Blackorby and Murty [2007] prove that, with a monopoly and under one hundred percent 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. In this paper, we relax the assumption of one hundred percent profit taxation and allow the consumers to receive profit incomes from ownership of shares in the monopoly firm. We find that, 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.