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1. Chapter 6: An Introduction to
Benefit-Cost Analysis
"Information is a source of learning. But unless it is organized, processed, and
available to the right people in a format for decision making, it is a burden, not a
benefit."
William Pollard
“The Freedom of Information Act is the Taj Mahal of the Doctrine of Unanticipated
Consequences, the Sistine Chapel of Cost-Benefit Analysis Ignored.”
Antonin Scalia, Associate Justice, U.S. Supreme Court
2. Introduction
This chapter introduces the process and decision rules for benefit-cost analysis.
The chapter also introduces cost-effectiveness analysis, a decision model that can
be useful when a full comparison of dollar-valued benefits and costs is not possible
or not desirable.
Finally, the chapter presents a related model labeled weighted benefit cost analysis,
which allows the analyst to assign different values to different affected groups. One
application of these weights involves assigning higher values to the net benefits of
the poor.
4. Reviewing the Steps in a
Benefit-Cost Analysis
Let’s review Eugene Bardach’s 8 step process for policy analysis:
(1) define the problem,
(2) assemble evidence,
(3) select criteria for making the decision,
(4) identify the policy alternatives to be considered,
(5) predict the outcome of each alternative, (
6) confront the tradeoffs,
(7) make recommendations, and
(8) tell your story.
The primary focus of this chapter is on steps 3 through 7, but a brief review of the
process of defining and quantifying a policy problem may also be useful.
5. Identifying the Problem
The goal of most public policies is to reduce, eliminate, or prevent a particular
social or economic problem. Therefore, any convincing policy analysis should
have clear and detailed answers to a seemingly simple set of questions:
What is the problem?
When, where, and how often does the problem occur?
What are the causes of the problem?
How serious are the harms caused by the problem?
6. Identifying the Problem
Identifying the seriousness of the problem involves quantifying both the number of
people affected by the problem and the intensity of harm suffered by those people.
Some problems such as violating speed limits are very widespread but on average
not very harmful. On the other hand problems such as homelessness, airline
fatalities, or childhood cancer are comparatively rare but are very serious for their
victims.
Estimating the frequency of a given problem usually requires broadly based
statistics. For national problems in the U.S. the federal government is usually the
first place to search for statistical data.
Quantifying the harms of the problem often involves complex economic, statistical,
and interdisciplinary analysis. Examples will be considered throughout this book.
7. Assembling Information and Evidence
In order to understand any policy problem, careful consideration of the academic
and professional literature relating to this problem is important.
For most people research now begins with a search of electronic sources such as
on-line library catalogs and databases of academic or professional literature.
Different university library systems have different sets of resources for research, so
your professor and library staff may be important in setting up assignments for
researching a policy topic.
8. Select the Criteria for
Making the Decision
The most common economic rule for analyzing policy alternatives is the Kaldor-
Hicks criterion or fundamental rule of policy analysis discussed in Chapter 4.
This rule leads the analyst to rank projects according to their total net benefits, or
total benefits minus total costs.
However, in policy areas such as health and safety policy a direct comparison of
the dollar value of benefits and costs is controversial. In such cases policy
analysis models such as cost-effectiveness analysis, which does not rely on a
dollar value for lives saved, are sometimes used.
Finally, when analyzing policies for which the distribution of income or other net
benefits are important, relying on ethical criteria or assigning higher weights to the
net benefits of the poor may be appropriate.
9. Identifying the Policy Alternatives
In some cases several different policies might be used to address a problem.
For example, traffic congestion (see Chapter 12) might be reduced through
highway expansion, fees on rush hour drivers, regulations that encourage ride
sharing, and subsidies for mass transit or other substitutes for the automobile.
Different policies can be used either separately or in combination.
11. Marginal Analysis of Policy Decisions
When quantity can be produced in small units and perfect information exists, we
should continue to invest in a project as long as the marginal benefits of the
project are greater than its marginal costs.
Our optimal scale for the project will be where
the marginal benefits and marginal costs are equal
(See Figure 6-1).
12. Other Marginal Decision Rules
Ideally, when one is choosing how much to spend on each of several policies or
programs, she should allocate resources so that the marginal benefit for the last
dollar spent for one project equals the marginal benefit of the last dollar spent on
the other.
In equation form, for any three projects X, Y, and Z, the ideal allocation of funds
between the projects would occur where
This is basically the same formula as the utility maximization rule one sees in
introductory microeconomics classes.
If one has no budget constraint, each of these projects should be funded until its
marginal benefits equal its marginal costs, as in Figure 6-1. If each project’s
marginal benefits equal its marginal costs, each ratio in equation (6-1) will equal 1.
