Chapter 7: Cost Benefit Analysis

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Chapter 7 Cost Benefit Analysis

• The best way to evaluate a government policy is
  through the social welfare function Wf(U1, U2)
• BUT, this function is difficult to accurately
  calculate.
• A more practical way to evaluate public
  expenditure is through COST-BENEFIT ANALYSIS.

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Chapter 7 Cost-Benefit Analysis

• Present Value Calculations and Alternatives
• Public Sector Discount Rate
• Calculating Public Costs and Benefits
• Cost-Benefit Analysis Errors
• Distribution
• Uncertainty

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Math- Compound Interest

• Investment 100
• Interest rate 2

Year Calc. Amount
1 100 100.00
2 1001.02 102.00
3 1001.022 104.04
4 1001.023 106.12
5 1001.024 108.24
Derived Formula S P (1r)t S value after
t years P principle amount r interest rate t
years
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Compound Interest Example
The City loans 2 million to a local sports team,
to be paid back in 10 years at 3 interest. How
much will the City get? S P (1r)t S 2
million (10.03)10 S 2.69 million
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Math - Present Value
How much do I have to invest now to have a given
sum of money in the future? How much is a future
amount worth now? PV S/(1r)t PV present
value (money invested now) S sum needed in
future r real, compound interest rate t
years
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Present Value Example
If the City wins their bid for the Video Games
Olympics (VGO) in 5 years, they will gain 10
billion in economic activity. What is the
present value of that gain if interest rates are
4? PV S/(1r)t PV 10 billion/(10.04)5 P
V 8.22 billion
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Theory Discount Rate
Since the future value is discounted according
to the interest rate r, r is often referred to as
the DISCOUNT RATE. Similarly, (1r)t is often
referred to as the DISCOUNT FACTOR This PV
formula changes if a stream of income
occurs
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Math - Present Value of a stream
If an investment today yields future returns of
Rt, where t is the year of the return, then the
present value becomes
Note that failing to use present values to
discount future benefits can overestimate the
value of a project.
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Theory - Inflation
Typically, all prices in an economy change
(typically increase) with inflation. A 100 DVD
player today with 3 inflation will cost 103
next year. A 50,000 salary tied to inflation
will be 50,150 next year. NOMINAL VARIABLES are
the sticker price variables, the
variables/prices actually faced in that year.
(ie 103 DVD player) REAL VARIABLES are
variables after inflation has been factored out
(ie 100 DVD player)
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Inflation Rule
When doing financial calculations, the general
rule is that ALL VARIABLES MUST BE IN NOMINAL
TERMS OR ALL VARIABLES MUST BE IN REAL
TERMS. -Therefore if future revenues/costs are in
nominal terms, simply use the going interest rate
r -If future revenues/costs are in REAL terms,
the nominal interest rate must be converted into
the real interest rate through
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Math - Private Firm Evaluation
-In order to evaluate public projects, it is best
to begin with private projects -If a firm is
considering project X with costs and benefits Ctx
and Btx in year t, present value is
calculated
Where r is the firms rate of return or its
opportunity cost of funds.
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Theory - Present Value Criteria

• A firm will undertake projects based on the
  following
• A firm will only undertake projects whose PV is
  positive
• If given a choice between many mutually exclusive
  projects, it will chose the one with the highest
  PV

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Private Firm Evaluation
Note that r should represent a firms accurate
opportunity cost of funds -a high r favors
projects with a quick return (therefore an
incorrectly high r discriminates against long
projects) -a low r allows for project with a
longer return (therefore an incorrectly low r
discriminates against short projects)
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Math - Benefit-Cost Ratio
-One limited way to evaluate projects is using a
cost benefit ratio -Given a present value of
costs and benefits
-The BEFEFIT-COST ratio is B/C
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Benefit-Cost Ratio
-A project can be undertaken if B/Cgt1 -This
implies that B-Cgt0, similar to the present value
calculation considered earlier -The benefit-cost
ratio is poor for comparing between projects, as
it doesnt consider the amount of PV -3 net
PV could have a B/C value of 1.7 while 2,000,000
net PV could have a B/C value of only
1.1
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Theory - Public Sector Discount Rate

