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Chapter 7: Cost Benefit Analysis

The best way to evaluate a governmentpolicy is through the social welfarefunction W=f(U1, U2)

BUT, this function is difficult to accuratelycalculate.

A more pract icalway to evaluate publicexpenditure 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: $100Interest rate: 2%

Year Calc. Amount

1 100 100.00

2 100*1.02 102.00

3 100*1.022 104.04

4 100*1.023 106.12

5 100*1.024 108.24

Derived Formula:

S = P (1+r)t

S = value after t yearsP = principle amount

r = interest rate

t = years

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Compound Interest ExampleThe 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 (1+r)t

S = $2 million (1+0.03)10

S = $2.69 million

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Present Value Example

If the City wins their bid for the Video GamesOlympics (VGO) in 5 years, they will gain$10 billion in economic activity. What is thepresent value of that gain if interest ratesare 4%?

PV = S/[(1+r)t]

PV = $10 billion/[(1+0.04)5]

PV = $8.22 billion

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TheoryDiscount RateSince the future value is discounted

according to the interest rate r, ris oftenreferred to as the DISCOUNT RATE.

Similarly, (1+r)tis often referred to as theDISCOUNT FACTOR

This PV formula changes if a stream of incomeoccurs:

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Math - Present Value of a streamIf an investment today yields future returns of

Rt, where t is the year of the return, thenthe present value becomes:

TT

o

r

R

r

R

r

RRPV

)1(...

)1()1( 221

Note that failing to use present values to

discount future benefits can overestimatethe value of a project.

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Theory - InflationTypically, 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 stickerprice variables, the variables/prices actuallyfaced in that year. (ie: $103 DVD player)

REAL VARIABLESare variables afterinflation has been factored out (ie: $100DVD player)

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Inflation RuleWhen doing financial calculations, the general

rule is thatALL VARIABLES MUST BE IN NOMINAL TERMS

OR ALL VARIABLES MUST BE IN REAL TERMS.

-Therefore if future revenues/costs are in nominalterms, simply use the going interest rate r

-If future revenues/costs are in REAL terms, the

nominal interest rate must be converted intothe real interest rate through:

inflationnomrealrr

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Theory - Present Value Criteria

A firm will undertake projects based on thefollowing:

1) A firm will only undertake projects whosePV is positive

2) If given a choice between many mutually

exclusive projects, it will chose the one withthe highest PV

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Private Firm EvaluationNote 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 discriminatesagainst long projects)

-a low r allows for project with a longer return

(therefore an incorrectly low r discriminatesagainst 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:

T

X

T

XX

XX

r

C

r

C

r

C

CC )1(...)1()1(2

210

-The BEFEFIT-COST ratio is B/C

T

X

T

XX

XX

r

B

r

B

r

BBB

)1(

...

)1()1( 2

210

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Benefit-Cost Ratio

-A project can be undertaken if B/C>1

-This implies that B-C>0, similar to the presentvalue calculation considered earlier

-The benefit-cost ratio ispoorfor comparingbetween projects, as it doesnt considerthe amount of PV:

-$3 net PV could have a B/C value of 1.7while $2,000,000 net PV could have a B/C

value of only 1.1

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Theory - Pub l ic Secto r Discount Rate

In the private secto r, the discount rate, r, is

the opportunity cost of funds

-ie: the highest return on another

investment or through the bankForpubl ic pro jects, the public sectordiscount rate is harder to calculate

-Is the project funding through reducing:

1) Private investment or

2) Private consumption

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1) Private Inves tment Fund ing

Assume that funding a public projectdecreases private investment.

Ie: A new road costs $10,000, but theprivate secto rwould have used that$10,000 to make $2,000 20% return.

In this case the public sector discount rateis the private sectors before-tax return.

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2) Pr ivate Consumpt ion Funding

Assume that funding a public projectdecreases 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 rateis the private sectors after-tax return.

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Pub l ic Secto r Discoun t Rate Dif f icu l ty

Typically, government funding decreasesbothprivate consumption and privateinvestment.

