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                             Answers to Exercises for Chapter 14

1. The construction of a dam that would provide hydroelectric power would result in the
loss of two streams: one that is now used for sport fishing; and another that does not
support game fish but is part of a wilderness area.
        a. Imagine that a contingent valuation method is used to estimate the social cost of
        the loss of each of these streams. Would you be equally confident in the two sets
        of estimates?
        b. Consider two general approaches to asking contingent valuation questions about
        the streams. The first approach attempts to elicit how much compensation people
        would require to give up the streams. The second approach attempts to elicit how
        much people would be willing to pay to keep the streams. Which approach would
        you recommend? Why?

         1.a. As noted in the chapter, CV studies of use goods appear to give answers generally
consistent with methods based on observed behaviors. CV studies of non-use goods have not
been validated through comparisons with behavioral methods because the latter are not available.
Furthermore, they are especially prone to the many of the CV biases discussed in the text.
Consequently, one would likely place more confidence in valuations of use than non-use. In this
context, one would likely be more confident in the CV estimate of the value of sport fishing on
the first stream than CV estimates of the existence value of either of the two streams.

        1.b. If either WTA or WTP could be estimated by CV methods with the same degree of
confidence, then the first approach would be the most appropriate because it corresponds exactly
to the project under consideration. However, most experts believe that WTP estimates are so
much more reliable than WTA estimates that the former should always be used, even in a case
like this where WTA is conceptually more appropriate. See, for example, National Oceanic and
Atmospheric Administration, "Report of the NOAA Panel on Contingent Valuation," Federal
Register, 58, no. 10, (1993), pp. 4602-4614.

 2. A number of residents of Dullsville have complained to the mayor that the center of
town looks shabby compared to the centers of many other nearby towns. At the mayor’s
request, the Parks Department has put together a proposal for converting the town square
parking lot into a sitting park with flower displays—it modeled the design on a similar
park in the neighboring town of Flowerville. The annualized cost of installing and
maintaining the park, and relocating parking to nearby Short Street, would be about
$120,000. With about 40,000 households paying property taxes, the project would cost an
average household about $3 per year.
       You have been asked to give advice about conducting a survey to measure the
       benefits of the project.
       a. The Parks Department proposes conducting a telephone survey. Does this seem
       like an appropriate survey vehicle?
       b. How might a random sample be drawn for a telephone survey?
       c. Write a statement that could be read by the interviewer to describe the project.
       d. Write questions to implement the open-ended WTP method.
       e. Propose a procedure for implementing the dichotomous choice method.
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        2.a. As the project and the questions that need to be asked to value it are relatively
simple, a telephone survey is a reasonable approach. It is likely to be much less expensive than
personal interviews and likely to have a higher response rate than would be obtained from a mail
survey.

       2.b. One commonly used procedure is to generate random numbers between "0000" and
"9999" to be used with the telephone exchange for the town. A personal computer could be used
to generate a list of telephone numbers that match the random numbers and check to eliminate
duplicate numbers. Callers could then try numbers on the list until the target sample size is
obtained.

         If the exchange extends beyond the town, then a screening question would be asked
initially to see if the respondent lived within the town -- assuming only town residents are given
standing. If standing is not limited to town residents, then telephone exchanges covering an area
in which people could reasonably be expected to care about the project should be the basis for
sampling.

      2.c. An appropriate statement would fully describe the project, how it will be funded, and
whether the respondent is answering as an individual or as the representative of a household. For
example:

THE TOWN OF DULLSVILLE IS CURRENTLY CONSIDERING REPLACING THE
PARKING LOT IN THE TOWN SQUARE WITH A SITTING PARK. THE PARK, SIMILAR
TO THE ONE IN THE CENTRAL SQUARE OF FLOWERVILLE, WOULD INCLUDE
DISPLAYS OF ANNUAL FLOWERS. THE DISPLACED PARKING SPACES WOULD BE
RELOCATED TO NEARBY SHORT STREET. THE COSTS OF INSTALLING AND
MAINTAINING THE PARK AND RELOCATING PARKING WOULD BE PAID FOR
THROUGH THE TOWN'S PROPERTY TAX. IF YOU ARE A RENTER, YOU SHOULD
ASSUME THAT THE TAXES WOULD BE PASSED ALONG TO YOU IN YOUR RENT.
TO HELP THE TOWN DETERMINE THE DESIRABILITY OF THE PARK, PLEASE
ANSWER THE FOLLOWING QUESTIONS. YOUR ANSWERS SHOULD BE FOR YOU
PERSONALLY AND NOT INCORPORATE THE VIEWS OF OTHER MEMBERS OF YOUR
HOUSEHOLD.

Respondents might be asked if they are familiar with the Flowerville Park. If they are not, then
more description of the proposed park might be given.

