Fall 2008 Final Exam Solution

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.

Question 1A

PV of construction costs = $545M.  PV of the externality on residents = $40M.  Total costs = $585M.  PV of benefits = $570M.  Net PV = - $15M.  Don't build the line.

Question 1B

PV of CS if the wind farm is built = $78M.  Expected net PV of the line including the wind farm = $16.  Decision changes: build the line.

Question 2A

Expected value of evaluating the regulation = $0.5M.  The government should proceed.

Question 2B

Expected value of hiring the consultant = $46M.  The city should hire the consultant.  The consultant is not very likely to report that the project would succeed (8% chance) but if it does, the project can proceed and the payoff will be very large.  Note that answering this problem correctly requires the use of conditional probabilities.

 Question 3A

Q=34, P=$82, profit = $1312.

Question 4A

Q=40, P=$45, profit = $800.   Note that this problem was set up with P and Q as small integers for clarity on the exam.  In a real-world case, they would be measured in thousands and profit would be in millions (e.g., 40,000 vehicles at a price of $45,000 with $800 million profit).

Question 4B

PV of monopoly profit = $9970.  Expected PV of developing the car = $-1508.  No, the firm would not proceed.

Question 4C

Expected value to the firm = $0.  If the project is successful, Q=80 and CS per year = $1600.  PV of CS = $32,000.  Expected PV of CS = $8000.  Expected value to the government (includes only direct payments, not PS or CS to avoid double counting) = $-4000.  Net gain in expected value to society over all = $0 + $8000 - $4000 = $4000.  Net gain of $4000 relative to 4B, where the project is not undertaken.