COST-BENEFIT ANALYSIS

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COST-BENEFIT ANALYSIS
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It is best to think of the cost-benefit approach
as a way of organizing thought rather than as a
substitute for it. Michael Drummond
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Cost-Benefit Analysis

• Cost-benefit analysis (CBA) is the implicit or
  explicit assessment of the benefits and costs
  (i.e., pros and cons, advantages and
  disadvantages) associated with a particular
  choice.
• Benefits and costs may be monetary (pecuniary) or
  non-monetary (non-pecuniary, psychic).

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For private decisions, such as taking martial
arts classes or going to a movie on Saturday
night, we are often not aware of any internal
process of consideration of costs and benefits,
but behave as though we do.An individual will
choose an action ifBenefits (B) gt Costs (C)
orNet Benefits (NB) B - C gt 0.
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Joan will smoke if B gt C. For Joan, Bs are
taste/oral satisfaction, relaxation, diet
control, and improved work performance. Cs
are expense, health consequences, value of time
spent, discomfort/inconvenience of
smoking-allowed areas, and disapproval of
others. For the continuous choice of how many
cigarettes to smoke, Joan will smoke the number
of cigarettes which yield the greatest net
benefits.
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CBA is most commonly used for public decisions
policy proposals, programs, and projects, e.g.,
dams, bridges, traffic circles, riverfront parks,
libraries, drunk driving laws, and anything else
the government might fund. CBA can be used to
rank alternative projects as well as evaluating
the social value of one particular project.
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• Even if CBA is not explicit, any decision, public
  or private, reveals a cost-benefit calculus
  consistent with the observed choice.
• Example Ashenfelter, Orley and Michael
  Greenstone, Using Mandated Speed Limits to
  Measure the Value of a Statistical Life,
  National Bureau of Economic Research Working
  Paper w9094, August 2002 (httpwww.nber.org/papers
  /w9094)

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Raising the maximum speed limit from 55 to 65
increased travel speed by about 2 mph (people
often exceed posted speed) ? saving 45 million
hours travel time per year, and inducing about
360 deaths per year (125,000 hours of life).Our
collective decision to drive faster infers that
45 million hours of travel time is worth more
that 360 deaths. Our decisions lead to changes
in benefits and costs regardless of whether we
make them explicit.
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• Example Knee Injury Getzen, Thomas E., Health
  Economics, Second Edition New York Wiley and
  Sons, 2004.
• Playing soccer, you injure your knee. Do you go
  to the emergency room (ER)?
• CBA usually takes the form of an explicit and
  formal presentation of a balance sheet, i.e., is
  it worth taking 3 hours and possibly 80 to go to
  the ER so that a doctor can alleviate pain and
  check for serious damage?

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Outlining benefits and costs assists rational
decision-making.1. Enumerate benefits and
costs. (Handout, Table 3.1)2. Quantify each
benefit and cost as accurately as possible
(usually expressed in dollars), given the
information at hand. (Handout, Table
3.2)Previously set appointment for Thursday
means the proper comparison is treatment today
vs. treatment Thursday (not treatment vs. no
treatment).
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Time lost - opportunity cost of time commonly
measured by the wage, e.g., 7/hour. Value of
athletic image - what you are willing to pay to
preserve your image, e.g., 40 for
crutchesValue of stopping pain with certainty
-the highest amount you would pay to stop the
pain for 10 days, e.g., by buying
painkillers.Expected value of stopping pain by
going to the ER probability that the ER visit
will result in stopping the pain times the value
of stopping the pain with certainty.
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Expected Value When values of costs or benefits
are not known with certainty, but are known with
probability, expected values are used. Expected
value of a benefit is E(B) ?i prob(Bbi) ?
bi where prob(Bbi) is the probability that the
benefit is worth bi .
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Knee Injury Cost of visit to ER50, 100 or
more expected value 80 80 is a weighted
average, where the weights are the probabilities
that alternative cost values will occur. That
is, if 50 will occur with probability
0.6, 100 will occur with probability 0.2,
and 150 will occur with probability 0.2, then
E(C).6 (50).2 (100).2 (150) 80
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Example Mauskopf, J.A. et. al, Economic Impact
of Treatment of HIV-Positive Pregnant Women and
their Newborns with Zidovudine Implications for
HIV Screening, JAMA 276 2, 132-8, July 10,
1996. Probability of maternal-to-fetal
transmission when the mother is HIV-positive No
Treatment 25.5 With Zidovudine Treatment
8.3 Lifetime cost of treatment of an infected
child from birth 98,915
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Expected value of cost of a lifetime pediatric
HIV infection probability of transmission ?
lifetime treatment costs No Treatment .255 ?
98,915 25,223 With Treatment .083 ? 98,915
8,210 Expected benefits of treatment
Expected costs averted by treatment 25,223
- 8,210 17,013 Cost of Zidovudine treatment
1,045 Expected Net Benefits 17,013 - 1,045
15,968 per HIV-positive pregnant woman
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If medical expenses are paid privately, the woman
will opt for the treatment. If the child will
be on public assistance for medical care (e.g.,
MedicaidOHP), it benefits society to treat the
mother with Zidovudine.
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Theory of Cost-Benefit Analysis