Ie: If $10,000 funding decreasedconsumption and investment by $5,000each, r = (20%)/2+(10%)/2=15%

-But it is hard to calculate impact onconsumption and investment, and thisimpact changes with each tax

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Theory - Soc ial Discount Rate

Some argue that a SOCIAL RATE OF

DISCOUNT is more appropriate, representingthe value SOCIETYplaces on decreasedconsumption.

SOCIAL DISCOUNT RATE is lessthan marketrate of return for 3 reasons:

1) Concern for future generations2) Paternalism

3) Market Inefficiency

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1) Concern for Futu re Generat ions

One may argue that the private sector has a high

discount rate, heavily discounting benefits tofuture generations

-Therefore the social discount rate should be

lower to take the future into accountBUT

-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 futureBUT

Should public preference be forced upon people?

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3) Market Ineff iciency

Often private investment results in posi t ive

externali t ies.-These positive externalities areUNDERPROVIDED

-A lower social discount rate can correct thisinefficiency

BUT

-How big is this externality?

-Would a subsidy make more sense (chapter 5)

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Publ ic Discount Rate Conc lusion

-The arguments for a social discount rate instead

of a market discount rate still fail to provide fora 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 percentforsensi t iv i ty analysis

-If PV is positive with all these rates, a good

argument exists for doing the project

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Theory - Valuing Publ ic Benef its and Costs

Private benefi tsand costsare easy to

calculaterevenueand expendi tures.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:

1) Market Prices (SMC)

2) Shadow/Adjusted Market Prices (SMC)3) Consumer/Producer Surplus (SMB)

4) Inferences from Economic Behavior

5) Valuing Intangibles

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1) Market Prices

If the First Fundamental Theorem o f Welfare

Economicsholds, then-P=SMC; we have Pareto Efficiency

-In this case market prices can be used for

project valuationEven if the Theorem fai ls, market prices are

often used because:

1) Market prices are simple and straightforward2) Other measures are:

a) Complicated and questionable

b) Time consuming and costly to calculate

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2) Ad jus ted Market Prices

The SHADOW PRICEof a commodity is its

underlying social marginal cost in an imperfectmarket

SHADOW PRICErelates to MARKET PRICE

depending on how the market reacts togovernment intervention.

Ie: a) Monopoly

b) Taxes

c) Unemployment

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2a) Monopoly and Shadow Price

In a monopo ly, P>MC

i) If use of a monopoly input increases itsproduction by the full amount,MC = SHADOW PRICE

ii) If the project consumes inputs that aretaken directly from the private consumer,

PMonopoly = SHADOW PRICEiii) If production is increased somewhat,

PMonopoly < SHADOW PRICE < MC

wei hted avera e

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2b) Tax and Shadow Price

Taxes fo rce Pconsumer>Pproducer

i) If production of the fully expands,Pproducer= SHADOW PRICE

ii) If the project consumes inputs that aretaken directly from the private consumer,Pconsumer= SHADOW PRICE

iii) If production increases somewhat,Pproducer< SHADOW PRICE < Pconsumer

(weighted average)

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2c) Unemployment and Shadow Price

Emp loyment in government projects can

come from other jobs o r the unemp loyed

i) If a worker is hired away from another job,WagePrivate Sector= SHADOW PRICE

ii) If the worker doesnt leave another job, thingsare 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 (in2011 Alberta had both high vacancies andhigher 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 Surp lus

Typically, private firms have little effect on the

price of a commodity in the marketThe 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 inroducer and consumer sur lus

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Consumer

Surplus

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Consumer Surplus

D

Q*

P*

Equilibrium

Or marketPrice

Q

P

Originally, consumer surplus is calculated as the area

below demand and above equilibrium price

S

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Consumer

Surplus

34

Consumer Surplus

D

Q*

P*

Q

P

If a government policy increases supply, consumer surplus

also increases.

