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Chapter 7: Cost Benefit Analysis

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Title: Chapter 7: Cost Benefit Analysis


1
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.

2
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

3
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
4
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
5
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
6
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
7
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
8
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.
9
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)
10
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
11
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.
12
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

13
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)
14
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
15
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
16
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

17
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.

18
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.

19
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

20
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

21
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

22
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?

23
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)

24
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

25
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

26
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

27
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

28
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)

29
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)

30
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?

31
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

32
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

33
Consumer Surplus
P
S
P
D
Q
Q
Originally, consumer surplus is calculated as the
area below demand and above equilibrium price
34
Consumer Surplus
P
S
S
P
P
D
Q
Q
Q
If a government policy increases supply, consumer
surplus also increases.
35
Producer Surplus
P
S
P
D
Q
Q
Originally, producer surplus is calculated as the
area above supply and below equilibrium price
36
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).
37
Old Surplus
P
S
S
P
P
D
Q
Q
Q
38
New Surplus
P
S
S
P
P
D
Q
Q
Q
39
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?)
40
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

41
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

42
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.

43
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

44
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)

45
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?

46
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?

47
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

48
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.

49
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.

50
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.

51
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

52
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.

53
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

54
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).

55
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

56
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.

57
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.

58
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.

59
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

60
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

61
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.

62
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.

63
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.

64
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

65
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

66
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
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