Time Inconsistency and Naivete-Based Price Discrimination

In many markets, consumers need to sign advance contracts with upfront fees and usage-based payments. Yet they may value consumptions inconsistently over time. They tend to overconsume temptation goods (e.g., credit cards), but underconsume aversion goods (e.g., gym visits), relative to initial plans. Nevertheless, consumers may be either sophisticated or naive in their beliefs about future consumptions. In this research we study how a firm can design optimal contracts to screen consumers with heterogeneous beliefs about time-inconsistent preferences. We show that the optimal contracts may involve distortions and reversals in the per-usage prices, relative to the first-best benchmark when consumers’ belief heterogeneity is absent. The optimal per-usage prices intended for the sophisticated versus the naive consumers may deviate from the marginal cost in opposite directions, concurrently. This two-sided pricing deviation is consistent with many real-world observations. We also show that, contrary to intuition, a higher degree of time inconsistency may reduce firm profit and increase social welfare. Meanwhile, reducing consumer naivete may harm the society. Our main results are robust to the presence of time-consistent consumers. Moreover, in settings with repeated consumptions, the firm can use history-dependent prices to facilitate naivete-based price discrimination