1
Exercises for Chapter 9
11. Imagine a wilderness area of 200 square miles in the Rocky Mountains. How would
you expect each of the following factors to affect people’s total willingness-to-pay for its
preservation?
a. The size of the total wilderness area still remaining in the Rocky Mountains.
b. The presence of rare species in this particular area.
c. The level of national wealth.
1.a. Other things equal, we would expect people to place a higher value on preserving
this particular area, the smaller the total stock of Rocky Mountain wilderness remaining. The
reason is that we generally expect declining marginal utility as more of any good is "consumed,"
whether through use or nonuse.
1.b. Other things equal, the "rarer" the wilderness area is in terms of either its physical
characteristics or the species that make it their habitat, the higher people's willingness to pay to
preserve it. One way to view rareness is in terms of the stock of comparable areas. People are
likely to have the largest willingness-to-pay for areas that are unique in some significant way,
because, if it is really unique, the area constitutes the total remaining stock.
1.c. Other things equal, the wealthier people are the more they are willing to pay for all
normal goods, including those that offer nonuse value. This may be one reason why
environmental movements appear stronger in more developed countries.
2. An analyst wishing to estimate the benefits of preserving a wetland has combined
information obtained from two methods. First, she surveyed those who visited the wetland-
fishers, duck hunters, and bird watchers-to determine their willingness-to-pay for these
uses. Second, she surveyed a sample of residents throughout the state about their
willingness-to-pay to preserve the wetland. This second survey focused exclusively on
nonuse values of the wetland. She then added her estimate of use benefits to her estimate
of nonuse benefits to get an estimate of the total economic value of preservation of the
wetland. Is this a reasonable approach? (Note: In responding to this question assume that
there was virtually no overlap in the persons contacted in the two surveys.)
2. There is a danger that summing the estimates will result in an overestimate of total
willingness-to-pay. The reason is that some of the respondents from the state-wide survey may
also be users and potential users. These respondents would probably give a smaller willingness-
to-pay for nonuse if they were first asked to give their willingness-to-pay for use.
It would be conceptually correct simply to ask respondents in the state-wide survey their
willingness-to-pay amounts for use and nonuse together. This approach is problematic, however,
if only a small fraction of state residents are users -- the sample may provide too few users to
make reliable estimates of use values. On the other hand, estimating nonuse values based only
on the responses of users would not be a good alternative because the users probably differ in
important ways from the general population -- users are probably more familiar with the wetland
and they also probably live closer.
, 2
Exercises for Chapter 10
11. (Spreadsheet required) The following table gives cost and benefit estimates in real
dollars for dredging a navigable channel from an inland port to the open sea.
Year Dredging and Patrol Costs Saving to Shippers Value of Pleasure Boating
($) ($) ($)
0 2548000 0 0
1 60000 400000 60000
2 60000 440000 175000
3 70000 440000 175000
4 70000 440000 175000
5 80000 440000 175000
6 80000 440000 175000
7 90000 440000 175000
The channel would be navigable for seven years, after which silting would render it
un-navigable. Local economists estimate that 75 percent of the savings to shippers would
be directly invested by the firms, or their shareholders, and the remaining 25 percent
would be used by shareholders for consumption. They also estimate that all government
expenditures come at the expense of private investment. The social marginal rate of time
preference is assumed to be 1.5 percent, the marginal rate of return on private investment
is assumed to be 4.5 percent, and the shadow price of capital is assumed to be 1.3.
Assuming that the costs and benefits accrue at the end of the year they straddle and
using the market-based interest rate approach, calculate the present value of net benefits of
the project using each of the following methods:
a. Discount at the marginal rate of return on private investment, as suggested by the
U.S. Office of Management and Budget.
b. Discount at the social marginal rate of time preference, as suggested by the U.S.
Environmental Protection Agency.
c. Discount using the shadow price of capital method.
d. Discount using the shadow price of capital method. However, now assume that
the social marginal rate of time preference is 2.0 percent, rather than 1.5 percent.
e. Discount using the shadow price of capital method. However, now assume that
the shadow price of capital is 1.1, rather than 1.3. Again assume that the social marginal
rate of time preference is 1.5 percent.
f. Discount using the shadow price of capital method. However, now assume that
only 50 percent of the saving to shippers would be directly invested by the firms or their
shareholders, rather than 75 percent. Again assume that the social marginal rate of time
preference is 1.5 percent and that the shadow price of capital is 1.3.
, 3
The spreadsheet as provided is set up to answer immediately parts a, b, and c.
