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

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ANSWERS TO EXERCISES (5th Edition)
Cost-Benefit Analysis: Concepts and Practice
By
Boardman, Greenberg, Vining and Weimer
This document contains answers to all of the exercises in our book. If you find an error please
contact: 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 file for each exercise.
For many exercises the spreadsheet contains a complete solution. This pertains, for example, to
Ex 9.6 (Chapter 9, exercise 6) and Ex 17.3. For such exercises, the instructor may wish to modify
the spreadsheet before making it available to students, for example, by keeping the raw data but
eliminating other material. Or the instructor may wish to ask a slightly different question. In Ex
17.3, for example, we provide the solution for Australia, Portugal and Brazil in the first sheet and
ask students to obtain solutions for Norway, New Zealand and Croatia. The solutions for these
countries are contained in the second sheet.
For some exercises, there are spreadsheets available that show the calculations behind the
answers in this answer key. Students are not aware that these spreadsheets are available, but
instructors may find them helpful.
Last revision: 22 May 2018

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Chapter 1 Exercises
Introduction to Cost-Benefit Analysis
1. Imagine that you live in a city that currently does not require bicycle riders to wear
helmets. Furthermore, imagine that you enjoy riding your bicycle without wearing a
helmet.
a) From your perspective, what are the major costs and benefits of a proposed city
ordinance that would require all bicycle riders to wear helmets?
b) What are the categories of costs and benefits from society’s perspective?
1.a. The most significant categories of costs to you as an individual are probably: the
purchase price of a helmet, the reduced pleasure of riding your bicycle while wearing a helmet,
diminished appearance when you take the helmet off (bad hair), and the inconvenience of
keeping the helmet available. The most significant categories of benefits are probably: reduced
risk of serious head injury (morbidity) and reduced risk of death (mortality).
1.b. There are a number of categories of costs and benefits that do not affect you (directly
or are insignificant), but which are important in aggregate. These are:
• program enforcement (a cost)
• reduced health care costs (a benefit), (although this may not be as high as one might
expect if bicyclists ride more aggressively because they feel safer; this is called off-
setting behaviour)
• increased pollution, due to cyclists switching to cars (a cost)
A social cost-benefit analysis would take account of these costs and benefits in addition
to your costs.
2. The effects of a tariff on imported kumquats can be divided into the following categories:
tariff revenues received by the treasury ($8 million); increased use of resources to produce
more kumquats domestically ($6 million); the value of reduced consumption by domestic
consumers ($13 million); and increased profits received by domestic kumquat growers ($5
million). A CBA from the national perspective would find costs of the tariff equal to $19
million-the sum of the costs of increased domestic production and forgone domestic
consumption ($6 million + $13 million). The increased profits received by domestic
kumquat growers and the tariff revenues received by the treasury simply reflect higher
prices paid by domestic consumers on the kumquats that they continue to consume and,
hence, count as neither benefits nor costs. Thus, the net benefits of the tariff are negative (-
$19 million). Consequently, the CBA would recommend against adoption of the tariff.
a) Assuming the agriculture department views kumquat growers as its primary
constituency, how would it calculate net benefits if it behaves as if it is a spender?
b) Assuming the treasury department behaves as if it is a guardian, how would it
calculate net benefits if it believes that domestic growers pay profit taxes at an
average rate of 20 percent?
2.a. If the agriculture department behaved as if it were a "spender," then the benefits
would probably be:

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• $5 million domestic grower profits (“constituents”)
• $8 million tariff revenue (income from foreigners)
Total benefits: $13 million
Costs would be $13 million (reduced consumption)
Net benefits: $0 million.
A spender might treat the additional resources devoted to domestic kumquat production
($6 million) as a cost (if the resources go to non-constituents) or as a benefit (if the recipients are
their constituents, such as labour). Either would be okay. However, the description of the
question implies that the growers are the primary constituents, thus we would lean towards the
view that a spender would not treat the $6 million as a benefit.
If the agriculture department behaved as if it were a "spender," then it might consider the
increased prices paid by domestic consumers as a cost. However, again we would argue that the
growers are the primary constituency and, therefore, a spender would probably ignore the
increased prices paid by domestic consumers. For this reason, a “spender” might also ignore the
$13 million loss in consumption benefits.
2.b. If the treasury department behaved as if it were a "guardian," then it would count
only the costs and benefits accruing to the government. If so, benefits would equal $9 million ($8
million in tariff revenue and $1 million = 20% x $5 million in profits tax) and costs would be
zero, so that net benefits would equal $9 million.
3. (Spreadsheet recommended) Your municipality is considering building a public
swimming pool. Analysts have estimated the present values of the following effects over the
expected useful life of the pool:
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 only available for this purpose. Also, the
construction and maintenance will have to be done by a non-municipal firm.
a) Assuming national-level standing, what is the net social benefit of the project?
b) Assuming municipal-level standing, what is the net social benefit of the project?
c) How would a guardian in the municipal budget office calculate the net benefit?
d) How would a spender in the municipal recreation department calculate the net
benefit?