SS

Q

P

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Producer

Surplus

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Producer Surplus

D

Q*

P*

Equilibrium

Or marketPrice

Q

P

Originally, producer surplus is calculated as the area above

supply and below equilibrium price

S

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Producer

Surplus

36

Producer Surplus

D

Q*

P*

Q

P

If a government policy increases supply, producer surplus

also changes (depending on who is producing the good).

SS

Q

P

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Old Surplus

D

Q*

P*

Q

P

SS

Q

P

Consumer

Surplus

Producer

Surplus

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Producer

Surplus

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New Surplus

D

Q*

P*

Q

P

SS

Q

P

Consumer

Surplus

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Gained Surplus

D

Q*

P*

Q

P

SS

Q

P

Note that since producer surplus is lost, businesses are hurt,

possibly having negative consequences (unemployment?)

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4) Inferences from Econom ic Behavior

If no market exists for a commodity, other

strategies must be used to estimatecosts 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

busie: Edmonton bridge construction slows traffic

until its done; closing of Keillor Road

increases travel time

And time is money

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The theory of leisure-income choice states that

people will work up until the point where theirwage is equal to their value of one extra hourof leisure.

If AFTER-TAX WAGE > Leisure value, theperson will work

If AFTER-TAX WAGE < Leisure value, theperson will relax

Therefore one could value time saved as the

AFTER-TAX WAGE RATE.

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BUT:

1) Some people cant choose how many hoursthey work (ie: as involuntary unemployment)

2) Not all time away from a job is equal

-ie: someone who likes the bus may have alower opportunity cost of time

-ie: someone who hates the morning commute

may have a higher opportunity cost of time

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Alternately, one could compare the cost of slow

and fast travelie: (Cost of a taxi)-(Cost of the bus) = value of

time saved by using a taxi

BUTOther things affect choice of travel (fear of taxis,

income, environmental concerns)

Typically, travelling time cost is estimated atabout 50% of before-tax wage rate

(Small, 1992)

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4b) The Value Of L ife

L ife is p riceless

But

Resources ($) are lim ited

Therefore

Life has a do l lar value attached

A community hospital has $1 million in funding.Does it spend it on an MRI to catch obscurediseases and save 4 young adult lives, or onflu clinics to save 10 elderly lives?

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4b) The Value Of L ife Question

Approximately 200 people die of the flesh-eating

disease (Necrotizing Fasciitis) each year.Assume that if all the resources spent on theinternet were redirected to this disease

(internet would shut down), these deathswould be prevented.

Is it worth it?What if only youtube shut down?

Itunes?

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4b) The Value Of L ife

Unfo rtunately, as an aggregate society we

need to quanti fy th e value of l i fe.

Two methods o f assign ing f in i te value to

human l i fe are:

i) Lost Earnings

ii) Probability of Death

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4b i) Los t Earn ings

Law courts often consider the present value of a

persons lifelong earnings when assigningcompensation to relatives of fatal accidents.

This is one way to estimate the value of life

BUTIt assigns a value (benefit) of ZERO to the old

and retired.

Since everyone in society carries a cost, costbenefit analysis would execute the old and

retired. This is unacceptable.

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4bi i) Probab i l i ty o f Death

A better value of life is determined through

varying the probability of death. (As mostprojects affect the probability of death; theydont guarantee avoiding death forever).

People often accept a probability of death to savetime 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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4bi i) Probab i l i ty o f 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 reasonableprojects (ie: safety rails) and argues againstunreasonable projects (ie: Asbestos removal:$100 million per life saved)

-This approach is still controversal. A new cancertreatment reducing probability of death by0.01% takes on new meaning if you need the

treatment.

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5) Valuing In tang ibles

Some costs and benef i ts seem impossib le 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 thecheapest possible

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5a) Intang ibles can ru in everyth ing

-if you complain or believe that an intangible costor benefit is big enough, you can approve ordeny many projects

ie: Losing the Oilers would be unbearable, we

should build them a new arena!

The piece of mind is worth it, buy thewarrantee!

