Optimal criteria for selecting price discrimination metrics when buyers have log-normally distributed willingness-to-pay

This paper investigates how a monopoly seller should determine the optimal set of pricing variables (pricing metrics) for third-degree price discrimination applications in which buyers have log-normally distributed willingness-to-pay (WTP). In a setup that closely resembles linear and probit regressions, this paper shows that when the monopoly seller is restricted to using one metric and no price discrimination cost exists, the pricing metric that best reduces the residual variance of buyers’ willingness-to-pay is the one that maximizes revenue. Equivalently, the explanatory power of willingness-to-pay is the ordering criterion. This paper also shows that this criterion is not universally true when willingness-to-pay follows other distributions. When the seller incurs price discrimination costs associated with different metrics, the ordering criterion becomes the explanatory power of each pricing metric divided by its cost. This paper also discusses how to apply this model to solve real-world pricing problems with contingent valuation models or using probit regression.