Taxing a monopolist

We consider a simple, self-financing and informationally undemanding scheme to reduce the deadweight loss due to a monopolist's market power. Essentially, we propose taxing the monopolist and applying the tax revenue to generate a public demand for his output. It turns out that a favorable scenario for such a reform to generate an 'efficiency increase' (i.e. to increase total output) is an elasticity of market demand with an absolute value of less than 3 (a seemingly 'realistic' condition). We also consider the case for the implementation of the first best, and compare specific and ad-valorem taxes as a way to finance the public demand.