# Solution Manual for Environmental and Natural Resource Economics, 10th Edition

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Chapter 3
Evaluating Trade-Offs: BenefitโCost Analysis and Other
Decision-Making Metrics
Chapter 3 presents three decision-making metrics that can be used to evaluate policy options. The bulk of
the chapter covers benefit-cost analysis, and explores the connection between static efficiency and
maximizing net benefits. The first equimarginal principle and pareto optimality are introduced. Present
value is reviewed and there is a discussion of which discount rate is best. Some difficulties associated
with measuring benefits are raised, and there is a discussion of how to estimate costs. Cost effectiveness
analysis and impact analysis are discussed as options to benefit-cost analysis. Since resources are limited
it is not possible to undertake all ventures that might be desirable. The government for example has
limited resources and cannot possibly address and solve every single environmental problem. Students
need to understand how to wisely use scarce resources and this chapter provides a framework for
allocating scarce resources.
โผ
Teaching Objectives
1. Understand that all actions have benefits and costs, and all benefits and costs are valued in terms of
their effect on humanity.
2. Understand that (total) benefit is measured as the area under the demand curve, and total cost is
measured as the area under the supply (or marginal cost) curve.
3. Define net benefit graphically as the difference between total benefit and total cost.
4. Explain that all costs should be measured as opportunity costs.
5. Define present value and the discount rate. Illustrate the basic discounting equations.
6. Calculate the present value of net benefits and show how benefit-cost analysis can be used to evaluate
specific options.
7. Define optimality and economic efficiency.
8. Distinguish between static efficiency and dynamic efficiency. Use the equimarginal principle to
illustrate both efficiency and inefficiency.
9. Define the concept of Pareto optimality.
10. Apply these concepts to real world examples.
11. Discuss several issues in estimating benefits such as the difference between primary and secondary
effects.
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โข Environmental and Natural Resource Economics, Tenth Edition, Global Edition
12. Explain the different approaches to cost estimation.
13. Understand how to quantify risk and how to decide how much risk is acceptable.
14. Discuss how to choose the discount rate, and explain the difference between the social and private
discount rate.
15. Discuss cost effectiveness analysis and impact analysis as alternatives to benefit cost analysis when
benefit data is lacking.
โผ
Outline
I. Normative Criteria for Decision-Making
A. Benefit-cost analysis provides a method for determining whether or not an action should be
supported. Most simply, if the benefits exceed the costs, then the action should be supported.
1. Benefits can be derived from the demand curve for the good or service.
2. Total willingness to pay or total benefit is the area under the demand curve from the
origin to the chosen quantity.
3. Costs are measured by the marginal cost curve.
4. All costs should be measured as opportunity costs. Opportunity cost is the net benefit
foregone when an environmental service is lost to a different use.
5. Marginal opportunity cost is the cost of producing the last unit.
6. Total cost is the sum of the marginal costs or the area under the marginal opportunity cost
curve up to the chosen quantity. This will also be the area under the supply curve in purely
competitive markets.
7. Net benefit is the excess of benefits over costs or the area under the demand curve that lies
above the supply curve. This is also consumer plus producer surplus.
B. Benefit-cost analysis requires comparing benefits and costs that usually occur at different
points in time. The concept of present value allows us to incorporate the time value of money
and to compare dollars today to dollars in some future period by translating everything back to
its current worth.
1. The present value of benefits, $B, received n years from now is $Bn /(1 + r)n, where r is the
discount rate.
2. The present value of a stream of benefits {B0,โฆ,Bn} received over a period of n years is the
sum from time i = 0 until year n of $Bi /(1 + r)i.
3. Discounting is the process of calculating present value.
C. Finding the Optimal Outcome
1. An allocation is efficient or has achieved static efficiency if the net benefit from the use of
those resources is maximized by that allocation. If at an allocation marginal cost is greater
than marginal benefit, then net benefits are less than the maximum possible, and the
allocation is inefficient (too much has been produced). Likewise, if marginal benefit is
greater than marginal cost, net benefits can be increased by increasing the allocation. Thus,
an efficient allocation will be achieved when marginal benefit and marginal cost are equal.
