Public economics

• Cost benefit analysis: A set of practical procedures based on welfare

economics to guide public expenditure decisions

Projecting Present Dollars into the Future

R=$ T=years r=interest rate

How much will $1000 earn in 2 years at an interest rate of 10%?

R0 = $1000

R1 = $1000*(1+.01) = $1010

R2 = $1010*(1+.01) = $1020.10

R2 = $1000*(1+.01)2 = $1020.10

RT = R0*(1+r)T

8-2

Projecting Future Dollars into the Present

How much will $1000 earned in 2 years at an interest rate of 10% be worth today?

Since RT = R0*(1+r)T

R0 = RT/(1+r)T Present Value

discount ratediscount factor

Low r – more future-oriented and benefits projects in which returns are concentrated further into the futureHigh r – more present-oriented and benefits projects in which returns are concentrated closer into the future

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Present Value of a Stream of Money

8-4

R 0 R1 R2 R3 R4 R5 R6 R7 R8 …. Rn

T= 1 2 3 4 5 ……n

Flow of income at different dates

Each income converted into its present value

Present Value of a Stream of Money

PV RR

r

R

r

R

rT

T

01 2

21 1 1( ) ( ). . .

( )

8-5

R stream of money at different dates

r market rate of return => discount factor

PV max you pay today to get that stream (or a given amount) in the future

Private Sector Project EvaluationPresent Value Criterion

We consider streams of net returns

TTT

r

CB

r

CB

r

CBCBPV

)1(...

)1(1 22211

00

Note choice of r is critical:

8-6

Private Sector Project Evaluation: Present Value CriterionLet us compare two projects mutually exclusive in terms of PV

TTT

r

CB

r

CB

r

CBCBPV

)1(...

)1(1 22211

00

Annual Net Return PV of R&D vs. Advertising

Year R&D Advertising r = R&D Advertising

0 -$1,000 -$1,000 0 $150 $200

1 600 0 0.01 128 165

2 0 0 0.05 46 37

3 550 1,200 0.07 10 -21

Note choice of r is critical: • Low r benefits Advertising; High r benefits R&D. Why? Is it

odd result? 8-7

How to choose r

It must reflect as close as possible a firm’s actual opportunity costBorrowing firm: market rate of returnInvesting firm: opportunity cost (risk free bonds

return rate)With taxes: r = 0.10 tax = 0.25r net of taxes is 0.75

Present value criterion

• Only project with positive NPV will be chosen• Of two mutually exclusive the one with higher

NPV will be chosenNote= initial outlay is the same for both!Not needed for it to compare in appropriate way

2 projectsWe use the same rBack to the example diapo 7

Private Sector Project Evaluation Internal Rate of Return

0)1(

...)1(1 22211

00

TTT CBCBCB

CBPV

Project Year 0 Year 1 ρ Profit PV

X -$100 $110 10% $4 3.77

Y -$1,000 $1,080 8% $20 18.87

IRR: Discount rate that would make a project’s NPV zero

If firm can lend/borrow freely at 6% rate of interest= > profits are 4$ for X = (10-6) and 20$ for Y = (80-60)

8-10

Private Sector Project Evaluation Internal Rate of Return

Project Year 0 Year 1 ρ Profit PV

X -$100 $110 10% $4 3.77

Y -$1,000 $1,080 8% $20 18.87

IRR: Discount rate that would make a project’s NPV zero

We can compare projects of different size but the this criterion is flawed when comparing projects of much differing sizes if Although X has the higher IRR, Y yields the higher profit. Note that the PV criteria, using r=6%, would prefer Y.

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• If project are mutually exclusive, and if they differ in size, internal rate of return gives poor guidance

• This result rests on the assumptionn that projects are mutually exclusive o/wise we could duplicate project X ten times…

• NPV no problem with different amounts, we get guidance (initial investment is also important for other kind of considerations eg credit rationing, real guarantees etc …)

Private Sector Project Evaluation Benefit-Cost Ratio

TT

r

B

r

B

r

BBB

)1(...

)1(1 221

0

TT

r

C

r

C

r

CCC

)1(...

)1(1 221

0

Benefit-cost ratio = B/CMust be > 1 to be accepted

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Problems with the Benefit-Cost Ratio: Toxic waste dump

Project B C B/CI $250 $100 2.5II $200 $100 2.0

Suppose now that $40 of crop damage need to be added to project I

I: Subtract $40 from B?

$210 $100 2.1

ORI: Add $40 to

C?$250 $140 1.79

Benefit-Cost criterion can lead to incorrect inference “Costs or Negative Benefits?”

No problem with NPV8-14

Private Sector Project Evaluation

The Present-Value Criterion is the most reliable evaluation guide

– Both IRR and Benefit-Cost Ratio Criteria can lead to incorrect inferences

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What is the Appropriate Discount Rate for Government Projects

• Based on Returns in Private Sector:• Problem: money comes from taxes => families’ income =>

less consumption => rate of return is market rate after taxes => (available income)

• 1000 euro income 5% return 50% taxes=> => Cost opportunity?• possibly less investment: the market rate (before taxes) on

private investment (value for the society)=> why before taxes?

• Weighted average? Which proportion?

8-16

What is the Appropriate Discount Rate for Government Projects

• Social Discount Rate: the rate at which society is willing to trade off present consumption for future consumption (not individual)

• Lower than the MKT rate of return, why?– Arguments for SDR:

• Paternalism / not farsighted enough• Market Inefficiency/ externalities => investment

underprovided=> Lower rate, but which one?

