Behavior-based price discrimination and elastic demand

Existing studies on Behaviour-based price discrimination (BBPD) typically show that firms offer discounts to encourage consumers located middle of the line segment to switch in a duopoly model. However, in practice, some firms offer both this discount and a discount to encourage consumers with lower preferences for the product itself to buy at the same time. I introduce heterogeneity of consumer willingness to pay and relax the assumption that the market is fully covered. Then, there are three purchase histories: bought from a firm, bought from another firm, and bought nothing. I assume that the two firms offer three different prices according to the purchase histories under BBPD. In the second period, firms offer discounts not only for rival customers but also for customers who bought nothing. On the other hand, firms offer higher prices for consumers who purchase the same goods over two periods in the second period than in the first period. This paper shows that BBPD does not lower all prices in the second period and does not increase consumer surplus.