This Document Contains Chapters 15 to 19 Chapter 15 Exercises Valuing Impacts from Observed Behavior: Indirect Market Methods 1. Child care services in a small Midwestern city cost $30 per day per child. The high cost of these services is one reason why very few mothers who are on welfare work; given their low potential wages, virtually no welfare mothers are willing to pay these high costs. To combat this problem, the city establishes a new program: in exchange for their welfare benefits, a group of welfare recipients is required to provide day care for the children of other welfare recipients who obtain private-sector employment. The welfare mothers who use these day care services are required to pay a fee of $3 per day per child. These services prove very popular; 1,000 welfare children receive them each day and an additional 500 welfare children are on a waiting list. Do the mothers of the 1,000 children who receive services under the program value these services at $30,000 ($30 x 1,000) a day, $3,000 a day ($3 x 1,000), or at a value that is greater than $3,000 but less than $30,000? Explain. 1. On one hand, the fact that there is a long waiting list for day care services when welfare mothers are required to pay only $3 per day per child suggests that many welfare mothers are willing to pay well over $3 to receive this service. Hence, the welfare mothers who receive day care under the program must value it at considerably more than $3,000. On the other hand, the fact that virtually no welfare mothers are willing to pay $30 per day per child for day care suggests that $30,000 surely greatly exceeds the value that the welfare mother who receive day care under the program place on it. Unfortunately, in the absence of more information about willingness to pay, benefits from the program cannot be valued more precisely. We know only that they are likely to be substantially over $3,000 and substantially less than $30,000. 2. A worker, who is typical in all respects, works for a wage of $50,000 per year in a perfectly safe occupation. Another typical worker does a job requiring exactly the same skills as the first worker, but in a risky occupation with a known death probability of 1 in 1,000 per year, and receives a wage of $58,000 per year. What value of a human life for workers with these characteristics should a cost-benefit analyst use? 2. The workers require an additional $8,000 to accept a higher death risk of .001. The value of life implied by this is $8,000/.001 = $8,000,000. 3. (Instructor-provided spreadsheet recommended.) Happy Valley is the only available camping area in Rural County. It is owned by the county, which allows free access to campers. Almost all visitors to Happy Valley come from the six towns in the county. Rural County is considering leasing Happy Valley for logging, which would require that it be closed to campers. Before approving the lease, the county executive would like to know the magnitude of annual benefits that campers would forgo if Happy Valley were to be closed to the public. An analyst for the county has collected data for a travel cost study to estimate the benefits of Happy Valley camping. On five randomly selected days, he recorded the license plates of vehicles parked overnight in the Happy Valley lot. (As the camping season is 100 days, he assumed that this would constitute a 5 percent sample.) With cooperation from the state motor vehicle department, he was able to find the town of residence of the owner of each vehicle. He also observed a sample of vehicles from which he estimated that each vehicle carried 3.2 persons (1.6 adults), on average. The following table summarizes the data he collected:
Town Miles from Happy Valley Population (thousands) Number of Vehicles in Sample Estimated Number of Visitors for Season Visit Rate (Visits per 1,000 People)
A 22 50.1 146 3,893 77.7
B 34 34.9 85 2,267 65.0
C 48 15.6 22 587 37.6
D 56 89.9 180 4,800 53.4
E 88 98.3 73 1,947 19.8
F 94 60.4 25 666 11.0
Total 14,160
In order to translate the distance traveled into an estimate of the cost campers faced in using Happy Valley, the analyst made the following assumptions. First, the average operating cost of vehicles is $0.36 per mile. Second, the average speed on county highways is 50 miles per hour. Third, the opportunity cost to adults of travel time is 40 percent of their wage rate; it is zero for children. Fourth, adult campers have the average county wage rate of $9.25 per hour. The analyst has asked you to help him use this information to estimate the annual benefits accruing to Happy Valley campers. Specifically, assist with the following tasks: a. Using the preceding information, calculate the travel cost of a vehicle visit (TC) from each of the towns. b. For the six observations, regress visit rate (VR) on TC and a constant. If you do not have regression software available, plot the points and fit a line by sight. Find the slope of the fitted line. c. You know that with the current free admission, the number of camping visits demanded is 14,160. Find additional points on the demand curve by predicting the reduction in the number of campers from each town as price is increased by $5 increments until demand falls to zero. This is done in three steps at each price: First, use the coefficient of TC from the regression to predict a new VR for each town. Second, multiply the predicted VR of each town by its population to get a predicted number of visitors. Third, sum the visitors from each town to get the total number of predicted visits. d. Estimate the area under the demand curve as the annual benefits to campers. 