– Example: Discounting and the Economics of Climate Change, future damages

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Importance in global climate changes• This topic has recently been very controversial and

highly debated. Since there is such a strong probability that the world will suffer significantly in the future due to global change in temperature, finding the correct social discount rate for the benefits of reducing CO2 emissions and other harmful greenhouse gases is very important.

• giving future generations less weight than the current generation is 'ethically indefensible.'

• To someone, weighting generations equally leads to paradoxical and even nonsensical results."

• The range in the social discount rate for a cost-benefit analysis in this issue range from zero to over 3%.

Importance in global climate changes• The Stern Review on the Economics of Climate

Change is one such report that argues for zero discounting of future generations.

• While William D. Nordhaus of Yale • "examines a model of climate change that is similar

to the one used in the Stern Review but with a 3 percent social discount rate that slowly declines to 1 percent in 300 years rather than the 0.1 percent discount rate used in the Stern Review. In his model, the welfare of future generations is given less weight than the current generation’s welfare. He finds that preventive measures like a tax on carbon emissions are certainly required. But they are of a much smaller magnitude than those recommended in the [Stern] report.

Government Discounting in Practice• U.S. Office of Management and Budget (OMB)

requires federal agencies to use a variety of discount rates, depending on the agency and the type of project– One using real discount rate of 7%– One using real discount rate of 3%

• Evidence shows that government’s incorrect use of discounting has favored policies that increase revenue in the short run, but reduce it in the long run

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Valuing Public Benefits and CostsPrivate sector ignore social costs and externalities

• Use Market Prices?• Although imperfect…• Use Adjusted Market

Prices in imperfect markets? => Shadow price= underlying social MC of a good–Monopoly ITC marginal cost < market price –More or less production?–(pag 158)

• Use Consumer Surplus?

Pounds of avocados per year

Pric

e pe

r pou

nd

of a

voca

dos

Da

Sad

A0

Sa’

$1.35

$2.89b

c g

A1

e

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Valuing Public Benefits and CostsInferences from Economic Behavior

• How to place a value on the time saved by a proposed project like a new highway?– Earnings? After tax wage– Other methods

• How to place a value on a life saved by a proposed project such as a 4-lane divided highway? – Lost earnings? PV– Probability of death

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Valuing Public Benefits and CostsIntangibles

• Intangibles can subvert cost-benefit exercises• C/B tools can reveal limits on valuing

intangibles• Cost-effectiveness analysis might be best in

the presence of intangible benefits– Comparing the costs of various alternatives that

attain similar benefits to determine which one is the cheapest

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Games Cost-Benefit Analysts PlayCommon Errors

• The Chain-Reaction Game– Including secondary profits (but not costs)

• The Labor Game– Including project workers’ wages as a benefit

(rather than what it is, which is a cost)

• The Double-Counting Game– Including benefits from all possible projects, when

only one project can be undertaken

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Distributional Considerations

Should who gains and who loses be taken into account? Should benefits and costs be weighted?•NO: Hicks-Kaldor Criterion – a project should be undertaken if it has positive net present value, regardless of distributional consequences•NO: Let the government costlessly correct any undesirable distributional aspects•NO: Relies too much on value judgments and politics

8-25

Uncertainty

Project Benefit Probability CE**

X $1,000 1.00 $1,000

Y

0 0.50

$1,000$2,000 0.50

**Certainty Equivalents (Expected Value)

8-26

An Application: Are Reductions in Class Size Worth It?

• Discount rate• Costs• Benefits• The Bottom Line and Evaluation

8-27

Use (and Nonuse) by Government

• Using Cost-Benefit Analysis• Not Using Cost-Benefit Analysis

– Clean Air Act– Endangered Species Act– Food, Drug, and Cosmetic Act

8-28

Chapter 8 Summary

• Cost-Benefit analysis is used to evaluate potential public sector projects

• Present value of future expected costs and benefits must be calculated in order to allow correct comparisons

• Although the IRR and B-C Ratio are used to evaluate projects, the NPV criterion has fewer biases and problems

• Choice of the discount rate is critical• The costs and benefits of public projects can be measured

using market prices in the absence of market failures. Otherwise, shadow prices or consumer surplus can be used

CONT

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Chapter 8 Summary (cont)

• Quantifying the value of time and life, is necessary in measuring benefits, but using earnings as a proxy has limitations

• Whether the distribution of future costs and benefits on various groups of people should be included in C-B analysis is under debate

• Uncertainty of future costs and benefits can be included through the use of certainty equivalents

8-30

Appendix: Calculating the Certainty Equivalent Value

Income per year

Util

ity

CE E + y

U(E)

U*

U(E + y)

U

Expected income

Certainty Equivalent

8-31

O

Inflation

PV RR

r

R

r

R

r

TT

T T

0

12

22 2

1

1 1

1

1 1

1

1 1

( )

( )( )

( )

( ) ( ). . .

( )

( ) ( )

How to incorporate inflation – price level increases – into the procedure? Given: ∏ = inflation rate

However, (1+∏) terms cancel out, leaving the PV equation from previous slide!

CAUTION: $ values and r values must be measured consistently – if real values are used for R, the r must be measured in real terms

8-32