Components of optimal price under logit demand

Amiya Basu, Tridib Mazumdar, Sevilimedu Raj

Research output: Contribution to journalArticle

4 Citations (Scopus)

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

Fingerprint

Logit
demand
Nonlinear equations
Profitability
value added
Costs
Insensitivity
marginal costs
System of Nonlinear Equations
market
Linear Approximation
Approximation
Weighted Sums
Closed-form Solution
Nash Equilibrium
Profit
Demand
Values
profit
customer

Keywords

  • Logit models of competition
  • Marketing
  • Pricing

ASJC Scopus subject areas

  • Information Systems and Management
  • Management Science and Operations Research
  • Statistics, Probability and Uncertainty
  • Applied Mathematics
  • Modeling and Simulation
  • Transportation

Cite this

Components of optimal price under logit demand. / Basu, Amiya; Mazumdar, Tridib; Raj, Sevilimedu.

In: European Journal of Operational Research, Vol. 182, No. 3, 01.11.2007, p. 1084-1106.

Research output: Contribution to journalArticle

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