2021 S2 ECON8039/3004 HEALTH ECONOMICS TUTORIAL WEEK 11 Q1: TB CH12, Q11 11 Suppose there is a test, o, that yields the distribution of test outcomes for good drugs and bad drugs seen in Figure 12.9. In this case, is it possible to create a rule for P bad drugs good drugs Figure 12.9. Bad drug and good drug distributions for Exercise 11. T+ accepting and rejecting drugs that yields no Type I or Type II error? If so, be sure to show this threshold rule explicitly on the graph above. If not, explain why this is impossible. + reject these drugs approve these drugs Type I error: a false positive decision; a bad drug gets approved for sale. Type II error: a false negative decision; a good drug gets rejected. bad drugs good drugs Density Type I error 1 Type Il error +T Q2: TB CH12, Q12 12 Explain why the following statement is true, or provide a counter-example: A receiver- operator characteristic curve, which plots the Type I error of a test against the Type II error from that same test, always slopes downward. See Figure 12.8(b) for an example of this kind of curve. The statement is true. Assuming that the distribution of T has full support, then increasing the threshold always (weakly) decreases the Type-1 error, and (weakly) increases the Type-2 error. Thus the receiver-operator characteristic curve always slopes downward. (a) Five possible thresholds (b) Receiver-operator characteristic (ROC) curve T: Density bad drugs good drugs Type I error · T T2 Ts · T'3 · TA > B Type II error
Q3: TB CH12, Q14 14 Establishing a new drug in the market. Bhattacharya and Vogt (2003) study the pric- ing strategies of pharmaceutical companies that bring new drugs to market. They observe that new drugs often debut at relatively low prices and get more expensive over time. They interpret this strategy as an attempt by the drug company to establish its drug in the minds of doctors and patients before trying to extract monopolistic profits. Recall our fictional drug for carpal tunnel syndrome called BHTnl which was introduced in Section 12.1. a Suppose demand for the new drug is Q=1,000-P where P is the price that the monopolistic firm sets. What price will the firm choose to maximize profits II = PQ? We assume the cost of producing the drug is negligible throughout this problem. max PQ max P (1000-p) For wort P : 1000-P-P = 0 > p+ = 500 b Now suppose that Bhattacharya and Vogt are on to something when they say that drug companies must manage the stock of knowledge about their drug. Imagine a two-period model where the drug company is trying to maximize the sum of profits over two periods. In the first period, the monopolistic firm will price low to build buzz about BHTn1, and in the second period the firm will capitalize on its popularity. Demand in year 1 (Q1) and demand in year 2 (Q2) are