3.a. The travel cost from each town consists of two components (admission is free). The first is vehicle operating expense, estimated as $0.12 per mile times the round-trip distance. The second is the opportunity cost of time, which is estimated as the travel time of adults multiplied by 40 percent of the wage rate. For example, the travel cost for a visit from Town A, which is 22 miles from Happy Valley (44 miles round trip), is: ($0.36/m)(44 m) + (0.40)($9.25/h)(1.6 adults)(44 m)/(50 m/h) = $21.05/vehicle-visit Because there are 3.2 persons/vehicle, the average travel cost per person is: $21.05/3.2 = $6.50/person. The costs per person (and the cost/trip) for the towns are thus: 3.b. The estimated regression equation (standard errors in parentheses, R2 = 0.96) is: The estimated equation indicates that each dollar of additional travel cost reduces the visit rate by 2.88 visits per 1000 residents. 3.c. Consider, for example, the impact of a $10 admission fee. The following table summarizes the calculation procedure:
Town New Visit Rate Predicted Visits
A 77.7-2.88*10 = 48.9 2,451
B 65.0-2.88*10 = 36.2 1,264
C 37.6-2.88*10 = 8.8 138
D 53.4-2.88*10 = 24.6 2,213
E 19.8-2.88*10 = -9.0 0
F 11.0-2.88*10 = -17.8 0
Total 6,065
Note that a $10 admission fee leads to a prediction of negative visit rates for Towns E and F. As visit rates cannot be negative, we set these predicted visit rates to zero. Summing the predicted number of visits for the towns gives a total 6,062 visits. Repeating this procedure leads to the following points on the derived demand curve:
Admission Fee ($) Predicted Visits
0 14,160
5 9,338
10 6,065
15 3,410
20 1,268
25 288
30 0
Demand falls to zero between $25 and $30. (The calculated choke price is $26.98, but the accuracy of the estimation procedure does not justify such a precise prediction) 3.d. To estimate the area under this demand curve, multiply the average heights of adjacent points times their width, $5, and sum: Therefore, our estimate of the annual benefits from camping in Happy Valley is $137,245. Chapter 16 Exercises Contingent Valuation: Using Surveys to Elicit Information about Costs and Benefits 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, 1993, 58(10), 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. 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? 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 ensure 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 (annual payment in dollars) Fraction of Respondents 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? 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. Chapter 16 Case Study Exercises Using Contingent Valuation to Estimate Benefits from Higher Education 1. a. Why did Blomquist and his colleagues believe that contingent valuation was needed to fully assess the value of a 10 percent expansion of KCTCS? b. Did their findings suggest that they were correct? 1.a. Blomquist and his colleagues believed that community-wide benefits (e.g., effects on citizenship, crime, and economic growth) and private non-monetary benefits (e.g., effects on child rearing and health) from education could not be captured without a stated preference approach such as contingent valuation. In other words, they thought there was missing markets problems. 1.b. Yes, their findings, if correct, suggest that willingness-to-pay for the expansion was well in excess of the private financial gains that would have resulted. 2. Blomquist and his colleagues predict that willingness-to-pay for a 10 percent expansion of KCTCS would be around $92.7 million. Do you think that this is a reasonable estimate? Why or why not? 2. There are a number of arguments and counter-arguments concerning the reasonableness of the $92.7 million estimate. Two of these appear below: First, in using the contingent value survey to estimate willingness-to-pay for a 10 percent expansion in estimates KCTCS the researchers attempted to control for noncommitment bias, a key potential problem with contingent valuation surveys, and they provide evidence that their method is valid. However, their findings may still be subject to other potential problems with contingent valuations, which are discussed in Chapter 13, such as hypotheticality. Second, the surveys on which the willingness-to-pay estimates were based may not be very representative of Kentucky households. The survey response rate in the larger of the two sample populations was only 29 percent. Moreover, only around half of the surveys that were returned were unusable because of wording errors in many of the survey questionnaires and had to be discarded. Finally, only surveys from respondents who indicated they would definitely pay the amount they stated they were willing-to-pay were used in the analysis. However, the researchers compared the demographic characteristics of the respondents who provided usable surveys with those for Kentucky residents surveyed in the U. S. Census and found them similar. Chapter 17 Exercises Shadow Prices from Secondary Sources 1. (Instructor-provided spreadsheet recommended.) Suppose 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 (before tax) hourly wage in the county in which the majority of users of the road work is $18.30/hour. The average income tax rate is 25 percent. Further assume that the average social cost of an accident (excluding the value of lost lives) is 1.5 percent of the value of a statistical life. 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, the value of life and the cost of an accident (excluding the value of lost lives) as a fraction of the VSL. 1. Here is a summary from the spreadsheet:
