8.Return to Figure 5.2 and consider the following criteria for prescription:
a.Maximize effectiveness at least cost [Note: Be careful—this is a tricky question].
b.Maximize effectiveness at a fixed cost of $10,000.
c.Minimize costs at a fixed-effectiveness level of 4,000 units of service.
d.Achieve a fixed-effectiveness level of 6,000 units of service at a fixed cost of $20,000.
e.Assuming that each unit of service has a market price of $10, maximize net benefits.
f.Again assuming that each unit of service has a market price of $10, maximize the ratio of
benefits to costs.
Indicate which of the two main programs (program I and program II) should be selected under
each of these criteria, and describe the conditions under which each criterion may be an adequate
measure of the achievement of objectives.
FIGURE 5.2
Cost-effectiveness comparisons using four criteria of adequacy.
Source: Adapted from E. S. Quade, Analysis for Public Decisions (New York: American
Elsevier, 1975), p. 93.
To answer this question, we must look at the relation between costs and effectiveness, rather than
view costs and effectiveness separately. Yet this is where the complications begin (see Figure
5.2): (1) If we are dealing with a type I (equal-cost) problem and costs are fixed at $20,000 (C2),
program II is preferable because it achieves the higher level of effectiveness while remaining
within the fixed-cost limitation. (2) If we are confronted with a type II (equal-effectiveness)
problem and effectiveness is fixed at 6,000 units of service (E2), program I is preferable. (3) If,
on the other hand, we are dealing with a type III (variable-cost-variable-effectiveness) problem,
for which costs and effectiveness are free to vary, program II is preferable, because the ratio of
effectiveness to costs (called an effectiveness-cost ratio) is greatest at the intersection
of E1 and C1. Here program II produces 4,000 units of service for $10,000, that is, a ratio of 4,000
to 10,000 or 0.4. By contrast, program I has an effectiveness-cost ratio of 0.32 (8,000 units of
service for $25,000 = 8,000/25,000 = 0.32).10 Finally, (4) if we are dealing with a type IV (equalcost-equal-effectiveness) problem, for which both effectiveness and costs are fixed at E2 and C2,
neither program is adequate. This dilemma, which permits no adequate solution, is known
as criterion over specification.
The lesson of this illustration is that it is seldom possible to choose between two alternatives on
the basis of either costs or effectiveness. Although it is sometimes possible to convert
measures of effectiveness into dollar benefits, which permits us to calculate net income benefits
by subtracting monetary costs from monetary benefits, it is frequently difficult to establish
convincing dollar equivalents for important policy outcomes. What is the dollar equivalent of a
life saved through traffic safety programs? What is the dollar value of international peace and
securiy promoted by United Nations educational, scientific, and cultural activities? What is the
dollar value of natural beauty preserved through environmental protection legislation? Such
questions will be examined further when we discuss cost-benefit analysis; but it is important here
to recognize that the measurement of effectiveness in dollar terms is a complex and difficult
problem.11
Sometimes it is possible to identify an alternative that simultaneously satisfies all criteria of
adequacy. For example, the broken-line curve in Figure 5.2 (Program III) adequately meets
fixed-cost as well as fixed-effectiveness criteria and also has the highest ratio of effectiveness to
costs. As this situation is rare, it is almost always necessary to specify the level of effectiveness
and costs that is regarded as adequate.
Questions of adequacy cannot be resolved by arbitrarily adopting a single criterion. For example,
net income benefits (dollars of effectiveness minus dollar costs) are not an appropriate criterion
when costs are fixed and a single program with the highest benefit-cost ratio can be repeated
many times. This is illustrated in Table 5.4, in which program I can be repeated 10 times up to a
fixed-cost limit of $40,000, with total net benefits of $360,000 (i.e., $36,000 × 10). Program I
therefore has the highest benefit-cost ratio. But if program I cannot be repeated—that is, if only
one of the three programs must be selected—program III is preferable because it yields the
greater net benefits, even though it has the lowest benefit-cost ratio.
