Suppose that a monopoly faces the short-run cost function \(C=1,000+2 Q^{2}\) and the inverse demand curve \(p=500-0.5 Q\). How does charging the monopoly a per-unit tax of \(t=100\) affect the monopoly optimum and its profits? If a profits tax were instead imposed, would it affect the monopoly optimum? What would be the rate of a profits tax that raises the same amount of tax revenue as the specific tax?