        2.d. The open-ended question could be quite simple, though it may be best to phrase it
slightly differently for homeowners and renters.

Version for property owners:

WHAT IS THE MAXIMUM AMOUNT THAT YOU WOULD BE WILLING TO PAY EACH
YEAR IN HIGHER PROPERTY TAXES TO HAVE THE PARK INSTALLED AND
MAINTAINED?
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Version for renters:

WHAT IS THE MAXIMUM AMOUNT THAT YOU WOULD BE WILLING TO PAY EACH
YEAR IN HIGHER RENT TO HAVE THE PARK INSTALLED AND MAINTAINED?

        2.e. The first question that must be answered concerns the prices that are to be offered.
As you know that the annual cost would be roughly $3 per household per year, you would
probably want to pick your spread of prices around this amount. As some people may view the
new parking as less desirable than the old parking, you should probably include some negative
prices as well as positive prices. Perhaps equally spaced prices from negative $5 to positive $25
would be a reasonable range for a project such as this.

         The second question is randomization. In this case, because the telephone randomization
is likely to be quite effective, the main concern is to insure that there are no systematic
differences due to the telephone interviewers. Therefore, you would probably want to give each
interviewer equal numbers of the different prices. If you were concerned about changes in the
interviewers skill or attention over the course of the survey, then you could give them the set of
different prices in random order.

3. Consider a project that would involve purchasing marginal farmland that would then be
allowed to return to wetlands capable of supporting migrant birds. Researchers designed a
survey to implement the dichotomous choice method. They reported the following data:

     Stated Price           Fraction of
 (annual payment          Respondents
       in dollars)     Accepting Stated
                        Price (percent)

                0                   98

                5                   91

               10                   82

               15                   66

               20                   48
               25                   32

               30                   20

               35                   12
               40                    6

               45                    4

               50                    2



What is the mean willingness-to-pay for the sampled population?
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        3. The mean WTP for the sample is approximately the price increment times the sum of
the fractions of acceptance:
($5)[0.98 + 0.91 + ... + 0.02] = ($5)(4.61) = $23.05.
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                                    Exercises for Chapter 15

1. A 40-mile stretch of rural road with limited access is used primarily by regional
commuters and business travelers to move between two major interstate highways. The
legal speed limit on the road is currently 55 miles per hour (mph) and the estimated
average speed is 61 mph. Traffic engineers predict that if the speed limit were raised to 65
mph and enforcement levels were kept constant, the average speed would rise to 70 mph.
        Currently, an average of 5,880 vehicles per day use the stretch of road --
approximately half are commuters and half are business travelers. Traffic engineers do
not expect that a higher speed limit will attract more vehicles. Vehicles using the road
carry, on average, 1.6 people. Traffic engineers predict that raising the speed limit on this
stretch of road would result in an additional 52 vehicle crashes involving, on average, 0.1
fatalities annually. They also predict that operating costs would rise by an average of
$0.002 per mile per vehicle.
        The average hourly wage in the county in which the majority of users of the road
work is $18.30/hour.
        Estimate the annual net benefits of raising the speed limit on the road from 55 mph
to 65 mph. In doing this, test the sensitivity of your estimate of annual net benefits to
several alternative estimates of the value of time savings and the value of life that you have
selected from the chapter.

         1. (There is also an answer to this question in an Excel file. The numbers differ slightly
due to rounding). The major benefit of the increase in the speed limit arises from a reduction in
travel time. The major costs arise from increases in fatalities, accidents, and vehicle operating
expenses.

TIME SAVED:
Time saved per vehicle = 40/61 – 40/70 = 0.084309 hrs

Number of passengers per year = 5880x365x1.6 = 3.434 million

Vehicle-hour savings = 0.0843 x 3.434 million = 289,510 hours

Value of time savings (business travelers at full wage rate; commuters at 0.5 times after-tax wage
rate)
 = [(.5)($18.30)+(.5)(.5)(.7)($18.30)]x289,510 = $3,576,172

This assumes the average person faces a tax rate of 30%. Strictly speaking the wages for
business travellers should include hourly benefits.

