Post on 04-Feb-2023
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4 Cost-Benefit Analysis
Public Finance, 8th EditionRosen and Gayer, Chapter 8
Adapted by Chairat Aemkulwat for Theory of Public Expenditures
2943410
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OutlineI. Introduction
II. Present value
III. Private sector project evaluation
IV. Discount rate for government projects
V. Valuing public benefits and costs
VI. Cost-benefit “games”
VII. Distributional considerations
VIII. Uncertainty
ชยรตน เอ+ยมกลวฒน Theory of Public Expenditures 2943410
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I. Introduction
• การวเคราะหตนทน-ผลประโยชนหมายถง เคร;องมอท;ใชในทางปฏบต สาหรบเปนแนวทางในการตดสนใจการใชจายหรอการลงทนภาครฐ– Cost-benefit analysis is a set of practical
procedures for guiding public expenditure decisions.
I. Introduction
4
II. Present Value• Project evaluation usually requires
comparing costs and benefits from different time periods
• Dollars or baht across time periods are not immediately comparable, because of
1) inflation and 2) returns in the market.
II. Present Value
5
Present Value:Present Dollars into the Future• Suppose you invest $1000 today in the bank . .
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
II. Present Value
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Present Value:Present Dollars into the Future
• Define– R = initial investment amount– r = rate of return on investment– T = years of investment
• The future value (FV) of the investment is:
( )FV R r T= +1
II. Present Value
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Present Value:Future Dollars into the Present
• Suppose someone promises to pay you $100 one year from now.
• What is the maximum amount you should be willing to pay today for such a promise?
• เรากาลงสญเสยผลประโยชนท6เราควรไดจากการปลอยก – You are forgoing the interest that you could earn on
the money that is being loaned.
II. Present Value
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Present Value:Future Dollars into the Present
• มลคาปจจบนของเงนกอนในอนาคต คอ จานวนเงนกอนสงสดท7เรายนดจายวนน< เพ7อสทธในการไดรบเงนกอนในอนาคต– The present value of a future amount of
money is the maximum amount you would be willing to pay today for the right to receive the money in the future.
II. Present Value
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Present Value:Present Dollars into the Future
• Define– R = amount to be received in future– r = rate of return on investment– T = years of investment
• The present value (PV) of the investment is:
( )PV R
r T=+1
II. Present Value
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Projecting Future Dollars into the Present
R0 = RT/(1+r)T PV =
discount ratediscount factor
In previous equation, r is often referred to as the discount rate,
and (1+r)-T or 1/(1+r)T is the discount factor.
FV = RT = R0*(1+r)T
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Present Value:Future Dollars into the Present
• Finally, consider a promise to pay a stream of money, $R0 today, $R1 one year from now, and so on, for T years.
( ) ( ) ( )PV R R
rRr
RrTT= +
++
++ +
+0
1 221 1 1...
II. Present Value
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Present Value:
Future Dollars into the Present
• Present value is an enormously important
concept
• A $1,000,000 payment 20 years from now
is only worth today:
– $376,889 if r=.05
– $148,644 if r=.10
II. Present Value
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Present Value:Inflation
• Nominal amounts are valued according to the level of prices in the year the return occurs.
• Real amounts are valued according to the level of prices in one particular year.
• Inflation affects both the payout stream and the discount factor, and these two cancel each other out.
II. Present Value
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Present Value:Inflation
II. Present Value
( ) ( ) ( )1 2
0 2(1 ) (1 ) (1 )...
(1 ) 1 (1 ) 1 (1 ) 1T
TR R RPV R
r r rp p p
p p p- - -
= + + + +- + - + - +
• Inflation affects both the payout stream and the discount factor, and these two cancel each other out.
16
11.4
4.9 4.3
10.2
4.5 5.0
9.3 9.8 10.3
5.4 5.2 5.9 5.4 5.6 5.8
4.6 5.5
9.5
13.3 12.2
11.2
8.6 8.1 8.3 8.0 8.1
5.7
(2.8)
(7.6)
4.6 4.5 3.4
6.1 7.2
6.3
4.2 5.0 5.4
1.7
(0.7)
7.5
0.8
7.2
2.7
1.0
3.0 3.3 3.9
(10.0)
(5.0)
0.0
5.0
10.0
15.0
20.0
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
GROWTH RATES 1970-2017 Thailand Korea, Rep.
