This Document Contains Chapters 1 to 7 ANSWERS TO EXERCISES (5th Edition) Cost-Benefit Analysis: Concepts and Practice By Boardman, Greenberg, Vining and Weimer This document contains answers to all of the exercises in our book. If you find an error please contact: [email protected]. For some exercises, the text indicates that an “instructor-provided spreadsheet” is available. These spreadsheets are in separate Excel files – one file for each exercise. For many exercises the spreadsheet contains a complete solution. This pertains, for example, to Ex 9.6 (Chapter 9, exercise 6) and Ex 17.3. For such exercises, the instructor may wish to modify the spreadsheet before making it available to students, for example, by keeping the raw data but eliminating other material. Or the instructor may wish to ask a slightly different question. In Ex 17.3, for example, we provide the solution for Australia, Portugal and Brazil in the first sheet and ask students to obtain solutions for Norway, New Zealand and Croatia. The solutions for these countries are contained in the second sheet. For some exercises, there are spreadsheets available that show the calculations behind the answers in this answer key. Students are not aware that these spreadsheets are available, but instructors may find them helpful. Last revision: 22 May 2018 Chapter 1 Exercises Introduction to Cost-Benefit Analysis 1. Imagine that you live in a city that currently does not require bicycle riders to wear helmets. Furthermore, imagine that you enjoy riding your bicycle without wearing a helmet. a) From your perspective, what are the major costs and benefits of a proposed city ordinance that would require all bicycle riders to wear helmets? b) What are the categories of costs and benefits from society’s perspective? 1.a. The most significant categories of costs to you as an individual are probably: the purchase price of a helmet, the reduced pleasure of riding your bicycle while wearing a helmet, diminished appearance when you take the helmet off (bad hair), and the inconvenience of keeping the helmet available. The most significant categories of benefits are probably: reduced risk of serious head injury (morbidity) and reduced risk of death (mortality). 1.b. There are a number of categories of costs and benefits that do not affect you (directly or are insignificant), but which are important in aggregate. These are: • program enforcement (a cost) • reduced health care costs (a benefit), (although this may not be as high as one might expect if bicyclists ride more aggressively because they feel safer; this is called off-setting behaviour) • increased pollution, due to cyclists switching to cars (a cost) A social cost-benefit analysis would take account of these costs and benefits in addition to your costs. 2. The effects of a tariff on imported kumquats can be divided into the following categories: tariff revenues received by the treasury ($8 million); increased use of resources to produce more kumquats domestically ($6 million); the value of reduced consumption by domestic consumers ($13 million); and increased profits received by domestic kumquat growers ($5 million). A CBA from the national perspective would find costs of the tariff equal to $19 million-the sum of the costs of increased domestic production and forgone domestic consumption ($6 million + $13 million). The increased profits received by domestic kumquat growers and the tariff revenues received by the treasury simply reflect higher prices paid by domestic consumers on the kumquats that they continue to consume and, hence, count as neither benefits nor costs. Thus, the net benefits of the tariff are negative (-$19 million). Consequently, the CBA would recommend against adoption of the tariff. a) Assuming the agriculture department views kumquat growers as its primary constituency, how would it calculate net benefits if it behaves as if it is a spender? b) Assuming the treasury department behaves as if it is a guardian, how would it calculate net benefits if it believes that domestic growers pay profit taxes at an average rate of 20 percent? 2.a. If the agriculture department behaved as if it were a "spender," then the benefits would probably be: • $5 million domestic grower profits (“constituents”) • $8 million tariff revenue (income from foreigners) Total benefits: $13 million Costs would be $13 million (reduced consumption) Net benefits: $0 million. A spender might treat the additional resources devoted to domestic kumquat production ($6 million) as a cost (if the resources go to non-constituents) or as a benefit (if the recipients are their constituents, such as labour). Either would be okay. However, the description of the question implies that the growers are the primary constituents, thus we would lean towards the view that a spender would not treat the $6 million as a benefit. If the agriculture department behaved as if it were a "spender," then it might consider the increased prices paid by domestic consumers as a cost. However, again we would argue that the growers are the primary constituency and, therefore, a spender would probably ignore the increased prices paid by domestic consumers. For this reason, a “spender” might also ignore the $13 million loss in consumption benefits. 