• Public Policy Objective Choose the level of
  output of a good or service to maximize net
  social benefits (NSB)
• NSB TSB TSC
• where
• TSB total social benefits
• TSC total social costs

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• Marginal Social Benefit (MSB) additional social
  benefits from one more unit of output
• Marginal Social Cost (MSC) additional social
  costs of producing one more unit of output
• MSB d TSB/d Q
• MSC d TSC/d Q
• Q quantity of a publicly provided good or
  service
• NSB are max when MSB MSC ?
• Social Decision Rule Choose Q for which MSB
  MSC

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Present Value
Future, as well as present, benefits and costs
must be included in the analysis. But costs and
benefits that accrue in the future are worth less
than costs and benefits today. Economic agents
and society as a whole will maximize the present
value of expected net benefits.
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Costs and benefits may occur over different
periods of time, e.g., costs for a dam built
today may be spent primarily during the initial
period of the project, but benefits will accrue
over the lifetime of the dam. To account for
all costs and benefits in the same units across
time periods, we calculate the present value of
net benefits PV(NB) ?t NB/(1r)t
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Present Value Worksheet 100 invested today at
an annual interest rate (r) of 4 will be worth
104 in 1 year. Present value (PV) of 104 next
year when r.04 is 100. That is, 104
tomorrow is worth 100 today. PV F/(1 r),
where F is a fixed sum of money to be received
next year.
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Discount Rate What value of r should be used? r
rate of discount of future consumption or rate
of time preference The higher the social
discount rate, the higher the social value of
consumption today relative to consumption
tomorrow.
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Conventional to use 3-5 or the T-Bill interest
rate since it represents the cost of borrowing at
virtually no risk. Results can be sensitive to
the discount rate chosen.Researchers often
conduct a sensitivity analysis to see how
sensitive the results are to changes in
assumptions about the discount rate, costs, and
benefits.
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Value of life Does society view life as
infinitely valuable?
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Many public programs and projects involve the
prevention of loss of life dams, maintaining
roads, traffic signs, provision of health care,
employment of firefighters, etc. How do
economists value a life saved (death averted) in
the cost-benefit calculus?
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• 1. Human Capital Approach
• Value of life present value of lifetime
  earnings
• ( lifetime productivity in competition)
• represents productivity gains from extending life
  (benefit side)
• or
• productivity losses from early death (cost side)
• for society as a whole, represents a loss in
  national output due to mortality

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Method often used in court cases, e.g., court
awards the family of a man who dies at 35 in a
car accident the amount of his expected PV of
lifetime earnings 650,000
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• Problems with human capital approach
• People who are not working for pay (e.g.,
  homemakers, students, retirees) are valued at 0!
  (Even for the employed, time away from the job is
  valued at 0.)
• Implies that people with higher wages have higher
  social value.
• Does not account for labor market imperfections,
  e.g., discrimination.

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2. Willingness-to-pay (WTP) Approach Value of
life is estimated from the amounts that people
are WTP to reduce the probability of dying.
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• Suppose the cost of a safety device (e.g., smoke
  detectors, seat belts, radon gas detectors) which
  reduces the probability of death by 1 in 10,000
  is 100, and people are WTP the 100.
• Recall net benefits are maximized when
• marginal benefit (MB) marginal cost (MC).
• Benefit of 1 more safety device (MB)
• (change in probability of dying) ?
  (value of life)
• Cost of 1 more safety device MC
• Assuming people are maximizing NB, MB MC?
• MC (change in probability of dying) ? (value
  of life)
• Value of life MC/(change in probability of
  dying)
• 100 ? (1/10,000)
• Value of life 1 million

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• Advantages.
• Measures total value of life (not just labor
  market value)
• Includes foregone earnings and nonmarket value of
  life
• Disadvantages.
• Estimates vary widely
• Price may be less than true WTP, value will be
  understated