Envir 235 – The government is considering a regulation

Envir 235 – The government is considering a regulation

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.

(3 points)How many “statistical lives” are saved each year by the regulation?

(10 points)Fill in the following table:

VSL, $million

6 6.3 9


Discount rate, r 0.05


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.

(2 points)Discuss your results. What would your recommendation be as far as implementation of this regulation goes?

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 r=0.01 PV using r=0.05 PV using r=0.1

0 1000000000 1000000000 1000000000




(5points)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 Distance to lake S, miles Population

A 10 100

B 20 200

C 30 300

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 hourtotal 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)=3-0.1*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.

(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 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.

(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?(T?? )??NPV(T)=?_(t=1)^???V/?(1+r)?^t =(V(1+r))/(1-(1/(1+r)))=V/r??, where V is the annual payment (e.g., annual value of ecosystem services) and r is the discount rate.

(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 Benefit, $ Cost, $ Ratio (B/C)

A 30 10 3

B 20 5 4

C 15 10 1.5

D 60 30 2

E 5 5 1

F 10 5 2

(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.

(3 points)What if you can repeat projects? How does your answer to (a) change?

(3 points)What if the size of your budget is reduced to $30? How does your answer to (a) change?

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