Cost-Benefit Analysis (Rosen Chapter 12 )

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.