Here are the final numerical results for each section of the exam. You can use them to check your work if you do the exam for practice. If you have trouble with the problems, or don't get the answers shown here, stop by during office hours or make and appointment and we can go over them.
Relative to BAU, the NPV of policy C is $4.285M and the NPV of policy P is $5.105M. Both are better than BAU and policy P is the best.
(a) The EV of the startup is $208k. The EU is 280, which is less than the utility of the job, which is 316; the researcher will not launch the startup. The CE is $78,400, which is much less than the EV because the researcher is risk averse.
(b) The EU is now 331 and the researcher will accept the offer. Not required but the CE of the offer is $109.4k, which beats the $100k risk-free job.
The NPV of adopting C without the report is $720M. The expected NPV of adopting S without the report is $590M. If the report costs X dollars, the expected NPV of purchasing it and then choosing the best policy given H or L is $738M - X. The most the city would pay for the report is the difference between that and the next best payoff ($720M) or $18M.
(a) EV = -$50B. The government won't do it.
(b) The EV of the study is $10B. The government would do it. A few of the intermediate results that are needed along the way: probability of rG = 60%; conditional probability of G given rG = 75%; probability of rB = 40%; conditional probability of B given rB = 87.5%.
Q = 64; P = $4160; profit = $480.
Q = 40; P = $8200; profit = $320k.
(a) Expected NPV = -$283k. The firm would not undertake the project.
(b) PV of CS = $6.818M. Expected PV = $1.909M.
New expected NPV to the firm = $293k; the firm would undertake the project. Expected NPV to the government, including the CS, the profits if the vaccine succeeds, and less the grant = $1.332M.