2.b. If the treasury department behaved as if it were a "guardian," then it would count only the costs and benefits accruing to the government. If so, benefits would equal $9 million ($8 million in tariff revenue and $1 million = 20% x $5 million in profits tax) and costs would be zero, so that net benefits would equal $9 million. 3. (Spreadsheet recommended) Your municipality is considering building a public swimming pool. Analysts have estimated the present values of the following effects over the expected useful life of the pool: The national government grant is only available for this purpose. Also, the construction and maintenance will have to be done by a non-municipal firm. a) Assuming national-level standing, what is the net social benefit of the project? b) Assuming municipal-level standing, what is the net social benefit of the project? c) How would a guardian in the municipal budget office calculate the net benefit? d) How would a spender in the municipal recreation department calculate the net benefit? 3.a-d. The spreadsheet available from the instructor web page facilitates the following estimates of net benefits (millions of dollars):
Social CBA Social CBA County County
National Standing County Standing Guardians Spenders
-0.2 1.1 -6.9 8.9
We recommend that instructors delete the cell entries under these columns and distribute the spreadsheet to students. As this is a very simple use of a spreadsheet, it makes a good introduction for students who have not used them before. As an alternative, instructors can distribute the spreadsheet as provided and give the students a different set of costs and benefits. Chapter 2 Exercises Conceptual Foundations of Cost-Benefit Analysis 1. Many experts claim that, although VHS came to dominate the video recorder market, Betamax was a superior technology. Assume that these experts are correct, so that, all other things equal, a world in which all video recorders were Betamax technology would be Pareto superior to a world in which all video recorders were VHS technology. Yet it seems implausible that a policy that forced a switch in technologies would be even potentially Pareto improving. Explain. 1. Obviously, the switch itself from Betamax to VHS would be costly: the stocks of existing VHS tapes and equipment would lose their value and equipment for producing them would have to be retired earlier than would otherwise be the case. As the replacement would almost certainly occur gradually, there would be a transition period during which positive “network” externalities, the benefits from having compatible systems, would be reduced. More generally, it is important to keep in mind the distinction between Pareto efficient outcomes and Pareto efficient moves. If everyone were at least as well off, and some were better off, in some alternative to the status quo, then the alternative would be considered Pareto superior. Yet, if the move to the alternative were sufficiently costly, then it would not be Pareto improving. Only if the move were costless, the common assumption in the comparison of alternative equilibria in economic theory, would the Pareto efficiency of outcomes correspond to the Pareto efficiency of moves. In the real world, moves are rarely costless so that policy alternatives are best thought of as moves rather than as outcomes. 2. Let’s explore the concept of willingness to pay with a thought experiment. Imagine a specific sporting, entertainment, or cultural event that you would very much like to attend-perhaps a World Cup match, the seventh game of the World Series, a Bruce Springsteen concert, or an opera starring Renée Fleming performance. a. What is the most you would be willing to pay for a ticket to the event? b. Imagine that you won a ticket to the event in a lottery. What is the minimum amount of money that you would be willing to accept to give up the ticket? c. Imagine that you had an income 50 percent higher than it is now, but that you didn’t win a ticket to the event. What is the most you would be willing to pay for a ticket? d. Do you know anyone who would sufficiently dislike the event that they would not use a free ticket unless they were paid to do so? e. Do your answers suggest any possible generalizations about willingness to pay? 2.a. The most I would be willing to pay for a ticket to the event is $500. 