Source: Tradingeconomicscom
17
11.4
4.9 4.3
10.2
4.5 5.0
9.3 9.8 10.3
5.4 5.2 5.9 5.4 5.6 5.8 4.6
5.5
9.5
13.3 12.2
11.2
8.6 8.1 8.3 8.0 8.1
5.7
(2.8)
(7.6)
4.6 4.5 3.4
6.1 7.2
6.3
4.2 5.0 5.4
1.7
(0.7)
7.5
0.8
7.2
2.7 1.0
3.0 3.3 3.9
(10.0)
(5.0)
0.0
5.0
10.0
15.0
20.0
25.0
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
GROWTH RATE 1970-2019 Thailand China
Source: Tradingeconomicscom
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11.4
4.9 4.3
10.2
4.5 5.0
9.3 9.8 10.3
5.4 5.2 5.9
5.4 5.6 5.8 4.6
5.5
9.5
13.3 12.2
11.2
8.6 8.1 8.3 8.0 8.1
5.7
(2.8)
(7.6)
4.6 4.5 3.4
6.1 7.2
6.3
4.2 5.0 5.4
1.7
(0.7)
7.5
0.8
7.2
2.7
1.0
3.0 3.3 3.9
(10.0)
(5.0)
0.0
5.0
10.0
15.0 19
7019
7119
7219
7319
7419
7519
7619
7719
7819
7919
8019
8119
8219
8319
8419
8519
8619
8719
8819
8919
9019
9119
9219
9319
9419
9519
9619
9719
9819
9920
0020
0120
0220
0320
0420
0520
0620
0720
0820
0920
1020
1120
1220
1320
1420
1520
1620
17
Growth Rate 1970-2017 Thailand Malaysia
Source: Tradingeconomicscom
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Thailand vs Malaysia Compared
2556 2557 2558 2559 2560 2561 THB
2013 2014 2015 2016 2017 2018
Malaysia 4.7 6.0 5.1 4.2 5.9 4.7
Thailand 2.7 1.0 3.0 3.3 3.9 4.1
Differnce 5.0 2.1 0.9 2.0 0.6
Economic Value
GDP at 2018 price 13,932,560 14,069,720 14,494,612 14,970,404 15,601,188 16,314,417
i=0% 706,625 300,233 140,831 309,548 97,887 1,555,122
i=2% 764,873 318,610 146,520 315,739 97,887 1,643,628
i=5% 858,907 347,557 155,266 325,025 97,887 1,784,641
4 3 2 1 0
Source: www.bot.or.th EC_EI_027-2
Thailand 2014 2015 2016 2017 2018
Nominal GDP 13,230 13,747 14,534 15,452 16,314
Real GDP at constant price 9,232 9,511 9,823 10,237 10,708
GDP Deflator 143.3 144.5 148.0 150.9 152.4
Economic growth 1.0% 3.0% 3.3% 4.2% 4.6%
GDP deflator (base = 2018) 106.34 105.44 103.01 100.97 100.00
Real GDP(2018 price) 14,070 14,495 14,970 15,601 16,314 21
Thailand GDP Data 2013-1018
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III. Private Sector Project Evaluation
• Suppose there are two projects, X and Y.
• Each entails certain benefits and costs, denoted as BX, CX, BY, and CY.
• Need to ask:– Is the project admissible?– Is the project preferable?
III. Present Sector Project Evaluation
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Private Sector Project Evaluation
• Admissible: Are the benefits greater than the costs?
• Preferable: Are the net benefits the highest?
• โครงการสวนใหญเก0ยวของกบกระแสผลประโยชนและตนทนหลายชวงเวลา– Most projects involve a stream of benefits and costs
over time.
III. Present Sector Project Evaluation
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Private Sector Project Evaluation
• Define:
Bti =
Cti =
Benefits from project i at time t
Costs from project i at time t• Then the present value of project i is:
( ) ( )( )
( )( )
PV B CB C
rB C
ri i i
i iTi
Ti
T= - +-
++ +
-
+0 0
1 1
1 1...
III. Present Sector Project Evaluation
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Private Sector Project Evaluation
• The present value criteria for project evaluation are that:– A project is admissible only if its present
value is positive.
– When two projects are mutually exclusive, the preferred project is the one with the highest present value.
III. Present Sector Project Evaluation
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Private Sector Project Evaluation
• Two different projects (R&D or Advertising).
• The discount rate plays a key role in deciding
what project to choose, because the cash
inflows occur at different times.
• The lower the discount rate, the more
valuable the back-loaded project (โครงการท)มผลประโยชนสงในชวงทายๆ - advertising).
III. Present Sector Project Evaluation
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Private Sector Project Evaluation
TTT
rCB
rCB
rCBCBPV
)1(...
