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Solution Manual for Cost-Benefit Analysis: Concepts and Practice , 5th Edition

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    1 ANSWERS TO EXERCISES ( 5 th Edition) Cost - Benefit Analysis: Concepts and Practice B y Boardman, Greenberg, Vining and Weimer This document contains answers to all of the exerci ses in our book. If you find an error please contact: Anthony.Boardman@Sauder.ubc.ca . For some exercises, the text indicates that an “instructor - provided spreadsheet” is available. These spreadsheets are in separate Excel files – one f ile for each exercise. For many exercises the s preadsheet contains a complete solution. Thi s pertains, for example, to Ex 9 . 6 (Chapter 9 , exercise 6 ) and Ex 1 7 . 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 1 7 .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 the se spreadsheets are available, but instructors may find them helpful. Last revision: 22 May 2018

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    2 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 consu mption 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 domes tic 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:

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    3 • $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, t he 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 consu mers 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. ( S preadsheet recommended) Your municipality is considering b uilding a public swimming pool. Analysts have estimated t he present values of the following effects over the expected useful life of the pool: PV (million dollars) National Government grant: 2.2 Construction and maintenance costs: 12.5 Personnel costs: 8.2 Revenue from municipal residents: 8.6 Revenue from non - residents: 2.2 Use value benefit to municipal residents: 16.6 Use value benefit to non - residents: 3.1 Scrap value: 0.8 The national government grant is on ly available for this purpose. Also, the construction and maintenance will hav e to be done by a non - municipal firm. a) Assuming n ational - level standing, what is the net social benefit of the project? b) Assuming municipal - leve l 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) H ow would a spender in the municipal recreation department calculate the net benefit ?

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    4 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.

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    5 Chapter 2 Exercises Conceptual Foundations of Cost - Benefit Analysis 1. Many experts claim that, although VHS came to dominat e the video recorder market , Beta max 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 exp lore 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 tic ket 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 did n’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. Students’ answers will vary (they should be > or = 0). 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

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    6 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. 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 nucle ar 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

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    7 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 $ 2 0 million and costs of $ 16 million; project F, a forest preserve with some recreational facilities, has estimated benefits of $ 26 million and costs of $ 2 0 million; project W, a wilderness area with restricted public access, has estimated benefits of $ 10 mi llion 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 benefi ts of project W by $ 2 million. Even in the absence of any of the other projects, the r oad has estimated benefits of $4 million. a. Calculate the benefit - cost ratio and net benefits for each possible alternative to the status quo. Note that there are seven possible alternatives to the status quo: R, F, and W, both with and without the road, and the road alone. b. If only one of the seven alternatives can be selected, which should be selected according to the CBA decision rule? 4.a. The seven possible alternatives to the status quo have the following costs (millions), benefits (millions), benefit/cost ratios, and net benefits (millions): Alternative B C B/C Ratio NB ($) ($) ($) Project R without road 20 16 1.25 4 Project R with road 36 24 1.50 12 Project F without road 26 2 0 1.30 6 Project F with road 36 28 1.38 8 Project W without road 10 2 5.00 8 Project W with road 8 10 0.80 - 2 Road alone 4 8 0.50 - 4 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. N avy 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 a nd maintaining the facilities. The major category of benefit was

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    8 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 je w ellery 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 jewel lery that is stolen falls. Specifically, without the increase in surveillance, jewel le ry with a retail value of $ 900,000 would have been stolen. This stolen jewe l l e ry would have been fenced by the jewel lery 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 $ 9 00,000, 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 $ 2 00,000 net loss: $ 9 00,000 - $500,000 - $600,000 = - $ 2 00,000. 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: $ 9 00,000 - $500,000 = $ 4 00,000. 7. ( S preadsheet recommended . ) Excessive and improper use of antibiotics is contributing to the resistance of many dis eases to existing antibiotics. Consider a regulatory program in the United States that would monitor antibiotic prescribi ng 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 b e $180 million (all annually). The annual benefits of the program are esti mated 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 wo rld. 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

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    9 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.