2.b. Most people would be willing to pay less to obtain something than the amount of compensation they would require to give the same thing up willingly if they already owned it. This difference has been frequently observed and economists refer to it as “the difference between willingness to pay and willingness to accept.” Though some of the difference may be attributable to the lower wealth level of the individual in the first case than in the second case, it almost certainly also reflects the way people perceive gains and losses. 2.c. Willingness to pay depends on people’s wealth. If a person’s income rises, then the person is wealthier and is likely to be willing to pay more for goods such as tickets to recreational events. (Recreational events are normal goods.) 2.d. Different people can have very different willingness-to-pay amounts for the same good. Indeed, it is quite likely that some people would have a negative willingness to pay for a recreational event that others would be willing to pay large positive amounts to attend – tastes differ. In CBA, it is important to keep in mind that a project effect may simultaneously be viewed by some as a benefit and by others as a cost. 2.e. Yes, the answers suggest that willingness to pay is highly subjective and varies based on personal interest, the uniqueness of the event, and individual financial situations. Generally, people are willing to pay more for events they are passionate about or that are rare and highly anticipated. 3. How closely do government expenditures measure opportunity cost for each of the following program inputs? a. Time of jurors in a criminal justice program that requires more trials. b. Land to be used for a nuclear waste storage facility that is owned by the government and located on a military base. c. Labor for a reforestation program in a small rural community with high unemployment. d. Labor of current government employees who are required to administer a new program. e. Concrete that was previously poured as part of a bridge foundation. 3.a. Most jurisdictions pay jurors a small per diem and reimburse them for commuting and meal expenses. For most jurors, these payments fall short of the opportunity costs of their time. For employed workers, a more reasonable estimate of the opportunity cost of their time would be their wage rates. Note that, from the social perspective, it makes no difference whether or not workers continue to receive their wages while on jury duty. Society is forgoing their labor, which the market values at their wage rates. For those not employed, the opportunity cost is the value they place on their forgone leisure. 3.b. Assume that the government does not charge itself for the use of land that it owns. As long as the land could be used for something other than a nuclear waste facility, the government’s accounting would underestimate the opportunity cost of the land. If the land could be sold to private developers, for example, then its market price would be a better reflection of its opportunity cost. If the fact that the land is on a military base precludes its sale to private developers, then the opportunity cost of the land would depend on the other uses to which it could be put by the government. 3.c. Government expenditures on wages would overestimate the opportunity cost if the workers would have otherwise been unemployed. The opportunity cost of the workers is the value they place on the leisure time that they are giving up. 3.d. As the employees are already on the government payroll, the diversion of their time to the program would not involve additional expenditures. The opportunity cost of their time depends on how they would have been using it in the absence of the program. If the government efficiently used labor, then the opportunity cost of their time would be measured by their wage rates. If the government inefficiently used labor, so that the value of output given up per hour diverted is less than their wage rate, then the opportunity cost would be less than the wage rate. 3.e. Once it is in place, the concrete has zero opportunity cost if it cannot be salvaged and reused, regardless of whether or not the government has yet paid the bill for it. This is the classic case of a “sunk cost.” Indeed, imagine that if the bridge project were to be cancelled. Then, for safety reasons, the concrete would have to be removed, requiring the use labor and equipment. Consequently, with respect to the bridge project, the opportunity cost of the concrete is negative – not having to remove it is a benefit of continuing the project! 