Endogenous third-degree price discrimination in Hotelling model with elastic demand

Abstract

We relax two common assumptions in the Hotelling model with third-degree price discrimination: inelastic demand and exogenously assumed price discrimination. Based on the constant elasticity of substitution representative consumer model, we allow firms to endogenously choose whether to acquire consumer information and price discriminate. We find that when the information cost is sufficiently low, there exist two symmetric sub-game perfect Nash equilibria irrespective of the demand elasticity: both firms acquiring information and price discriminating, and neither firm acquiring information and charging a uniform price. This implies that the widely discussed prisoners’ dilemma, in which both firms are exogenously assumed to price discriminate, is not in fact a dilemma. A comparison of social welfare shows that when the demand elasticity is large enough, price discrimination improves social welfare. This is in contrast to the finding—price discrimination harms social welfare—in the existing literature assuming perfect inelastic demand.