Solution Manual for Cost-Benefit Analysis: Concepts and Practice , 5th Edition
Solution Manual for Cost-Benefit Analysis: Concepts and Practice , 5th Edition simplifies tough problems, making them easier to understand and solve.
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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
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
1
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
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
2
Chapter 1 Exercises
Introduction to Cost-Benefit Analysis
1. Imagine that you live in a city that currently does not require bicycle riders to wear
helmets. Furthermore, imagine that you enjoy riding your bicycle without wearing a
helmet.
a) From your perspective, what are the major costs and benefits of a proposed city
ordinance that would require all bicycle riders to wear helmets?
b) What are the categories of costs and benefits from society’s perspective?
1.a. The most significant categories of costs to you as an individual are probably: the
purchase price of a helmet, the reduced pleasure of riding your bicycle while wearing a helmet,
diminished appearance when you take the helmet off (bad hair), and the inconvenience of
keeping the helmet available. The most significant categories of benefits are probably: reduced
risk of serious head injury (morbidity) and reduced risk of death (mortality).
1.b. There are a number of categories of costs and benefits that do not affect you (directly
or are insignificant), but which are important in aggregate. These are:
• program enforcement (a cost)
• reduced health care costs (a benefit), (although this may not be as high as one might
expect if bicyclists ride more aggressively because they feel safer; this is called off-
setting behaviour)
• increased pollution, due to cyclists switching to cars (a cost)
A social cost-benefit analysis would take account of these costs and benefits in addition
to your costs.
2. The effects of a tariff on imported kumquats can be divided into the following categories:
tariff revenues received by the treasury ($8 million); increased use of resources to produce
more kumquats domestically ($6 million); the value of reduced 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:
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:
3
• $5 million domestic grower profits (“constituents”)
• $8 million tariff revenue (income from foreigners)
Total benefits: $13 million
Costs would be $13 million (reduced consumption)
Net benefits: $0 million.
A spender might treat the additional resources devoted to domestic kumquat production
($6 million) as a cost (if the resources go to non-constituents) or as a benefit (if the recipients are
their constituents, such as labour). Either would be okay. However, 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?
• $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?
4
3.a-d. The spreadsheet available from the instructor web page facilitates the following
estimates of net benefits (millions of dollars):
Social CBA Social CBA County County
National Standing County Standing Guardians Spenders
-0.2 1.1 -6.9 8.9
We recommend that instructors delete the cell entries under these columns and distribute
the spreadsheet to students. As this is a very simple use of a spreadsheet, it makes a good
introduction for students who have not used them before.
As an alternative, instructors can distribute the spreadsheet as provided and give the
students a different set of costs and benefits.
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.
5
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
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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6
almost certainly also reflects the way people perceive gains and losses.
2.c. Willingness to pay depends on people’s wealth. If a person’s income rises, then the
person is wealthier and is likely to be willing to pay more for goods such as tickets to
recreational events. (Recreational events are normal goods.)
2.d. Different people can have very different willingness-to-pay amounts for the same
good. Indeed, it is quite likely that some people would have a negative willingness to pay for a
recreational event that others would be willing to pay large positive amounts to attend – tastes
differ. In CBA, it is important to keep in mind that a project effect may simultaneously be
viewed by some as a benefit and by others as a cost.
3. How closely do government expenditures measure opportunity cost for each of the
following program inputs?
a. Time of jurors in a criminal justice program that requires more trials.
b. Land to be used for a 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
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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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
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.
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.
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.
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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 + (
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 + (
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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.
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.
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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: -
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: -
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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:
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:
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Subject
Economics