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

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1ANSWERS TO EXERCISES (5thEdition)Cost-Benefit Analysis: Concepts and PracticeByBoardman, Greenberg, Vining and WeimerThis document contains answers to all of the exercises in our book. If you find an errorpleasecontact:Anthony.Boardman@Sauder.ubc.ca.For someexercises,the text indicates that an “instructor-provided spreadsheet” is available.These spreadsheets arein separate Excel files–one file for each exercise.For many exercisesthe spreadsheet contains a complete solution.This pertains, for example, toEx 9.6(Chapter9, exercise6) and Ex 17.3.For suchexercises,the instructor may wish to modifythe spreadsheet before making it available to students, for example, by keeping the raw data buteliminating other material. Or the instructor may wish to ask a slightly differentquestion. In Ex17.3, for example, we provide the solution for Australia, Portugal and Brazil inthe first sheetandask students to obtain solutions for Norway, New Zealand and Croatia. The solutions for thesecountries are contained inthe second sheet.For some exercises, thereare spreadsheets available that showthe calculations behind theanswers in this answer key. Students are not aware that these spreadsheets are available, butinstructors may find them helpful.Last revision:22May 2018

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2Chapter 1 ExercisesIntroduction to Cost-Benefit Analysis1. Imagine that you live in a city that currently does not require bicycle riders to wearhelmets. Furthermore, imagine that you enjoy riding your bicycle without wearing ahelmet.a)From your perspective, what are the major costsand benefits of a proposed cityordinance 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: thepurchase 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 ofkeeping the helmet available. The most significant categories of benefits are probably: reducedrisk 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 (directlyor 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 mightexpect 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 additionto 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 producemore kumquats domestically ($6 million); the value of reduced consumption by domesticconsumers ($13million); and increased profits received by domestic kumquat growers ($5million). A CBA from the national perspective would findcosts of the tariff equal to $19million-the sum of the costs of increased domestic production and forgone domesticconsumption ($6 million + $13 million). The increased profits received by domestickumquat growers and the tariff revenues received by the treasury simply reflect higherprices paid by domestic consumers on the kumquats that they continue to consume and,hence, count as neither benefits nor costs. Thus, the net benefitsof the tariff are negative (-$19million). Consequently, the CBA would recommend against adoption of the tariff.a)Assuming the agriculture department views kumquat growers as its primaryconstituency, 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 itcalculate net benefits if it believes that domestic growers pay profit taxes at anaverage rate of 20 percent?2.a.If the agriculture department behaved as if it were a "spender," then the benefitswould probably be:

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3•$5 million domestic grower profits (“constituents”)•$8 million tariffrevenue (income from foreigners)Totalbenefits: $13 millionCosts would be $13million (reduced consumption)Net benefits: $0million.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 aretheir constituents, such as labour). Eitherwould be okay.However, the description of thequestion implies that the growers arethe primary constituents, thus wewould lean towards theview that a spender wouldnottreat the $6 million as a benefit.If the agriculture department behaved as if it were a "spender," then it might consider theincreased prices paid by domestic consumers as a cost. However, again wewould argue that thegrowers are the primary constituency and, therefore, a spender would probably ignore theincreased 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 countonly the costs and benefits accruing to the government. If so, benefits would equal $9 million ($8million in tariff revenue and $1 million= 20% x $5 millionin profits tax) and costs would bezero, so that net benefits would equal $9 million.3. (Spreadsheet recommended) Yourmunicipalityis considering building a publicswimming pool.Analysts have estimatedthepresent values of the following effects over theexpected useful life of the pool:PV(million dollars)National Governmentgrant:2.2Construction and maintenance costs:12.5Personnel costs:8.2Revenue from municipalresidents:8.6Revenue from non-residents:2.2Use valuebenefitto municipalresidents:16.6Use valuebenefitto non-residents:3.1Scrap value:0.8The national governmentgrant is only available for this purpose.Also, theconstruction and maintenance will have to be done by a non-municipalfirm.a)Assuming national-level standing, what isthenet social benefitof the project?b)Assuming municipal-level standing, what is thenetsocial benefitof the project?c)How would a guardian in the municipalbudget office calculatethe net benefit?d)How would a spender in the municipalrecreation department calculatethenetbenefit?

