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Suppose you are working for the Colorado state
government in the highway department.- cost-benefit analysis of road repairs
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Measuring Current Costs
We need the social marginal cost.
- equal to its opportunity cost
Cost of Asphalt:1 bag asphalt costs $100
- next best use = sell to someone else
- competitive market
- opportunity cost = price
1 million bags x $100 = $100,000,000
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Cost of Labor:
In a perfectly competitive market, the opportunity cost isequal to the wage.
Suppose instead an imperfect market with some
unemployment among construction workers. (due tominimum wage of $20)
Suppose the value of one hour of leisure is $10.
The opportunity cost of hiring an unemployed worker is
$10. The opportunity cost of hiring an employed worker
is $20.
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Suppose we hire 500,000 previously unemployed
workers and 500,000 previously employed workers.
The opportunity cost of the labor is:
500,000 x $10 + 500,000 x $20
= $5,000,000 + $10,000,000
= $15,000,000
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Even though the government is paying out $20,000,000
in cash, the opportunity cost is $15,000,000.
The cash cost of the labor cost has two parts:
- opportunity cost
- transfer of rents
Rents are payments to resource acquisition that exceed
those necessary to employ the resource.
In this case the rents are a transfer from the government
to previously unemployed workers.
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Measuring Future Costs
Use the Present Discounted Value.
The PDV of a long-term stream of payments is:
PDV = payment amount
interest rate
Use 7% as the interest rate.
PDV = $10,000,000
0.07
= $143,000,000
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Measuring Current Benefits
Valuing Driving Time Saved:
Various Approaches:
- wages (2009 average wage $19.29)- overstate if value of leisure < wage
(cant work overtime)
- understate if there are non-monetaryaspects of the job
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- Contingent Valuation (ask individuals to valuean option that they are not currently doing)
- reveled preference (let individuals actions
reveal their value)- gas station natural experiment
Lets use $19.00 as the value of an hour of time.500,000 x $19 = $9,500,000
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Valuing a life saved:
Various Approaches:
- wages
- a worker under age 50 will spend 10-20%
of all future hours working
- value of life is 5-10 times future lifetime
earnings
- Contingent Valuation
- $963,000 to $26,000,000
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- revealed preference
- see how much pay to reduce odds of dying
- if airbag costs $350 and there is a 1 in
10,000 chance that it would save the life
then the value of a life is at least $3.5 million
- look at compensating differentials
- compare 2 jobs, one has 1% higher risk ofdeath in a year and pays $30,000 more
- value life at $3 million
Kip Viscusi of Harvard says: $8.7 million
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- government revealed preference
- look at existing government programs
and see how much they spend to save lives
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Lets use $8.7million as the value of a life.
$8,700,000 x 5 lives = $43,500,000
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Discounting Future Benefits
Very tricky!
- choice of discount rate matters a lot
- how to treat future generations benefits?
Lets use 7%.
Total Benefits = $9,500,000 + $43,500,000
= $53,000,000
PDV = $53,000,000
0.07
= $757,142,857
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$8.7 million / life $43.5 million
$53 million
$757 million
$499 million
The project should be undertaken.