The Limits of Price Discrimination When the Market Is Unknown

Irfan Tekdir

Papers from arXiv.org

Abstract: 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 $\pi\ln(\bar{v}/\pi)$ when producer surplus (the seller's profit) is $\pi$, this bound is reached without segmentation, and no market gives consumers more than $\bar{v}/e$.

Date: 2026-10, Revised 2026-10
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