In this case we need not distinguish between the short-run and the long-run because, in general, the monopolist always realizes some excess profits — both in the short-run and in the long-run.
Under these conditions, the imposition of a lump-sum tax will’ reduce the excess profits of the monopolist because it will increase his total fixed cost However, the MC curve of the monopolist will not be affected, and, hence, the equilibrium in the monopoly market will remain the same even in the buy-run, if the lump-sum tax does not exceed the supernormal profits of the monopolist.