Fall 2012 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 1

Net PV of plan A: $36.6k
Net PV of plan B: $50k 

Also OK:

Gross PV of BAU: -$200k (or -$210 if you count year 0)
Gross PV of A: -$163k (or -$173)
Gross PV of B: -$150k (or -$160)

Plan B is best: highest net gain from BAU.

Question 2

(a) EV of project: -$2M.  Do not proceed.

(b) EV of hiring the firm: $2.45M.  Hire the consultant and then proceed with the project.  Note that the firm changes the probabilities but it's still unknown whether the public will like the project until after it's done.  (This is an important real world issue: public participation in the early stages of projects often makes a big difference in public satisfaction with the end result.)

Question 3

PV of benefits if CD: $1,228B; PV of benefits if PC: $614B; PV of costs: $1,200B. Expected NPV of proceeding without the study: -$95B.  Expected NPV of doing the study and then using its results appropriately: $12.4B.  The government should definitely do the study.

Question 4

PV of income: $195.5k; C0: $134.4k; C1: $67.2k; saves $15.6k

Question 5

Q 24; P $20; profit $40.

Question 6

Q 13; P $132; profit $1690.

Question 7

PV of profits if the project is successful: $14,388.  Expected NPV of project: -$1,367.  The firm should not undertake the project.

Question 8

(a) Annual CS during the monopoly period: $845; annual CS after the monopoly period: $3,380; PV of CS if the project is successful: $12,218; expected PV given 60% chance of success: $7,331.

(b) New expected NPV to the firm: $633.  The firm would now proceed with the project.  To answer the efficiency part, either of the following arguments were OK:

Expected NPV of SS less all costs: 0.6*(12,218+14,388-8,000-3,000)+0.4*(-8,000-3,000) = $4,964.  
Expected NPV of CS less CV: 0.6*(12,218-3,000)+0.4*(-3,000) = $4,331.  

Since the ENPV of SS is positive, the overall gains exceed the costs and the policy is efficient. Alternatively, since it's already known that the gains exceed the costs for the firm, it's sufficient to show that the policy is good for consumers and taxpayers: that is, that the ENPV of CS is greater than the CV (the second calculation).  The difference between the two ENPVs is the ENPV to the firm.