Market Segmentation, Parallel Imports, and Incomplete Price Discrimination: The Welfare Effects of Regulations∗

We consider a regulated monopolist that faces a continuum of markets (e.g., [0, 1]) although a finite number k of prices must be charged. As a function of the integer k, we provide the optimal profit policy defined as the optimal market segmentation and the discriminatory prices. The social welfare is maximized for three prices, but the result is far below the benchmark, the welfare under the Ramsey price. As this price implies no profit, we study regulatory policies that yield a welfare closer to the benchmark, but compatible with "reasonable" profits. We show that a small amount of price discrimination can substantially enhanced the welfare when the monopolist is subject to an average price constraint.