Should a multiproduct monopolist whose "average price" is capped by regulation be allowed to engage in (third-degree) price discrimination? If the cap applies to a price index with weights proportional to demands at uniform prices, then price discrimination benefits consumers as well as the firm. But if -- perhaps more realistically -- it is the firm's average revenue that is capped, then consumers prefer uniform pricing. In this case total output is higher when discrimination is allowed, which increases welfare, but marginal utilities differ across markets, which is inefficient, and the overall effect is ambiguous. A small amount of discrimination is desirable, however. It is better not to allow price discrimination if the price cap is close to the level of marginal cost. The consequences of tightening the price cap when discrimination is allowed are also examined.
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