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COST-BENEFITCOST-BENEFIT

ANALYSISANALYSIS



“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 AnalysisCost-Benefit Analysis

Cost-benefit analysisCost-benefit analys

is (CBA) is the implicit or(CBA) is the implicit or

explicit assessment of the benefits and costs (i.e.,explicit assessment of the benefits and costs (i.e.,pros and cons, advantages and disadvantages)pros and cons, advantages and disadvantages)

associated with a particular choice.associated with a particular choice.

Benefits and costs may be monetary (pecuniary) orBenefits and costs may be monetary (pecuniary) ornon-monetary (non-pecuniary, “psychic”).non-monetary (non-pecuniary, “psychic”).



ForFor private decisions private decisions, such as taking martial arts, such as taking martial arts

classes or going to a movie on Saturday night, we areclasses or going to a movie on Saturday night, we are

often not aware of any internal process of often not aware of any internal process of

consideration of costs and benefits, but behave asconsideration of costs and benefits, but behave as

though we do.though we do.

An individual will choose an action if:An individual will choose an action if:

Benefits (B) > Costs (C)Benefits (B) > Costs (C)

ororNet Benefits (NB) = B - C > 0.Net Benefits (NB) = B - C > 0.



Joan will smoke if B > C.Joan will smoke if B > C.

For Joan, B’s are: taste/oral satisfaction, relaxation, dietFor Joan, B’s are: taste/oral satisfaction, relaxation, diet

control, and improved work performance.control, and improved work performance.

C’s are: expense, health consequences, value of timeC’s are: expense, health consequences, value of timespent, discomfort/inconvenience of “smoking-allowedspent, discomfort/inconvenience of “smoking-allowed

areas”, and disapproval of others.areas”, and disapproval of others.

For the continuous choice of how many cigarettes toFor the continuous choice of how many cigarettes tosmoke, Joan will smoke the number of cigarettes whichsmoke, Joan will smoke the number of cigarettes which

yield the greatest net benefits.yield the greatest net benefits.



CBA is most commonly used forCBA is most commonly used for public decisions public decisions – – policy proposals, programs, and projects, e.g., dams,policy proposals, programs, and projects, e.g., dams,

bridges, traffic circles, riverfront parks, libraries,bridges, traffic circles, riverfront parks, libraries,

drunk driving laws, and anything else thedrunk driving laws, and anything else the

government might fund.government might fund.

CBA can be used to rank alternative projects as wellCBA can be used to rank alternative projects as well

as evaluating the social value of one particularas evaluating the social value of one particular

project.project.



Even if CBA is not explicit, any decision, public orEven if CBA is not explicit, any decision, public orprivate, reveals a cost-benefit calculus consistent withprivate, reveals a cost-benefit calculus consistent with

the observed choice.the observed choice.

Example Exampl e: Ashenfelter, Orley and Michael Greenstone,: Ashenfelter, Orley and Michael Greenstone,

“Using Mandated Speed Limits to Measure the Value of a“Using Mandated Speed Limits to Measure the Value of a

Statistical Life,” National Bureau of Economic ResearchStatistical Life,” National Bureau of Economic Research

Working Paper w9094, August 2002Working Paper w9094, August 2002(http:www.nber.org/papers/w9094)(http:www.nber.org/papers/w9094)



Raising the maximum speed limit from 55 to 65Raising the maximum speed limit from 55 to 65

increased travel speed by about 2 mph (people oftenincreased travel speed by about 2 mph (people oftenexceed posted speed)exceed posted speed) saving 45 million hours travelsaving 45 million hours travel

time per year, and inducing about 360 deaths per yeartime per year, and inducing about 360 deaths per year

(125,000 hours of life).(125,000 hours of life).

Our collective decision to drive faster infers that 45Our collective decision to drive faster infers that 45

million hours of travel time is worth more that 360million hours of travel time is worth more that 360

deaths.deaths.

Our decisions lead to changes in benefits and costsOur decisions lead to changes in benefits and costs

regardless of whether we make them explicit.regardless of whether we make them explicit.