1.a. Using the marginal rate of return on private investment (4.5 percent) yields NPV =
$503,523. Thus, if the marginal rate of return on private investment is used as the discount rate,
then the project passes the net benefits test.
1.b. Using the social marginal rate of time preference (1.5 percent) yields NPV =
$878,428. Thus, if the social marginal rate of time preference is used as the discount rate, then
the project passes the net benefits test.
1.c. If we assume that all government expenditures on dredging and patrol displace
private investment, then we must multiply these costs by the shadow price of capital (1.3). We
should also multiply the 75 percent of the savings to shippers that they or their shareholders
invest by the shadow price of capital. For example, if shippers save $440,000 in a year, the
social value of these savings would be
(.25)($440,000) + (.75)($440,000)(1.3) = $539,000
Applying these adjustments to government expenditures and savings to shippers converts them to
consumption equivalents that can be added directly to the pleasure boating benefits, which are
direct consumption benefits. Once the costs and benefits for each year have been converted to
consumption equivalents, they can be discounted using the social marginal rate of time
preference (1.5 percent). This procedure results in NPV = $614,754, which passes the net
benefits test.
The spreadsheet must be modified to answer parts d, e, and f.
1.d. Using 2.0 as the marginal rate of time preference and the shadow price of capital
method results in NPV = $538,153, which does not pass the net benefits test. Note that the NPV
is not highly sensitive to modest changes in the marginal rate of time preference.
1.e. Using 1.1 as the shadow price of capital and 1.5 as the marginal rate of time
preference result in NPV = $790,536. Note that the NPV is not highly sensitive to modest
changes in the value of the shadow price of capital.
1.f. Assuming that 50 percent of the savings to shippers would be directly invested, but
again using 1.3 as the shadow price of capital and 1.5 as the marginal rate of time preference,
result in NPV = $399,969.
2. An analyst for a municipal public housing agency explained the choice of a discount rate
as follows: “Our agency funds its capital investments through nationally issued bonds. The
effective interest rate that we pay on the bonds is the cost that the agency faces in shifting
revenue from the future to the present. It is, therefore, the appropriate discount rate for
the agency to use in evaluating alternative investments.” Comment on the appropriateness
of this discount rate.
Exercises for Chapter 9
11. Imagine a wilderness area of 200 square miles in the Rocky Mountains. How would
you expect each of the following factors to affect people’s total willingness-to-pay for its
preservation?
a. The size of the total wilderness area still remaining in the Rocky Mountains.
b. The presence of rare species in this particular area.
c. The level of national wealth.
1.a. Other things equal, we would expect people to place a higher value on preserving
this particular area, the smaller the total stock of Rocky Mountain wilderness remaining. The
reason is that we generally expect declining marginal utility as more of any good is "consumed,"
whether through use or nonuse.
1.b. Other things equal, the "rarer" the wilderness area is in terms of either its physical
characteristics or the species that make it their habitat, the higher people's willingness to pay to
preserve it. One way to view rareness is in terms of the stock of comparable areas. People are
likely to have the largest willingness-to-pay for areas that are unique in some significant way,
because, if it is really unique, the area constitutes the total remaining stock.
1.c. Other things equal, the wealthier people are the more they are willing to pay for all
normal goods, including those that offer nonuse value. This may be one reason why
environmental movements appear stronger in more developed countries.
2. An analyst wishing to estimate the benefits of preserving a wetland has combined
information obtained from two methods. First, she surveyed those who visited the wetland-
fishers, duck hunters, and bird watchers-to determine their willingness-to-pay for these
uses. Second, she surveyed a sample of residents throughout the state about their
willingness-to-pay to preserve the wetland. This second survey focused exclusively on
nonuse values of the wetland. She then added her estimate of use benefits to her estimate
of nonuse benefits to get an estimate of the total economic value of preservation of the
wetland. Is this a reasonable approach? (Note: In responding to this question assume that
there was virtually no overlap in the persons contacted in the two surveys.)
2. There is a danger that summing the estimates will result in an overestimate of total
willingness-to-pay. The reason is that some of the respondents from the state-wide survey may
also be users and potential users. These respondents would probably give a smaller willingness-
to-pay for nonuse if they were first asked to give their willingness-to-pay for use.