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43.a-d.The spreadsheet available from the instructor web page facilitates the followingestimates of net benefits (millions of dollars):Social CBASocial CBACountyCountyNational StandingCounty StandingGuardiansSpenders-0.21.1-6.98.9We recommend thatinstructors delete the cell entries under these columns and distributethe spreadsheet to students. As this is a very simple use of a spreadsheet, it makes a goodintroduction for students who have not used them before.As an alternative, instructors can distribute the spreadsheet as provided and give thestudents a different set of costs and benefits.

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5Chapter 2 ExercisesConceptual Foundations of Cost-Benefit Analysis1. Many experts claim that, although VHScame todominatethe video recorder market,Betamax was a superior technology.Assume that these experts are correct, so that, allother things equal, a world in which all video recorders were Betamax technology would bePareto superior to a world in which all videorecorders were VHS technology.Yet it seemsimplausible that a policy that forced a switch in technologies would be even potentiallyPareto improving.Explain.1.Obviously, the switch itself from Betamax to VHS would be costly: the stocks ofexisting VHS tapes and equipment would lose their value and equipment for producing themwould have to be retired earlier than would otherwise be the case. As the replacement wouldalmost 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 efficientoutcomes and Pareto efficient moves. If everyone were at least as well off, and some were betteroff, in some alternative to the status quo, then the alternative would be considered Paretosuperior. Yet, if the move to the alternative were sufficiently costly, then it would not be Paretoimproving. Only if the move were costless, the common assumption in the comparison ofalternative equilibria in economic theory, would the Pareto efficiency of outcomes correspond tothe Pareto efficiency of moves. In the real world, moves are rarely costless so that policyalternatives are best thought of as moves ratherthanas outcomes.2. Let’s explore the concept of willingness topay with a thought experiment. Imagine aspecific sporting, entertainment, or cultural event that you would very much like to attend-perhaps a World Cup match, the seventh game ofthe World Series, a Bruce Springsteenconcert, oran opera starring Renée Flemingperformance.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 minimumamount 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 youdidn’t win a ticket to the event.What is the most you would be willing to pay for aticket?d.Do you know anyone who would sufficiently dislike the event that they would notuse a free ticket unless they were paid to do so?e.Do your answers suggest any possible generalizations about willingnesstopay?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 ofcompensation 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 differencebetween willingness to pay and willingness to accept.”Though some of the difference may beattributable to the lower wealth level of the individual in the first case than in the second case, it

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6almost 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 theperson is wealthier and is likely to be willing to pay more for goods such astickets torecreational events. (Recreational events are normal goods.)2.d.Different people can have very different willingness-to-pay amounts for the samegood. Indeed, it is quite likely that some people would have a negative willingness to pay for arecreational event that others would be willing to pay large positive amounts to attend–tastesdiffer. In CBA, it is important to keep in mind that a project effect may simultaneously beviewed by some as a benefit and by others as a cost.3. How closely do government expenditures measure opportunity cost for each of thefollowing 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 thatis owned by the governmentand located on a military base.c.Labor for a reforestation program in a small rural community with highunemployment.d.Labor of current government employees who are required to administer a newprogram.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 andmeal 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 betheir wage rates. Note that, from the social perspective, it makes no difference whether or notworkers continue to receive their wages while on jury duty. Society is forgoing their labor, whichthe market values at their wage rates. For those not employed, the opportunity cost is the valuethey 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, thegovernment’s accounting would underestimate the opportunity cost of the land. If the land couldbe sold to private developers, for example, then its market price would be a better reflection ofits opportunity cost. If the fact that the land is on a military base precludes its sale to privatedevelopers, then the opportunity cost of the land would depend on the other uses to which itcould be put by the government.3.c.Government expenditures on wages would overestimate the opportunity cost if theworkers would have otherwise been unemployed. The opportunity cost of the workers is thevalue 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 timeto the program would not involve additional expenditures. The opportunity cost of their timedepends on how they would have been using it in the absence of the program. If the governmentefficiently used labor, then the opportunity cost of their time would be measured by their wage

