Esrm/Econ/Envir 235
Problem Set #4 Problem 1 (15 points). The government is considering a regulation which would require a more stringent safety
standard for passenger cars. The regulation imposes upfront costs on the industry in the amount of $100 million, as
well as an increase of $300 dollars in the price of each vehicle sold. Assume 1 million vehicles will be sold every
year. However, the government estimates that the regulation will reduce the annual risk of death from 1/100,000
to 1/200,000 for all drivers (not only the new vehicle buyers). In total, there are 10 million drivers affected by the
regulation annually. The regulation is going to be effective immediately and is estimated to be in place for 20 years.
a. (3 points) How many “statistical lives” are saved each year by the regulation? b. (10 points) Fill in the following table:
VSL,
$million
6 6.3 9 0
Discount
rate, r 0.05
0.1 Since regulations are effective immediately, 50 lives are saved every year, starting at t=0 (first year of the
program).
Hint: In each cell of the table, you want to write the Present Value of the policy for that VSL and discount
rate combination. For computing each PV-- Develop a spreadsheet in Excel, with your columns being: time
(year 0 to year 19), then benefits (VSL * “statistical lives saved”), costs, net benefit, and discounted net
benefit (NB/(1+r)^t). Sum up the discounted NBs across all years and enter the numbers in the table. You
might as well include your spreadsheet when you turn in the assignment, but it’s not required. c. (2 points) Discuss your results. What would your recommendation be as far as implementation of
this regulation goes? 1 Problem 2 (10 points). Traditional (exponential) discounting. Using a spreadsheet program, graph the
changes in the present value of 1 billion dollars over time. Use a one year step, starting at year t=0
(today) up to year t=99. Set up a table of the following format, and compute the present values under
different assumptions about the discount rate. Put time on the horizontal axis, the present values on the
vertical axis, and graph all the present value curves on the same graph (we have 3 different discount
rates, so you should have 3 curves on the graph).
t PV using
PV using
PV using
r=0.01
r=0.05
r=0.1
0 1000000000 1000000000 1000000000
1
2
…
99 (5 points) What is the present value of 1 billion dollars at t=99 (i.e., in one hundred years)? Discuss the
importance of the choice of a discount rate for evaluating, for example, environmental damages
removed into a fairly distant future. Problem 3 (15 points). Travel cost method and a value of a recreation site.
Consider a situation where there is a lake, call it S (for site), which is visited for recreation by the
residents of 3 towns: A, B, and C. Town populations and distances to the lake are given in the following
table: Town
A
B
C Distance to lake S, miles
10
20
30 Population
100
200
300 2 The hourly wage rate is $12 in all three towns, and, because of differing topographic conditions and road
quality, it takes residents from all the three towns 1 hour total to drive to the lake and come back to their
town. Assume that the value of time spent driving is 1/3 of the hourly wage rate. Further assume that
everyone drives vehicles that have 20 mpg fuel economy, and everyone drives alone. The price of gas is
$4/gallon. Trips are single-purpose trips (for recreation only).
Researchers estimated that the individual recreation demand function can be expressed as: Trips per
Year = 3 – 0.1*Cost of Single Trip.
Hint: Follow the in-class example to derive the 3 demand curves. To do that, do the following:
1) Convert the individual demand function into an inverse demand function. We have Q(P)=30.1*P, so P(Q)=30-10*Q.
2) Recognize that a travel cost from each town introduces “a tax” of sorts, so the individual
demand curve for a town becomes P(Q) = 30 – Travel Cost – 10*Q. Calculate the travel costs for each
town (remember, a trip involves going to the lake and coming back), and arrive at the 3 individual
demand curves.
3) Use the individual demand curves to find the number of visits, etc. Remember to multiply that
value by the town’s population to get the right number for the town. a. (5 points) The local government is considering charging fees for lake access. Assume that the fee
revenue will not affect the quality of the lake. Fill in the missing values in the following table
Fee charged
per trip, $ Number of
trips from
town A (trips
per year) Number of
trips from
town B
(trips per
year) Number of
trips from
town C (trips
per year) Total number
of recreators at
the lake (visits
per year) 0 (current
situation)
5
10
20 3 b. (5 points) Assuming the lake has no non-use value, what is the total annual economic value of
lake S (assuming no fees are being charged)?
Hint: Draw the three individual demand curves, find the total WTP (when fee=0), multiply those
by the population, and add them up to get the full benefit. See the in-class travel cost example
spreadsheet. c. (4 points) Assuming a discount rate of r=0.05 (5 percent), what is the net present economic
value of the lake S, where the lake is assumed to exist forever (in perpetuity). Hint: make use of
the following formula (based on the result about convergent geometric series):
∞ lim NPV ( T )=∑ T→∞ t=1 V (1+ r) V
V
=
=
t
(1+r ) 1−( 1 ) r , where V is the annual payment (e.g., annual
1+r value of ecosystem services) and r is the discount rate.
d. (1 point) Does a project which permanently enhances lake water quality and costs $100,000
today pass the benefit-cost test? Problem 4 (10 points). Budget allocation. Suppose you are charged with allocating a fixed budget among
independent projects. The projects and their benefits and costs are given by the following table:
Project
A
B
C
D
E
F Benefit, $
30
20
15
60
5
10 Cost, $
10
5
10
30
5
5 Ratio (B/C)
3
4
1.5
2
1
2 a. (4 points) Assuming projects are not divisible and are not repeatable, how would you allocate a
$50 budget if your goal is to maximize the benefit obtained? Explain your selection, and
compute the benefit you obtain.
b. (3 points) What if you can repeat projects? How does your answer to (a) change? c. (3 points) What if the size of your budget is reduced to $30? How does your answer to (a)
change?
4 5

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