Behavior-based price discrimination with a general demand

This paper offers a complete picture of the impact of behavior-based price discrimination on profits, consumer surplus, and welfare in markets with a general demand function, where consumers and firms can discount the future at different discount factors. Regardless of the demand function considered, in comparison to uniform pricing, BBPD reduces firms´ second-period prices and profits. In contrast, we show that new results arise regarding the impact of BBPD on first-period prices. Under perfectly inelastic and CES demand, the firm-side effect is null and the consumer-side e¤ect fully explains the increase in first-period prices. This is no longer the case when the price elasticity of demand varies with price level. Specifically, we show that the firm-side effect can lead firms to raise first-period prices, even when consumers are myopic. We also show that, depending on the demand function considered, the consumer side effect can act to reduce or increase first-period prices. The overall impact of BBPD on first-period prices depends on the interplay between these two effects. Our analysis reveals that the output effect and consumer switching plays an important role in explaining the impact of BBPD on welfare. When discount factors are equal, BBPD may have a positive or negative impact on consumer surplus and social welfare, which contrasts with the result that BBPD is beneficial for consumers under a unit and CES demand. For a linear demand function, we identify the regions for firms and consumers discount factors where BBPD can simultaneously enhance or reduce total discounted profits, consumer surplus, and social welfare.