Welfare of Price Discrimination and Market Segmentation in Duopoly

We study welfare consequences of third-degree price discrimination and market segmentation in a duopoly market with captive and contested consumers. A market segmentation divides the market into segments that contain different proportions of captive and contested consumers. Firm-optimal segmentation divides the market into two segments and in each segment only one firm has captive consumers. In contrast to the existing literature with exogenous segmentation, price discrimination under firm-optimal segmentation unambiguously reduces consumer surplus for all markets. Consumer-optimal segmentation divides the market into a maximal symmetric segment and the remainder, and yields the lowest producer surplus among all segmentations.