Inefficient allocations do not maximize net benefit.
2. The first equimarginal principle says that net benefits are maximized when the marginal
benefits from the allocation equal the marginal costs.
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Chapter 3 Evaluating Trade-Offs: BenefitโCost Analysis and Other Decision-Making Metrics
3.
4.
5.
11
An allocation is Pareto optimal if no other feasible allocation could benefit some people
without any negative effects on at least one other person.
Allocations that do not satisfy Pareto optimality are suboptimal.
An allocation has achieved dynamic efficiency if it maximizes the present value of net
benefits.
II. Applying the Concepts
A. This section presents some examples of actual studies in which benefit-cost analysis has been
used. The benefits and costs of U.S. air pollution control policy are discussed as are preservation
versus development conflicts. The boxed Examples 3.2 and 3.3 in this chapter are useful case
studies to discuss in class.
B. Issues in Benefits Estimation
Benefit-cost analysis involves judgments on:
โข
Which effects should be included (e.g., should secondary effects be included)?
โข
How many people incur benefits and costs and are the benefits and costs the same for each
person?
โข
How to handle intangible values or those that cannot be reliably assigned a monetary value.
What should be counted might vary depending on the nature of the local economy. Thus it will
vary by place and time. How these variables are measured is also important. Students may have
trouble, for example, with the idea that the additional labor hired for a project will not be
counted in an analysis if it is simply a transfer of labor that would already be employed
elsewhere. A natural reaction is to include this on the benefit side when it is actually simply a
rearrangement of productively employed resources. The quantification of intangible benefits
will also likely be a stumbling block. The importance of sensitivity analysis should be stressed.
C. Approaches to Cost Estimation
Estimating cost is typically more straightforward than estimating some types of benefits.
Difficulties involve estimating expected future costs and getting reliable cost information
from firms. Some common approaches include the following:
1. The survey approach involves asking polluters about their control costs.
2. The engineering approach uses engineering information to estimate the technologies
available and the costs of purchasing and using those technologies.
3. The combined approach uses both 1 and 2.
D. Treatment of Risk
For many environmental issues, scientific uncertainty complicates benefit-cost analysis. Thus,
identifying and quantifying risks and then deciding how much risk is acceptable is important.
Since it is very tedious and sometimes unfeasible to do a benefit-cost analysis for every possible
outcome, we usually must utilize expected values.
1. A dominant policy is one that confers the highest net benefits in every outcome.
2. The expected value of net benefits is the sum over the possible outcomes of the present
value of net benefits of that outcome weighted by its probability of occurrence. The policy
selected should be the one with the highest expected present value of net benefits.
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Tietenberg/Lewis
3.
4.
โข Environmental and Natural Resource Economics, Tenth Edition, Global Edition
The above approach assumes risk neutrality. Whether or not it makes sense for the
government to assume that society on the whole is risk neutral (versus risk loving or
risk averse) should be discussed.
The evaluation of irreversible decisions requires extra caution.
E. Choosing the Discount Rate
The discount rate is defined as the social opportunity cost of capital. The discount rate will
have two components: the riskless cost of capital and the risk premium. The rate on long-term
government bonds is a common choice as a measure of the cost of capital. This can then be
adjusted by a risk premium to reflect the level of riskiness of the particular project being
considered.
The appropriate rate to use will depend on the nature and expected lifetime of the project, who is
doing the financing, and the level of risk. The power of the discount rate to sway a decision one
way or another should not be overlooked (Example 3.4). Sensitivity analysis to the choice of the
discount rate should be performed. Numerical examples will facilitate the explanation of these
concepts. A simple homework assignment will also help illustrate discounting. For example, an
assignment could be designed such that the present value of net benefits flips from being greater
than zero to less than zero with a change in discount rates. A 10-year project with equal
expected annual benefits and differing annual costs, for example, could be put into a spreadsheet.
Students can be asked to evaluate the project using both rates and to make a decision. Variations
on this type of exercise can include changes in estimated benefits or costs or a change in the
expected lifetime of the project.