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    10 Chapter 3 Exercises Microeconomic Foundations of Cost - Benefit Analysis 1. A person’s demand for gizmos is given by the following equation: q = 6 – 0.5 p + 0.000 2 I where , q is the quantity demanded at price p when the person’s income is I . Assume initiall y that the person’s income is $6 0,000. 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 $8 0,000, 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(6 0,000) 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

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    11 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 $ 8 0,000, the demand for gizmos is given by q = 6 – 0.5p + (0.0002)(80,000) = 22 – 0.5p. For p=$10, q=1 7 ; and for p=$12, q=1 6 . The change in consumer surplus is thus (12 - 10)(1 6) + (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 equilibriu m, the price of a good equals $4 0 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 $ 4 0 to $ 3 4 . 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 $3 4 , the quantity supplied falls to q = - 10+.5(34 ) = 7 units.

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    12 The producer surplus is the area of the new triangle formed by the price line p = $3 4 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 $3 4 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 = $3 4 ), 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 - $3 4 )( 7 ) = $ 42 and the area of the triangle is (.5)($40 - $3 4 )( 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) = X a Y (1 - a) where 0<a<1. Let the person’s budget be B. The feasible amounts of consumption must satisfy the following equation: B = pX+Y where p is the unit price of X and the price of Y is set to 1. Solving the budget constraint for Y and substituting into the utility function yields U = X a (B - pX) (1 - a) Using calculus, it can be shown that utility is maximized by choosing X=aB/p Also, it can be shown that the area under the Marshallian demand curve for a price increase from p to q yielding a change in consumption of X from x p to x q is given by ΔCS = [aBln(x q ) - p x q ] - [aBln(x p ) - p x p ] - (q - p)x q When B=100, a=0.5, and p=.2, X=250 maximizes utility, which equals 111.80. If price is raised to p=.3, X falls to 204.12. a. Increase B until the utilit y raises to its initial level. The increase in B needed to

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    13 return utility to its level before the price increase is the compensating va riation for the price increase. (It can be found by guessing values until utility reaches its original level.) b. Compare ΔCS, as measured with the Marshallian demand curve, to the compensating variation. 3. This is the first significant spreadsheet exercise. It is intended to make clear the meaning of compensating variation and its relationship to the change in consumer surplus measured under the Marshallian demand schedule. It is very important that students master this exercise before attempting Exercise 7 .4 , which introduces a secondary market. The provided spreadsheet shows the compensating variation, change in consumer surplus, and equivalent variation for a change in price from $0.20 to $.40. The numbers shown are as follows: Compensating variation: - $41.42 Change in consumer surplus: - $38.04 Equivalent variation: - $29.29 Note that the compensating variation and equivalent variation bracket the change in consumer surplus. Also note that the discrepancy between these money metrics and the change in consumer surplus is quite large. This results because the good makes up such a large fraction of the consumer’s expenditure so that the income effect that puts a wedge between the money metrics is very large. Solving iterative for a price change from $.20 to $.30 yields the following: Compensating variation: - $22.47 Change in consumer surplus: - $21.37 Equivalent variation: - $18.35

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    14 Chapter 4 Exercises Valuing Impacts from Observed Behavior: Direct Estimation of Demand Schedules 1. Consider the example presented in Figure 4. 3. Compute the annual loss in consumer surplus for the price increase from $1.25 to $1.75. a. Assume a linear demand curve as per equation (4.7) b. Assume a constant elasticity demand curve as per equation (4.8) 1.a. The loss in consumer surplus is the sum of the loss to consumers on trips they continue to take ($1.75 - $1.25)(13.1 million) = $7.05 million plus the deadweight loss equal to 0.5($1.75 - 1.35)(14.5 million - 13.1 million) = $0.35 million for a total loss of $7.4 million. 1.b. Assuming a constant - elasticity demand curve, the quantity demand only falls to 13.6 million trips per year. The total reduction in social benefits equals the area under the constant elasticity demand curve, which is given by p q q p p o 0 1 / 1 1 ) 1 ( −   w here ß 0 = 15.2, ß 1 = - 0.2 and ρ = [1+ 1/ß 1 ] = - 4. Using a calculator enables us to find the area under the demand schedule to be $1.34 million. The deadweight loss is thus $1.34 million - ($1.25)(14.5 million - 13.6 million) = $0.216 million. The additional cost of the trips that consumer continue to take (13.6 million) times the added cost per trip ($0.5) = $6.8 million. Thus the total loss in consumer surplus is $6.8 million plus $0.216 million or $7.016 million, which is less than the loss in part a based on the linear demand schedule. 2. (Regression software required ; instructor - provided spreadsheet recommended .) An analyst was asked to predict the gross social benefits of building a public swimming pool in Dryville, which has a population of 70,230 people and a media n household income of $31,500. The analyst identified 24 towns in the region that alre ady had public swimming pools. H e conducted a telephone interview with the recreation department in each town to find out what fee it charged per visit (FEE) and how many visits it had duri ng the most recent summer season (VISITS). In addition, he was able to find each town’s population (POP) and median household income (INCOME) in the most recent census. His data are as follows: Town Visits Fee ($) Income ($) Population 1 168,590 $0.00 20,600 36,879 2 179,599 $0.00 33,400 64,520 3 198,595 $0.00 39,700 104,123 4 206,662 $0.00 32,600 103,073 5 170,259 $0.00 24,900 58,386 6 209,995 $0.25 38,000 116,592 7 172,018 $0.25 26,700 49,945 8 190,802 $0.25 20,800 79,789 9 197,019 $0.25 26,300 98,234 10 186,515 $0.50 35,600 71,762

