On page 246 in Rosen Discussion question number 5 is a benefit cost problem

Below is an example of how you might respond to the question.

5.            a.   Bill is willing to pay \$0.25  to save 5 minutes, so he values time at \$.05 per minute.

The subway saves him 10 minutes per trip, or \$0.50.

The value of 10 trips per year is \$5.

The cost of each trip is \$0.40, or \$4 per year.

The annual net benefit to Bill is therefore \$1.

Formula for PV of a perpetuity = A/r

The present value of the benefits = \$5/0.25 = \$20;

the present value of the costs is  \$4/0.25 = \$16.

b.         Total benefits = \$20 x 55,000 =\$1,100,000.

Total costs \$16 x 55,000 = \$880,000

Net benefit = \$220,000

Formula for PV of a value in a single year = A/(1+r)t

c.  Costs = \$1.25 x 55,000= \$68,750

Benefits= 62,500/1.25+ 62,500/(1.25) 2=\$90,000

Net benefit \$21,250.

d. Subway project has a higher present value.

If a dollar to the “poor” is valued the same as a dollar to the “middle class,” choose the subway project.

e. Let X = distributional weight.

Set

NPV project 1 = NPV of project 2 with weight on benefits to the poor

220,000 = -68,750 +X ((62,500/1.25) + 62,500 /(1.25)2)

X=3.21.