Solving Share Equations in Logit Models Using the LambertW Function
Review of Marketing Science, 2011

Though individual demand and supply equations can readily be expressed in logit models, closed-form solutions for equilibrium shares and prices are intractable due to the presence of products of polynomial and exponential terms. This hinders the employment of logit models in theoretical studies, and also makes it difficult to develop reduced-form expressions for share and price as a function of exogenous variables for use in empirical studies.

In this paper, Professor Ashwin Aravindakshan and co-author Brian Ratchford from the University of Texas, Dallas propose that a mathematical function called the ‘LambertW’ be employed in solving logit models for equilibrium shares and prices. The authors derive closed form solutions for price and share in both the monopoly case as well as in the presence of competition.