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Price regulation of a multi-market monopolist, with the cap based on average revenue, can cause welfare to be below the unregulated level. In a model with linear demands and constant but unequal marginal costs, a sufficient condition for this welfare effect is that the cap equals the average revenue that would be earned with marginal cost pricing. Relaxation of the price cap can lower all prices. Welfare with uniform pricing at the level of the price cap can be above or below the average revenue welfare level.