• In the private sector, the discount rate, r, is
  the opportunity cost of funds
• -ie the highest return on another investment or
  through the bank
• For public projects, the public sector discount
  rate is harder to calculate
• -Is the project funding through reducing
• 1) Private investment or
• 2) Private consumption

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1) Private Investment Funding

• Assume that funding a public project decreases
  private investment.
• Ie A new road costs 10,000, but the private
  sector would have used that 10,000 to make
  2,000 20 return.
• In this case the public sector discount rate is
  the private sectors before-tax return.

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2) Private Consumption Funding

• Assume that funding a public project decreases
  private consumption.
• Ie If the private sector consumes 10,000, that
  could have made 20 return, or 2,000. If tax is
  50, they are effectively giving up 1,000 or 10
  return.
• In this case the public sector discount rate is
  the private sectors after-tax return.

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Public Sector Discount Rate Difficulty

• Typically, government funding decreases both
  private consumption and private investment.
• Ie If 10,000 funding decreased consumption and
  investment by 5,000 each, r (20)/2(10)/215
  
• -But it is hard to calculate impact on
  consumption and investment, and this impact
  changes with each tax

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Theory - Social Discount Rate

• Some argue that a SOCIAL RATE OF DISCOUNT is more
  appropriate, representing the value SOCIETY
  places on decreased consumption.
• SOCIAL DISCOUNT RATE is less than market rate of
  return for 3 reasons
• Concern for future generations
• Paternalism
• Market Inefficiency

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1) Concern for Future Generations

• One may argue that the private sector has a high
  discount rate, heavily discounting benefits to
  future generations
• -Therefore the social discount rate should be
  lower to take the future into account
• BUT
• -The government is not fully omniscient and
  benevolent towards future generations
• -Plus projects with long-term benefits should
  have long-term profits, expressed in the rate of
  return

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2) Paternalism

• Even if people are selfish, they may not be
  far-sighted enough to take the future into
  account (Ill never get sick I dont need to
  save)
• -The government would use the discount rate
  people would use if they knew better
• -the government is paternalistic forcing
  decreased consumption now in order to save for
  the future
• BUT
• Should public preference be forced upon people?

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3) Market Inefficiency

• Often private investment results in positive
  externalities.
• -These positive externalities are UNDERPROVIDED
• -A lower social discount rate can correct this
  inefficiency
• BUT
• -How big is this externality?
• -Would a subsidy make more sense (chapter 5)

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Public Discount Rate Conclusion

• -The arguments for a social discount rate instead
  of a market discount rate still fail to provide
  for a specific discount rate
• -Typical discount rates fall between the
  before-tax and after-tax private sector rates of
  return
• -The Treasury Board Secretariat (1976)
  recommended the use of a social discount rate of
  10 per cent, and of 5 and 15 percent for
  sensitivity analysis
• -If PV is positive with all these rates, a good
  argument exists for doing the project

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Theory - Valuing Public Benefits and Costs

• Private benefits and costs are easy to calculate
  revenue and expenditures.
• Public benefits and costs are harder to calculate
  since SOCIAL costs and benefits may not be
  reflected in market prices.
• Some approaches and considerations are
• Market Prices (SMC)
• Shadow/Adjusted Market Prices (SMC)
• Consumer/Producer Surplus (SMB)
• Inferences from Economic Behavior
• Valuing Intangibles

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1) Market Prices

• If the First Fundamental Theorem of Welfare
  Economics holds, then
• -PSMC we have Pareto Efficiency
• -In this case market prices can be used for
  project valuation
• Even if the Theorem fails, market prices are
  often used because
• Market prices are simple and straightforward
• Other measures are
• Complicated and questionable
• Time consuming and costly to calculate

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2) Adjusted Market Prices

• The SHADOW PRICE of a commodity is its underlying
  social marginal cost in an imperfect market
• SHADOW PRICE relates to MARKET PRICE depending on
  how the market reacts to government intervention.
• Ie a) Monopoly
• b) Taxes
• c) Unemployment

