1) Suppose a firm, Neurotech, owns the patent needed to produce a pill that cures alzheimer's disease, and thus is the only firm that can produce and sell this pill. Given that this is a huge scientific/medical breakthrough, the pill only needs to be taken once and there are no close substitutes for this pill. a) Draw a diagram representing this market, be sure to show the profit maximizing quantity and price of the Neurotech pill. Draw standard cost curves such that the firm is making positive profits, and clearly show the area on your graph that corresponds with the firm's profits. Make sure to label all relevant curves. b) Now draw the diagram again, but shading in consumer surplus, producer surplus, and deadweight loss. c) If the government were to regulate the price of Neurotech pills to maximize total surplus, what price should be set (assume the firm cannot shut down for now)? Show the price in your diagram, the corresponding quantity that Neurotech will provide, and explain why this price is the efficient price. d) Now let's examine Neurotech's situation more precisely. The total cost function of the firm is given by C(Q) = 32000 + 6Q, with Q measured in millions. Market inverse demand is given by P=6350-4Q. Find formulas for the MR curve, MC curve, and AC curve. e) Solve for the profit maximizing Q and P, and monopoly profit. Sketch the AC curve, MC curve, MR curve, and demand curve, labeling the profit maximizing quantity of pills and the monopoly price per pill. In no more than two sentences indicate how these cost curves differ from what you drew in part (a) and why they are reasonable for a pharmaceutical product. f) Suppose that due to political pressure, the government decides to regulate the price, requiring Neurotech to charge the efficient price. What would be the price, quantity, and the profits for Neurotech, in this case? Is this a sustainable policy? g) If the government wants Neurotech to charge the lowest price that allows it to stay in business, what price should the government require? You do not need to calculate this price, just explain how the government would find this price. Would the quantity that corresponds to this price be higher, lower, or the same as the efficient quantity found in part (f)