Consider a monopoly with the market demand D(p) = 120 p, where p 120. The monopoly's total cost function is C(Q) = 2Q.

a) Find the monopoly's optimal output Q_M and price p_M . For questions below, suppose that the monopoly is regulated by the government that set the highest price p_H = 64. That is, the monopoly can produce any output Q, but cannot set the price above 64.

b) Find the marginal revenue function of the regulated monopoly (Note: depending on the level of output, the formula for the marginal revenue can be different).

c) Find the optimal output Q_R and price p_R of the regulated monopoly.