Designing Optimal Menu of Subscription Plans under Time-inconsistent Preferences: An Empirical Investigation

Abstract

We empirically study how time-inconsistent preferences shape the optimal menu design of prepaid volume subscription plans for a firm. Using data from a gym, we first show that users systematically overpay for attending private training sessions due to under- and over-usages, a phenomenon consistent with time-inconsistent preferences. We then estimate a structural model and find that most users’ usage preferences at the planner stage exceed that at the doer stage. Counterfactual analysis reveals that the firm can exploit such a gap in preferences by introducing an “anchor” plan which offers a high quantity allowance with large price discount to target those users. It can then expand the menu by adding plans with smaller allowances to capture lower-preference individuals. This strategy sharply contrasts with the rational-expectations benchmark, under which the anchor plan would never be offered. While offering subscription plans would significantly increase the firm profit, the impact on consumer welfare is ambiguous: it improves users’ surplus from the planner’s perspective but reduces that from the doer’s standpoint. Our findings offer actionable managerial guidance on how to design subscription menus when behavioral biases are prevalent among consumers.