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2a) Monopoly and Shadow Price

• In a monopoly, PgtMC
• i) If use of a monopoly input increases its
  production by the full amount, MC SHADOW PRICE
• ii) If the project consumes inputs that are
  taken directly from the private consumer,
  PMonopoly SHADOW PRICE
• iii) If production is increased somewhat,
• PMonopoly lt SHADOW PRICE lt MC
• (weighted average)

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2b) Tax and Shadow Price

• Taxes force PconsumergtPproducer
• i) If production of the fully expands, Pproducer
  SHADOW PRICE
• ii) If the project consumes inputs that are
  taken directly from the private consumer,
  Pconsumer SHADOW PRICE
• iii) If production increases somewhat, Pproducer
  lt SHADOW PRICE lt Pconsumer
• (weighted average)

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2c) Unemployment and Shadow Price

• Employment in government projects can come from
  other jobs or the unemployed
• i) If a worker is hired away from another job,
  WagePrivate Sector SHADOW PRICE
• ii) If the worker doesnt leave another job,
  things are more complicated
• -is the worker taking someone elses
  job? WagePrivate Sector SHADOW PRICE
• -would the worker have found a job?
• -what is the workers opportunity cost of
  leisure?

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2c) Unemployment and Shadow Price

• -Forcasting future employment is difficult
• -Fully understanding unemployment is difficult
  (in 2011 Alberta had both high vacancies and
  higher unemployment due to imperfect job matches)
• -Without a major recession, it is assumed that
• WagePrivate Sector SHADOW PRICE

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3) Consumer/Producer Surplus

• Typically, private firms have little effect on
  the price of a commodity in the market
• The government, however, can have a huge impact
  on the price of a commodity in a market
• -How should the project be valued?
• -Pre-project prices?
• -Post-project prices?
• -Somewhere in between?
• -A good alternative is to calculate change in
  producer and consumer surplus

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Consumer Surplus
P
S
P
D
Q
Q
Originally, consumer surplus is calculated as the
area below demand and above equilibrium price
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Consumer Surplus
P
S
S
P
P
D
Q
Q
Q
If a government policy increases supply, consumer
surplus also increases.
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Producer Surplus
P
S
P
D
Q
Q
Originally, producer surplus is calculated as the
area above supply and below equilibrium price
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Producer Surplus
P
S
S
P
P
D
Q
Q
Q
If a government policy increases supply, producer
surplus also changes (depending on who is
producing the good).
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Old Surplus
P
S
S
P
P
D
Q
Q
Q
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New Surplus
P
S
S
P
P
D
Q
Q
Q
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Gained Surplus
P
S
S
P
P
D
Q
Q
Q
Note that since producer surplus is lost,
businesses are hurt, possibly having negative
consequences (unemployment?)
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4) Inferences from Economic Behavior

• If no market exists for a commodity, other
  strategies must be used to estimate costs or
  benefits such as
• a) The value of time
• b) The value of life
• i) Lost earnings
• ii) Probability of Death

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4a) The Value Of Time

• Often public projects save time, or (temporarily
  or permanently) cost time
• ie Edmonton LRT saves time compared to the bus
• ie Edmonton bridge construction slows traffic
  until its done closing of Keillor Road increases
  travel time
• And time is money

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4a) The Value Of Time

• The theory of leisure-income choice states that
  people will work up until the point where their
  wage is equal to their value of one extra hour of
  leisure.
• If AFTER-TAX WAGE gt Leisure value, the person
  will work
• If AFTER-TAX WAGE lt Leisure value, the person
  will relax
• Therefore one could value time saved as the
  AFTER-TAX WAGE RATE.