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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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Chapter 2 Exercises
Conceptual Foundations of Cost-Benefit Analysis
1. Many experts claim that, although VHS came to dominate the video recorder market,
Betamax was a superior technology. Assume that these experts are correct, so that, all
other things equal, a world in which all video recorders were Betamax technology would be
Pareto superior to a world in which all video recorders were VHS technology. Yet it seems
implausible that a policy that forced a switch in technologies would be even potentially
Pareto improving. Explain.
1. Obviously, the switch itself from Betamax to VHS would be costly: the stocks of
existing VHS tapes and equipment would lose their value and equipment for producing them
would have to be retired earlier than would otherwise be the case. As the replacement would
almost certainly occur gradually, there would be a transition period during which positive
“network” externalities, the benefits from having compatible systems, would be reduced.
More generally, it is important to keep in mind the distinction between Pareto efficient
outcomes and Pareto efficient moves. If everyone were at least as well off, and some were better
off, in some alternative to the status quo, then the alternative would be considered Pareto
superior. Yet, if the move to the alternative were sufficiently costly, then it would not be Pareto
improving. Only if the move were costless, the common assumption in the comparison of
alternative equilibria in economic theory, would the Pareto efficiency of outcomes correspond to
the Pareto efficiency of moves. In the real world, moves are rarely costless so that policy
alternatives are best thought of as moves rather than as outcomes.
2. Let’s explore the concept of willingness to pay with a thought experiment. Imagine a
specific sporting, entertainment, or cultural event that you would very much like to attend-
perhaps a World Cup match, the seventh game of the World Series, a Bruce Springsteen
concert, or an opera starring Renée Fleming performance.
a. What is the most you would be willing to pay for a ticket to the event?
b. Imagine that you won a ticket to the event in a lottery. What is the minimum
amount of money that you would be willing to accept to give up the ticket?
c. Imagine that you had an income 50 percent higher than it is now, but that you
didn’t win a ticket to the event. What is the most you would be willing to pay for a
ticket?
d. Do you know anyone who would sufficiently dislike the event that they would not
use a free ticket unless they were paid to do so?
e. Do your answers suggest any possible generalizations about willingness to pay?
2.a. 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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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 nuclear waste storage facility that is owned by the government
and located on a military base.
c. Labor for a reforestation program in a small rural community with high
unemployment.
d. Labor of current government employees who are required to administer a new
program.
e. Concrete that was previously poured as part of a bridge foundation.
3.a. Most jurisdictions pay jurors a small per diem and reimburse them for commuting and
meal expenses. For most jurors, these payments fall short of the opportunity costs of their time.
For employed workers, a more reasonable estimate of the opportunity cost of their time would be
their wage rates. Note that, from the social perspective, it makes no difference whether or not
workers continue to receive their wages while on jury duty. Society is forgoing their labor, which
the market values at their wage rates. For those not employed, the opportunity cost is the value
they place on their forgone leisure.
3.b. Assume that the government does not charge itself for the use of land that it owns.
As long as the land could be used for something other than a nuclear waste facility, the
government’s accounting would underestimate the opportunity cost of the land. If the land could
be sold to private developers, for example, then its market price would be a better reflection of
its opportunity cost. If the fact that the land is on a military base precludes its sale to private
developers, then the opportunity cost of the land would depend on the other uses to which it
could be put by the government.
3.c. Government expenditures on wages would overestimate the opportunity cost if the
workers would have otherwise been unemployed. The opportunity cost of the workers is the
value they place on the leisure time that they are giving up.
3.d. As the employees are already on the government payroll, the diversion of their time
to the program would not involve additional expenditures. The opportunity cost of their time
depends on how they would have been using it in the absence of the program. If the government
efficiently used labor, then the opportunity cost of their time would be measured by their wage

