COST-BENEFIT
ANALYSIS
“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
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”).
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 if:
Benefits (B) > Costs (C)
or
Net Benefits (NB) = B - C > 0.
Joan will smoke if B > C.
For Joan, B’s are: taste/oral satisfaction, relaxation, diet
control, and improved work performance.
C’s 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.
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.
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
(http:www.nber.org/papers/w9094)
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.
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?
Outlining benefits and costs assists rational decisionmaking.
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).
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 crutches
Value 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.
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(B=bi)  bi
where
prob(B=bi) is the probability that the benefit is worth $ bi .
Knee Injury
Cost of visit to ER=$50, $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
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
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
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., Medicaid–OHP), it benefits society to treat the
mother with Zidovudine.
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
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
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.
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/(1+r)t
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.
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.
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.
Value of life
Does society view life as infinitely valuable?
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?
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
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
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.
2.
Willingness-to-pay (WTP) Approach
Value of life is estimated from the amounts that
people are WTP to reduce the probability of dying.
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
•
•
•
•
•
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