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7rates. If the government inefficiently used labor, so that the value of output given up per hourdiverted 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 andreused, regardless of whether or not the government has yet paid the bill for it. This is the classiccase of a“sunk cost.”Indeed, imagine that if the bridge project were to be cancelled. Then, forsafety 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: ProjectR, a recreational facility, has estimated benefits of $20 million and costs of $16million;project F, a forest preserve with some recreational facilities, has estimated benefits of $26million and costs of $20 million; project W, a wilderness area with restricted public access,has estimated benefits of $10million and costs of $2million.In addition, a road could bebuilt for a cost of $8million that would increase the benefits of project R by $16million,increase the benefits of project F by $10million, and reduce the benefits of project W by $2million.Even in the absence of any of the other projects, the road has estimated benefits of$4million.a.Calculate the benefit-cost ratio and net benefits for each possible alternative to thestatus quo. Note that there are seven possible alternatives to the status quo: R, F,and W, both with and without the road, and the road alone.b.If only one of the seven alternatives can be selected, which should be selectedaccording to the CBA decision rule?4.a.The seven possible alternatives to the status quo have the following costs (millions),benefits (millions), benefit/cost ratios, and net benefits (millions):AlternativeBCB/C RatioNB($)($)($)Project R without road20161.254Project R with road36241.5012Project F without road26201.306Project F with road36281.388Project W without road1025.008Project W with road8100.80-2Road alone480.50-44.b.Even though Project W without the road has the largest benefit/cost ratio, Project Rwith the road offers the largest net benefits among the possible projects and therefore would beselected by the CBA decision rule.5. An analyst for theU.S. Navy was asked to evaluate alternatives for forward-basing adestroyer flotilla.He decidedto do the evaluation as a CBA.The major categories of costswere related to obtaining and maintaining the facilities.The major category of benefit was

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8reducedsailing time to patrol routes.The analyst recommended the forward basewith thelargest net benefits.The admiral, his client, rejected the recommendation because the CBAdid not include the risks to the forward bases from surprise attack and the risks of beingunexpectedly ejected from the bases because of changes in politicalregimes of the hostcountries.Was the analyst’s work wasted?5.The analyst was mistaken in attempting to apply CBA as a decision rule to alternativepolicies that had impacts that could not easily be monetized. Nevertheless, the analysis could berestructured as a multigoal analysis with three goals: maximize economic efficiency, reducevulnerability to surprise attack, and reduce risks from political changes in host country. In thisanalysis, the net benefits estimated in the CBA can be taken as a criterion for ranking alternativesin terms of maximizing economic efficiency. Thus, CBA is useful in this evaluation not as adecision rule, but rather as a way of systematically measuring progress toward one of severalimportant goals.6. Because of a recent wave of jewellery store robberies, a city increases police surveillanceof jewellery stores. The increased surveillance costs the city an extra $500,000 per year, butas a result, the amount of jewellery that is stolen falls.Specifically, without the increase insurveillance, jewellery with a retail value of $900,000would have been stolen.This stolenjewellery would have been fenced by the jewellery thieves for $600,000.What is the netsocial benefit resulting from the police surveillance program?6.As a result of the increase in surveillance, the jewellery stores (or their insurancecompanies) receive benefits of $900,000, taxpayers incur costs of $500,000, and the jewelleryrobbers 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 appropriateapproach, 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 tothe resistance of many diseases to existing antibiotics.Consider a regulatory program inthe United States that would monitor antibiotic prescribing by physicians.Analystsestimate the direct costs of enforcement to be $40 million, the time costs to doctors andhealth professionals to be $220 million, and the convenience costs to patients to be $180million (all annually).The annual benefits of the program are estimated to be $350 millionin avoided resistance costs in the United States, $70 million in health benefits in the UnitedStates from better compliance with prescriptions, and $280 million in avoided resistancecosts in the rest of the world.Does the program have positive net benefitsfrom the nationalperspective?If not, what fraction of benefits accruing in the rest of the world would have to

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9be counted for the program to have positive net benefits?7.The provided spreadsheet shows the following:Millions ofDollarsRegulatory program to monitorRegulatory enforcement40antibiotic prescribing by U.S.Time cost to doctors220physicians to reduce theConvenience cost to patients180spread of resistant strainsTotal U.S. Costs440Avoided U.S. resistance costs350Better drug compliance70Total U.S. Benefits420Avoided non-U.S. resistance costs280Fraction counted as U.S. Benefits0U.S. Net Benefits-20To determine what fraction of benefits to non-U.S. resistance costs would have to beincluded in the CBA to show zero benefits can be determined by changing the value of cell C13until U.S. Net Benefits rise to zero. Any larger fraction will then yield positive net benefits. Thenet benefits are about $20,000 when the fraction equals .0715. This might be a good time to talkto students about rounding–here, $20,000 should be rounded to zero.