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rates. If the government inefficiently used labor, so that the value of output given up per hour
diverted is less than their wage rate, then the opportunity cost would be less than the wage rate.
3.e. Once it is in place, the concrete has zero opportunity cost if it cannot be salvaged and
reused, regardless of whether or not the government has yet paid the bill for it. This is the classic
case of a “sunk cost.” Indeed, imagine that if the bridge project were to be cancelled. Then, for
safety reasons, the concrete would have to be removed, requiring the use labor and equipment.
Consequently, with respect to the bridge project, the opportunity cost of the concrete is negative
– not having to remove it is a benefit of continuing the project!
4. Three mutually exclusive projects are being considered for a remote river valley: Project
R, a recreational facility, has estimated benefits of $20 million and costs of $16 million;
project F, a forest preserve with some recreational facilities, has estimated benefits of $26
million and costs of $20 million; project W, a wilderness area with restricted public access,
has estimated benefits of $10 million and costs of $2 million. In addition, a road could be
built for a cost of $8 million that would increase the benefits of project R by $16 million,
increase the benefits of project F by $10 million, and reduce the benefits of project W by $2
million. Even in the absence of any of the other projects, the road has estimated benefits of
$4 million.
a. Calculate the benefit-cost ratio and net benefits for each possible alternative to the
status quo. Note that there are seven possible alternatives to the status quo: R, F,
and W, both with and without the road, and the road alone.
b. If only one of the seven alternatives can be selected, which should be selected
according to the CBA decision rule?
4.a. The seven possible alternatives to the status quo have the following costs (millions),
benefits (millions), benefit/cost ratios, and net benefits (millions):
Alternative B C B/C Ratio NB
($) ($) ($)
Project R without road 20 16 1.25 4
Project R with road 36 24 1.50 12
Project F without road 26 20 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. Navy was asked to evaluate alternatives for forward-basing a
destroyer flotilla. He decided to do the evaluation as a CBA. The major categories of costs
were related to obtaining and maintaining the facilities. The major category of benefit was

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reduced sailing time to patrol routes. The analyst recommended the forward base with the
largest net benefits. The admiral, his client, rejected the recommendation because the CBA
did not include the risks to the forward bases from surprise attack and the risks of being
unexpectedly ejected from the bases because of changes in political regimes of the host
countries. Was the analyst’s work wasted?
5. The analyst was mistaken in attempting to apply CBA as a decision rule to alternative
policies that had impacts that could not easily be monetized. Nevertheless, the analysis could be
restructured as a multigoal analysis with three goals: maximize economic efficiency, reduce
vulnerability to surprise attack, and reduce risks from political changes in host country. In this
analysis, the net benefits estimated in the CBA can be taken as a criterion for ranking alternatives
in terms of maximizing economic efficiency. Thus, CBA is useful in this evaluation not as a
decision rule, but rather as a way of systematically measuring progress toward one of several
important goals.
6. Because of a recent wave of jewellery store robberies, a city increases police surveillance
of jewellery stores. The increased surveillance costs the city an extra $500,000 per year, but
as a result, the amount of jewellery that is stolen falls. Specifically, without the increase in
surveillance, jewellery with a retail value of $900,000 would have been stolen. This stolen
jewellery would have been fenced by the jewellery thieves for $600,000. What is the net
social benefit resulting from the police surveillance program?
6. As a result of the increase in surveillance, the jewellery stores (or their insurance
companies) receive benefits of $900,000, taxpayers incur costs of $500,000, and the jewellery
robbers incur costs of $600,000.
The answer to this question depends on whether the jewellery robbers are given standing.
After all, they are (unfortunately) part of society.
If the robbers are given standing, society suffers a $200,000 net loss:
$900,000 - $500,000 - $600,000 = -$200,000.
If the robbers are not given standing, which would appear to be the more appropriate
approach, society enjoys a $500,000 net benefit from the surveillance project:
$900,000 - $500,000 = $400,000.
7. (Spreadsheet recommended.) Excessive and improper use of antibiotics is contributing to
the resistance of many diseases to existing antibiotics. Consider a regulatory program in
the United States that would monitor antibiotic prescribing by physicians. Analysts
estimate the direct costs of enforcement to be $40 million, the time costs to doctors and
health professionals to be $220 million, and the convenience costs to patients to be $180
million (all annually). The annual benefits of the program are estimated to be $350 million
in avoided resistance costs in the United States, $70 million in health benefits in the United
States from better compliance with prescriptions, and $280 million in avoided resistance
costs in the rest of the world. Does the program have positive net benefits from the national
perspective? If not, what fraction of benefits accruing in the rest of the world would have to

