A monopolist has an inverse demand curve given by p(y) = 12-y and a cost curve given by c(y) = y².

1. What will be its profit maximizing level of output? ________
2. Suppose the government decides to put a tax on this monopolist so that for each unit it sells it has to pay the government $2. What will be its output under this form of taxation? ________
3. Suppose now that the government puts a lump sum tax of $10 on the profits of the monopolist. What will be its output? __________