Equity. The criterion of equity is closely related to legal and social rationality and refers to the
distribution of effects and effort among different groups in society. An equitable policy is one for
which effects (e.g., units of service or monetary benefits) or efforts (e.g., monetary costs) are
fairly or justly distributed. Policies designed to redistribute income, educational opportunity, or
public services are sometimes prescribed on the basis of the criterion of equity. A given program
might be effective, efficient, and adequate—for example, the benefit-cost ratio and net benefits
may be superior to those of all other programs—yet it might still be rejected on grounds that it
will produce an inequitable distribution of costs and benefits. This could happen under several
conditions: Those most in need do not receive services in proportion to their numbers, those who
are least able to pay bear a disproportionate share of costs, or those who receive most of the
benefits do not pay the costs.
The criterion of equity is closely related to competing conceptions of justice or fairness and to
ethical conflicts surrounding the appropriate basis for distributing resources in society. Such
problems of “distributive justice,” which have been widely discussed since the time of the
ancient Greeks, may occur each time a policy analyst prescribes a course of action that affects
two or more persons in society. Although we may seek a way to measure social welfare, that
is, the aggregate satisfaction experienced by members of a community. Yet individuals and
groups within any community are motivated by different values, norms, and institutional rules.
What satisfies one person or group often fails to satisfy another. Under these circumstances, the
analyst must consider a fundamental question: How can a policy maximize the welfare of
society, and not just the welfare of particular individuals or groups? The answer to this question
may be pursued in several different ways:
1.Maximize individual welfare. The analyst can attempt to maximize the welfare of all
individuals simultaneously. This requires that a single transitive preference ranking be
constructed on the basis of all individual values. Arrow’s impossibility theorem, as we
have seen, demonstrates that this is impossible even when there are only two persons and three
alternatives.
2.Protect minimum welfare. The analyst can attempt to increase the welfare of some persons
while still protecting the positions of persons who are worse off. This approach is based on
the Pareto criterion, which states that one social state is better than another if at least one
person is better off, and no one is worse off. A Pareto optimum is a social state in which it is
not possible to make any person better off without also making another person worse off.
3.Maximize net welfare. The analyst can attempt to increase net welfare (e.g., total benefits
less total costs) but assumes that the resulting gains could be used to compensate losers. This
approach is based on the Kaldor-Hicks criterion: One social state is better than another if
there is a net gain in efficiency (total benefits minus total costs) and if those who gain can
compensate losers. For all practical purposes, this criterion, which does not require that losers
actually be compensated, avoids the issue of equity.
4.Maximize redistributive welfare. The analyst can attempt to maximize redistributional
benefits to selected groups in society, for example, the racially oppressed, poor, or sick. One
redistributive criterion has been put forth by philosopher John Rawls: One social state is better
than another if it results in a gain in welfare for members of society who are worst off.12
DEMONSTRATION EXERCISE
Return to Chapter 1 and reread Case 1.1 (Saving Lives and Saving Time). Then read Case
5.1 (Opportunity Costs of Saving Lives—The 55 mph Speed Limit) below. Prepare a short
analysis in which you answer these questions:
■What assumptions govern estimates of the value of time lost driving? Are some assumptions
more tenable than others? Why?
■What is the best way to estimate the value of time? Justify your answer.
■What is the best way to estimate the cost of a gallon of gasoline? Justify your answer.
■Driving speeds and miles per gallon estimates may be based on official statistics on highway
traffic from the Environmental Protection Agency and the Department of Energy or on
engineering studies of the efficiency of gasoline engines. Which is the more reliable? Why?
What are the consequences of using one source rather than another?
■What is the value of a life saved? Explain.
■Which policy is preferable, the 55 mph speed limit or the 65 mph limit that was abandoned in
1994?
CASE 1.1 THE GOELLER SCORECARD—MONITORING AND FORECASTING TECHNOLOGICAL
IMPACTS
CASE 1.1 THE GOELLER SCORECARD—MONITORING AND FORECASTING
TECHNOLOGICAL IMPACTS
When advanced technologies are used to achieve policy goals, sociotechnical systems of
considerable complexity is created. Although it is analytically tempting to prepare a
comprehensive economic analysis of the costs and benefits of such policies, most practicing
analysts do not have the time or the resources to do so. Given the time constraints of policy
making, many analyses are completed in a period of several days to a month, and in most cases
policy analyses do not involve the collection and analysis of new data. Early on in a project,
policy makers and their staffs typically want an overview of the problem situation and the
potential impacts of alternative policies. Under these circumstances, the scorecard is appropriate.