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10Chapter 3 ExercisesMicroeconomic Foundations of Cost-Benefit Analysis1.A person’s demand for gizmos is given by the following equation:q= 6–0.5p+ 0.0002Iwhere,qis the quantity demanded at pricepwhen the person’s income isI.Assumeinitially that the person’s income is $60,000.a.At what price will demand fall to zero? (This is sometimes called the choke pricebecause 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 incomewere $80,000, what would be the consumer surplus loss from a price risefrom $10 to $12?1.a. q = 6–0.5p + 0.0002Iq = 6–0.5p + 0.0002(60,000)q = 18–0.5pAt the choke price, q = 0:0 = 18-0.5pp = $361.b.q = 18-.5(10) =13If the market price is $10, then the consumer will demand13gizmos.1.c. The price elasticity of demand equals approximately (∆q/∆p)(p/q). For a lineardemand 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 percentreduction in quantity demanded. Note that for a linear demand curve, the price elasticity ofdemand 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 thetriangle under the (inverse) demand schedule and above the price. The height of the triangle isthe 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 to12gizmos. 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 thearea of trapezoid resulting from the reduction in the size of the consumer surplus triangle. The

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11trapezoid, 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 twoareas together, we have (2)(12) + (2)(1)/2 = $25, which is the same result as that obtained bysubtracting 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 incomesituation illustrates the dependence of willingness to pay on income.2.At the current market equilibrium, the price of a good equals $40 andthe quantityequals 10 units.At this equilibrium, the price elasticity of supply is2.0.Assume that thesupply 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 ofΔq/Δp, and then, find the value ofa.)b.Calculate the producer surplus in the market.c.Imagine that a policy results in price falling from $40 to $34. By how much doesproducer surplus fall?d.What fraction of the lost producer surplus is due to the reduction in the quantitysupplied 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+.5pAt the market equilibrium: 10 = a + (.5)(40)a =-10Therefore, 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 + 2qNext, find the producer surplus as the area between the price line (p=$40) and the inversesupply schedule from quantity zero to quantity 10. Note that this area forms a triangle withheightequal to the price minus the price at zero quantity (40-20=20) and base equal to thequantity (10). The area of the triangle is thus (.5)(20)(10) = $100. Therefore, the producersurplus in this market is $100.2.c.Using the supply schedule, we see that at a price of $34, the quantitysupplied falls toq =-10+.5(34) =7units.

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12The producer surplus is the area of the new triangle formed by the price line p = $34andthe inverse supply schedule from quantity zero to7units. Thearea of this triangle is (.5)(34-20)(7) = $49. Thus, the decline in price from $40 to $34results 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 bythe original price line (p = $40), thenew price line (p = $34), the price axis, and the segment ofthe inverse supply schedule between the old quantity (q = 10) and the new quantity (q =7). Thistrapezoid can be divided into a rectangle over the quantity still supplied and a triangle over thequantity no longer supplied. The area of the rectangle is ($40-$34)(7) = $42and the area of thetriangle is (.5)($40-$34)(10-7) = $9. (Note that these amounts sum to $51, the total producersurplus loss.) Thus,$9of the producer surplus loss is due to the reduction in the quantity soldand the remaining$42of the loss is due to producers receiving less for each unit that theycontinue to sell.3.(This question pertains toAppendix3A; instructor-provided spreadsheetrecommended).Imagine a person’s utility function over two goods, X and Y, where Yrepresents dollars. Specifically, assume a Cobb-Douglas utility function:U(X,Y) = XaY(1-a)where 0<a<1.Let the person’s budget be B.The feasible amounts of consumption must satisfy thefollowing equation:B=pX+Ywhere 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 yieldsU = Xa(B-pX)(1-a)Using calculus, it can be shown that utility is maximized by choosingX=aB/pAlso, it can be shown that the area under the Marshallian demand curve for a priceincrease from p to q yielding a change in consumption of X from xpto xqis given byΔCS = [aBln(xq)-pxq]-[aBln(xp)-pxp]-(q-p)xqWhen B=100, a=0.5, and p=.2, X=250 maximizesutility, which equals 111.80.If price israised to p=.3, X falls to 204.12.a.Increase B until the utility raises to its initial level.The increase in B needed to