PS3 - $300. Giving your boyfriend the best

birthday gift everpriceless.

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5b) In tang ible Value L im it

Decisions can reveal the value of an intangible:

Ie: If, for the Oilers Arena,(Cost-Benefits)=$50 million, and the cityDOES build the arena, the Oilers are worth at

least $50 millionIe: If the cost of a laptop is $1000, with a $200

warrantee, and the laptop failure rate is 5%,

(Cost-Benefits)=$200-$50=$150, andsomeone DOESNT buy the warrantee, laptop

peace of mind is worth less than $150

5c) Cheapest Method to ach ieve

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5c) Cheapest Method to ach ieve

Intangibles

Cos t-effect iveness analys iscan be used tochosean option to achieve a benefit that cantbe 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).

Th C B fi A l i E

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Theory - Cos t-Benef i t Analys is Errors

Weve already discussed a variety of issues with

cost-benefit analysis.Tresch (2002) noted the following common errors

in cost-benefit analysis:

1) The Chain-Reaction Game

2) The Labour Game

3) The Double-Counting Game

1) Th Ch i R ti G

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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 millionBUT, if you considersecondary benefi ts, one

must also considersecondary COSTS

ie: Moving the arena from the Northeast wouldhurt Northeastern businesses by $X million.

Often secondary benefits are simply transfers

across individuals.

2) Th L b G

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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 involuntaryunemployed, social cost is less than wage.

3) Th D b l C t i G

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3) The Doub le-Count ing Game

One cant count the benefit of two mutual ly

exclus iveuses of a commodity (ie: sellingand farming on farmland)

ie: If the government provides housing for lowincome families, the benefit is either:

1) Housing low income families

Or2) Selling the house on the market

Not both.

Th Th P b l f Di t ib t i

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Theory - The Prob lem of Distr ibut ion

In PRIVATE projects, distribution is irrelevant

-if the present value is positive, it is assumedthat the winners COULD compensate thelosers

-The POTENTIAL PARETOIMPROVEMENT CRITERION

-The HICKS-KALDOR CRITERION

-Public projects can be based on thisPOTENTIAL gain in social welfare

-Some can endure cost as long as others

gain more benefits

Th Add d P b l f Di t ib t i

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The Added Prob lem of Distr ibu t ion

ON TOP of the cost-benefit calculation, one could

also be concerned about DISTRIBUTION.

We can AVOID this problem by assuming that:

1) The government can costlessly transferbetween winners and losers

2) This transfer is nondistortionary

This assumption is difficult to justify

Th Add d P b l f Di t ib t i

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The Added Prob lem of Distr ibu t ion

We can ADDRESS this problem by assuming that

certain members of society are especiallydeserving

-A dollar benefit to these members is greater

than a dollar benefit to othersBUT:

1) Who is more deserving (poor, disabled, hard

workers, women, men)?2) How much more than a dollar ($1.10, $2)?

POLITICS now complicates the issue.

Th Th P b l f U t i t

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Theory The Prob lem of Uncertainty

Often the costs and benefits of a project are

UNCERTAIN.(ie: Vaccines MAY prevent the swine flu, orthey may go to people who were at no risk.)

Costs and Benefits must therefore be convertedto CERTAINTY EQUIVALENTS the amount

of certain cost or benefit that a person wouldtrade for an uncertain cost or benefit scheme.

U t i t E l 1

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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 $20,000 with a probability of 0.5E($)=$0(0.5)+$20,000(0.5)=$10,000

If a contestant would take the chance UNTIL hiswinnings increased to $4,000, that would behis CERTAINTY EQUIVALENT.


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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% failurerate on laptops over 4 years.

Ninva: Benefit=$600

Whale: Benefit=$1000(0.75)+0(0.25)=$750

If Jonah is indifferent between laptops, he has a

CERTAINTY EQUIVALENT of $600

Chapter 7 Summary

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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 return>r>after-tax return

Alternatively, social discount rates argue forless 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

Chapter 7 Summary

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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

econ 350 chapter07

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