Example Exampl e: Knee Injury: Getzen, Thomas E.,: Knee Injury: Getzen, Thomas E., Health Health

Economics Economics, Second Edition New York: Wiley and, Second Edition New York: Wiley and

Sons, 2004.Sons, 2004.

Playing soccer, you injure your knee. Do you goPlaying soccer, you injure your knee. Do you go

to the emergency room (ER)?to the emergency room (ER)?

CBA usually takes the form of an explicit andCBA usually takes the form of an explicit and

formal presentation of a balance sheet, i.e., is itformal presentation of a balance sheet, i.e., is it

worth taking 3 hours and possibly $80 to go to theworth taking 3 hours and possibly $80 to go to theER so that a doctor can alleviate pain and check ER so that a doctor can alleviate pain and check

for serious damage?for serious damage?



Outlining benefits and costs assists rational decision-Outlining benefits and costs assists rational decision-

making.making.

1. Enumerate benefits and costs.1. Enumerate benefits and costs. (Handout, Table 3.1)(Handout, Table 3.1)

2. Quantify each benefit and cost as accurately as possible2. Quantify each benefit and cost as accurately as possible

(usually expressed in dollars), given the information at(usually expressed in dollars), given the information athand. (Handout, Table 3.2)hand. (Handout, Table 3.2)

Previously set appointment for Thursday means thePreviously set appointment for Thursday means the

proper comparison is treatment today vs. treatmentproper comparison is treatment today vs. treatment

Thursday (not treatment vs. no treatment).Thursday (not treatment vs. no treatment).



Time lost Time lost - opportunity cost of time commonly measured- opportunity cost of time commonly measured

by the wage, e.g., $7/hour.by the wage, e.g., $7/hour.

Value of Value of athletic imageathletic imag e - what you are willing to pay to- what you are willing to pay to

preserve your image, e.g., $40 for crutchespreserve your image, e.g., $40 for crutches

Value of Value of stopping painstop ping pain with certainty -the highest amountwith certainty -the highest amount

you would pay to stop the pain for 10 days, e.g., byyou would pay to stop the pain for 10 days, e.g., by

buying painkillers.buying painkillers.

Expected value of stopping pain by going to the ER =Expected value of stopping pain by going to the ER =

probability that the ER visit will result in stopping theprobability that the ER visit will result in stopping the

pain times the value of stopping the pain with certainty.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 AnalysisTheory of Cost-Benefit Analysis

Public Policy Objective: Choose the level of outputPublic Policy Objective: Choose the level of output

of a good or service to maximize net social benefitsof a good or service to maximize net social benefits

(NSB)(NSB)

NSB = TSB – TSCNSB = TSB – TSC

wherewhere

TSB = total social benefitsTSB = total social benefits

TSC = total social costsTSC = total social costs



Marginal Social Benefit (MSB) = additional social benefitsMarginal Social Benefit (MSB) = additional social benefits

from one more unit of outputfrom one more unit of output

Marginal Social Cost (MSC) = additional social costs of Marginal Social Cost (MSC) = additional social costs of

producing one more unit of outputproducing one more unit of output

MSB = d TSB/d QMSB = d TSB/d Q

MSC = d TSC/d QMSC = d TSC/d Q

Q = quantity of a publicly provided good or serviceQ = quantity of a publicly provided good or service

NSB are max when MSB = MSCNSB are max when MSB = MSC Social Decision Rule Social Decision Rule: Choose Q for which MSB = MSC: Choose Q for which MSB = MSC



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.

Present ValuePresent Value



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 rateConventional to use 3-5% or the T-Bill interest rate

since it represents the cost of borrowing at virtually nosince it represents the cost of borrowing at virtually no

risk.risk.

Results can be sensitive to the discount rate chosen.Results can be sensitive to the discount rate chosen.

Researchers often conduct a sensitivity analysis to seeResearchers often conduct a sensitivity analysis to see

how sensitive the results are to changes in assumptionshow sensitive the results are to changes in assumptions

about the discount rate, costs, and benefits.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.

HHow 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.

detectors seat belts radon gas detectors) which



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 whenmarginal 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 = MCMC = (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

Ad



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

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