public expenditures

1. Chapter 4: Cost-Benefit Analysis
Chapter 4 Cost-Benefit Analysis
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved.
McGraw-Hill/Irwin

2. Chapter 4: Cost-Benefit Analysis
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Introduction
Cost-benefit analysis
Building a factory
Benefits from improving the safety of a highway
Mistakes to avoid
Benefits from building a highway
Reducing global warming
Paying for a costly medical treatment
Intervening militarily

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Cost-Benefit Analysis
• A project should be undertaken if its benefit to
society exceeds its costs to society.
Cost-benefit analysis is the measuring of the costs
and the benefits of a project to help decide:
• Whether to undertake the project
• The scale of the project
Who uses cost-benefit analysis?
• Private firms
• Individuals
• Government

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Cost-Benefit Analysis
The optimal scale
of the project is Q*.
Q*
$
Scale of the
project (Q)
MSB
MSC
Figure 4.1

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A Private Firm: Building a Factory
Should a firm build another factory?
Assumptions:
• The factory will be built in one year (Year 0)
• The factory will last one year (Year 1) before
wearing out
• The construction cost in Year 0 = $100,000
• The profit from the factory in Year 1 = $110,000

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A Private Firm: Building a Factory
Building with borrowing:
Will the firm build if the interest rate is 5%? 15%?
The firm borrows $100,000
in Year 0 to pay for the
construction cost
The present discounted value (PV) of a future amount at
a future date is the amount you would need to put in the
bank today to have that future amount by that future date.

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A Private Firm: Building a Factory
Multi-year profits
• $55,000 in Year 1
• $60,500 in Year 2
• r = 10%
PV of profits = $55,000
(1+r)
$60,500
(1+r)2
+
= $100,000
= $50,000 + $50,000
$55,000
(1.10)
$60,500
(1.21)
+
=
Example

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A Private Firm: Building a Factory
PV of $110,000 in Year 1 = $110,000
(1+r)
Table 4.1
r = 5% r = 15%
PV of Profit $104,762 $95,652
Cost of Project $100,000 $100,000
Correct Decision Build Don’t Build
• This is true even when a firm uses their own
money to finance the construction of the factory.

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Government: Building a Highway
Costs
• Current construction costs
• Discounted future maintenance costs
Benefits
• What drivers are willing to pay to use the
highway in all future years measured as the
discounted dollar value of time saved

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Government: Building a Highway
Measuring benefit of time saved through
Increased Output
• Estimate how much more output commuters could
produce at work if they decreased commute time
Example
• Commuter is paid $20/hr
• Saves 1 hour of commute time each day because of
the new highway
• Commuter works 250 days a year
• Time savings = (250 days)(1 hour)($20) = $5000

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Government: Building a Highway
Measuring benefit of time saved through
Revealed Preference
• Look at commuter location preferences and estimate
how home prices differ depending on commute time.
Example
• Two identical homes in two different suburbs
• One house is associated with a shorter commute
• The house associated with the shorter commute costs
$20,000 more than the other house.
• The difference in price “reveals” the value of time saved

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Government: Building a Highway
Measuring benefit of time saved through
Contingent Valuation
• Pose a hypothetical question that asks commuters
how much they would be willing to pay to reduce their
daily commute by one hour.
Issues
• Critics argue surveys produce unreliable results because
answers may be sensitive to wording, presentation, etc.
• Supporters argue that actual market behavior is also
subject to similar problems
• Supporters argue surveys improve with experience

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Benefits of Improving the Safety of a Highway
The safer the highway, the greater the cost of building it.
Measuring the value of lives saved through
Increased Output
• Estimate how much that person would
have produced over the rest of his life.
Issues
• If person A is paid more than person B, then person A is
valued higher than person B
• How do you value the surviving family’s suffering?

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Benefits of Improving the Safety of a Highway
Measuring the value of lives saved through
Revealed Preference
• Estimate how much people actually pay to reduce
their chance of dying
• Compensating Differential
Measuring the value of lives saved through
Contingent Valuation
• Pose a hypothetical question that asks commuters
how much they would be willing to pay to reduce
their chance of death on the highway from 2 in 1000
to 1 in 1000

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Benefits of Improving the Safety of a Highway
• The value of the life of a person we don’t
know personally
Measuring the value of lives saved through
The Value of a Statistical Life
• Approximately $8 million
• Is the VSL different for a young person
as compared to an old person?

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Mistakes to Avoid
• Counting job creation as a benefit
• Double counting the same benefit
• Counting secondary benefits

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Reducing Global Warming
How much should each country cut back on its
emissions of greenhouse gasses?
Costs: carbon fuel use
must be reduced
Benefits: reduced
global warming
• Uncertainty and the risk of catastrophe
• The social discount rate is the rate analysts use
to compute the present value of future benefits
• A cost-effectiveness analysis focuses on
achieving the given objective at a minimum cost

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Paying for a Costly Medical Treatment
Patients and families want the best care, which
tends to be costly. Should the insurer pay for the
care?
A medical treatment costs $1 million, and it will extend
the life of the patient by 1 year.
• What if the patient is 100?
Example
• What if the patient is 80?
• What if the patient is 20?

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Intervening Militarily
Should a particular military intervention be undertaken?
Costs: military budget cost, cost of lives lost,
suffering of veterans, disability payments, etc.
Benefits: historians, military scientists,
international relations experts, and political
scientists will determine the benefits.

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Cost-benefit analysis
Building a factory
Benefits from improving the safety of a highway
Mistakes to avoid
Benefits from building a highway
Reducing global warming
Paying for a costly medical treatment
Intervening militarily
Summary

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Preview of Chapter 5:
Social Security
Four ways to prepare for retirement
The U.S. Social Security system
Reforming Social Security