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    15 11 152,679 $0.50 38,900 40,178 12 137,413 $0.50 21,700 22,928 13 158,056 $0.50 37,900 39,031 14 157,424 $0.50 35,100 44,685 15 179,490 $0.50 35,700 67,882 16 164,657 $0.75 22,900 69,625 17 184,428 $0.75 38,600 98,408 18 183,822 $0.75 20,500 93,429 19 174,510 $1.00 39,300 98,077 20 187,820 $1.00 25,800 104,068 21 196,318 $1.25 23,800 117,940 22 166,694 $1.50 34,000 59,757 23 161,716 $1.50 29,600 88,305 24 167,505 $2.00 33,800 84,102 a. Show how the analyst could use these data to predict the gross benefits of opening a public swimming pool in Dryville and allowing free admission. b. Predict gross benefits if admission is set at $1.00 and Dryville has margi nal excess tax burden of 0.25. In answering this question, assume that the fees are used to reduce taxes that would otherwise have to be collected from the citizens of Dryville to pay for expenses incurred in operating the pool. 2. The following tables provide the basic statistical analysis. The provided spreadsheet also provides estimates. Table 1: Summary of Variables Variable | Obs Mean Std. Dev. Min Max --------- --- + ----------------------------------------------------- ------------------------------------------------ VISITS 24 177191.5 17876.56 137423 209995 FEE 24 .6041667 .5413182 0 2 INCOME 24 30675 6843.674 20500 39700 POP 24 75488.25 27360.7 22928 117940 Table 2: Correlation Matrix | VISITS FEE INCOME POP ------- ---- - + ------------------------------------ --------------------------------------- VISITS 1.0000 FEE - 0.2516 1.0000 INCOME 0.0861 0.0582 1.0000 POP 0.8309 0.2077 0.1217 1.0000

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    16 Table 3: Regression on VISITS on FEE Only Source | SS df MS Number of obs = 24 --------- + ------------------------------ --------- F( 1, 22) = 1.49 Model 465177728 1 465177728 Prob > F = 0.2357 Residual 6.8850e+09 22 312952817 R - square = 0.0633 --------- - + ------------------------------ --------- Adj R - square = 0.0207 Total 7.3501e+09 23 319571291 Root MSE = 17690 VISITS | Coef. Std. Err. T P>|t| [95% Conf. Interval] -------- -- + -------------------------------------------------------------------- ------------------------------------ FEE - 8307.932 6814.326 - 1.219 0.236 - 22439.98 5824.115 _cons 182210.9 5476.248 33.273 0.000 170853.8 193567.9 Table 4: Regression of VISITS on FEE, INCOME, and POP Source | SS df MS Number of obs = 24 --------- + ------------------------------ ----------- F( 3, 20) = 48.14 Model 6.4561e+09 3 2.1520e+09 Prob > F = 0.0000 Residual 894055106 20 44702755.3 R - square = 0.8784 --------- + ------------------------------ ----------- Adj R - square = 0.8601 Total | 7.3501e+09 23 319571291 Root MSE = 6686.0 VISITS | Coef. Std. Err. T P>|t| [95% Conf. Interval] -------- ---- - + -------------------------------------------------------------------- ---------------------------------- FEE - 14638.37 2634.376 - 5.557 0.000 - 20133.58 - 9143.158 INCOME - .0011269 .2053551 - 0.005 0.996 - .4294902 .4272364 POP .6030525 .0524211 11.504 0.000 .4937039 .7124011 _ con 140546.7 7135.002 19.698 0.000 125663.4 155430.1 2.a. Using the regression results presented in Table 4 and rounding, we can write the demand equation estimated from the sample as: VISITS S = 140547 – 14638*FEE - 0.001127*INCOME + 0.6031*POP To predict a demand curve for Dryville, we set INCOME=$31,500 and POP=70,200, the values for Dryville. The resulting ordinary demand curve for Dryville is: VISITS dv = 182849 – 14638*FEE