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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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Chapter 3 Exercises
Microeconomic Foundations of Cost-Benefit Analysis
1. A person’s demand for gizmos is given by the following equation:
q = 6 – 0.5p + 0.0002I
where, q is the quantity demanded at price p when the person’s income is I. Assume
initially that the person’s income is $60,000.
a. At what price will demand fall to zero? (This is sometimes called the choke price
because it is the price that chokes off demand.)
b. If the market price for gizmos is $10, how many will be demanded?
c. At a price of $10, what is the price elasticity of demand for gizmos?
d. At a price of $10, what is the consumer surplus?
e. If price rises to $12, how much consumer surplus is lost?
f. If income were $80,000, what would be the consumer surplus loss from a price rise
from $10 to $12?
1.a. q = 6 – 0.5p + 0.0002I
q = 6 – 0.5p + 0.0002(60,000)
q = 18 – 0.5p
At the choke price, q = 0:
0 = 18 -0.5p
p = $36
1.b. q = 18 -.5(10) =13
If the market price is $10, then the consumer will demand 13 gizmos.
1.c. The price elasticity of demand equals approximately (∆q/∆p)(p/q). For a linear
demand curve, such as the one used in this problem, ∆q/∆p equals the slope of the demand curve,
which in this exercise is -0.5. Therefore, the price elasticity of demand equals (-0.5)(10/9) =
-0.556. That is, when price equals $10, a one percent rise in price results in a 0.556 percent
reduction in quantity demanded. Note that for a linear demand curve, the price elasticity of
demand is not constant – its absolute value increases as price increases.
1.d. Thinking of a diagram with price on the vertical axis, consumer surplus is the
triangle under the (inverse) demand schedule and above the price. The height of the triangle is
the choke price minus the market price (36-10=26) and the base is the amount demanded (13).
The area of the triangle is (26)(13)/2 = $169.
1.e. A price rise to $12 reduces demand to 12 gizmos. The new consumer surplus is (36-
12)(12)/2 = $144. The reduction in consumer surplus, therefore, is $169-$144 = $25.
An alternative way to calculate the change in consumer surplus is to recognize it as the
area of trapezoid resulting from the reduction in the size of the consumer surplus triangle. The

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trapezoid, in turn, can be thought of as a rectangle with sides equal to the price increase (12-
10=2) and the new consumption level (12) and a triangle with a height equal to the price increase
(2) and a base equal to the reduction in the quantity demanded (13-12=1). Adding these two
areas together, we have (2)(12) + (2)(1)/2 = $25, which is the same result as that obtained by
subtracting the areas of the triangles.
1.f. When income equals $80,000, the demand for gizmos is given by q = 6 – 0.5p +
(0.0002)(80,000) = 22 – 0.5p.
For p=$10, q=17; and for p=$12, q=16. The change in consumer surplus is thus (12-
10)(16) + (2)(1)/(2) = $33. The larger change in consumer surplus for the higher income
situation illustrates the dependence of willingness to pay on income.
2. At the current market equilibrium, the price of a good equals $40 and the quantity
equals 10 units. At this equilibrium, the price elasticity of supply is 2.0. Assume that the
supply schedule is linear.
a. Use the price elasticity and market equilibrium to find the supply schedule. (Hint:
the supply schedule has the following form: q = a + (Δq/Δp)p. First, find the value of
Δq/Δp, and then, find the value of a.)
b. Calculate the producer surplus in the market.
c. Imagine that a policy results in price falling from $40 to $34. By how much does
producer surplus fall?
d. What fraction of the lost producer surplus is due to the reduction in the quantity
supplied and what fraction is due to the fall in price received per unit sold?
2.a. elasticity = (∆q/∆p)(p/q)
2.0 = (∆q/∆p)(40/10)
(∆q/∆p) = .5, which is the slope of the supply schedule.
Assuming linearity, q = a+.5p
At the market equilibrium: 10 = a + (.5)(40)
a = -10
Therefore, the supply schedule is q = -10 + .5p.
2.b. First, find the “inverse” supply schedule, which gives price as a function of quantity:
p = 20 + 2q
Next, find the producer surplus as the area between the price line (p=$40) and the inverse
supply schedule from quantity zero to quantity 10. Note that this area forms a triangle with
height equal to the price minus the price at zero quantity (40-20=20) and base equal to the
quantity (10). The area of the triangle is thus (.5)(20)(10) = $100. Therefore, the producer
surplus in this market is $100.
2.c. Using the supply schedule, we see that at a price of $34, the quantity supplied falls to
q = -10+.5(34) = 7 units.

