logit models of competition
  • Marketing
  • Pricing

ASJC Scopus subject areas

  • Computer Science(all)
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management

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