(6-1)
MCz
MBz
MCy
MBy
MCx
MBx
14. Formulas for Comparing Benefits and Costs
When information is not complete enough for marginal analysis, it is possible to
compare the total or average benefits and costs of a policy using at least three
different formulas, net benefits, the benefit/cost ratio, and the rate of return.
Net Benefits = Total Benefits – Total Costs
Benefit/Cost Ratio = Total Benefits/Total Costs
Rate of Return = 100% • (Total Benefits-Total Costs)/Total Costs
These measurements are sometimes consistent, but in others they can produce
different rankings for alternative projects.
In cases where these measurements are not consistent, a clear preference exists in
economics for the net benefits measure as the best decision rule.
15. Your Turn 6-3:
One design for new windmill complex costs $9 million to construct, will produce
$15 million worth of power, and will require $2 million in operating and
maintenance costs. A second design will cost $6 million to construct, produce $10
million worth of power, and will require $2 million in operating and maintenance
costs. Find the net benefits, benefit/cost ratio, and percentage rate of return on
each of these two projects.
Project 1: net benefits = ____ benefit/cost ratio = ____ rate of return=____
Project 2: net benefits = ____ benefit/cost ratio = ____ rate of return=____
Which option is best according to each measure?
17. Accepting or rejecting a single project
This situation has two variants, accepting or rejecting one project or separately
considering each of a series of projects.
The decision rule in this case is very simple. Approve the project if the net benefits
are greater than zero, so that society experiences a net gain in well-being.
If total benefits are greater than total costs, then the benefit/cost ratio will be
greater than one and the rate of return will be greater than zero. All these
outcomes will lead the analyst to recommend approval of the program.
Your turn 6-5: Would you recommend building the wind farm project in Your Turn
6-3 above? Why or why not?
18. Choosing One of Several Possible Projects
This type of situation occurs when determining the best use of a plot of land or a
particular choice among competing designs for a building or highway project.
The recommended rule for this decision is to choose the project with the highest
net benefits.
Rank these alternatives in terms of their net benefits. Then calculate the benefit
cost ratio and rate of return for each alternative. Note that the benefit/cost ratios
for the industrial park and the outlet mall are not consistent with the net benefit
ranking.
HOUSING INDUSTRIAL
PARK
OUTLET
MALL
VACANT
LOT
Benefits $1,000,000 $1,250,000 $1,600,000 $1,000
Costs $1,100,000 $900,000 $1,200,000 $1,000
Net Benefits
B/C ratio
Rate of Return
19. Choosing an Optimal Budget
An optimal budget is one that maximizes possible net gains to society as a whole.
Therefore an optimal budget will fund all projects with positive net benefits for
society.
If marginal analysis is possible, an optimal budget would be sufficient so that each
project or department is funded to the point where its marginal benefits equal its
marginal costs, so that each ratio in equation 6-1 will equal 1.
20. Choosing Which Projects to Fund Within a
Fixed Budget
Making this choice involves the following steps.
Calculate the benefit/cost ratio for each choice. Immediately reject any project
which does not have a B/C ratio greater than one.
Rank the projects according to their Benefit/Cost ratio.
Choose the highest B/C ratio, then the next highest, and so forth until you cannot
go further without breaking your budget.
If you must skip one or more projects due to budget considerations, choose the
remaining programs with the highest benefit/cost ratios that fit into the budget.
21. Your Turn 6-8:
Assume that you have plenty of available land but only $3 million to spend.
Following the 4 steps above, choose the projects from the following table that
should be approved within this budget. Then verify that these projects provide the
greatest total net benefits.
Now assume that your budget has not been determined. Calculate the optimal
budget for land development given these possible projects.
Table 6-2: Project Choices Given a Budget
HOUSING INDUSTRIAL
PARK
OUTLET
MALL
GOLF
COURSE
POWER
PLANT
VACANT
LOT
Benefits $1,000,000 $1,250,000 $1,600,000 $1,500,000 $4,200,000 $1,000
Costs $1,100,000 $900,000 $1,200,000 $900,000 $3,000,000 $1,000
B/C ratio
Net benefits
22. Choosing the Scale of a Policy with Limited
Information
See Table 6-3 below. In 2001 the Environmental Protection Agency chose one of
the following maximum allowable levels of Arsenic. Which one would you choose,
if any, and why?
If half the cancer case resulted in death, and each life saved by the standard is
assumed to be worth $6 million dollars, recalculate the health benefits and
consider the choices again. Which level of arsenic would be chosen now? The
answer may depend on which number of cancer cases you choose.