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4a) The Value Of Time

• BUT
• Some people cant choose how many hours they work
  (ie as involuntary unemployment)
• Not all time away from a job is equal
• -ie someone who likes the bus may have a lower
  opportunity cost of time
• -ie someone who hates the morning commute may
  have a higher opportunity cost of time

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4a) The Value Of Time

• Alternately, one could compare the cost of slow
  and fast travel
• ie (Cost of a taxi)-(Cost of the bus) value of
  time saved by using a taxi
• BUT
• Other things affect choice of travel (fear of
  taxis, income, environmental concerns)
• Typically, travelling time cost is estimated at
  about 50 of before-tax wage rate (Small, 1992)

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4b) The Value Of Life

• Life is priceless
• But
• Resources () are limited
• Therefore
• Life has a dollar value attached
• A community hospital has 1 million in funding.
  Does it spend it on an MRI to catch obscure
  diseases and save 4 young adult lives, or on flu
  clinics to save 10 elderly lives?

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4b) The Value Of Life Question

• Approximately 200 people die of the flesh-eating
  disease (Necrotizing Fasciitis) each year.
  Assume that if all the resources spent on the
  internet were redirected to this disease
  (internet would shut down), these deaths would be
  prevented.
• Is it worth it?
• What if only youtube shut down?
• Itunes?

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4b) The Value Of Life

• Unfortunately, as an aggregate society we need to
  quantify the value of life.
• Two methods of assigning finite value to human
  life are
• i) Lost Earnings
• ii) Probability of Death

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4bi) Lost Earnings

• Law courts often consider the present value of a
  persons lifelong earnings when assigning
  compensation to relatives of fatal accidents.
• This is one way to estimate the value of life
• BUT
• It assigns a value (benefit) of ZERO to the old
  and retired.
• Since everyone in society carries a cost, cost
  benefit analysis would execute the old and
  retired. This is unacceptable.

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4bii) Probability of Death

• A better value of life is determined through
  varying the probability of death. (As most
  projects affect the probability of death they
  dont guarantee avoiding death forever).
• People often accept a probability of death to
  save time or make money in their everyday lives
  (driving without snow tires, driving a small car,
  taking a dangerous job).
• The change in probability of death and money
  value can be used to calculate value of life.

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4bii) Probability of Death

• Studies have used this device to put the value of
  a life between 4 million US and 10 million US
  (Viscusi, 2006)
• -This is a great range, but still allows
  reasonable projects (ie safety rails) and argues
  against unreasonable projects (ie Asbestos
  removal 100 million per life saved)
• -This approach is still controversal. A new
  cancer treatment reducing probability of death by
  0.01 takes on new meaning if you need the
  treatment.

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5) Valuing Intangibles

• Some costs and benefits seem impossible to value
  (ie pride at winning Olympics)
• 3 issues arise from intangibles
• a) Intangibles can subvert the entire
  cost-benefit exercise.
• b) Cost-benefit analysis can force planners to
  put a limit on the value of intangibles
• c) Even if intangibles cant be measured,
  alternative measures be examined to find the
  cheapest possible

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5a) Intangibles can ruin everything

• -if you complain or believe that an intangible
  cost or benefit is big enough, you can approve or
  deny many projects
• ie Losing the Oilers would be unbearable, we
  should build them a new arena! The piece of
  mind is worth it, buy the warrantee!
• PS3 - 300. Giving your boyfriend the best
  birthday gift ever priceless.

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5b) Intangible Value Limit

• Decisions can reveal the value of an intangible
• Ie If, for the Oilers Arena, (Cost-Benefits)5
  0 million, and the city DOES build the arena, the
  Oilers are worth at least 50 million
• Ie If the cost of a laptop is 1000, with a 200
  warrantee, and the laptop failure rate is
  5,(Cost-Benefits)200-50150, and someone
  DOESNT buy the warrantee, laptop peace of mind
  is worth less than 150

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5c) Cheapest Method to achieve Intangibles

• Cost-effectiveness analysis can be used to chose
  an option to achieve a benefit that cant be
  measured.
• ie If you cant put a value on health, you
  dont need a gym membership (600/year), when you
  can walk or run outside or at a mall (0/year).

