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.
NPV to government: G = $10.1 M; T = $15.8 M; T is better because costs fall more than CS. NPV of to firm: T = $0.2 M.
Manager's expected utility: C = 330; N = 310; manager prefers C. Donor's expected value: C = $110 K; N = $240 K; donor prefers N. Manager's expected utility with donor's offer: N = 372; manager would now choose N. Not required: expected value of the new deal to the donor = $230 K, which is still better than C.
PV of costs: M = $350 K; A = $650 K. PV of benefits: H = $1567 K; L = $313 K. Expected values: M = $88.7 K; A = $165 K; A is better.
The maximum the foundation would be willing to pay for the test is $1.6 M. Some intermediate details: if the study isn't done, the best option would be C with a payoff of $30 M. With the study, the probability of a report that benefits would be H (rH) is 64% and the probability of a report that benefits would be L (rL) is 36%. If rH occurs, the probability that benefits are actually H is 25% and the best action is N; if rL occurs, the probability that benefits are actually H is 4/36 or 11.11% and the best action is C.
Q = 214; P = $68 ; profit = $272.
Q = 60; P = $1530; profit = $90,000.
(a) ENPV = -$192 K. Firm would not undertake it.
(b) If the project works, PV of CS during the patent period = $561 K; PV of CS after the patent expires = $1357 K; total PV of CS = $1918 K. Accounting for the chance of success: expected PV of CS = $288 K.
ENPV to the firm under each policy: G = $8.2 K; P = $33.3 K; either policy would induce the firm to undertake the project. Expected cost to the government: G = $200 K; P = $225 K; the government would choose G.
Extra credit: if there are many firms, the government is clearly better off with P. The maximum payout under P is $1.5 M, but under G the payout would be $1.6 M for 8 firms and it would go even higher if the number of firms was larger.