3. Suppose a monopolist's per-period demand curve for a new computer chip is given by p= 1000.25q, and its marginal cost (mc) is $20. (a) What is the monopolist's profit-maximizing price and quantity, pm and qm ? Graph the market for the computer chip. (b) What is the socially optimal quantity of output, q ? (c) What is the per-period value of the innovation to society, v, if the innovation is competitively supplied instead? (d) Calculate per-period consumer surplus, deadweight loss, and monopoly profit. (e) Calculate the (discounted) present value of the patent to the monopolist if r=0.05 (or 5%) and the number of periods the patent last is n=20 years. Recall that T=[1(1/1+r)n]/r. (f) What is the social value of the invention, i.e. S=v/rvT