topic 4 cost benefit analysis (with page 41)
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Cost-BenefitAnalysisEC3351 Topic 4
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Cost-Benefit Analysis
Cost-Benefit Analysis (CBA) = measurement,estimation and comparison of a project’s costsand benefits
General decision rules:
• A project should be undertaken if its benefit
exceeds its cost• The scale of the project should be increased as
long as MB > MC
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CBA of Government Projects
A private sector firm considers the costs and
benefits to itself
A government considers the costs and benefits
to everyone in society
•
Not just costs and benefits that accrue togovernment itself!
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An expressway project
A city
government is
planning an
infrastructureproject:
A North South
Expressway
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Costs of expressway
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Construction Annual Maintenance
Cement (tons) 1 million 50,000
Labor (hours) 100 million 5 million
Simplifying
assumptions
Construction
starts and
finishes this year
Maintenance
starts next year
Continues everyyear …
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Benefits of expressway
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Annual Benefits
Saved Time (hours) 5 million
Saved Lives 20
Simplifying assumptions Benefits starts this year
Continue every year …
E.g. 10 minutes per day x 150,000 commuters
x 200 commute days a year
= 300 million minutes a year
= 5 million hours a year
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Counting Secondary Benefits
Retailers at a shopping centre near an exit to newexpressway will gain profit. Should this profit be countedas a benefit?
Retailers at a shopping centre far from expressway willlose profit. Should this loss be counted as a reduction inbenefit?
If you count one, you should count the other; otherwiseexclude both
In a large full-employment economy, these secondarygains and losses will cancel out
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Task of CBA
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Cost Quantity Value Total
Cement 1 million tons
Labor 100 million hours
Maintenance
(starts next year)
Benefit (Yearly) Quantity Value Yearly Total
Saved time 5 million hours
Saved lives 20 lives
Total Cost over time:
Total Benefit over time:
Yearly:
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Three valuation problems in CBA
1. If market prices are available, do they reflect
costs and benefits correctly? If not, how to
adjust?
2. If market prices are not available, how to
measure costs and benefits?
3. How to compare costs and benefits
happening over a long period of time?
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Outline
1. Valuation with market prices
2. Valuation with no market prices
3. Valuation across Time4. Issues with CBA
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1. Valuation with market prices
Value of inputs used (cement, labor) usually
have market prices available for valuation
For a public sector project, the correct measure
is the marginal opportunity cost to society of
using the input
• This may differ from the market price due to
market distortions
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Impact of imperfect competition
If cement is provided by a monopoly, then P >MC of cement production. Between the two (P,MC) which is better indicator of Opp. Cost to
society?• If monopoly doesn’t expand production at all,
opp. cost falls on ____________ P is betterindicator
• If monopoly expands production by the full 1million tons, then opp. cost falls on other
_______________MC is better indicator
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Impact of taxes and subsidies
Suppose cement production is done in a
competitive market, but is taxed, so P > MC.
Again, look at cement production response to
the project!
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Impact of Unemployment
If the economy has full employment, hiring aworker-hour for the project will reduce availablelabor for rest of economy
•
Thus, opp. cost of hiring one worker-hour =market wage rate
If the economy is in recession, hiring a worker-hourneed not be at the expense of the rest of economy
• Then, opp. cost of hiring one worker-hour = valueof one hour of leisure time for unemployed
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Common Mistake:Counting Job Creation as a Benefit
Politicians often tout the employment effects of
public sector projects
• “Build the expressway because 10,000 jobs
will be created!”
This implicitly values wages paid as a benefit of
the project!
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Impact of Large Scale Projects
A public sector project may be large enough to
change market prices
In that case, measurement of benefits and costs
will have to involve estimating price changes
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Task of CBA
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Cost Quantity Value Total
Cement 1 million tons
Labor 100 million hours
Maintenance
(starts next year)
Benefit (Yearly) Quantity Value Yearly Total
Saved time 5 million hours
Saved lives 20 lives
Total Cost over time:
Total Benefit over time:
Yearly:
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Outline
1. Valuation with market prices
2. Valuation with no market prices
2.1 Value of Time
2.2 Value of Life
3. Valuation across Time
4. Issues with CBA
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Valuation with no market prices
Some costs (e.g. noise) and many benefits
(commuting time saved, lives saved) don’t have
market prices
• Other examples: defense, national prestige,
ecological diversity, aesthetics
An intangible is a benefit or cost for which there
is no obvious method of assigning a dollar value
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2.1 Value of Time
There are 3 valuation methods for intangibles
1. Use a measurable proxy
2. Ask people for their hypothetical responses to
different scenarios: Contingent Valuation3. Use actual market behavior to uncover peoples’
valuations: Revealed Preference
We apply the 3 methods to measuring the value ofcommuting time saved by the expressway project.