4. Three mutually exclusive projects are being considered for a remote river valley: Project R, a recreational facility, has estimated benefits of $20 million and costs of $16 million; project F, a forest preserve with some recreational facilities, has estimated benefits of $26 million and costs of $20 million; project W, a wilderness area with restricted public access, has estimated benefits of $10 million and costs of $2 million. In addition, a road could be built for a cost of $8 million that would increase the benefits of project R by $16 million, increase the benefits of project F by $10 million, and reduce the benefits of project W by $2 million. Even in the absence of any of the other projects, the road has estimated benefits of $4 million. a. Calculate the benefit-cost ratio and net benefits for each possible alternative to the status quo. Note that there are seven possible alternatives to the status quo: R, F, and W, both with and without the road, and the road alone. b. If only one of the seven alternatives can be selected, which should be selected according to the CBA decision rule? 4.a. The seven possible alternatives to the status quo have the following costs (millions), benefits (millions), benefit/cost ratios, and net benefits (millions): 4.b. Even though Project W without the road has the largest benefit/cost ratio, Project R with the road offers the largest net benefits among the possible projects and therefore would be selected by the CBA decision rule. 5. An analyst for the U.S. Navy was asked to evaluate alternatives for forward-basing a destroyer flotilla. He decided to do the evaluation as a CBA. The major categories of costs were related to obtaining and maintaining the facilities. The major category of benefit was reduced sailing time to patrol routes. The analyst recommended the forward base with the largest net benefits. The admiral, his client, rejected the recommendation because the CBA did not include the risks to the forward bases from surprise attack and the risks of being unexpectedly ejected from the bases because of changes in political regimes of the host countries. Was the analyst’s work wasted? 5. The analyst was mistaken in attempting to apply CBA as a decision rule to alternative policies that had impacts that could not easily be monetized. Nevertheless, the analysis could be restructured as a multigoal analysis with three goals: maximize economic efficiency, reduce vulnerability to surprise attack, and reduce risks from political changes in host country. In this analysis, the net benefits estimated in the CBA can be taken as a criterion for ranking alternatives in terms of maximizing economic efficiency. Thus, CBA is useful in this evaluation not as a decision rule, but rather as a way of systematically measuring progress toward one of several important goals. 6. Because of a recent wave of jewellery store robberies, a city increases police surveillance of jewellery stores. The increased surveillance costs the city an extra $500,000 per year, but as a result, the amount of jewellery that is stolen falls. Specifically, without the increase in surveillance, jewellery with a retail value of $900,000 would have been stolen. This stolen jewellery would have been fenced by the jewellery thieves for $600,000. What is the net social benefit resulting from the police surveillance program? 6. As a result of the increase in surveillance, the jewellery stores (or their insurance companies) receive benefits of $900,000, taxpayers incur costs of $500,000, and the jewellery robbers incur costs of $600,000. The answer to this question depends on whether the jewellery robbers are given standing. After all, they are (unfortunately) part of society. If the robbers are given standing, society suffers a $200,000 net loss: $900,000 - $500,000 - $600,000 = -$200,000. If the robbers are not given standing, which would appear to be the more appropriate approach, society enjoys a $500,000 net benefit from the surveillance project: $900,000 - $500,000 = $400,000. 7. (Spreadsheet recommended.) Excessive and improper use of antibiotics is contributing to the resistance of many diseases to existing antibiotics. Consider a regulatory program in the United States that would monitor antibiotic prescribing by physicians. Analysts estimate the direct costs of enforcement to be $40 million, the time costs to doctors and health professionals to be $220 million, and the convenience costs to patients to be $180 million (all annually). The annual benefits of the program are estimated to be $350 million in avoided resistance costs in the United States, $70 million in health benefits in the United States from better compliance with prescriptions, and $280 million in avoided resistance costs in the rest of the world. Does the program have positive net benefits from the national perspective? If not, what fraction of benefits accruing in the rest of the world would have to be counted for the program to have positive net benefits? 7. The provided spreadsheet shows the following:
Millions of Dollars
Regulatory program to monitor Regulatory enforcement 40
antibiotic prescribing by U.S. Time cost to doctors 220
physicians to reduce the Convenience cost to patients 180
spread of resistant strains Total U.S. Costs 440
Avoided U.S. resistance costs 350
Better drug compliance 70
Total U.S. Benefits 420