)1(1 23322
11 +-
++++
++-
+-=
Annual Net Return
Year R&D Advertising0 - $1,000 - $1,0001 600 02 0 03 550 1,200
AdmissiblePreferablePresent Value Criteria
PV
R = R&D Advertising
0 $150 $200
0.01 128 165
0.03 86 98
0.05 46 37
0.07 10 -21
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Private Sector Project Evaluation
• Several other criteria are often used for project evaluation, but can give misleading answers– Internal rate of return (IRR)– Benefit-cost ratio (B/C)
III. Present Sector Project Evaluation
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Private Sector Project Evaluation
• The internal rate of return, ρ, is defined as the ρthat solves the equation:
( ) ( )( )
( )( )
01 10 01 1= - +-+
+ +-
+B C
B C B CT TTr r
...
• The IRR is the discount rate that would make the present value of the project equal to zero.– Admissible if ρ>r.
– The flawed analysis would choose an admissible project with the higher internal rate of return, ignoring scale.
III. Present Sector Project Evaluation
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Internal Rate of Return
0)1(
...)1(1 23322
11 -+-
++++
++-
+-= TTT CBCBCBCBPV
rrr
Project Year 0 Year 1 ρ Profit PV
X -$100 $110 10% $4 3.77
Y -$1,000 $1,080 8% $20 18.87
Assume the firm can borrow and lend freely at a
6 percent rate of return
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Private Sector Project Evaluation• The benefit-cost ratio divides the discounted
stream of benefits by the discounted stream of costs. In this case:
B=stream of benefits and C=stream of costs:
( ) ( )B B B
rBrT
T= ++
+ ++
01
1 1...
( ) ( )C C C
rCrTT= +
++ +
+0
1
1 1...
III. Present Sector Project Evaluation
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Private Sector Project Evaluation
• Admissibility using the benefit-cost ratiorequires:
BC> 1
• This ratio is virtually useless for comparing across admissible projects, however.
• Ratio can be manipulated by counting benefits as “negative costs” and vice-versa.
III. Present Sector Project Evaluation
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Project 1: Project waste Dump
B=250; C=100
Project 2: Wastes sent to Saturn
B=200; C=100
• Neglect seepage-induced crop damage of $40– Reduction of dump benefits. B=210; B/C=2.1
– An increase in cost C=140; B/C = 1.79
Private Sector Project Evaluation
2.0 1B BC C= >
III. Present Sector Project Evaluation
2.5 1B BC C= >
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Problems with the Benefit-cost RatioMethod B C B/C
I $250 $100 2.5
II $200 $100 2.0
I: Subtract $40 mistake
from B
$210 $100 2.1
I: Add $40 mistake to C
$250 $140 1.79
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IV Discount Rate for Government Projects
• Government decision making involves present value calculations.
• Costs, benefits, and discount rates are somewhat different from private sector.
IV. Present Sector Project Evaluation
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Discount Rate for Government Projects• Less consensus on appropriate discount rate in
public sector. One possibility are rates based on returns in private sector.– Assumes all of the money that is raised would have
been invested in a private sector project.– In reality, funding comes from a variety of sources –
investment and consumption.– Funding that come from consumption should be
discounted at the after-tax discount rate.– Hard in reality to determine what proportions of
funding come from consumption or investment.
IV. Present Sector Project Evaluation
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Discount Rate for Government Projects• Another possibility is the social rate of
discount – which measures the valuation society place on consumption that is sacrificed in the present.
• Differs from market returns because it:– Accounts for concern about future generations– Involves paternalism– May solve some market inefficiency such as positive
externalities
IV. Present Sector Project Evaluation
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Discount Rate for Government Projects
• In reality, federal agencies are required to use a real rate of return of 7%, on the assumption that this measures the before-tax rate of return in the private sector.
• Some use 2% real return instead, thought to measure the after-tax rate of return.
IV. Present Sector Project Evaluation
41
Thailand vs Malaysia Compared
2556 2557 2558 2559 2560 2561 THB
2013 2014 2015 2016 2017 2018
Malaysia 4.7 6.0 5.1 4.2 5.9 4.7
Thailand 2.7 1.0 3.0 3.3 3.9 4.1
Differnce 5.0 2.1 0.9 2.0 0.6
Economic Value
GDP at 2018 price 13,932,560 14,069,720 14,494,612 14,970,404 15,601,188 16,314,417
i=0% 706,625 300,233 140,831 309,548 97,887 1,555,122
i=2% 764,873 318,610 146,520 315,739 97,887 1,643,628
i=5% 858,907 347,557 155,266 325,025 97,887 1,784,641
4 3 2 1 0
Source: www.bot.or.th EC_EI_027-2
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V. Valuing Public Benefits and Costs
• Recall that the discount rate, benefits, and costs are needed to compute the present value of a project.
