Nonlinear Pricing with Underutilization: A Theory of Multi-part Tariffs
研究了当商品使用能为卖家创收且买家可自由处置时，最优定价为多部定价，其中部分层级边际价格为零。该模型解释了免费产品、免费试用和无限订阅等常见定价方案，并发现自由处置会损害生产者与消费者福利。
We study the nonlinear pricing of goods whose usage generates revenue for the seller and of which buyers can freely dispose. The optimal price schedule is a multi-part tariff, featuring tiers within which buyers pay a marginal price of zero. We apply our model to digital goods, for which advertising, data generation, and network effects make usage valuable, but monitoring legitimate usage is infeasible. Our results rationalize common pricing schemes including free products, free trials, and unlimited subscriptions. The possibility of free disposal harms producer and consumer welfare and makes both less sensitive to changes in usage-based revenue and demand.