The Goeller scorecard, named after Bruce Goeller of the RAN D Corporation, is appropriate
for this purpose. Table C1.1 shows the impacts of alternative transportation systems. Some of the
impacts involve transportation services used by members of the community, whereas others
involve impacts on low-income groups. In this case, as Quade observes, the large number of
diverse impacts are difficult to value in dollar terms, making a benefit-cost analysis impractical
and even impossible.50 Other impacts involve financial and economic questions such as
investments, jobs created, sales, and tax revenues. Other impacts are distributional because they
involve the differential effects of transportation. ■
TABLE C1.1
Scorecard
Social Impacts
CTOL
VTOL
TACV
Passengers (million miles)
7
4
9
Per trip time (hours)
2
1.5
2.5
Per trip cost ($)
$17
$28
$20
Reduced congestion (%)
0%
5%
10%
TRANSPORTATION
FINANCIAL
Investment ($ millions)
$150
$200
$200
Annual subsidy ($ millions)
0
0
90
Added jobs (thousands)
20
25
100
Added sales ($millions)
50
88
500
Noise (households)
10
1
20
Added air pollution (%)
3%
9%
1%
Petroleum savings (%)
0%
−20%
30%
Displaced households
0
20
500
Taxes lost ($millions)
0
0.2
2
Landmarks destroyed
None
None
Fort X
7%
1%
20%
2%
16%
40%
ECONOMIC
COMMUNITY
DISTRIBUTIONAL
Low-income trips (%)
Low-income household
Noise annoyance (%)
Source: Goeller (1974); Quade, Analysis for Public Decisions (1975), p. 60.
Note: Conventional takeoff and landing aircraft (CTOL); vertical takeoff and landing aircraft
(VTOL); tracked air-cushion vehicle (TACV).
CASE 5.1 OPPORTUNITY COSTS OF SAVING LIVES-THE 55 MPH SPEED LIMIT41
Conducting a benefit-cost analysis is not only a technical matter of economic analysis. It is also a
matter of identifying, and if necessary challenging, the assumptions on which benefit-cost
analysis is based. This can be seen if we examine the case of the National Maximum Speed Limit
of 1974.
Table 5.11 describes steps in conducting a benefit-cost analysis and a critique of the assumptions
underlying the analysis. The case shows, among other things, that all steps in conducting a
benefit-cost are sensitive to these assumptions. ■
TABLE 5.11
Measuring the Costs and Benefits of the 55 mph Speed Limit: A Critical
Appraisal
Steps
Critique
Costs
1. The major cost of the National Maximum Speed
Law (NMSL) was the additional time spent
driving as a result of slower speeds. To calculate
the number of hours spent driving in 1973, divide
the total number of vehicle miles traveled on
interstate highways by the average highway speed
(65 mph) and then multiply by the average
occupancy rate per vehicle, which is
approximately 1.77 persons.
Why use 1973 mileage without any
adjustment? The average growth rate in
travel before 1973 was 4 percent.
Therefore, the formula should be
Next, find the number of hours spent driving in
1974 by dividing total vehicle miles traveled on
interstate highways by the average highway speed
in 1974 (58 mph). The NMSL caused some people
to cancel trips and others to find alternative modes
of transportation; as a result, time calculations
based on 1974 mileage would be an
underestimate. Therefore, we should use the 1973
mileage of 525 million miles.
Using the following formula, where VM is vehicle
miles, S is average speed, R is average occupancy
rate, and H is the number of hours lost,
The number of hours lost driving in 1974, based
on this equation, is estimated to be 1.72 billion.