III. Divergence of Social and Private Discount Rates
A. Private market decisions or outcomes may differ from societyโs decisions. This will be the case
if individual rates of time preference differ and if private risk premiums differ from social risk
premiums. The risk premium is the amount required to compensate capital owners for potential
differences between expected and actual returns. Different discount rates will result in market
outcomes that are not efficient. Asking your students about their rates of time preference in
relation to an expected sum of money or student loans should result in a variety of responses.
Topics such as gambling or speeding on the highway can spark discussion (and interesting
stories) and help to illustrate rates of time preference and variations in risk perceptions.
B. A Critical Appraisal
Concern over the reliability of benefit and cost estimates is commonplace and should not be
ignored. Unreliable estimates limit the value of a benefit-cost analysis. Ex-post benefit-cost
analysis can be useful for fine-tuning the methodology of future benefit-cost analyses. Some
examples from ex-post analysis are presented.
Accounting stance, or the geography of who benefits and who pays, should also receive attention.
Whether the costs and benefits are measured at the local, national or international level will
affect the results. (See, for example, Howe, C.W. โProject Benefits and Costs from National and
Regional Viewpoints: Methodological Issues and Case Study of the Colorado-Big Thompson
Project,โ Natural Resources Journal 261 (Winter 1987): 5โ20.)
The pros and cons of benefit-cost analysis should be overviewed and outlined at this point.
Teaching students to think critically about these issues is important.
IV. Cost-Effectiveness Analysis
Cost-effectiveness analysis is a useful alternative to benefit-cost analysis when the measurement
of benefits is impossible, or estimates are unavailable. This alternative involves the
minimization of the costs of achieving a policy target, such as an emission standard. A
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Chapter 3 Evaluating Trade-Offs: BenefitโCost Analysis and Other Decision-Making Metrics
13
minimum-cost solution requires the equalization of the marginal costs of all possible alternatives
(Second Equimarginal Principle). Various proposed standards can thus be compared for their
cost effectiveness.
A numerical example of this concept will be extremely helpful.
V. Impact Analysis
Environmental impact statements attempt to quantify consequences of an action. Impact analysis
is useful when the data needed for either a benefit-cost analysis or a cost-effectiveness analysis
is unavailable. These present the analyst with as much raw information as is available without
any optimization or benefit-cost analysis. More sophisticated environmental impact statements
sometimes include benefit-cost analysis or a cost-effectiveness analysis.
โผ
Common Student Difficulties
Students with a limited background in economics will have trouble with the equimarginal principle and
will frequently confuse total and marginal cost. Simple numerical examples that illustrate the
maximization of net benefits in terms of equalizing marginal cost and marginal benefit should help. They
may also have difficulty with the concept of optimization and Pareto optimal allocations. This might be a
good place to also start talking about the role of government intervention.
The concept of discounting might also be problematic for some students. Examples they can relate to
(all students will likely have a high rate of time preference for money) will illustrate present value and
the role of the discount rate. Asking them if they would like $100 today or $100 on the day they graduate
should nicely illustrate the time value of money. If they are skeptical, this type of question should help
prove to them that most people have positive rates of time preference (prefer benefits sooner and costs
later).
โผ
Suggested Classroom Exercises
Total Benefit and Total Cost: an example that illustrates the difference between total benefit and cost
and marginal benefit and cost will be very useful. Use the equations given below and have the students
calculate total benefit, total cost, marginal benefit, and marginal cost for values of X ranging from 35 to
45. Next have the students graph total benefit and total cost on one graph, and marginal benefit and
marginal cost on the other graph. Have them find the optimal value of X.
TB = 314X – 1.6X2
MB = 314 – 3.2X
TC = 50X + 1.7X2
MC = 50 + 3.4X
The Discount Rate: An in-class example or problem set related to discounting will not only let the
students learn with a hands-on example, but will likely ease their minds about the difficulty of the concept.
