State whether the statement is true of false and explain.

1. The deadweight loss represent the sum of added consumer and producer surplus if the firm would produce the quantity where P = MC.
2. A specific tax imposed on a monopolist may increase the price by more than the tax.
3. An ad valorem tax imposed on a monopolist will reduce the deadweight loss generated by the monopolist.
4. What is the advantage of the government imposing an ad valorem tax over a specific tax when facing a monopoly?