Health Care Analytics

Assignment #3

Spring 2022

Note that in order to receive full credit for each problem, you must not only report the answer to each question asked, but also explain how you arrived at that answer. Simply stating your final answer will not result in the award of full points even if your answer is correct.

Problem 1: (5 points)

Suppose that a drug is in either Phase I, or II or III of the drug approval process with equal probability. If the drug is in Phase I, it has 0.1 probability of being successful, if it is in Phase II, it has 0.15 probability of success and if it is in Phase III, it has 0.25 probability of success. What is the overall probability that the drug will be successful?

Problem 2:

Consider a lottery, where you can either invest $100 or do nothing. If you do nothing, then have your original wealth of w. If you invest $100, then with probability 0.2, your total wealth will be w + 600, and with probability 0.8, your total wealth will be w 100. Assume that you are a risk neutral individual. What is your certainty equivalent (CE) of this lottery?

Problem 3:

Why do the profits of both the manufacturer and the distributor increase if the manufacturer offers to buy back unsold inventory?

Problem 4:

Consider a newsvendor model with random yield uncertainty. With probability 0.6, the entire production quantity is good and with probability 0.4, it is bad and has to be discarded. The revenue is r = 8 and the cost is c = 3. Assume that demand follows a Normal distribution with mean 600 and standard deviation 150. What is the optimal production quantity?

Problem 5:

Consider a pharmacy that has to decide how many seasonal allergy drugs to order before allergy season begins. The revenue from selling each drug is r = $10, the cost of purchasing each drug is c = $4 and each unsold drug can be salvaged at v = $2/drug. From historical data, the pharmacy determines the demand for this product, as provided below.