2. Suppose a monopoly rm has a demand I; = 45 0.510 (the inverse demand is p : 90 2g) and the rm's cost is C : 100 + 2192. So xed costs are 100 and variable costs are 2q2. (a) (b) (C) (d) (6) What is the total revenue as a function of q? (Recall that the total revenue function is the inverse demand, or price, times q). Show that marginal revenue as a function of q is equal to 90 4g [recall that marginal revenue is the derivative of total revenue). What is the marginal cost and average cost as a function of .9? Set marginal cost equal to marginal revenue and solve for the prot max imizing output, q. What is the associated price and prot? Graph the inverse demand, marginal revenue, marginal cost, and aver age cost and label the producer surplus, consumer surplus, and \"dead weight loss" (the difference between consumer plus producer surplus at the monopoly price and at the output where price equals marginal cost. Calculate the \"dead weight loss\" using the formula for the area of a tri angle