Avoided non-U.S. resistance costs 280
Fraction counted as U.S. Benefits 0
U.S. Net Benefits -20
To determine what fraction of benefits to non-U.S. resistance costs would have to be included in the CBA to show zero benefits can be determined by changing the value of cell C13 until U.S. Net Benefits rise to zero. Any larger fraction will then yield positive net benefits. The net benefits are about $20,000 when the fraction equals .0715. This might be a good time to talk to students about rounding –here, $20,000 should be rounded to zero. Chapter 3 Exercises Microeconomic Foundations of Cost-Benefit Analysis 1. A person’s demand for gizmos is given by the following equation: q = 6 – 0.5p + 0.0002I where, q is the quantity demanded at price p when the person’s income is I. Assume initially that the person’s income is $60,000. a. At what price will demand fall to zero? (This is sometimes called the choke price because it is the price that chokes off demand.) b. If the market price for gizmos is $10, how many will be demanded? c. At a price of $10, what is the price elasticity of demand for gizmos? d. At a price of $10, what is the consumer surplus? e. If price rises to $12, how much consumer surplus is lost? f. If income were $80,000, what would be the consumer surplus loss from a price rise from $10 to $12? 1.a. q = 6 – 0.5p + 0.0002I q = 6 – 0.5p + 0.0002(60,000) q = 18 – 0.5p At the choke price, q = 0: 0 = 18 - 0.5p p = $36 1.b. q = 18 -.5(10) = 13 If the market price is $10, then the consumer will demand 13 gizmos. 1.c. The price elasticity of demand equals approximately (∆q/∆p)(p/q). For a linear demand curve, such as the one used in this problem, ∆q/∆p equals the slope of the demand curve, which in this exercise is -0.5. Therefore, the price elasticity of demand equals (-0.5)(10/9) = -0.556. That is, when price equals $10, a one percent rise in price results in a 0.556 percent reduction in quantity demanded. Note that for a linear demand curve, the price elasticity of demand is not constant – its absolute value increases as price increases. 1.d. Thinking of a diagram with price on the vertical axis, consumer surplus is the triangle under the (inverse) demand schedule and above the price. The height of the triangle is the choke price minus the market price (36 – 10 = 26) and the base is the amount demanded (13). The area of the triangle is (26)(13)/2 = $169. 1.e. A price rise to $12 reduces demand to 12 gizmos. The new consumer surplus is (36-12)(12)/2 = $144. The reduction in consumer surplus, therefore, is $169-$144 = $25. An alternative way to calculate the change in consumer surplus is to recognize it as the area of trapezoid resulting from the reduction in the size of the consumer surplus triangle. The trapezoid, in turn, can be thought of as a rectangle with sides equal to the price increase (12 – 10 = 2) and the new consumption level (12) and a triangle with a height equal to the price increase (2) and a base equal to the reduction in the quantity demanded (13 – 12 = 1). Adding these two areas together, we have (2)(12) + (2)(1)/2 = $25, which is the same result as that obtained by subtracting the areas of the triangles. 1.f. When income equals $80,000, the demand for gizmos is given by q = 6 – 0.5p + (0.0002)(80,000) = 22 – 0.5p. For p = $10, q = 17; and for p = $12, q = 16. The change in consumer surplus is thus (12 - 10)(16) + (2)(1)/(2) = $33. The larger change in consumer surplus for the higher income situation illustrates the dependence of willingness to pay on income. 2. At the current market equilibrium, the price of a good equals $40 and the quantity equals 10 units. At this equilibrium, the price elasticity of supply is 2.0. Assume that the supply schedule is linear. a. Use the price elasticity and market equilibrium to find the supply schedule. (Hint: the supply schedule has the following form: q = a + (Δq/Δp)p. First, find the value of Δq/Δp, and then, find the value of a.) b. Calculate the producer surplus in the market. c. Imagine that a policy results in price falling from $40 to $34. By how much does producer surplus fall? d. What fraction of the lost producer surplus is due to the reduction in the quantity supplied and what fraction is due to the fall in price received per unit sold? 2.a. elasticity = (∆q/∆p)(p/q) 2.0 = (∆q/∆p)(40/10) (∆q/∆p) = .5, which is the slope of the supply schedule. Assuming linearity, q = a + .5p At the market equilibrium: 10 = a + (.5)(40) a = -10 Therefore, the supply schedule is q = -10 + .5p. 2.b. First, find the “inverse” supply schedule, which gives price as a function of quantity: p = 20 + 2q Next, find the producer surplus as the area between the price line (p = $40) and the inverse supply schedule from quantity zero to quantity 10. Note that this area forms a triangle with height equal to the price minus the price at zero quantity (40 - 20 = 20) and base equal to the quantity (10). The area of the triangle is thus (.5)(20)(10) = $100. Therefore, the producer surplus in this market is $100. 