On the Optimality of Three-Part Tariff Plans: When Does Free Allowance Matter?

Two- (2PTs) and three-part tariffs (3PTs) are widely used for selling goods, to compensate workers, and in procurement contracts. They are practical alternatives to complex nonlinear tariffs in on-demand services and technology industries and are more profitable than the restrictive per-unit and unlimited-use pricing. A 2PT imposes both a fixed (access) fee and a per-unit (usage) fee, and a 3PT generalizes it by bundling some free units (an allowance) into the fixed fee. Intuitively, bundling free allowance provides an additional lever to the firm, enabling it to charge differential marginal rates to improve profitability. However, designing a 3PT is a challenging problem, and the optimal solution is known only when the market has homogeneous consumers or two discrete segments. We advance theory about optimal 3PT design by developing a reformulation that simplifies the solution procedure for the general case and generates new theoretical and practical insights. Our analysis reveals, surprisingly, that whe...