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13return utility to its level before the price increase is the compensating variation forthe price increase.(It can be found by guessing values until utility reaches itsoriginal level.)b.Compare ΔCS, as measured with the Marshallian demand curve, to thecompensating variation.3.This is the first significant spreadsheet exercise. It is intended to make clear themeaning of compensating variation and its relationship to the change in consumer surplusmeasured under the Marshallian demand schedule.It is very important that students master thisexercise before attempting Exercise7.4, 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 asfollows:Compensating variation:-$41.42Change in consumer surplus:-$38.04Equivalent variation:-$29.29Note that the compensating variation and equivalent variation bracket the change inconsumer surplus. Also note that the discrepancy between these money metrics and the change inconsumer surplus is quite large. This results because the good makes up such a large fraction ofthe consumer’s expenditure so that the income effect that puts a wedge between the moneymetrics is very large.Solving iterative for a price change from $.20 to $.30 yields the following:Compensating variation:-$22.47Change in consumer surplus:-$21.37Equivalent variation:-$18.35

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14Chapter 4 ExercisesValuing Impacts from Observed Behavior: Direct Estimation of Demand Schedules1.Consider theexample presented in Figure 4.3.Compute the annual loss in consumersurplus for the price increase from $1.25 to $1.75.a.Assume a lineardemand curveas per equation (4.7)b.Assume a constantelasticity demand curveas per equation (4.8)1.a.The loss in consumer surplus is the sum of the loss to consumers on trips theycontinue to take ($1.75-$1.25)(13.1 million) = $7.05 million plus the deadweight loss equal to0.5($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 13.6million trips per year. The total reduction in social benefits equals the area under the constantelasticity demand curve, which is given bypqqppo01/11)1(−whereß0= 15.2, ß1=-0.2 and ρ = [1+ 1/ß1] =-4.Using a calculator enables us to find the areaunder 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 thatconsumer 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.) Ananalyst was asked to predict the gross social benefits of building a public swimming pool inDryville, which has a population of 70,230 people and a median household income of$31,500.The analyst identified 24 towns in the region that already had public swimmingpools.He conducted a telephone interview with the recreation department in each town tofind out what fee it charged per visit (FEE) and how many visits it had during the mostrecent summer season (VISITS).In addition,he was able to find each town’s population(POP) and median household income (INCOME) in the most recent census.Hisdata are asfollows:TownVisitsFee ($)Income($)Population1168,590$0.0020,60036,8792179,599$0.0033,40064,5203198,595$0.0039,700104,1234206,662$0.0032,600103,0735170,259$0.0024,90058,3866209,995$0.2538,000116,5927172,018$0.2526,70049,9458190,802$0.2520,80079,7899197,019$0.2526,30098,23410186,515$0.5035,60071,762

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1511152,679$0.5038,90040,17812137,413$0.5021,70022,92813158,056$0.5037,90039,03114157,424$0.5035,10044,68515179,490$0.5035,70067,88216164,657$0.7522,90069,62517184,428$0.7538,60098,40818183,822$0.7520,50093,42919174,510$1.0039,30098,07720187,820$1.0025,800104,06821196,318$1.2523,800117,94022166,694$1.5034,00059,75723161,716$1.5029,60088,30524167,505$2.0033,80084,102a.Show how the analyst could use these data to predict the gross benefits of opening apublic swimming pool in Dryville and allowing free admission.b.Predict gross benefits if admission is set at $1.00 and Dryville has marginal excesstax burden of 0.25.In answering this question, assume that the fees are used toreduce taxes that would otherwise have to be collected from the citizens of Dryvilleto pay for expenses incurred in operating the pool.2.The following tables provide the basic statistical analysis. The provided spreadsheetalso provides estimates.Table 1: Summary of VariablesVariable |ObsMeanStd. Dev.MinMax------------+-----------------------------------------------------------------------------------------------------VISITS24177191.517876.56137423209995FEE24.6041667.541318202INCOME24306756843.6742050039700POP2475488.2527360.722928117940Table 2: Correlation Matrix|VISITSFEEINCOMEPOP------------+---------------------------------------------------------------------------VISITS1.0000FEE-0.25161.0000INCOME0.08610.05821.0000POP0.83090.20770.12171.0000

