We analyze oligopolistic third-degree price discrimination relative to uniform pricing when markets are covered. Pricing equilibria are critically determined by supply-side features such as the number of firms and their marginal cost differences. It follows that each firm's Lerner index under uniform pricing is equal to the weighted harmonic mean of the firm's relative margins under discriminatory pricing. Uniform pricing then lowers average prices and raises consumer surplus. We can calculate the gain in consumer surplus and loss in firms' profits from uniform pricing based only on the market data of the discriminatory equilibrium (i.e., prices and quantities).

中文翻译：

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市场被覆盖时寡头垄断中的三级价格歧视*

我们分析了市场覆盖时相对于统一定价的寡头垄断三级价格歧视。定价均衡主要由供给方特征决定，例如企业数量及其边际成本差异。由此可见，统一定价下每个公司的勒纳指数等于歧视性定价下公司相对利润的加权调和平均值。统一定价会降低平均价格并提高消费者剩余。我们可以仅根据歧视均衡的市场数据（即价格和数量）来计算统一定价带来的消费者剩余收益和企业利润损失。