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    17 The inverse demand curve is: FEE = 12.49 – (1/14638)* VISITS The “ choke price, ” the price at which demand falls, to zero is FEE=$12.49. When price is zero, VISITS dv = 182,849. The area under this demand curve from VISITS dv =0 to VISITS dv =182,849 is computed as: (.5)($12.49)(182,849)=$1,141,892 which is an estimate of the annual gross social benefits of the Dryville pool based on the observed demand behavior in the sample of towns with pools. 2.b. To predict the benefits with a $1.00 fee, we must subtract the consumer surplus reduction caused by fewer visits from the above estimate. At a fee of $1.00, VISITS dv =168,207. The consumer surplus loss resulting from the reduction in visits by 14,638 is computed as: (.5)($1.00)(14,638) = $7,319 Therefore, the gross benefit from swimming when there is a $1.00 fee is ($1,141,892 - $7,319)=$1,134,573. Of this, $168,211 would be received as revenues by the government of Dryville, while $966,362 would be received by swimmers as consumer surplus. Although the $168,211 in revenue that Dryville would realize is a transfer from swimmers to the town, it would result in an additional benefit in the form of reduced excess burden of taxation. This amount is (.25)($168,211)=$42,053. So the total gross benefits would be: ($1,134,573+$42,053)=$1,176,626. Of course, the marginal excess burden resulting from the government expenditure needed to construct the pool must also be taken into account.

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    18 Chapter 4 Case Study Exercises Use of Demand Schedules in Regulatory Impact Analyses 1. (Instructor provided spreadsheet recommended) Figure C4.1 shows the effect of adding 183.6 million dozen eggs to the cage free market assuming a price elasticity of supply of 0.5. Recalculate the equilibrium price and quantity and the change in social surplus assuming a price elasticity of supply equal to 0.75. 1. Using the spreadsheet provided to instructors, but changing the price elasticity of supply to 0.75, the new equilibrium price and quantity, $3.38 and 1,110 million dozen, respectively, can be determined by finding the row such that the quantities in the Demand and Supply 1 columns are approximately equal. The gain in social surplus in the cage free market, analogous to triangle abc in Diagram C4.1, is equal to (0.5)(1110 million dozen - 1005 million dozen)($3.78 per dozen - $3.38 per dozen) =$21 million. 2. An overlook in the state’s Scenic Park offers a spectacular view of Angel’s Lake and the surrounding countryside. The overlook is accessible to people in wheelchairs by a special park bus that takes about 60 minutes to reach the overlook. The overlook is accessible to people not in wheelchairs by a tram that takes 15 minutes to reach the overlook. During the most recent park season, 600 people in wheelchairs visited the park. A local economist has estimated that the demand schedule for overlook visits by people in wheelchairs is linear and has a price elasticity of demand equal to - 0.8. Assume that people in wheelchairs value their recreational time at $10 per hour. What is the annual benefit of making the tram accessible to people in wheelchairs? 2. Making the tram wheelchair accessible would reduce the time costs of using the overlook from 120 minutes (bus ride up and back down again) to 30 minutes (tram up and back down again). Thus, the time savings per visit would be 90 minutes, effectively reducing the time costs from $20 to $5 per visit. The formula for the change in quantity can be found by rearranging the elasticity equation: ΔQ=εQΔP/P. For ε= - 0.8, P=$20, Q=600, and ΔP= - $15, yields an increase in visits of 360. The increase in consumer surplus is the reduced cost of the original 600 visits, $9,000 (600 times $15), plus the value of the additional 360 visits, $2,700 (0.5 times 360 times $15). Thus, the total annual gain in consumer surplus is $11,700.