BENEFITS:
Leisure travellers 927,158
Business travellers 2,649,024
Value of time saved 3,576,182
COSTS:
Operating cost 171,696
Fatal crash cost 1,100,000
Non-fatal crash cost 8,580,000
COSTS: 9,851,696
Net Benefits -6,275,514
Sensitivity Analysis:
VSL (Millions)
4 5 6 11 13
Cost of 0.05 1,973,328 2,774,486 2,648,486 2,018,486 1,766,486
An Accident 1 -2,672 304,486 -315,514 -3,415,514 -4,655,514
(as % VSL) 2 -2,082,672 -2,295,514 -3,435,514 -9,135,514 -11,415,514
4 -6,242,672 -7,495,514 -9,675,514 -20,575,514 -24,935,514
This table indicates that the estimated 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). See the spreadsheet for sensitivity analysis with respect to the value of time saved. For an explanation about how to compute these numbers, see the Excel file. 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. 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. 3. (Instructor-provided spreadsheet recommended.) Assuming that the elasticity of the value of statistical life with respect to income is between 0.5 and 1.2 and that the value of statistical life in the United States is between $4 million and $13 million, ranges of values of a statistical life for Australia, Portugal, and Brazil are found in the first page of the spreadsheet, based on both equation (17.4) and equation (17.5). Data on per capita income were obtained from the Quick Reference Tables section of the World Bank site http://siteresources.worldbank.org/DATASTATISTICS/Resources/GNI.pdf, using the Altas method figures. Using the same source of data on per capita income, calculate ranges of the value of a statistical life for Norway, New Zealand and Croatia. 3. The World Bank website contains the following table (unless it has been updated): Given this information, the provided spreadsheet shows:
Gross National Income per capita 2008, Atlas Method US dollars
Australia $40,350
Portugal $20,560
Brazil $7,350
United States $47,580
It also computes the following VSLs (in US$) using equation (17.4) and using equation (17.5). Note that the VSL for the lower income country (Brazil) is negative using equation (17.4). For this country in particular it makes more sense to compute the VSLs (in US$) using equation (17.5). The World Bank table shows that the GDP per capita of Norway, New Zealand and Croatia are:
Gross National Income per capita 2008, Atlas Method US dollars
Norway $87,070
New Zealand $27,940
Croatia $13,570
United States $47,580
Sheet 2 of the spreadsheet provides VSLs (in US$), based on equations (17.4) and (17.5). Note that this procedure used does not take account of differences in the underlying mortality risk levels or attitudes towards risk in these countries, which may be important. Chapter 17 Case Study Exercises Shadow Pricing a High School Diploma 1. How would the shadow price of a high school diploma change if the labor force participation rate for increase? Assuming that the labor participation rates increase proportionally across the education categories and earnings of those working do not change, then the present values of the average compensation would increase proportionately so that the shadow price would increase. If higher were inducing more people to enter the workforce, and the wage increase were higher for the better educated, then the shadow price would increase even more. 2. (Instructor provided spreadsheet required) How much would the shadow price of a diploma change if the probabilities of high school graduates obtaining no further education, some college, and college graduation were 26 percent, 38 percent, and 36 percent, respectively, as assumed by WSIPP? The answer can be found by changing three cell values on the Benefits Calculations sheet of the spreadsheet: F10 should be changed from 34 to 26 percent, F16 from 31 to 38 percent, and F22 from 35 to 36 percent. These changes would increase the productivity estimate to $247 thousand, the productivity estimate adjusted for education costs to $195 thousand, the productivity estimated adjusted for externalities to $339 thousand, and the productivity estimated adjusted for both education costs and externalities to $286 thousand. Note to instructors: If you provide students access to the spreadsheet, then they can be encouraged to investigate the impact of changes in assumptions they find interesting on the shadow price. Chapter 18 Exercises Cost-Effectiveness Analysis and Cost-Utility Analysis 1. A public health department is considering five alternative programs to encourage parents to have their preschool children vaccinated against a communicable disease. The following table shows the cost and number of vaccinations predicted for each program:
Program Cost ($) Number of Vaccinations
A 20,000 2,000
B 44,000 4,000
C 72,000 6,000