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16Table 3: Regression on VISITS on FEE OnlySource |SSdfMSNumber of obs=24---------+---------------------------------------F( 1,22)=1.49Model4651777281465177728Prob > F=0.2357Residual6.8850e+0922312952817R-square=0.0633----------+---------------------------------------Adj R-square=0.0207Total7.3501e+0923319571291Root MSE=17690VISITS |Coef.Std. Err.TP>|t|[95% Conf. Interval]----------+--------------------------------------------------------------------------------------------------------FEE-8307.9326814.326-1.2190.236-22439.985824.115_cons182210.95476.24833.2730.000170853.8193567.9Table 4: Regression of VISITS on FEE, INCOME, and POPSource |SSdfMSNumber of obs=24---------+-----------------------------------------F( 3,20)=48.14Model6.4561e+0932.1520e+09Prob > F=0.0000Residual8940551062044702755.3R-square=0.8784---------+-----------------------------------------Adj R-square=0.8601Total |7.3501e+0923319571291Root MSE=6686.0VISITS|Coef.Std. Err.TP>|t|[95% Conf. Interval]-------------+------------------------------------------------------------------------------------------------------FEE-14638.372634.376-5.5570.000-20133.58-9143.158INCOME-.0011269.2053551-0.0050.996-.4294902.4272364POP.6030525.052421111.5040.000.4937039.7124011_ con140546.77135.00219.6980.000125663.4155430.12.a.Using the regression results presented in Table 4 and rounding, we can write thedemand equation estimated from the sample as:VISITSS= 140547–14638*FEE-0.001127*INCOME + 0.6031*POPTo predict a demand curve for Dryville, we set INCOME=$31,500 and POP=70,200, the valuesfor Dryville. The resulting ordinary demand curve for Dryville is:VISITSdv= 182849–14638*FEE

