On the Optimality of Three-Part Tariff Plans

Abstract

Two and three-part tariffs are widely used, for selling goods, to compensate workers, and in procurement contracts. They are practical alternatives to complex non-linear tariffs in on-demand services and technology industries and are more profitable than the restrictive per-unit and unlimited-use pricing. A two-part tariff (2PT) imposes both a fixed (access) fee and a per-unit (usage) fee, and a three-part tariff (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 when the market demand follows an increasing price elasticity (or, approximately, when consumer distribution follows an increasing hazard rate), the optimal 3PT outcomes are identical to optimal 2PT outcomes. This result generalizes to a menu of tariffs. In contrast, the free allowance in a 3PT may be truly impactful when market demand is multimodal or corresponds to distinct segments with sharp across-segment differences, or when consumers have certain tariff biases. Our results help explain how and when 3PT matters, and can help managers make informed decisions about how to design and employ non-linear pricing.