An exact pricing algorithm for revenue maximization under the logit demand function

TL;DR

This paper introduces an exact, closed-form pricing algorithm for revenue maximization under the logit demand function, improving over heuristic methods and demonstrating significant revenue gains.

Contribution

It develops a novel analytical solution using the Lambert W function to determine the optimal price under the logit demand model, correcting common heuristic practices.

Findings

Optimal price is consistently lower than the inflection point.

Average 20% price reduction leads to 15% revenue increase.

Numerical experiments validate the effectiveness of the proposed algorithm.

Abstract

Determining the optimal selling price is a challenge in revenue management, especially in markets characterized by nonlinear and price-sensitive demand. While traditional models, such as linear, power, and exponential demand functions, offer analytical convenience, they often fail to capture realistic purchase dynamics, leading to suboptimal pricing. The logit demand function addresses these limitations through its bounded, S-shaped curve, offering a more realistic representation of consumer behavior. Despite its advantages, most existing literature relies on heuristic approaches, such as pricing at the inflection point, which prioritizes maximum price sensitivity but does not guarantee maximum revenue. This study proposes a novel, exact pricing algorithm that analytically derives the revenue-maximizing price under the logit demand function using the Lambert W function. By providing a closed-form solution, the approach eliminates reliance on heuristic iterative methods and corrects the common practice of considering the inflection point price as market price. In fact, we demonstrate that the optimal price is consistently lower than the inflection-point price under reasonable assumptions, leading to lower prices for consumers and higher revenue for sellers. Numerical experiments illustrate the proposed algorithm and examine the changes in the optimality gap as demand function parameters vary. Results indicate that the optimal price is consistently lower than the inflection-point price, with an average 20% price reduction accompanied by a 15% increase in revenue.