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Value of Time by Proxy
The idea here is that time is valuable because it
can be used to increase output
Thus, a proxy for the value of time would be the
wage rate of the average commuter
• E.g. wage rate is $10/hr
• Then saving 5 million hours has the value of
$50 million
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Value of Time by Contingent Valuation
Ask commuters in a survey:
“How much would you pay to cut your daily
commute by 10 minutes?”
• Easy to administer
• For some kind of intangibles (e.g. value of
preserving the Grand Canyon), surveys are the
only way to determine value
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Value of Time by Contingent Valuation
But answers may be highly sensitive to context, e.g.how the questions are asked (framing)
1. “How much would you pay to cut your daily
commute by 10 minutes?”2. “Considering the time you could spend with
your children, how much would you pay to cutyour daily commute by 10 minutes”
3. “How much would you pay to cut commutetime from Upper Thompson to City Hall by 10minutes?”
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Value of Time by Revealed Preference
Examine existing consumer behavior to tease outhow much they value time
• E.g. Time expended to get a discount
•Large corporate petrol stations sold petrol at lowerprice (by $0.395/gallon) than small independentpetrol stations
• On average, people were willing to wait 14.6 minutes
longer to buy 10.5 gallons of petrol at the largecorporate stations
• Value of 1 hour is thus $0.395 x 10.5 x 60/14.6 = $17
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Value of Time by Revealed Preference
E.g. compare prices of houses that differ only by
travel time to downtown
In practice, use regression analysis to control for
other salient differences
• This is called Hedonic Price Analysis
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Common Mistake: Double Counting
Property values along expressway exits will rise
But this merely reflects the value of savedcommute time, which is already being counted
in benefits
Thus, if rise in property value is separately
counted as a benefit, that is double-counting!
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2.2 Value of Life
Society cannot function if life is considered priceless• Should governments force hospitals to spend $1
million to extend the life of a 100-year-old patientto 101 years?
People do not behave as if life is priceless
• Driving is a risky activity, but people willingly do it
In CBA, a finite value of life is estimated, using the 3methods
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Value of a Life by Proxy
Use the expected value of lifetime earnings
Some uncomfortable implications
• Mens’ lives are more valuable than womens’
• The younger you are the more valuable your life
• High earner’s life is more valuable
• Life in UK is dear; life in India is cheap
• You have no value outside your working capacity!
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Value of a life by Contingent Valuation
Ask commuters in a survey: “How much would
you pay to cut your probability of death by from
2 in 10,000 to 1 in 10,000?”
Again, framing matters
• E.g. People might pay more to avoid gruesome
deaths
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Value of a Life by Revealed Preference
Look at how much consumers actually spend on
safety devices such as car airbags
• E.g. airbag costs $350 but lowers Pr(death) by
1:10,000, then value of life is $3.5 million
• Do consumers really understand these risks
when they are making purchase decisions?
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Look at compensating differential in wagesobtained from doing risky jobs
• E.g. job in oilrig raises Pr(death) by 0.1% but pays
$10,000 more annually, then value of life is $10
million
• People who take on dangerous jobs may be
more risk-loving than the general population
• Do workers fully understand the risks they
face?
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Estimates of “Value of a Statistical Life”
0100020003000400050006000
700080009000
Estimated Value of a Statistical Life by Country
(1995 USD)
VSL
32Source: Miller (2000)
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Estimates of
“Value of a
StatisticalLife”
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Source: Viscusi and Aldy (2003)
http://www.nber.org/papers/w9487.pdfhttp://www.nber.org/papers/w9487.pdf
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Task of CBA
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Cost Quantity Value Total
Cement 1 million tons $1,000/ton $1 billion
Labor 100 million hours $10/hr $1 billion
Maintenance
(starts next year)
Benefit (Yearly) Quantity Value Yearly Total
Saved time 5 million hours
Saved lives 20 lives
Total Cost over time:
Total Benefit over time:
Yearly: $100 million
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Outline
1. Valuation with market prices
2. Valuation with no market prices
3. Valuation across Time3.1 Discounting and Present Value
3.2 What discount rate to use?
4. Issues with CBA
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3.1 Discounting and Present Value
Suppose the market interest rate is 5% per year
The Present Value (PV) of “$110 in one year’s time”
= $___ today that will yield $110 in one year’s time,• Ans: $110 / 1.05 = $104.76
The process of converting a future value into its PVis called discounting, and the interest rate used iscalled the discount rate
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Using PV to compare $ values over time
Is $100 today better, or $110 in two year’s time?