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

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18Chapter 4 Case StudyExercisesUse of Demand Schedules in Regulatory Impact Analyses1.(Instructor provided spreadsheet recommended)FigureC4.1 shows the effect of adding183.6 million dozen eggs to the cage free market assuming a price elasticity of supply of0.5. Recalculate the equilibrium price and quantity and the change in social surplusassuming a price elasticity of supplyequal to0.75.1.Using the spreadsheet provided to instructors,but changing the price elasticity ofsupply to 0.75,thenewequilibrium price and quantity, $3.38 and 1,110 million dozen,respectively, can be determined by finding the row such that the quantities in the Demandand Supply 1 columns are approximately equal. The gain in social surplus in the cage freemarket,analogous totriangle abc in Diagram C4.1, is equal to (0.5)(1110 million dozen-1005 million dozen)($3.78 per dozen-$3.38 per dozen) =$21million.2.An overlook in the state’s Scenic Park offers a spectacular view of Angel’s Lake and thesurrounding countryside. The overlook is accessible to people in wheelchairs by aspecial park bus that takes about 60 minutes to reach the overlook. The overlook isaccessible to people not in wheelchairs by a tram that takes 15 minutes to reach theoverlook. During the most recent park season, 600 people in wheelchairs visited thepark. A local economist has estimated that the demand schedule for overlook visits bypeople 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. Whatis theannual benefit ofmaking the tram accessible to people in wheelchairs?2.Making the tram wheelchair accessible would reduce the time costs of using theoverlook from 120 minutes (bus ride up and back down again) to 30 minutes (tram upand back down again). Thus, the time savings per visit would be 90 minutes, effectivelyreducing the time costs from $20 to $5 per visit. The formula for the change in quantitycan befound 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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19Chapter 5 ExercisesValuing Impacts inOutput Markets1.Suppose the government is considering an increase in the toll on a certain stretch ofhighway from $.40 to $.50. At present, 50,000 cars per week use that highway stretch; afterthe toll is imposed, it is projected that only 45,000 cars per week will use the highwaystretch.Assuming that the marginal cost of highway use is constant (i.e., the supply schedule ishorizontal) and equal to $.40 per car,what is thechange in social surplusattributable tothe increase in the toll?(Hint: The toll increase will cause thesupply schedule, not thedemand schedule, to shift.)1. The net cost to society is the deadweight loss caused by the increased toll and theresulting fall in the number of cars using the highway. The value of this deadweight loss is(.5)(.50-.40)(50,000-45,000) = $250. The increased toll paid by the remaining drivers–(.50-.40)(45,000)–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 producesanother 3 billion barrels of crude oil per year. The world price of crude oil is $90 perbarrel. Assuming linear curves, economists estimate the price elasticity of domestic supplyto 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 $30per 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 countryimposing the import fee, but that the domestic price will increase by $30per barrel.Also assume that only producers, consumers, and taxpayers within the country havestanding.Determine the quantity consumed, the quantity produced domestically,and the quantity imported after the imposition of the import fee.Then estimate theannual social benefits of the import fee.b.Economists have estimated that the marginal excess burden of taxation in thecountry is 0.25 (see Chapter 3). Re-estimatethe social net benefits assuming that 20percent of the increase in producer surplus is realized as tax revenueunder theexisting tax system.In answering this question, assume that increases in taxrevenues less the cost of administrating the import fee are used to reduce domestictaxes.c.The reduction in the country’s demand for imports may affectthe world price ofcrude oil.Assuming that the import fee reduces the world price from $90to $80perbarrel, and thus, the after-tax domestic price is $80+ $30= $110per barrel, a netincrease in domestic price of $20per barrel, repeat the analysis done in parts a andb.2.a.The imposition of the import fee would have the following effect on the domesticmarket: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 billionChange in domestic supply:.25 = (∆q/∆p)(p/q)∆q = (.25)∆p(q/p)∆q = (.25)($30)(3 billion)/($90)∆q = .25 billionThus, after imposition of the fee, domestic consumption will fall to 5.8 billion barrels peryear, domestic production will rise to 3.25 billion barrels per year, and imports will fall to 2.55billion 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 fromadditional .25 billion barrels producedRevenue = (.25 billion)($120) = $30 billion/yearProduction costs (area under supply schedule) =(.5)($120-$90)(.25 billion) + ($90)(.25 billion) = $26.25 billion/yearNet change in surplus from new production =$30 billion/year-$26.25 billion/year = $3.75 billion/yearB. Surplus from higher prices on original production =($120-$90)(3 billion) = $90 billion/yearTotal change in producer surplus =$3.75 billion + $90 billion = $93.75 billion/yearChange in consumer surplus:C.“Deadweight loss”from reduced consumption =(.5)($120-$90)(.2 billion) = $3 billion/yearD. Additional payments on quantity still consumed =($120-$90)(5.8 billion) = $174 billion/yearTotal change in consumer surplus =(-$3 billion) + (-$174 billion) =-$177 billion/yearChange in tax revenues:E. Import fee applied to new import level:($30)(2.55 billion) = $76.5 billion/yearF. Administrative costs-$.25 billion/year

