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We analyse the effect of competition on quality in hospital markets with regulated prices, considering both the effect of (i) free patient choice (monopoly versus competition) and (ii) increased competition through lower transportation costs (increased substitutability). With partly altruistic providers and a convex cost function that is non-separable in activity and quality, we show - in both cases - that the effect is generally ambiguous. In contrast to the received theoretical literature, this is consistent with, and potentially explains, the mixed empirical evidence.