Table 6-3: Alternate Arsenic Standard Benefits and Costs
ARSENIC STANDARD 3 PPB 5 PPB 10 PPB 20 PPB
Compliance Costs
(millions of 1999 $)
$698-792 $415-472 $180-206 $67-77
Estimated Health
Benefits (millions of 1999 $)
$214-491 $191-356 $140-198 $66-75
Cancer Cases Avoided 57-138 51-100 37-56 19-20
Source: U.S. EPA, 2001
23. Choosing an optimal scale and allocation
among different groups
The analysis of this issue of both total scale and allocation involves several steps,
displayed graphically in Figure 6-2. First one needs to calculate the marginal
benefits of a given program for various groups.
Then one adds the marginal benefit curves horizontally to find the marginal
benefits of the total budget.
One then finds the quantity where the sum of the
marginal benefits meets the marginal cost (Qtotal), as
well as the dollar value of the marginal cost at this
quantity.
So far we have determined the optimal scale.
24. Allocating an Optimal Budget Across
Different Programs
In order to allocate the budget efficiently across the
two programs one should set the marginal benefit
curve of each program equal to the dollar value of
the marginal cost of the last unit produced.
The quantities at which the individual marginal
benefits equal this marginal cost dollar value (Q1
and Q2) are the optimal quantities that should be
allocated to each program.
One might also notice that if MB1 = MCtotal and MB2
= MCtotal, this result also meets the marginal rule for
an optimal budget in equation 6-1.
26. The Net Benefits of an Output
Tax on Polluters
The previous chapter contained an example of the
effects of a tax on a polluting industry.
Because this policy leads to higher prices and
lower output, consumer surplus falls.
Because the firm experiences lower output and
lower after-tax revenue per unit, producer surplus
also falls.
The government and those experiencing external
harm from the pollution benefit from the policy.
The net benefits of this policy are most easily found
by calculating the change in the surplus of each
group and then adding the net effects.
27. The Net Benefits of an Output
Tax on Polluters
The net benefit of imposing the pollution tax equals $101.25, which equals the
original value of the deadweight loss that was eliminated by the tax.
The net benefits to both consumers and producers are negative, while the
government and the outsiders suffering harm from the pollution gain.
In principle, the winners could compensate the losers, but according to the Kaldor-
Hicks criterion this is not required.
Table 6-4: Net Benefits to Different Stakeholders
CONSUMER
SURPLUS
PRODUCER
SURPLUS
EXTERNAL
SURPLUS
GOVERNMENT
SURPLUS
TOTAL
NET GAINS
Before tax $1,012.5 $1,012.5 -$506.25 $0 $1,518.75
With tax $648 $648 -$324 $648 $1,620.00
Difference=
net benefits
of tax
-$364.5 -$364.5 $182.25 $648 $101.25
29. Cost-Effectiveness Analysis
For some policies, the benefits of a policy are not directly measured in terms of
money either because no monetary values have been estimated or because the
analyst cannot or will not use monetary values to measure the benefit.
Weighing of costs and benefits when benefits are not measured in dollars is
referred to as cost-effectiveness analysis. The primary measurement tool in such
studies is the cost/effectiveness ratio.
Definition: Cost-effectiveness ratio = total cost/total non-monetary effect.
The basic decision rule for this formula is to choose the alternative with the lowest
cost per unit of effect.
30. Cost Effectiveness Analysis
under Ideal Conditions
Cost-effectiveness analysis can work reasonably well as a policy tool if it is
used to compare policy alternatives with either equal total costs or equal
total effects.
31. Example: The COPS program
In 1994 Congress passed President Clinton’s Community Oriented Policing Services
(COPS) program, which added 100,000 officers to police departments.
Assume that this goal can be accomplished by offering grants to local law enforcement
agencies or by opening a national police training center.
Salaries and training costs are $5,000,000,000 for each program.
The training center costs $100,000,000 to build and maintain.
The grants include $10,000,000 in expected waste and fraud, and also include
$10,000,000 in administrative costs.
Given these assumptions the total cost of the training center is $5,100,000,000 ($5.1
billion) and the total cost of the grants equals $5,020,000,000 ($5.02 billion).
Therefore the cost per officer (the cost/effectiveness measure for this scenario) =
$5,100,000,000/100,000 or $51,000 for the training center and $5,020,000,000/100,000 =
$50,200 for the grants. The grants are more cost effective and would be recommended.
32. Cost Effectiveness Under Less
Than Ideal Conditions
If two alternative policies have unequal effects and unequal total costs, cost-
effectiveness analysis is less reliable as a decision tool. Let’s begin with an example
and then analyze the limits of this approach.