• For private company:– Benefits = revenues received– Costs = firm’s payments for inputs
V. Valuing Public Benefits and Costs
43
Valuing Public Benefits and Costs
• For public sector, market prices may not reflect social benefits and costs.– Externalities, for example
• Several ways of measuring benefits and costs– Market prices– Adjusted market prices– Consumer surplus– Inferences from economic behavior– Valuing intangibles
V. Valuing Public Benefits and Costs
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Valuing Public Benefits and Costs
• Market prices– In a properly functioning competitive
economy, the price of a good simultaneously reflects its marginal social cost of production and its marginal value to consumers.
– Ignores market imperfections– Easy to gather
V. Valuing Public Benefits and Costs
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Valuing Public Benefits and Costs
• Adjusted market prices– If markets are imperfect, prices generally do
not reflect true marginal social cost.– Shadow price of a commodity is its true,
underlying marginal social cost, which can sometimes be estimated.
– Examples where insights can be gleaned include monopoly price, taxes, and unemployment.
V. Valuing Public Benefits and Costs
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Valuing Public Benefits and Costs
• Consumer surplus– Public sector projects can be large and
change market prices.– Figure 8.1 measures the change in consumer
surplus from a government irrigation project that lowers the cost of agricultural production.
V. Valuing Public Benefits and Costs
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Valuing Public Benefits and Costs
Pounds of avocadosper 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 Costs
• In this figure, the change in consumer surplus is area bcgd.
• Provided the government planner can accurately measure the demand curve, the project’s benefit can be measured with this change.
V. Valuing Public Benefits and Costs
49
Valuing Public Benefits and Costs
• Inferences from Economic Behavior
• Many times a good in question is not explicitly traded, so no market price exists.
• Examples:– Value of time– Value of life
V. Valuing Public Benefits and Costs
50
Valuing Public Benefits and Costs
• Value of time
• In cost-benefit analysis, need to estimate the value of time to take advantage of theory of leisure-income choice.
– After-tax wage is often used
– But hours of work not always a “choice,” and not all uses of time away from job equivalent.
V. Valuing Public Benefits and Costs
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Valuing Public Benefits and Costs
• Researchers have examined value of time by travel commuting choices.– Trains are more expensive, but less time-
consuming, than buses. The same is true about non-stop airline flights versus those with a layover.
– Estimates are that value of time approximately half of the before-tax wage.
V. Valuing Public Benefits and Costs
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Valuing Public Benefits and Costs
• Value of life
• The mindset that “life is priceless” presents obvious difficulties for cost-benefit analysis.
• If the benefits of a saved life are infinite, any project that leads to even a single life saved has an infinitely high present value.
V. Valuing Public Benefits and Costs
53
Valuing Public Benefits and Costs
• Economists use two methods to assign finite
values to human life:
– Lost earnings: Net present value of individual’s
after-tax earnings over lifetime.
• Taken literally, no loss for aged, infirm, or severely
handicapped
– Probability of death: Most projects affect probabilityof death (e.g., cancer research). People are willing to
accept increases in the probability of death for a finite amount of money.
V. Valuing Public Benefits and Costs
54
Valuing Public Benefits and Costs
• Examples:
– Purchasing a more expensive, safer car with a lower probability of death versus a less expensive, less safe car.
– Occupational choice: Riskier jobs have higher wages, all else equal
– Willingness to pay for safety devices like smoke alarms.
