市场未知时价格歧视的边界
The Limits of Price Discrimination When the Market Is Unknown
Irfan Tekdir
AI 速览：在仅知可能价值集合、不知具体价值分布的情况下，刻画市场与市场分割所能产生的消费者剩余与生产者剩余组合。
Bergemann, Brooks, and Morris (2015) characterize the consumer and producer surplus pairs that segmentation can produce when the distribution of values is known. I fix only the set of possible values and characterize the pairs that some market and some segmentation can produce. They form a convex polygon. Its outer edge is the largest efficient surplus a market can have when its uniform-price profit is capped, net of that profit, and truncated equal-revenue markets attain it. At the values no segmentation is needed; strictly between two values, reaching the frontier requires splitting a market into two extremal markets. With a continuum of values up to $\bar{v}$, consumer surplus is at most $π\ln(\bar{v}/π)$ when producer surplus (the seller's profit) is $π$, this bound is reached without segmentation, and no market gives consumers more than $\bar{v}/e$.