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    19 Chapter 5 Exercises Valuing Impacts in Output Markets 1 . Suppose the government is considering an increase in the toll on a certain stretch of highway from $.40 to $.50. At present, 50,000 cars per week use that highway stretch; after the toll is imposed, it is projected that only 4 5 ,000 cars per week will use the highway stretch. Assuming that the marginal cost of highway use is constant (i.e., the supply schedule is horizontal) and equal to $.40 per car, what is the change in social surplus attributabl e to the increase in the toll? (Hint: T he toll increase will cause the supply schedule, not the demand schedule, to shift.) 1 . The net cost to society is the deadweight loss caused by the increased toll and the resulting fall in the number of cars using the highway. The value of this deadweight loss is (.5)(.50 - .40)(50,000 - 4 5 ,000) = $ 25 0. The increased toll paid by the remaining drivers – (.50 - .40)(4 5 ,000) – can be viewed as a transfer from the drivers to the government. 2 . A country imports 3 billion barrels of crude oil per year and domestically produces another 3 billion barrels of crude oil per year. The world price of crude oil is $90 per b arrel. Assuming linear curves , economists estimate the price elasticity of domestic supply to be 0.25 and the price elasticity of domestic demand to be 0.1 at the current equilibrium. a. Consider the changes in social surplus that would result from imposition of a $ 30 per barrel import fee on crude oil that would involve annual administrative costs of $ 250 million. Assume that the world price will not change as a result of the country imposing the import fee, but that the domestic price will increase by $ 30 per barrel. Also assume that only producers, consumers, and taxpayers wit hin the country have standing. Determine the quantity consumed, the quantity produced domestically, and the quantity imported after the imposition of the import f ee. Then estimate the annual social benefits of the import fee. b. Economists have estimated that the marginal excess burden of taxation in the country is 0 .25 (see Chapter 3). Re - estimate the social net benefits assuming that 20 percent of the increase in producer surplus is realized as tax revenue under the existing tax system. In answering this question, assume that increases in tax revenues less the cost of administrating the import fee are used to reduce domestic taxes. c. The reduction in the country’s demand for imports may affect the world price of crude oil. Assuming that the import fee reduces the world price from $ 90 to $ 80 per barrel, and thus, the after - tax domestic price is $ 80 + $ 30 = $ 110 per barrel, a net increase in domestic pric e of $20 per barrel, repeat the analysis done in parts a and b. 2 .a. The imposition of the import fee would have the following effect on the domestic market: Change in quantity consumed: - .1 = (∆q/∆p)(p/q) ∆ q = ( - .1) ∆ p(q/p)

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    20 ∆ q = ( - .1)($30)(6 billion)/($90) ∆ q = - .2 billion Change in domestic supply: .25 = (∆q/∆p)(p/q) ∆ q = (.25) ∆ p(q/p) ∆ q = (.25)($30)(3 billion)/($90) ∆ q = .25 billion Thus, after imposition of the fee, domestic consumption will fall to 5.8 billion barrels per year, domestic production will rise to 3.25 billion barrels per year, and imports will fall to 2.55 billion barrels per year (5.8 billion – 3.25 billion). The changes in surplus to producers, consumers, and tax - payers is as follows: Change in domestic producer surplus: A. Surplus from additional .25 billion barrels produced Revenue = (.25 billion)($120) = $30 billion/year Production costs (area under supply schedule) = (.5)($120 - $90)(.25 billion) + ($90)(.25 billion) = $26.25 billion/year Net change in surplus from new production = $30 billion/year - $26.25 billion/year = $3.75 billion/year B. Surplus from higher prices on original production = ($120 - $90)(3 billion) = $90 billion/year Total change in producer surplus = $3.75 billion + $90 billion = $93.75 billion/year Change in consumer surplus: C. “ Deadweight loss ” from reduced consumption = (.5)($120 - $90)(.2 billion) = $3 billion/year D. Additional payments on quantity still consumed = ($120 - $90)(5.8 billion) = $174 billion/year Total change in consumer surplus = ( - $3 billion) + ( - $174 billion) = - $177 billion/year Change in tax revenues: E. Import fee applied to new import level: ($30)(2.55 billion) = $76.5 billion/year F. Administrative costs - $.25 billion/year