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The producer surplus is the area of the new triangle formed by the price line p = $34 and
the inverse supply schedule from quantity zero to 7 units. The area of this triangle is (.5)(34-
20)(7) = $49. Thus, the decline in price from $40 to $34 results in a loss of producer surplus of
$100-$49 = $51.
2.d. The loss in producer surplus can be thought of as the area of the trapezoid formed by
the original price line (p = $40), the new price line (p = $34), the price axis, and the segment of
the inverse supply schedule between the old quantity (q = 10) and the new quantity (q = 7). This
trapezoid can be divided into a rectangle over the quantity still supplied and a triangle over the
quantity no longer supplied. The area of the rectangle is ($40-$34)(7) = $42 and the area of the
triangle is (.5)($40-$34)(10-7) = $9. (Note that these amounts sum to $51, the total producer
surplus loss.) Thus, $9 of the producer surplus loss is due to the reduction in the quantity sold
and the remaining $42 of the loss is due to producers receiving less for each unit that they
continue to sell.
3. (This question pertains to Appendix 3A; instructor-provided spreadsheet
recommended). Imagine a person’s utility function over two goods, X and Y, where Y
represents dollars. Specifically, assume a Cobb-Douglas utility function:
U(X,Y) = Xa Y(1-a)
where 0<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 = Xa (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 xp to xq is given by
ΔCS = [aBln(xq) -pxq] - [aBln(xp)-pxp] - (q-p)xq
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 utility raises to its initial level. The increase in B needed to

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return utility to its level before the price increase is the compensating variation 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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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 byp
qq pp
o
01/1 1
)
1
( −


where ß0 = 15.2, ß1 = -0.2 and ρ = [1+ 1/ß1] = -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 median household income of
$31,500. The analyst identified 24 towns in the region that already had public swimming
pools. He conducted a telephone interview with the recreation department in each town to
find out what fee it charged per visit (FEE) and how many visits it had during the most
recent summer season (VISITS). In addition, he was able to find each town’s population
(POP) and median household income (INCOME) in the most recent census. His data are as
follows:
Town Visits Fee ($)
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 marginal 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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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:
VISITSS = 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:
VISITSdv = 182849 – 14638*FEE

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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,
VISITSdv = 182,849. The area under this demand curve from VISITSdv=0 to VISITSdv=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, VISITSdv=168,207.
The consumer surplus loss resulting from the reduction in visits by 14,638 is computed as:
(.5)($1.00)(14,638) = $7,319
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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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 45,000 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 attributable to
the increase in the toll? (Hint: The 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)(50,000-45,000) = $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 produces
another 3 billion barrels of crude oil per year. The world price of crude oil is $90 per
barrel. 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 within the country have
standing. Determine the quantity consumed, the quantity produced domestically,
and the quantity imported after the imposition of the import fee. 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 price 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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∆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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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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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 market demand and supply curves 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) = $1.00. Hence, their total loss of surplus is
($1.00)(100) = $100. 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 $3.00 [=
(.5)($2 + $4)]. Thus, their total loss in surplus is ($4.00-$3.00)(100) = $100, 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 - $100 - $550 = -$150.
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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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 estimate 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 in 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 unemployed 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 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 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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