It would be conceptually correct simply to ask respondents in the state-wide survey their
willingness-to-pay amounts for use and nonuse together. This approach is problematic, however,
if only a small fraction of state residents are users -- the sample may provide too few users to
make reliable estimates of use values. On the other hand, estimating nonuse values based only
on the responses of users would not be a good alternative because the users probably differ in
important ways from the general population -- users are probably more familiar with the wetland
and they also probably live closer.
, 2
Exercises for Chapter 10
11. (Spreadsheet required) The following table gives cost and benefit estimates in real
dollars for dredging a navigable channel from an inland port to the open sea.
Year Dredging and Patrol Costs Saving to Shippers Value of Pleasure Boating
($) ($) ($)
0 2548000 0 0
1 60000 400000 60000
2 60000 440000 175000
3 70000 440000 175000
4 70000 440000 175000
5 80000 440000 175000
6 80000 440000 175000
7 90000 440000 175000
The channel would be navigable for seven years, after which silting would render it
un-navigable. Local economists estimate that 75 percent of the savings to shippers would
be directly invested by the firms, or their shareholders, and the remaining 25 percent
would be used by shareholders for consumption. They also estimate that all government
expenditures come at the expense of private investment. The social marginal rate of time
preference is assumed to be 1.5 percent, the marginal rate of return on private investment
is assumed to be 4.5 percent, and the shadow price of capital is assumed to be 1.3.
Assuming that the costs and benefits accrue at the end of the year they straddle and
using the market-based interest rate approach, calculate the present value of net benefits of
the project using each of the following methods:
a. Discount at the marginal rate of return on private investment, as suggested by the
U.S. Office of Management and Budget.
b. Discount at the social marginal rate of time preference, as suggested by the U.S.
Environmental Protection Agency.
c. Discount using the shadow price of capital method.
d. Discount using the shadow price of capital method. However, now assume that
the social marginal rate of time preference is 2.0 percent, rather than 1.5 percent.
e. Discount using the shadow price of capital method. However, now assume that
the shadow price of capital is 1.1, rather than 1.3. Again assume that the social marginal
rate of time preference is 1.5 percent.
f. Discount using the shadow price of capital method. However, now assume that
only 50 percent of the saving to shippers would be directly invested by the firms or their
shareholders, rather than 75 percent. Again assume that the social marginal rate of time
preference is 1.5 percent and that the shadow price of capital is 1.3.
, 3
The spreadsheet as provided is set up to answer immediately parts a, b, and c.
1.a. Using the marginal rate of return on private investment (4.5 percent) yields NPV =
$503,523. Thus, if the marginal rate of return on private investment is used as the discount rate,
then the project passes the net benefits test.
1.b. Using the social marginal rate of time preference (1.5 percent) yields NPV =
$878,428. Thus, if the social marginal rate of time preference is used as the discount rate, then
the project passes the net benefits test.
1.c. If we assume that all government expenditures on dredging and patrol displace
private investment, then we must multiply these costs by the shadow price of capital (1.3). We
should also multiply the 75 percent of the savings to shippers that they or their shareholders
invest by the shadow price of capital. For example, if shippers save $440,000 in a year, the
social value of these savings would be
(.25)($440,000) + (.75)($440,000)(1.3) = $539,000
Applying these adjustments to government expenditures and savings to shippers converts them to
consumption equivalents that can be added directly to the pleasure boating benefits, which are
direct consumption benefits. Once the costs and benefits for each year have been converted to
consumption equivalents, they can be discounted using the social marginal rate of time
preference (1.5 percent). This procedure results in NPV = $614,754, which passes the net
benefits test.
The spreadsheet must be modified to answer parts d, e, and f.
1.d. Using 2.0 as the marginal rate of time preference and the shadow price of capital
method results in NPV = $538,153, which does not pass the net benefits test. Note that the NPV
is not highly sensitive to modest changes in the marginal rate of time preference.
1.e. Using 1.1 as the shadow price of capital and 1.5 as the marginal rate of time
preference result in NPV = $790,536. Note that the NPV is not highly sensitive to modest
changes in the value of the shadow price of capital.
1.f. Assuming that 50 percent of the savings to shippers would be directly invested, but
again using 1.3 as the shadow price of capital and 1.5 as the marginal rate of time preference,
result in NPV = $399,969.
2. An analyst for a municipal public housing agency explained the choice of a discount rate
as follows: “Our agency funds its capital investments through nationally issued bonds. The
effective interest rate that we pay on the bonds is the cost that the agency faces in shifting
revenue from the future to the present. It is, therefore, the appropriate discount rate for
the agency to use in evaluating alternative investments.” Comment on the appropriateness
of this discount rate.