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Theory - Cost-Benefit Analysis Errors

• Weve already discussed a variety of issues with
  cost-benefit analysis.
• Tresch (2002) noted the following common errors
  in cost-benefit analysis
• The Chain-Reaction Game
• The Labour Game
• The Double-Counting Game

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1) The Chain-Reaction Game

• Often proposals consider SECONDARY profits
  arising from their benefits.
• ie A downtown arena produces 1 million profit
  itself and increases local business profit by 4
  million
• BUT, if you consider secondary benefits, one must
  also consider secondary COSTS
• ie Moving the arena from the Northeast would
  hurt Northeastern businesses by X million.
• Often secondary benefits are simply transfers
  across individuals.

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2) The Labour Game

• Often a project calls creating employment a
  benefit.
• BUT wage rates are a COST.
• As mentioned earlier, for the truly involuntary
  unemployed, social cost is less than wage.

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3) The Double-Counting Game

• One cant count the benefit of two mutually
  exclusive uses of a commodity (ie selling and
  farming on farmland)
• ie If the government provides housing for low
  income families, the benefit is either
• 1) Housing low income families
• Or
• 2) Selling the house on the market
• Not both.

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Theory - The Problem of Distribution

• In PRIVATE projects, distribution is irrelevant
• -if the present value is positive, it is assumed
  that the winners COULD compensate the losers
• -The POTENTIAL PARETO IMPROVEMENT
  CRITERION
• -The HICKS-KALDOR CRITERION
• -Public projects can be based on this POTENTIAL
  gain in social welfare
• -Some can endure cost as long as others gain
  more benefits

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The Added Problem of Distribution

• ON TOP of the cost-benefit calculation, one could
  also be concerned about DISTRIBUTION.
• We can AVOID this problem by assuming that
• The government can costlessly transfer between
  winners and losers
• This transfer is nondistortionary
• This assumption is difficult to justify

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The Added Problem of Distribution

• We can ADDRESS this problem by assuming that
  certain members of society are especially
  deserving
• -A dollar benefit to these members is greater
  than a dollar benefit to others
• BUT
• Who is more deserving (poor, disabled, hard
  workers, women, men)?
• How much more than a dollar (1.10, 2)?
• POLITICS now complicates the issue.

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Theory The Problem of Uncertainty

• Often the costs and benefits of a project are
  UNCERTAIN.
• (ie Vaccines MAY prevent the swine flu, or they
  may go to people who were at no risk.)
• Costs and Benefits must therefore be converted to
  CERTAINTY EQUIVALENTS the amount of certain
  cost or benefit that a person would trade for an
  uncertain cost or benefit scheme.

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Uncertainty Example 1

• Many game shows give an opportunity for the
  winner to keep their winning or RISK IT ALL (ie
  pick whats in case 2).
• Assume a suitcase can hold 0 with a probability
  of 0.5 and 20,000 with a probability of 0.5
• E()0(0.5)20,000(0.5)10,000
• If a contestant would take the chance UNTIL his
  winnings increased to 4,000, that would be his
  CERTAINTY EQUIVALENT.

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Uncertainty Example 2

• Jonah wants a laptop. He can buy a Whale laptop
  worth 1000 or a Ninva laptop worth 600 with a
  4-year warrantee. (Same price)
• From Gartner (2006) we can infer a 25 failure
  rate on laptops over 4 years.
• Ninva Benefit600
• Whale Benefit1000(0.75)0(0.25)750
• If Jonah is indifferent between laptops, he has a
  CERTAINTY EQUIVALENT of 600

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Chapter 7 Summary

• Since costs and benefits occur over time, their
  PRESENT VALUE must be calculated
• Typically, the public sector discount rate (r)
  is
• before tax returngtrgtafter-tax return
• Alternatively, social discount rates argue for
  less than public sector discount rates
• Costs and benefits can be measured at market
  prices or shadow prices
• Labour costs are calculated considering
  unemployment and chance to remain unemployed

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Chapter 7 Summary

• Consumer and Producer surplus can be effective
  ways of measuring costs and benefits
• The prices of some nonmarket commodities (time,
  life) have to be inferred from observing behavior
• Some intangible benefits cannot be measured
• In cost benefit analysis, never count secondary
  benefits without secondary costs, view wages as a
  benefit, or double-count
• Distributional issues and uncertainty further
  confuse cost-benefit analysis