D 104,000 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. What is the incremental cost-effectiveness ratio of program D? d. If the health department believes that each vaccination provides social benefits equal to $10, then which program should it adopt? 1. There is a spreadsheet available which shows the calculations. 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. The incremental cost-effectiveness ratio of program D is $16/vaccination. 1.d. Given a shadow price of $10/vaccination, the health department will be indifferent between doing program A and not doing any program. 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 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 death (D), the worst outcome. After fully describing the meaning of FR and D, 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 death? 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: 2.b. Calculating expected values over outcomes: 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. (Instructor-provided spreadsheet recommended) 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 (Millions of Dollars) QALYs Saved Incremental Cost (Millions of 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 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. 3. 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. Chapter 19 Exercises Distributionally Weighted CBA 1. A city is about to build a new sanitation plant. It is considering two sites, one located in a moderately high-income neighborhood and the other in a low-income neighborhood. Indeed, most of the residents in the latter neighborhood live below the poverty line. The city’s sanitation engineer insists that “the city needs the new plant and it has to go somewhere.” However, he is indifferent as to which neighborhood it is located in. The plant would operate at the same cost and as efficiently in either neighborhood, and about as many people would be affected by the air pollution emitted by the plant. The city hires an economist to study the two sites. The economist finds that the plant would cause a considerably larger fall in average property values in the higher income neighborhood than in the low-income neighborhood, given the more expensive homes that are located in it. Consistent with this, a contingent valuation study that the economist conducted finds that willingness to pay to avoid the sanitation plant is substantially higher in the higher income neighborhood than in the low-income neighborhood. The residents of the lower income neighborhood strongly prefer that the plant be built in the higher income neighborhood. In the face of the economist’s findings, what sort of arguments might they make? 1. The residents of the low-income neighborhood could begin by stressing the fact that they are presently considerably worse off than the residents of the higher income neighborhood and locating the sanitation plant in their neighborhood would exacerbate this situation. On the other hand, locating the plant in the higher income neighborhood would ameliorate the inequality. In addition, they can argue that the difference between the two neighborhoods in willingness to pay reflects the difference in income levels in the two neighborhoods; higher income people will always be willing to pay more for a normal good than lower income people, and clean air is probably a normal good. Basing the plant location on the finding from the contingent valuation study without first adjusting for the disparity in income between the two neighborhoods is inconsistent with a democratic ideal of "one man-one vote" by implicitly giving higher income households a larger number of votes. Finally, the residents of the low-income neighborhood might argue that while it is true that property values will fall by more in the higher income neighborhood, they as a result of their lower level of income, will suffer from a greater reduction in utility for each dollar reduction in property values than will the residents of the higher income neighborhood. 2. CBAs have been conducted of six proposed projects. None of these projects are mutually exclusive and the agency has a sufficient budget to fund those that will make society better off. The findings from the CBAs are summarized here in millions of dollars: Group I consist of households with annual incomes over $25,000, while Group II consists of households with annual incomes under $25,000. a. According to the net benefit rule, which of these projects should be funded? b. For which of the projects might distributional considerations be an issue? c. Compute internal distributional weights for the projects you selected in 2.b. Using these weights, indicate the circumstances under which each project might actually be undertaken. d. Recompute social net benefits for the six projects using a distributional weight of 1 for Group I and a distributional weight of 2 for Group II. Using these weight-adjusted net social benefit estimates, indicate the circumstances under which each project might actually be undertaken. In doing this, assume that the distributional weight for Group II is an upper bound-that is, it probably overstates society’s true generosity toward low-income households 2.a. According to the net benefit rule, all the projects with positive net social benefits should be funded. Therefore, Projects A, B, and, C should be funded; but Projects D, E, and F should not be funded. 