Example: S. Lumlord owns 50 apartments that are infested with cockroaches.
There are two methods of combating cockroach infestation, spraying and setting
traps. Spraying costs $25 per apartment and is 80 percent effective in eliminating
roaches in any single apartment. Setting traps costs $10 per apartment, but is only
40 percent effective in ridding each apartment of roaches.
Assuming that we measure effectiveness as the number of roach free
apartments, which method should Mr. Lumlord use?
33. S.Lumlord continued
The cost of spraying is $25•50 apts., or $1,250, while traps cost $10•50 or $500.
There will be 50•0.8, or 40 roach free apartments after spraying and 50•0.4, or 20
roach free apartments using traps.
The cost effectiveness ratios are $1,250/40 ($31.25/bug free apt.) for spraying and
$500/20 ($25/bug free apt.) for traps. According to this measure, traps cost less
per roach-free apartment, and are more cost-effective.
34. Problems With Cost-Effectiveness Analysis
This type of cost-effectiveness problem seems obvious enough, but some
important issues are unresolved.
First, there are 30 roach-infested apartments remaining after using traps but only
10 remaining after spraying.
Also, we have no way of knowing from cost effectiveness estimates how much
more valuable the apartments will be if they are roach-free, or how that value
affects the total benefits of each method.
It is quite possible that the added value of the extra 20 roach free apartments after
spraying would justify the added expense, but we cannot address this issue with
cost-effectiveness analysis.
35. Weighted Net Benefits
Assigning higher weights to the net benefits flowing to disadvantaged groups can
be easily justified on equity grounds and in a more limited way on efficiency
grounds as well.
The primary reason for weighing dollar valued net benefits to the least well-off
more highly is because the usual cost benefit calculation ignores the declining
marginal utility of consumption, an issue that was discussed at length in Chapter 3.
Other ethical theories may assign very different weights to the net benefits of
different groups. To take the most extreme example discussed in Chapter 3, John
Rawls’ difference principle, taken literally, would assign all of the weight to the net
benefits of the least well-off person.
36. Conclusion
This chapter introduced the basic economic tool for the analysis of public policy,
benefit-cost analysis, along with some related analytical tools.
The key elements of the chapter included the rules for various types of policy
decisions, the introduction of cost-effectiveness analysis for situations in which
either the benefits or costs cannot be quantified in dollar terms, and the
consideration of different weights for the net benefits of different groups.
Benefit-cost analysis and all of its related models are best thought of as tools for
organizing one’s thoughts and evidence about a policy’s effects, particularly its
efficiency effects. It does not actively consider equity, political practicality, or other
policy goals.
37. Kaldor-Hicks versus Ethical
Income Transfers
In Figure 6-4, the Kaldor-Hicks criterion weighs all incomes equally, so that a
neutral redistribution of net benefits doesn’t matter. The utilitarian graph in Figure
6-4 displays social indifference curves that are curved because of the declining
marginal utility of income for both persons. Equality is preferred given equal tastes.
38. Kaldor-Hicks versus Ethical
Income Transfers
In Figure 6-5 transfers are non-neutral. In this case no income redistribution is
justified under the Kaldor-Hicks criterion, while a modest amount of redistribution
is prescribed by utilitarianism and near equality is preferred according to the
Rawlsian social welfare function.
39. A Weighted Net Benefits Example
A modified form of Feldstein’s (1974) model is presented in the following
equation.
i
median
Y
Y
weight where α = the marginal social utility of income and Yi is the
income level of a particular group. Table 6-6 displays the weights produced by this formula
for a few values of alpha (α).
Table 6-6: Distributional Weights Using the Feldstein Formula
Unweighted
Income
Weight
(α=0)
weight
(α=1/2)
weight
(α=1)
20,000 1 1.414 2
40,000 (median) 1 1 1
60,000 1 .8165 2/3
40. Your Turn 6-13:
A training program provides total net benefits of $100,000 to a group of
disadvantaged youth. The program costs $120,000. The median income in this
society is $40,000. The youth have average incomes of $10,000, while those
paying for the program have average incomes of $80,000.
Calculate the weights for the $10,000 income group and $80,000 income group
using Feldstein’s formula, then calculate the weighted benefits and costs for each
group and determine the net benefits using each weight.
Table 6-7: A Weighted Net Benefits Example
Weight
(α=0)
Weight
(α=1/2)
Weight
(α=1)
$10,000 weight
$80,000 weight
Weighted benefits
to poor youth
Weighted costs
to quiche eaters
Weighted net
benefits of program