Question: A $1,000 tax incentive is used to encourage
people to purchase a vehicle that gets 40 miles per gallon instead of 25 miles
per gallon. It is expected that the tax
incentive will increase sales of the fuel efficient car from 1.0 million units
to 1.25 million units and will reduce the sale of the less fuel efficient car
by 0.25 million units? According to the
U.S. EPA, the consumption of one gallon of gasoline leads to the formation of
8,788 grams of carbon dioxide. On
average, each car is driven 15,000 miles per year for 8 years. How many fewer kilograms of CO^{2}
will be released because of this tax incentive?
What is the cost per reduced kilogram of CO^{2} from the
adoption of this tax incentive?
Answer: Cars are
driven for 15,000 miles per year for 8 years or a total of 120,000 miles. (8 x 15,000 = 120,000)
The tax credit affects gas consumption by 250,000 cars. The
total number of miles driven by the 250,000 cars is 3.0 x 10^{10} (1.2 x 10^{5} x 2.5 x 10^{5}
= 3.0x 10^{10})
Divide miles by miles per gallon to get gallons. 3.0x101^{0}/40 is 7.5x10^{8 }and
3.0x10^{10}/25 is 1.20x10^{9}.
Subtract: The
reduction in gas consumed is 4.50x10^{8} gallons.
Multiply by 8.788 kg to get the number of kilograms of CO^{2
}not formed because of the reduction in gas consumption. 8.788x4.50x10^{8}
is 3.95x10^{9}.
This is the answer to part one. Now the issue of cost:
All 1.25 vehicles get the tax credit. The total cost of the
credit is $1.250 billion (1,250,000 x 1,000 is 1.25 billion or 1.25 x 10^{9})
To get cost per kilograms of CO^{2} not created
divide by kilograms and get $0.32 ($1.25x10^{9}/3.95x10^{9} kg
is $0.32 per kg.)
Part two is solved.
The real world wrinkle: I have given you numbers for the number of
additional vehicles sold due to the tax credit.
In the real world there is a wrinkle to this problem. Analysts do not know what sales would have
been if the tax credit did not exist.
This affects the assessment of a wide range of tax credits from fuelefficient
vehicles to IRAs.
Calculation of reduced CO^{2}
from Tax Incentive


Miles per year for one
car (miles)

15000

Number of years average car
is driven (years)

8

Total miles driven over
the lifetime of one car (miles)

120000

Total miles driven by
250,000 Cars (miles)

3.00E+10

Gas consumed at 40 MPG
(gallons)

7.50E+08

Gas consumed at 25 MPG
(gallons)

1.20E+09

Reduction in gas consumed
(gallons)

4.50E+08

C0^{2} not formed
(kg)

3.95E+09

Calculation of Cost of
Tax Incentive


Number of cars receiving
tax credit (# cars)

1,250,000

Tax credit per car ($)

$1,000

Total amount spent on tax
credit ($)

$1,250,000,000

Cost of one kg reduction
in CO^{2} ($/kg)

$0.32

If you found this post
interesting you may also be interested in my previous post of fuel efficiency
issues.
Also, if you are interested
in personal finance consider www.financememos.com
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