2.c. Using the supply schedule, we see that at a price of $34, the quantity supplied falls to q = -10 + .5(34) = 7 units. The producer surplus is the area of the new triangle formed by the price line p = $34 and the inverse supply schedule from quantity zero to 7 units. The area of this triangle is (.5)(34 - 20)(7) = $49. Thus, the decline in price from $40 to $34 results in a loss of producer surplus of $100 - $49 = $51. 2.d. The loss in producer surplus can be thought of as the area of the trapezoid formed by the original price line (p = $40), the new price line (p = $34), the price axis, and the segment of the inverse supply schedule between the old quantity (q = 10) and the new quantity (q = 7). This trapezoid can be divided into a rectangle over the quantity still supplied and a triangle over the quantity no longer supplied. The area of the rectangle is ($40-$34)(7) = $42 and the area of the triangle is (.5)($40-$34)(10-7) = $9. (Note that these amounts sum to $51, the total producer surplus loss.) Thus, $9 of the producer surplus loss is due to the reduction in the quantity sold and the remaining $42 of the loss is due to producers receiving less for each unit that they continue to sell. 3. (This question pertains to Appendix 3A; instructor-provided spreadsheet recommended). Imagine a person’s utility function over two goods, X and Y, where Y represents dollars. Specifically, assume a Cobb-Douglas utility function: U(X,Y) = Xa Y(1-a) where 0 0, βm< (1-γqs)/2qm, βs < (1-γqm)/2qs, and γ < pmβs/ps + psβm/pm. For purposes of this exercise, assume that α = 1, βm = 0.01, βs = 0.01, and γ = -0.015. Also assume that the person has a budget of $30,000 and the price of qm, pm, is $100 and the price of qs, ps, is $100. Imagine that the policy under consideration would reduce pm to $90. The provided spreadsheet has two models. Model 1 assumes that the price in the secondary market does not change in response to a price change in the primary market. That is, ps equals $100 both before and after the reduction in pm. Step 1 solves for the quantities that maximize utility under the initial pm. Step 2 solves for the quantities that maximize utility under the new pm. Step 3 requires you to make guesses of the new budget level that would return the person to her original level of utility prior to the price reduction — keep guessing until you find the correct budget. (You may wish to use the Tools|Goal Seek function on the spreadsheet instead of iterative guessing.) Step 4 calculates the compensating variation as the difference between the original budget and the new budget. Step 5 calculates the change in the consumer surplus in the primary market. Model 2 assumes that ps = a + b qs. Assume that b = 0.25 and a is set so that at the quantity demanded in Step 2 of model 1, ps = 100. As there is no analytical solution for the quantities before the price change, Step 1 requires you to make guesses of the marginal utility of money until you find the one that satisfies the budget constraint for the initial pm. Step 2 repeats this process for the new value of pm. Step 3 requires you to guess both a new budget to return the person to the initial level of utility and a marginal utility of money that satisfies the new budget constraint. A block explains how to use Tools|Goal Seek to find the marginal utility consistent with your guess of the new budget needed to return utility to its original level. Step 4 calculates the compensating variation. Step 5 calculates the change in the consumer surplus in the primary market and bounds on the change in consumer surplus in the secondary market. Use these models to investigate how well the change in social surplus in the primary market approximates compensating variation. Note that as utility depends on consumption of only these two goods, there are substantial income effects. That is, a price reduction in either of the goods substantially increases the individual’s real income. Getting started: The values in the spreadsheet are set up for a reduction in pm from $100 to $95. Begin by changing the new primary market price to $90 and resolving the models. 4. The procedure for finding the compensating variation in Model 1 is the same as that used in Exercise 3.3. This exercise extends that approach in Model 2 to include a secondary market. As the iterative solution is a bit complicated, instructors may find it effective to have students work in teams. The spreadsheet shows the following values for the reduction in price from $100 to $95: Re-solving the spreadsheet for a reduction in price from $100 to $90 yields the following: Solution Manual for Cost-Benefit Analysis: Concepts and Practice Anthony E. Boardman, David H. Greenberg, Aidan R. Vining, David L. Weimer 9781108415996,9781108401296
