Optimal Contracts for Time-Inconsistent Consumers with Heterogeneous Beliefs

Abstract

In many markets (e.g., cell phones, video games), firms offer menus of contracts that include some tariffs charging per-usage prices above marginal cost and others below marginal cost. We term this puzzling phenomenon as two-sided deviations from marginal cost pricing, and present a potential explanation based on two well-recognized consumer characteristics. The first one is that consumers' actual consumptions may depart systematically from their initial plans (i.e., time-inconsistent preferences). In addition, consumers can be either sophisticated or naive in their beliefs about their time inconsistency (i.e., heterogenous beliefs). We characterize properties of the optimal contracts for a firm to screen the time-inconsistent consumers with heterogeneous beliefs. We articulate the conditions under which the optimal menu may account for two-sided deviations from marginal cost pricing. 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. Moreover, we confirm that our main results are robust to the presence of time-consistent consumers.

Keywords: time inconsistency, sophistication, naivete, screening, price discrimination