Optimal Three-Part Tariff Plans
研究电信运营商等服务业的三部分定价方案，提出一种基于全局利润上界的新方法，在消费者理性、存在心理成本、消费率确定或随机、消费者同质或异质等一般条件下，显式计算最优定价方案。
Service providers, such as cell phone carriers, often offer three-part tariff plans that consist of three levers: A fixed fee, an allowance of free units, and a price per unit above the allowance. In previous studies the optimal three-part tariff contract was characterized using the standard first-order conditions approach. Because this optimization problem is nonsmooth, however, it could only be solved in a few simple cases. In this study we employ a different methodology that is based on obtaining a global bound for the firm profit, and then showing that this bound is attained by the optimal plan. This approach allows us to explicitly calculate the optimal three-part tariff plan under quite general conditions, where consumers are rational, they have a general utility function, they experience psychological costs when they exceed the number of free units, they have deterministic or stochastic consumption rates, they are homogeneous or heterogeneous, and the firm costs are fixed or depend on the usage level. The online appendix is available at https://doi.org/10.1287/opre.2017.1609 .