2. To estimate the value of this time, begin with the
average wage rate for all members of the labor
force in 1974—$5.05. The value of one hour’s
travel is not $5.05 per hour because very few
persons would pay this sum to avoid an hour of
travel. We estimate that the people will pay up to
33 percent of their average hourly wage rate to
avoid an hour of commuting. The value of time
spent traveling is therefore about $1.68 per hour.
Using the above formula, the estimated
number of hours lost should be 1.95
billion—not 1.72 billion.
Why take a percentage of the $5.05 figure
based on what commuters would pay to
avoid an hour of travel? We should avoid
reducing the value of people’s time for
two reasons. First, the value of time in
cost to society is equal to what society
will pay for productive use of that time.
Time’s value is not what a commuter will
pay to avoid commuting because commuting
has other benefits, such as solitude for
thinking or the advantages of suburban
living. Second, the value of time spent
driving for a trucker is many times the
industrial wage rate. Discounting would
greatly underestimate the value of
commercial drivers.
3. Application of the cost figure ($1.68) to the time
lost figure (1.72 billion hours) results in an
estimated travel cost of $2.89 billion.
Applying the value of one hour’s time to
the hours lost as calculated above (1.95
billion) results in an estimated travel
cost of $9.85 billion.
4. The NMSL also has some enforcement costs.
Total enforcement cost should be about
Total enforcement costs for signs, advertising, and
$12 million-not $810,000.
patrolling are about $810,000.
a. New signs were posted. Cost estimates from 25
states for modification of speed limit signs
totaled $707,000; for 50 states, this results in an
OK.
estimated $1.23 million. Spread out over the
three-year life of traffic signs, we get an
estimate of $410,000.
b. The federal government engaged in an
advertising campaign encouraging compliance.
The Federal Highway Administration’s
advertising budget for 1974 was $2 million.
About 10 percent of this, or $200,000, was
spent to encourage compliance with the NMSL.
Assume that an additional amount of public
service advertising time was donated, for a total
of $400,000.
Not OK. The Federal Highway
Administration does other advertising.
Public service advertising estimate also
seems low.
Compliance costs pose some problems, but
they can be estimated. In 1973, some
5,711,617 traffic citations jumped by
1,713,636 to over 7.4 million. Each
c. Compliance costs are difficult to estimate. The
cost of highway patrols cannot be used because additional traffic citation includes an
these persons were patrolling highways before opportunity cost to society. If a law
enforcement officer were not issuing
the NMSL. Assume that states did not hire
additional personnel solely for enforcement of traffic tickets, he or she could be
the NMSL. Therefore, we assume that
solving other crimes. Assuming that it
enforcement of the NMSL will not entail any
requires 15 minutes for a law enforcement
additional costs above enforcement of previous officer to issue a speeding ticket, the
speed limits.
total cost of law enforcement is $2.9
million. This figure is based on the
average cost of placing a law enforcement
officer on the streets at $6.75 per hour.
This figure is clearly an underestimate
because it does not count time lost
waiting to catch speeders.
Approximately 10 percent of all speeders
will demand a court hearing. Estimating
an average of 30 minutes for each hearing
and an hourly court cost of $45 results
in an additional cost to society of $3.8
million for 171,000 cases. Given the
overloaded court dockets, this
opportunity cost may be even higher.
Benefits
Why estimate gasoline saved by comparing
1973 and 1974 miles-per-gallon figures in
relation to vehicle miles traveled? The
1. The most apparent benefit of the NMSL is the
federal figures for average miles per
amount of gasoline saved. The average gasoline
hour are estimates based on several
economy improves from 14.9 miles per gallon at assumptions. Given the conflict between
65 miles per hour to 16.1 at 58 miles per hour.
industry estimates, Environmental
Use this information to estimate the number of
Protection Agency estimates, and Energy
gallons of gasoline saved by traveling at lower
Department estimates, any miles-per-hour
speeds. Gallons saved will be calculated by the
estimate must be considered unreliable.
following formula, where VMT is vehicle miles
traveled on interstate highways (not all highways) The number of vehicle miles traveled is
and MPG is miles per gallon.
also based on gallons of fuel sold
multiplied by average miles per hour.