2.b. Projects B, C, D. Projects B and C would make the Group II, the low-income group, worse off, while making Group I, the high-income group, better off. Because these projects also would result in an increase in net social benefits, a trade-off exists between economic efficiency and distributional considerations. Project D also presents such a trade-off since it would make Group II, the low-income group, better off, while decreasing economic efficiency. None of the other projects present such a trade-off. Project E would make both groups worst off and decrease economic efficiency, while Project A would increase economic efficiency, but make neither group worst off. Finally, Project F would both reduce efficiency and redistribute income from households in the low-income group to households in the high-income group. 2.c. In answering this question, only Projects B, C, and D need be considered. The internal weights for these projects (that is, the weights at which these projects would just break-even) appear below: The weight for Project B suggests that this project should be undertaken unless society values each dollar of cost imposed on the low-income households in Group II at four times what it values each dollar of benefits received by the higher income households in Group I. This seems unlikely. Moreover, an argument presented near the end of the chapter suggests that distributional weights should probably not exceed 1.5 or 2.0. Projects C and D involve more difficult judgments. For example, even though Project C would result in positive net social benefits, it nevertheless should not be undertaken if society values each dollar of cost imposed on the low-income households by at least 50 percent more than each dollar of benefits received by the higher income households. Similarly, even though Project D would result in negative net social benefits, it should be undertaken if society values each dollar of benefits received by the low-income households by at least one-third more than each dollar of costs imposed on higher income households. 2.d. Assigning a distributional weight of 2 to Group II causes the signs of the net social benefit estimates to change for only two of the six projects. Project C changes from positive to negative, while Project D changes from negative to positive. The ultimate decision on whether to undertake these two projects would have to be made on the basis of judgment. As indicated in the question, the distributional weight for Group II that was used in computing the weight-adjusted net social benefit estimates is believed to be an upper bound. As suggested in the answer to 2.c., unless decision-makers believe that the true distributional weight for Group II is at least 1.5, Project C should be undertaken. And unless they believe that it is a bit over 1.33, Project D should not be undertaken. Chapter 19 Case Study Exercises The Tulsa IDA Account Project 1. You are a decision-maker who has to decide whether to adopt the Tulsa IDA program on a permanent basis relying, in part, on the information provided by the CBA described in this case study. a. The case study provides results for a range of distributional weights varying between 1 and 3. As a decision-maker would you prefer that those conducting the study had selected one weight and based the reported findings on that weight or, as is actually done, force you to decide on the appropriate weight? b. As the decision-maker which weight would you select? Why? Based on the weight you selected, what would you conclude about the merits of the program? Note: to the extent you can, base your answers on the information presented in Chapter 19 about the selection of weights. c. Imagine that participation in the Tulsa IDA had been limited to households with incomes below the federal poverty line, rather than to those with incomes below 150 percent of the poverty line; but the estimates of benefits and cost had been exactly the same as those presented in the case. How would that change your answers to (b)? 1.a. Those conducting the study may know more than you do about distributional weights and so be better able to selection the most appropriate one. However, you may know from reading the chapter that the most appropriate one is not really known and thus there is an advantage to seeing how findings change as the weights change. In the case of the Tulsa IDA program, you may find it useful to learn that the findings suggest that the program is unlikely to have positive net benefits unless the distributional weight is pretty large. 1.b. The choice is up to you. However, the chapter suggests that a weight from 1.5 to 2.0 provides a useful upper bound so you might select one of these values. Given that they are upper bounds, they would seem to imply that there is a high probability that the Tulsa IDA program will not produce positive net benefits. You could, of course even select a weight below 1.5, which would imply an even larger probability that the program will not produce positive net benefits. 1.c. If the program had been limited to a lower income group, that would strengthen the case for selecting a larger weight. For example, if you selected a weight of 1.5 in answering 1.b., you now might to select a weight of 2. Solution Manual for Cost-Benefit Analysis: Concepts and Practice Anthony E. Boardman, David H. Greenberg, Aidan R. Vining, David L. Weimer 9781108415996,9781108401296