ADDITIONAL VEHICLE OPERATING COSTS:
Number of vehicle miles = 5880 x 365 x 40 = 85.85 million miles

Additional operating cost = ($0.002/mile)x(85.85 million miles) = $171,700

ADDITIONAL FATAL ACCIDENT COSTS:
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Cost of Fatal Accident = 1.05*VSL (using Zaloshnja et al.’s estimate in Table 15-1), and VSL =
$4.0 million (Table 15-1):

Additional Fatal Accident Costs = (.1)(1.05)($4,000,000) = $420,000

ADDITIONAL INJURY COSTS:
Table 15-3 shows that the cost of a non-fatal crash varies between roughly 0.1 percent of the
VSL and 80 percent of the VSL. The actual distribution of crashes is heavily weighted towards
minor injuries. Suppose the average crash cost equals 2 percent of the VSL, then:

Additional injury costs = (52 accidents)(0.02)($4,000,000) = $4.16 million

NET BENEFITS:
Consequently, the annual net benefits = -$1,175,528 (in 2002 dollars)

SENSITIVITY ANALYSIS:

                                                     VSL (Millions)
                                             2            4           6
Cost of An Accident              1       2,154,486       904,486    -345,514
(as % VSL)                       2       1,114,486    -1,175,514 -3,465,514
                                 4        -965,514    -5,335,514 -9,705,514

This table indicates that annual net benefits are very sensitive to the assumption made about the
value of life and the cost of an accident (as a % of the VSL).


2. Analysts estimate that the expansion of the capacity of the criminal courts in a city would
require about 7,200 additional hours of juror time. The average wage rate in the county is
$15/hour. A recent survey by the jury commissioner, however, found that the average
wage for those who actually serve on juries under the present system, who are also
currently employed, is only $9/hour. The survey also found that about one-third of those
who actually serve on juries under the existing system do not hold jobs-for example, they
are homemakers, retirees, or unemployed.
       a. What shadow price should the analysts use for an hour of jury time?
       b. About a quarter of jurors do not receive wages from their employers while on
       jury duty. How does this affect your choice of the shadow price?

       2.a. Some people enjoy jury service, while others find it distasteful. In the absence of
information about willingness-to-pay to avoid jury service, it is reasonable to use information
about wage rates in determining the shadow price.

        A reasonable starting point would be to use the before-tax wage rate plus benefits of
those who currently serve to value the time of those who are currently working. This would
underestimate the correct shadow price, however, if the procedures used to draw the additional
jurors shifted the wage distribution of jurors more toward that of the county as a whole.
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       It would be an underestimate of the correct shadow price to attribute zero wages to those
who are not in the labor market -- most homemakers, unemployed, and retirees would not place a
zero value on their time. Thus, some fraction of the wage of those who are currently working
should probably be used in valuing the time of non-workers.

        The number of hours actually served on jury duty may underestimate the time costs of the
jury system. Jurors may experience added commuting time, which would reasonably be valued
at a shadow price equal to about 50 percent of their after-tax wage rate. Potential jurors may also
spend time avoiding jury service; this time probably has a shadow price close to the wage rate.
Further, those who do successfully avoid jury service are likely to be from among the higher
wage earners.


        2.b. As a first cut, it does not make a difference whether or not jurors receive wages
from their employers -- the opportunity cost of their time is approximately their wage rate.
Whether or not they receive wages from their employers does, however, determine who bears
these costs. The distributional effects of jury duty are also affected by the fact that jurors are
usually paid a fee by the courts, albeit, an amount that is usually much lower than their wage
rates. Thus, there may significant distributional effects that a broader analysis would want to
consider.
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                                    Exercises for Chapter 17

1. A public health department is considering five alternative programs to encourage
parents to have their preschool children vaccinated against a communicable disease. The
following table shows the cost and number of vaccinations predicted for each program:
            Program                           Cost ($)                  Number of Vaccinations

               A                               20,000                           2,000

               B                               44,000                           4,000

               C                               72,000                           6,000

               D                              112,000                           8,000

               E                              150,000                           10,000
       a. Ignoring issues of scale, which program is most cost-effective?
       b. Assuming that the public health department wishes to vaccinate at least 5,000
       children, which program is most cost-effective?
       c. If the health department believes that each vaccination provides social benefits
       equal to $20, then which program should it adopt?

       1. Use the ratio of cost to number of vaccinations as a measure of cost-effectiveness.

        1.a. Ignoring differences in scale, program A is most cost-effective with a cost-
effectiveness of $10/vaccination.

        1.b. Of the programs that yield at least 5,000 vaccinations, program C is most cost-
effective with a cost-effectiveness of $12/vaccination.

       1.c. Switching to a CBA, we find that program E offers the largest net benefits, $50,000,
and should therefore be adopted.

