Employing a general equilibrium framework, Blackorby and Murty prove that, with a monopoly and under 100% profit taxation and uniform lump-sum transfers, the utility possibility sets of economies with unit and ad valorem taxes are identical. This welfare equivalence is in contrast to most previous studies, which demonstrate the superiority of the ad valorem tax in a partial equilibrium framework. In this paper, we relax the assumption of 100% profit taxation and allow the consumers to receive profit incomes from ownership of shares in the monopoly firm. We find that, under certain regularity conditions, for any fixed vector of profit shares, the utility possibility sets of economies with unit and ad valorem taxes are not generally identical. But it does not imply that one completely dominates the other. Rather, the two utility possibility frontiers cross each other. Additionally, employing a standard partial equilibrium welfare analysis, we show that the Marshallian social surpluses resulting from the two tax structures are identical when the government can implement unrestricted transfers.