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We study price-cap regulation in a market in which a vertically integrated upstream monopolist sells an essential input to a downstream competitor. In the absence of regulation, entry benefits both firms, but may harm downstream consumers because the upstream monopolist can set a high input price that would push downstream prices above the unregulated monopoly level. However, if a regulator caps the incumbent's upstream and downstream prices, consumers and firms are better off after entry than under a price-cap monopoly. We extend our model to examine the concern that price caps may induce incumbents to forgo cost-reducing investments and dampen entrants' incentives to self-provision the input. [ABSTRACT FROM AUTHOR]