A monopolist has an inverse demand curve given by p(y) = 12 y and a cost curve given by c(y) = y 2 .

(a) What will be its profit-maximizing level of output, and the corresponding price?

(b) At the optimal output level, does price equal marginal cost? Explain why or why not with economic intuition.

(c) Suppose that the government taxes a lump sum of $10 of the firm's profits. What will be the firm's output and corresponding price? What fraction of the tax is passed on to the consumer? (d) 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 the firm's output and corresponding price? What fraction of the tax is passed on to the consumer? [Note: unlike the example in class, the demand curve does not have constant elasticity, so the fraction passed on may be 1.]