Question 5 (Monopoly) Suppose the demand curve of a monopolist is given by p(q) = 20 - q and the cost curve is given by c(q)=q² .

a) What is the firm's profit maximizing level of output? What are profits at this level of output?

b) Suppose the government imposes a quantity tax on the monopolist so that it has to pay $4 for every unit it sells. What is the profit-maximizing level of output? What are profits? (Hint: increase the marginal cost by $4)

c) What happens to the optimal level of output and profits if the government imposes a lump-sum tax on the monopolist (instead of a quantity tax)?