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We study the welfare effects of price discrimination in a duopoly with both
captive and contested consumers. Using a unified information design approach,
we characterize the best and worst market segmentations for producer surplus,
consumer surplus, and social surplus. The firm-optimal segmentation, which divides
the market into two nested segments, consistently reduces consumer welfare
relative to uniform pricing. The consumer-optimal segmentation, which divides
the market into a symmetric segment and a nested segment, may sometimes yield
a Pareto improvement but does not necessarily coincide with the social-optimal
segmentation.