2. Analysts wish to evaluate alternative surgical procedures for spinal cord injuries. The
procedures have various probabilities of yielding the following results:
       Full recovery (FR) — the patient regains full mobility and suffers no chronic pain.
       Full functional recovery (FFR) — the patient regains full mobility but suffers
       chronic pain that will make it uncomfortable to sit for periods of longer than about
       an hour and will interfere with sleeping two nights per week, on average.
       Partial functional recovery (PFR) — the patient regains only restricted movement
       that will limit mobility to slow-paced walking and will make it difficult to lift objects
       weighing more than a few pounds. Chronic pain is similar to that suffered under
       full functional recovery.
       Paraplegia (P) — the patient completely loses use of legs and would, therefore,
       require a wheelchair or other prosthetic for mobility, and suffers chronic pain that
       interferes with sleeping four nights per week, on average. Aside from loss of the use
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        of his or her legs, the patient would regain control of other lower body functions.
        a. Describe how you would construct a quality-of-life index for these surgical
outcomes by offering gambles to respondents. Test your procedure on a classmate, friend,
or other willing person.
        b. Assume that the index you construct on the basis of your sample of one
respondent is representative of the population of patients. Use the index to measure the
effectiveness of each of three alternative surgical procedures with the following
distributions of outcomes:
                                                    Surgical Procedures

                                    A                        B                        C

 FR                                .10                      .50                      .40

 FFR                               .70                      .20                      .45

 PFR                               .15                      .20                      .10

 P                                 .05                      .10                      .05

       c. Imagine that the surgical procedures involved different life expectancies for the
various outcomes. Discuss how you might revise your measure of effectiveness to take
account of these differences.

       2.a. Assign a value of 1 to full recovery (FR), the best outcome, and 0 to paraplegia (P),
the worst outcome. After fully describing the meaning of FR and P, you would offer the
respondent choices like the following:

         Which would you prefer, full functional recovery with certainty, or a 90 percent chance
of full recovery and a 10 percent chance of paraplegia?

      You would adjust the probabilities (chances) until the respondent is just indifferent
between the certain outcome and the gamble. For example, if the respondent were indifferent
between the choices given above, then your index would assign the value .9 to the outcome FFR.

       The process would be repeated for the outcome PFR. If the respondent were indifferent
between partial functional recovery with certainty and a 60 percent chance of full recovery and a
40 percent chance of paraplegia, then you would have the following quality-of-life index:

FR 1
FFR pFFR = .9
PFR pPFR = .6
P   0

       2.b. Calculating expected values over outcomes:
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Effectiveness(A) = (.1)(1)+(.7)(pFFR)+(.15)(pPFR)+(.05)(0)
          = .1+.7pFFR+.15pPFR

Effectiveness(B) = (.5)(1)+(.2)(pFFR)+(.2)(pPFR)+(.1)(0)
          = .5+.2pFFR+.2pPFR

Effectiveness(C) = (.4)(1)+(.45)(pFFR)+(.1)(pPFR)+(.05)(0)
          = .4+.45pFFR+.1pPFR

         2.c. The most straightforward approach would be to treat quality-of-life and longevity as
each contributing independently to utility. Each year of life would be weighted by the quality-
of-life index and discounted back to the present. In this way, a new index number would be
found for each combination of quality-of-life and longevity. The new index could be used as in
part b to measure effectiveness.

         If a sufficiently small number of combinations of quality-of-life and longevity appeared
as possible outcomes of the alternatives, then it might be feasible to present respondents with
choices between them and gambles involving extreme outcomes. This method would avoid the
restrictive assumption that quality-of-live and longevity have independent effects on utility. If
the possible outcomes included a large number of quality-of-life and longevity combinations,
then this alternative method would typically be impractical to implement through the available
survey resources.

3. (Spreadsheet provided) Two alternative mosquito control programs have been proposed
to reduce the health risks of West Nile disease in a state over the next five years. The costs
and effectiveness of each program in each of the next five years are displayed below:
                                  Alternative A                           Alternative B

                       QALYs Saved        Incremental Cost     QALYs Saved        Incremental Cost
                                             (Millions of                            (Millions of
                                              Dollars)                                Dollars)

      Year 1                1.0                   3.8               0.5                   1

      Year 2                0.5                   0                 0.5                   1

      Year 3                0.3                   0                 0.5                   1

      Year 4                0.1                   0                 0.5                   1

       a. Calculate CE ratios for each program without discounting.
       b. Calculate CE ratios discounting cost but not effectiveness assuming a discount
       rate of 4 percent.
       c. Calculate CE ratios discounting both costs and effectiveness at 4 percent.
       d. Assume that the uncertainty range for each of the yearly effectiveness
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       estimates is plus or minus 20 percent, and the uncertainty in each of the yearly cost
       estimates is 10 percent. Assuming uniform distributions of errors, produce Monte
       Carlo distributions of CE ratios for each program and compare them.

The provided spreadsheet provides the basis for answers to all parts.

                                                   Alternative A                    Alternative B
                                                    C/E ($m per )                   C/E ($M per Q)
3.a. CE without Discounting                    0             2.00                             2.00

3.b CE discounting only C                   0.04             2.00                               1.89

3.c. CE discounting C and E                 0.04             2.06                               2.00



3.d The spreadsheet is set up to do a Monte Carlos with 1000 trials for different assumptions
about uncertainty and the assumed discount rate.
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