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21Total change in tax revenues =$76.5 billion-$.25 billion = $76.25 billion/yearCBA from country’s perspective:Costs:Change in consumer surplus-$177.00 billion/yrBenefits:Change in domestic producer surplus$93.75 billion/yrNet gain to tax-payers$76.25 billion/yrNet benefits:-$7.00 billion/yrThe import fee would have negative net benefits of $7 billion/year and therefore does notpass the CBA test.Notice that over half of the loss in consumer surplus is offset by an increase in producersurplus. Note also that we can base our decision on only one year if we assume that none of theparameter values will change over time. If any of the parameters changed over time, then wewould have to extend the analysis to multiple periods. This would be the case, for example, if wethought 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 timepassed 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 benefitsare:Change in consumer surplus:-$177.00 billionAfter tax change in producer surplus:$75.00 billionNet gain to taxpayers:$95.00 billionNet gain to taxpayers times METB:$23.75 billionNet benefits:$16.75 billionNot only do tax-payers enjoy reductions in tax payments, but the reduction in tax paymentsresults in a reduction in deadweight loss. To calculate this latter benefit, we multiply the fiscalchange 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), butwould 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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22Change in domestic supply:.25 = (∆q/∆p)(p/q)∆q = (.25)∆p(q/p)∆q = (.25)($20)(3 billion)/($90)∆q = .167 billionThus, after the tax, 5.867 billion barrels are consumed, 3.167 billion barrels are domesticallyproduced, and 2.7 billion barrels are imported.Consumer surplus loss =(.5)(.134 billion)($110-$90) + (5.867 billion)($110-$90) = $118.68 billion/yearProducer 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/yearNet 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 theexisting 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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23Chapter 6 ExercisesValuing Impacts in Input Markets1.Consider a low-wage labor market. Workers in this market are not presently covered bythe minimum wage, but the government is considering implementing such legislation. Ifimplemented, this law would require employers in the market to pay workers a $5 hourlywage. Suppose all workers in the market are equally productive, the current marketclearing wage rate is $4 per hour, and that at this market clearing wage there are 600employed workers. Further suppose that under the minimum wage legislation, only 500workers would be employed and 300 workers would be unemployed. Finally, assume thatthe market demand and supply curves are linear and that the market reservation wage, thelowest 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 asa whole.1.As a consequence of the increase in the wage they must pay, employers losesurplusthat corresponds to the area of a trapezoid resulting from the reduction in the size of the surplustriangle under the demand curve for labor. The trapezoid, in turn, can be thought of as a rectanglewith sides equal to the wage increase ($5-$4 = $1) and the new employment level (500) and atriangle with a height equal to the wage increase ($1) and a base equal to the reduction in thenumber 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 $1increase 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 losesurplus. If these workers are assumed to be equally distributed along the market supply curvebetween the market reservation wage of $2and the market equilibrium wage of $4, their averageloss of surplus can be computed as (.5)($4-$2) = $1.00. Hence, their total loss of surplus is($1.00)(100) = $100. Alternatively, they can be viewed as losing $4 of earnings for each hourthey are unemployed, but gaining leisure that has an average hourly value to them of $3.00 [=(.5)($2+ $4)]. Thus, their total loss in surplus is ($4.00-$3.00)(100) = $100, the same amount ascomputed above.Finally, 200 workers are induced by the higher wage to enter the market. However,becausejobs are not available for these persons, they do not work either before or after theminimum 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-$100-$550 =-$150.Note that the total impact can also be computed asdeadweight loss, the triangle between the newand old wage and the supply of and demand for workers: (.5)($5-$4)(800-500) = $150.

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242.Assume that a typical unskilled rural worker in a developing country would be paid 2dubyas a week if he migrates to the city and finds a job. However, the unemployment ratefor 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 citythatwould use substantialnumbers of unskilled workers.Using your answer to a,suggest a reasonable upper bound estimate andlower bound estimate of the marketwage rate for unskilled workers that the government might use in conducting aCBA of the proposed project.2.a.Equation (16.1) indicates that the rural market wage equalsRW = 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 wagefor unskilled workers is their urban market wage, which is 2 dubyas per week, while a reasonablelower bound estimate is their rural market wage, which was estimated in 3.a to be 1.2 dubyas perweek.3.(Instructor-provided spreadsheet recommended.) A proposed government project in arural area with 100unemployedpersonswould require the hiring of 20 workers. Theproject 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 thatthe government makes random offers to the 100 unemployed until 20 of them acceptjobs.(First, generate a list of the reservation prices of 100 persons according to theformula $2+$18u where u is a random variable distributed uniformly [0,1].Second,work down the list to identify the first 20 workers with reservation wages less than$12.Third, sum the reservation wages of these 20 workers to get the opportunitycost of the labor used for the project.)b.Estimate the opportunity cost of the labor required for the project assuming thatthe government can identify and hire the 20 unemployed with the lowest reservationwages.c.Repeat part(a)15 times to get a distribution for the opportunity cost andcomputeits standard deviation.3.The purpose of this exercise is to explore the opportunity cost of unemployed labor andintroduce students to the use of random number generators.3. a. and b.Students should follow the directions on the spreadsheet. The opportunitycost 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 findthose with the lowest reservation wages).

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