V. Valuing Public Benefits and Costs
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Valuing Public Benefits and Costs
• Estimates suggest value of a life between $4,000,000-$9,000,000
• Can contrast this versus the cost per life saved:– Emergency floor lights on airplanes cost
about $900,000 per life saved
V. Valuing Public Benefits and Costs
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Valuing Public Benefits and Costs
• Valuing intangibles– National prestige, others
• Can be used to subvert entire cost-benefit analysis
• Could use difference between costs and benefits to make an argument on how large intangibles would have to be to make the project admissible
V. Valuing Public Benefits and Costs
Cost Benefit Analysis หรอ ม.44 (1)
• ม.44 "ปดประตหลายช0นในการตรวจสอบ"
• สวนมมมองของนกวชาการดานกฎหมายมหาชน คณะนตศาสตร จฬาฯ รศ.ดร.ณรงคเดช สรโฆษต หนไมพนความกงวลเรGองการใช "อานาจพเศษ" ตามมาตรา 44 ของรฐธรรมนญฉบบชGวคราว ซG งถกรบรองโดยรฐธรรมนญป 2560 ออกคาสGงเรงรดโครงการนY เขาชYใหเหนวา แมในคาสGงหวหนา คสช. จะอางถงการดาเนนการตองเปนไปตาม "ขอตกลงคณธรรม" หากผเกGยวของไมปฏบตตามขอตกลงนY ใหดาเนนการตามกฎหมาย แตปรากฎวาคาสGงหวหนาคสช. ฉบบเดยวกน กลบยกเวนการบงคบใชกฎหมายรวม 7 ฉบบ
60Source: https://www.bbc.com/thai/thailand-40369155
Cost Benefit Analysis หรอ ม.44 (2)
• ม.44 "ปดประตหลายช0นในการตรวจสอบ"
• "กฎหมายท, คสช.ใหยกเวน เปนกฎหมายมงขจดการทจรตท@งส@น ความหมายคอเจาหนาท,รฐไทยทาผด ยงโดนลงโทษตามกฎหมาย แตถาคนเสนอราคาทาผด หลดหมด ถอเปนการยกเวนการบงคบใชกฎหมายท,ไมควรยกเวน นอกจากน@ยงมความไมชดเจน หากรฐวสาหกจจนตองการใหบรษทใดบรษทหน,งของไทยมารบงานตอ จะสามารถเขามาไดโดยอตโนมตหรอไม" รศ.ดร.ณรงคเดชโยนคาถามข@นกลางวงเสวนา
61Source: https://www.bbc.com/thai/thailand-40369155
Cost/Benefit Analsis หรอ ม 44 (3)
• เขาบอกดวยวา คาส4งตามมาตรา 44 ไมเพยงตรวจสอบไมได เพราะถกรบรองโดยรฐธรรมนญ และแนวบรรทดฐานการพจารณาคดของศาลในประเดนท4เก4ยวของกบมาตรา 44 ยงใหความคมครองการรถไฟแหงประเทศไทย (รฟท.) ในการส4งการ การปฏบต ถอเปนการ "ปดประตหลายชQนในการตรวจสอบ"
• "ตอใหการออกคาส4งนQ เร4มตนดวยเจตนาด อยากสลายขอตดขด อยากพฒนาประเทศ ซ4 งทางกฎหมายมคาพดวาทาอยางไรกไดใหถงเปาหมาย แตแมเปาหมายด แตวธการไมถก กจะไปอยางน4นหรอ" รศ.ดร.ณรงคเดชระบ
62
63
VI. Cost-Benefit “Games”• Chain-Reaction game
– Include secondary benefits to make a proposal appear more favorable, without also including the secondary costs
• Labor game– Wages are viewed as benefits rather than
costs of the project
VI. Cost-Benefit “Games”
64
Cost-Benefit “Games”• Double counting game
– Benefits are erroneously counted twice
• 1) the increase in value of land
• 2) the present value of the stream of net income obtained from farming
VI. Cost-Benefit “Games”
65
VII. Distributional Considerations
• Hicks-Kaldor Criterion – a project should be undertaken if it has positive net present value, regardless of distributional consequences
• The Hicks-Kaldor criterion bases project selection on whether there is a potential Pareto improvement
VII. Distribution Considerations
66
Distributional Considerations
• Others view some groups in population as “more deserving” and argue this should be taken into account in project selection
• Government costlessly corrects any undesirable distributional aspects
VII. Distribution Considerations
68
Ans.
d. The subway project has a higher present value. If a dollar to the “poor” is valued the same as a dollar to the “middle class,” choose the subway project.
e. Let l = distributional weight. set– 220,000 = -68,750 + l[(62,500/1.25) + (62,500/1.252)]– l = 3.21– This distribution weight means that $1 of income to a poor person must be viewed as more
important than $3.21 to the middle class for the legal services to be done.
69
VIII. Uncertainty
• The results of many projects are uncertain (e.g., AIDS vaccine research or defense research).
• In risky projects, benefits or costs must be converted into certainty equivalents– the amount of certain income the individual would trade for a set of uncertain outcomes generated by project.
VIII. Uncertainty
70
Uncertainty
• Requires information on distribution of returns and risk aversion.
• Figure 8.2 shows a risky project (E,E+y) and a certain project (C) that give the same expected utility.
VIII. Uncertainty
72
Uncertainty – Certainty equivalent• ลกตานา – บณฑตศกษาท1จฬาลงกรณมหาวทยาลย คาดวาจะทาใหรายไดสงเพ1มขHน y บาท– Probability of ½
• Expected Income รายไดเฉล1ยของลกตานา = E+y/2 หรอจด
• Expected Utility = ½ U(E) + ½ U(E+y) หรอ จด C• Risk premium =• The project’s expected value be reduced by a risk premium
that depends on the shape of the utility function.
VIII. Uncertainty
I
I C-