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    21 Total change in tax revenues = $76.5 billion - $.25 billion = $76.25 billion/year CBA from country ’ s perspective: Costs: Change in consumer surplus - $177.00 billion/yr Benefits: Change in domestic producer surplus $93.75 billion/yr Net gain to tax - payers $76.25 billion/yr Net benefits: - $7.00 billion/yr The import fee would have negative net benefits of $7 billion/year and therefore does not pass the CBA test. Notice that over half of the loss in consumer surplus is offset by an increase in producer surplus. Note also that we can base our decision on only one year if we assume that none of the parameter values will change over time. If any of the parameters changed over time, then we would have to extend the analysis to multiple periods. This would be the case, for example, if we thought that the estimated elasticities were appropriate for the short - run, but not for the longer - run because producers and consumers would be better able to adjust to higher prices as time passed because they would have more opportunities to change their capital stocks. 2 .b. Assuming 20 percent of producer surplus is collected as taxes, the costs and benefits are: Change in consumer surplus: - $177.00 billion After tax change in producer surplus: $75.00 billion Net gain to taxpayers: $95.00 billion Net gain to taxpayers times METB: $23.75 billion Net benefits: $16.75 billion Not only do tax - payers enjoy reductions in tax payments, but the reduction in tax payments results in a reduction in deadweight loss. To calculate this latter benefit, we multiply the fiscal change by the METB. Taking account of the METB in this case makes an important difference: the tax would not pass the net benefits test if METB is zero (implicitly assumed in part a), but would pass the net benefits test if the METB is .25. 2 .c. The following changes in quantities result: Change in quantity consumed: - .1 = (∆q/∆p)(p/q) ∆q = ( - .1)∆p(q/p) ∆q = ( - .1)($20)(6 billion)/($90) ∆q = - .133 billion

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    22 Change in domestic supply: .25 = (∆q/∆p)(p/q) ∆q = (.25)∆p(q/p) ∆q = (.25)($20)(3 billion)/($90) ∆q = .167 billion Thus, after the tax, 5.867 billion barrels are consumed, 3.167 billion barrels are domestically produced, and 2.7 billion barrels are imported. Consumer surplus loss = (.5)(.134 billion)($110 - $90) + (5.867 billion)($110 - $90) = $118.68 billion/year Producer surplus gain = (.25 billion)($120) – [(.5)(.25 billion)($120 - $90) + (.25 billion)($90)] + (3 billion)(120 - $90) = (.5)(.167 billion)($110 - $90) + (3 billion)($110 - $90) = $61.67 billion/year Net taxpayer gain = ($30)(2.7 billion) - $.25 billion = $80.75 billion/yr. If the METB is assumed to be zero, then net benefits are $23.74 billion per year. Assuming that 20 percent of producer surplus is transferred to the government through the existing tax system and the METB is 0.25, the net social benefits are: (49.34) + (80.75+12.33) + (0.25)(80.75+12.33) – 118.68 = $47.01 billion/year.