Alternatively this problem can be done at home using a spreadsheet program. The spreadsheet problem set
below is a hypothetical example of two proposed uses for a coastal area. Obviously, you can think of many
different scenarios and sets of numbers. You can tell the students, for example, that a coral reef area will
either be protected or mined. A set of costs and benefits is given for a 10-year period. As you can see in
the answers, I have set this problem up so that the net present value changes from positive to negative with
a change in the discount rate. This is a nice illustration of the effect of the discount rate. The example is
also set up so that a different project would be pursued at a different rate. Additionally, the answers can be
calculated using a continuous discount rate if you are teaching your students both discrete and continuous
discounting. A discussion on the choice of the discount rate could be started here or saved for a later
chapter.
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โข Environmental and Natural Resource Economics, Tenth Edition, Global Edition
Problem Set 1. Discount rates
Project 1. Gringoland Marine Park
0
Costs (thousands of $)
Construction
Recurring costs
Foregone recreation
Benefits
Increased tourist revenue
Net
NPV @ 5%
NPV @ 10%
1
2
3
4
Years
5
6
7
8
9
10
1250
130 130 130 130 130
20 20 20 20 20 20
130
20
130
20
130 130
20 20
130
20
300 300 300 300 300 300
300
300
300 300
300
200
200
200 200
200
Project 2. Gringoland Coral Mining
Costs (thousands of $)
Extraction costs
Costs of coastal erosion
Benefits
Revenues from limestone
Net
NPV @ 5%
NPV @ 10%
3000
200 200 200 200 200 200
4500
Answers:
Project 1. Gringoland Marine Park
Years
0
1
2
3
4
5
6
7
8
9
10
130
130
130
130
130
130
130
130
130
130
20
20
20
20
20
20
20
20
20
20
20
300
300
300
300
300
300
300
300
300
300
300
โ970
150
150
150
150
150
150
150
150
150
150
Costs (thousands of $)
Construction
1250
Recurring costs
Foregone recreation
Benefits
Increased tourist revenue
Net
NPV
@
5
188.26
โ970 142.86 136.05
129.58 123.41 117.53 111.93
106.6 101.53 96.691
92.087
NPV
@ 10
โ48.31
โ970 136.36 123.97
112.7 102.45 93.138 84.671
76.974 69.976 63.615
57.831
Continuous r
NPV
@
5
181.14
โ970 142.68 135.73
129.11 122.81 116.82 111.12
105.7 100.55 95.644
90.98
NPV
@ 10
โ68.44
โ970 135.73 122.81
111.12 100.55
74.488 67.399 60.985
55.182
90.98 82.322
Continued
ยฉ2015 Pearson Education Limited
Chapter 3 Evaluating Trade-Offs: BenefitโCost Analysis and Other Decision-Making Metrics
15
Project 2. Gringoland Coral Mining
Years
0
1
2
3
4
5
6
7
8
9
10
200
200
200
200
200
200
200
200
200
200
1300
โ200
โ200
โ200
โ200
โ200
โ200
โ200
โ200
โ200
โ200
Costs (thousands of $)
Extraction costs
3000
Costs of coastal erosion
200
Benefits
Revenues from limestone
Net
4500
NPV
@
5
โ244.35
1300
โ190.5 โ181.4 โ172.8 โ164.5
โ156.7 โ149.2 โ142.1 โ135.4 โ128.9 โ122.8
NPV
@ 10
71.09
1300
โ181.8 โ165.3 โ150.3 โ136.6
โ124.2 โ112.9 โ102.6 โ93.3
โ172.1 โ163.7
โ155.8 โ148.2 โ140.9 โ134.1 โ127.5 โ121.3
โ163.7 โ148.2 โ134.1
โ121.3 โ109.8 โ99.32 โ89.87 โ81.31 โ73.58
โ84.82 โ77.11
Continuous r
NPV
@
5
โ234.86
1300
โ190.2 โ181
NPV
@ 10
97.92
1300
โ181
โผ
Essay Question
Consider a project that will require a sizeable expenditure today in order to realize a stream of net benefits
over the next 20 years. What happens to the present value of net benefits as the discount rate rises? Is it
likely that different people evaluating the same project would end up choosing different discount rates?
Discuss.
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