PV of “$110 in two year’s time”
= $110 / 1.052
= $99.77
$100 today is better, since $99.77 today wouldyield $110 two years from now, and $100 today
is certainly better than $99.77 today
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Discounting Benefits and Costs
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(benefits) =
(+)
(+) ⋯
(+)
(costs) =
(+)
(+) ⋯
(+)
A project provides benefits {B0, B1, B2 …. BT-1, BT}and costs {C0, C1, C2 …. CT-1, CT}
Assume for simplicity that the discount rate r isconstant across periods
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Discounting perpetual streams
For a perpetual stream of constant cost C,
starting next period (i.e. C0 = 0), PV is given by:
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(costs) = 0 ( 1 )
( 1 )2
( 1 )
⋯
=
( 1 ) 1
1
( 1 )
1
( 1 )2 ⋯
=
( 1 )
1
=
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E.g. Discounting for expressway project
Cost of maintenance is constant $100 million
(i.e. $108) per year, starting next year
Suppose discount rate is constant 7% per year
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= 0 $108
(1 0.07)
$108
(1 0.07)2
$108
(1 0.07) ⋯
≈ $1.43 billion
=
$108
0.07
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Task of CBA
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Cost Quantity Value Total
Cement 1 million tons $1,000/ton $1 billion
Labor 100 million hours $10/hr $1 billion
Maintenance
(starts next year)
Benefit (Yearly) Quantity Value Yearly Total
Saved time 5 million hours $20/hr $100 million
Saved lives 20 lives $8 million/life $160 million
Total Cost over time:
Total Benefit over time:
Yearly: $100 million
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3.2 What discount rate to use?
The Social Discount Rate (SDR) should reflect
the social opportunity cost of funds invested in
the project
There is no consensus on what constitutes the
appropriate SDR
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Using private sector rate of return
One approach: treat funds as being taken away
from private sector, affecting either investment
or current consumption
• If funds are taken from investment, then SDR
= B4-tax return on investment projects
• If funds are taken from consumption, then
SDR = after-tax return on investment projects
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Should SDR be lower thanprivate sector rate of return?
• Paternalism: people may be myopic they
over-discount
• For long term projects, future generations
aren’t well-represented by market rates
• See Seidman Ch 4 p. 90 for discussion about
Stern Review on the Economics of Climate
Change
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Outline
1. Valuation with market prices
2. Valuation with no market prices
3. Valuation across Time
4. Issues with CBA
4.1 Decision Rules
4.2 Distributional concerns4.3 Dealing with Uncertainty
4.4 To use or not to use CBA
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4.1 Decisions Rules
Net Present Value (preferred way)
Internal Rate of Return
Benefit-Cost Ratio
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Net Present Value
The Net Present Value of the project is given by
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= benefits − costs
The NPV criteria(1) Project should be done only if NPV > 0
(2) Between two mutually exclusive projects,
choose the one with higher NPV
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Internal Rate of Return
The Internal Rate of Return ρ = discount rate that makesNPV of a project = 0
The IRR criteria
(1) Project should be done only if ρ > r(2) Between two mutually exclusive projects, choose theone with higher ρ
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Project Benefits(1 year later)
Costs(today)
NPV(r = 7%)
IRR
A $110 $100 $2.80
B $220 $200 $5.60
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Benefit-Cost Ratio
The benefit-cost ratio = PV(benefits) / PV(costs)
The BCR criteria
(1) Project should be done only if BCR > 1
(2) if two projects are mutually exclusive, choosethe project with higher BCR
Problem: Suppose project results in $100 damageto environment
• Count as cost BCR denominator ↑
• Count as benefit BCR numerator ↓49
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4.2 Distributional Concerns
CBA is not concerned with the project’s
distribution of benefits and costs.
• If NPV is positive, you can potentially have
winners compensate losers, and still havewinners be better off
• Hicks-Kaldor Criterion: project is admissible if
it allows for a potential Pareto Improvement (which is satisfied if NPV is positive)
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Distributional Concerns
In principle, one can modify CBA to weigh
different people’s benefits and costs differently
• E.g. a $1 benefit to a poor person = $10
benefit to a rich person
But should CBA be thus modified? Or should
governments follow Hicks-Kaldor?
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4.3 Dealing with Uncertainty
If there is uncertainty, must make adjustments
to CBA
• Compute costs and benefits under alternative
scenarios
• Compute certainty equivalents (RG Chapter 8
Appendix, not required)
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4.4 To Use or Not to Use CBA
• Not popular with bureaucrats and politicianspushing their pet projects
• Not popular with environmentalists and
consumer advocates who do not accept valuationof intangibles
• US Clean Air Act, Endangered Species Actexplicitly prohibits CBA!
• Even when used, rarely the sole determinant• In Singapore, CBA is sometimes done, but almost
never published
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