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    23 Chapter 6 Exercises Valuing Impacts in Input Markets 1. Consider a low - wage labor market. Workers in this market are not presently covered by the minimum wage, but the government is considering implementing such legislation. If implemented, this law would require employers in the market to pay workers a $5 hourly wage. Suppose all workers in the market are equally productive, the current market clearing wage rate is $4 per hour, and that at this market clearing wage there are 600 employed workers. Further suppose that under the minimum wage legislation, only 500 workers would be employed and 300 workers would be unemployed. Finally, assume that the m arket demand and supply curve s are linear and that the market reservation wage, the lowest wage at which any worker in the market would be willing to work, is $ 2 . Compute the dollar value of the impact of the policy on employers, workers, and society as a whole. 1. As a consequence of the increase in the wage they must pay, employers lose surplus that corresponds to the area of a trapezoid resulting from the reduction in the size of the surplus triangle under the demand curve for labor. The trapezoid, in turn, can be thought of as a rectangle with sides equal to the wage increase ($5 - $4 = $1) and the new employment level (500) and a triangle with a height equal to the wage increase ($1) and a base equal to the reduction in the number of workers demanded (600 - 500=100). Adding these two areas together, we have (1)(500) + (1)(100)/2 = $550. The 500 workers who remain employed in the market each gain surplus equal to the $1 increase in the wage that they receive. Hence, their total increase in surplus is ($1)(500) = $500). The 100 workers who lose their jobs as a result of the minimum wage obviously lose surplus. If these workers are assumed to be equally distributed along the market supply curve between the market reservation wage of $ 2 and the market equilibrium wage of $4, their average loss of surplus can be computed as (.5)($4 - $ 2 ) = $1. 0 0. Hence, their total loss of surplus is ($1. 0 0)(100) = $1 0 0. Alternatively, they can be viewed as losing $4 of earnings for each hour they are unemployed, but gaining leisure that has an average hourly value to them of $ 3 . 0 0 [= (.5)($ 2 + $4)]. Thus, their total loss in surplus is ($4.00 - $ 3 . 0 0)(100) = $1 0 0, the same amount as computed above. Finally, 200 workers are induced by the higher wage to enter the market. However, because jobs are not available for these persons, they do not work either before or after the minimum wage is introduced. Hence, they neither gain nor lose surplus. Therefore, the total impact of the minimum wage on society as a whole equals: $500 - $1 0 0 - $550 = - $ 15 0. Note that the total impact can also be computed as deadweight loss, the triangle between the new and old wage and the supply of and demand for workers: (.5)($5 - $4)(800 - 500) = $150.

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    24 2 . Assume that a typical unskilled rural worker in a developing country would be paid 2 dubyas a week if he migrates to the city and finds a job. However, the unemployment rate for unskilled workers is 40 percent in the city. a. What does the Harris - Todaro model predict the worker’s rural wage is? b. Assume now that the government is considering funding a project in the city that would use substantial numbers of unskilled workers. Using your answer to a, suggest a reasonable upper bound estima te and lower bound estimate of the market wage rate for unskilled workers that the government might use in conducting a CBA of the proposed project. 2 .a. Equation (16.1) indicates that the rural market wage equals RW = UW(E/L) Because the rate of unemployment rate (U/L) is .4, the employment rate equals (L – U)/L = E/L = .6. Thus, the rural market wage equals 2 dubyas x .6 = 1.2 dubyas per week. 2 .b. As suggested in the chapter, a reasonable upper bound estimate of the market wage for unskilled workers is their urban market wage, which is 2 dubyas per week, while a reasonable lower bound estimate is their rural market wage, which was estimated in 3.a to be 1.2 dubyas per week. 3 . (Instructor - provided spreadsheet recommended.) A proposed government project i n a rural area with 100 unemployed persons would require the hiring of 20 workers. The project would offer wages of $12 per hour. Imagine that the reservation wages of the one - hundred unemployed fall between $2 and $20. a. Estimate the opportunity cost of the labor required for the project assuming that the government makes random offers to the 100 unemploye d until 20 of them accept jobs. (First, generate a list of the reservation prices of 100 persons according to the formula $2+$18u where u is a random variabl e distributed uniformly [0,1]. Second, work down the list to identify the first 20 workers with re servation wages less than $12. Third, sum the reservation wages of these 20 workers to get the opportunity cost of the labor used for the project.) b. Estimate the opportunity cost of the labor required for the project assuming that the government can identify and hire the 20 unemployed with the lowest reservation wages. c. Repeat part (a) 15 times to get a distribution for the opportunity cost and compute its standard deviation. 3 . The purpose of this exercise is to explore the opportunity cost of unemployed labor and introduce students to the use of random number generators. 3 . a. and b. Students should follow the directions on the spreadsheet. The opportunity cost of hiring the 20 workers will be larger in part a (the more realistic scenario) than in part b (an unrealistic scenario unless some method, such as the demand for bribes, can be used to find those with the lowest reservation wages).

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