Hence, this figure is also subject to
error.
Studies of the efficiency of gasoline
engines show that the effect of reducing
the average speed of free-flow interstate
highways would be to save 2.57 percent of
the normal gas used. In 1979, American
motorists consumed 106.3 billion gallons
of gasoline. Saving 2.57 percent would
total 2.73 billion gallons.
In 1974, the average price of gasoline was 52.8
cents per gallon. This market price, however, does
not reflect the social cost of gasoline, due to
government price controls on domestic oil. The
marginal (or replacement) cost of crude oil is the
price of foreign oil. Therefore, the price of
gasoline must reflect the higher cost of foreign oil.
Use the market price of gasoline in the absence of
Why use the market price? There is no way
to determine whether a marginal gallon of
gasoline will be imported or come from
domestic reserves. In addition, the costs
and benefits of the NMSL should not be
distorted simply because the U.S.
government does not have a market-
price controls, which is about 71.8 cents per
gallon. This figure yields an estimate of $2.50
billion in benefits through gasoline saved.
2. A major second-order benefit of the 55 mph limit
was a large drop in traffic fatalities, from 55,087
in 1973 to 46,049 in 1974. Part of the gain must
be attributable to reduction in traffic speeds.
Studies by the National Safety Council estimate
that up to 59 percent of the decline in fatalities
was the result of the speed limit. Applying this
proportion to the decline in fatalities provides an
estimated 5,332 lives saved. The consensus of
several studies is that a traffic fatality costs
$240,000 in 1974 dollars. Using this figure, the
value of lives saved in 1974 is estimated at
$1,279.7 million.
oriented energy policy. In 1974, gasoline
cost 52.8 cents per gallon, and
therefore, a gallon of gasoline saved was
worth 52.8 cents.
OK.
3. The NMSL also resulted in a reduction of nonfatal
injuries. Use the 59 percent figure found in the
fatality studies. Between 1973 and 1974, nonfatal
traffic injuries declined by 182,626. Applying the
estimated percentages results in 107,749 injuries
avoided. Generally, three levels of injuries are
indentified: (1) permanent total disability, (2)
permanent partial disability and permanent
disfigurement, and (3) nonpermanent injury. In
1971, the proportion of traffic injuries that
OK.
accounted for injuries in each category was 0.2
percent, 6.5 percent, and 93.3 percent,
respectively. The National Highway Traffic Safety
Administration estimated that in 1971, the average
cost of each type of injury was $260,300, $67,100,
and $2,465, respectively. The average injury,
therefore, cost $8,745 in 1974 dollars. Applying
this figure to our injury estimate results in $942.3
million as the social benefit of injury reduction.
4. The final benefit of the reduction in property
damage fell from 25.8 million to 23.1 million.
About 50 percent of this reduction was the result
of lower speeds. The NMSL saved 1.3 million
cases of property damage at an average cost of
$363. Therefore, the total benefit from property
damage prevented is $472 million.
OK.
Conclusion
The first estimate of the costs and benefits of the
NMSL results in the following figures (in millions):
Using different assumptions, the second
estimate of the costs and benefits of the
NMSL is as follows (in millions):
Costs
Costs
Time spent traveling
$2,890.0
Time spent traveling
$9,848.0
Enforcement
.8
Enforcement
12.0
$9,860.0
$2,890.8
Benefits
Benefits
Gasoline saved
$2,500.0
Gasoline save
$1,442.0
Lives saved
1.297.7
Lives saved
998.0
Injuries prevented
942.3
Injuries prevented
722.0
Property damage averted
472.0
Property damage adverted
236.0
$3,398.0
$5,212.0
Net benefits: $2,321.2 million
Net benefits: −$6,462 million
Benefits to costs ratio: 1.8
Benefits to costs ratio: .345
Source: The steps and data were suggested by Charles T. Clotfelter and John C. Hahn,
“Assessing the National 55 m.p.h. Speed Limit,” Policy Sciences 9 (1978): 281–94.The
critical comments are based on Charles A. Lave, “The Costs of Going 55,” Car and Driver.
May 1978, p. 12.
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