## Sunday, April 21, 2013

### Carbon dioxide emission reduction from a tax credit

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 CO2 will be released because of this tax incentive?  What is the cost per reduced kilogram of CO2 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 1010  (1.2 x 105 x 2.5 x 105 = 3.0x 1010)

Divide miles by miles per gallon to get gallons.  3.0x1010/40 is 7.5x108 and 3.0x1010/25 is 1.20x109.

Subtract:  The reduction in gas consumed is 4.50x108 gallons.

Multiply by 8.788 kg to get the number of kilograms of CO2 not formed because of the reduction in gas consumption. 8.788x4.50x108 is 3.95x109.

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 109)

To get cost per kilograms of CO2 not created divide by kilograms and get \$0.32 (\$1.25x109/3.95x109 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 fuel-efficient vehicles to IRAs.

 Calculation of reduced CO2 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 C02 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 CO2 (\$/kg) \$0.32

If you found this post interesting you may also be interested in my previous post of fuel efficiency issues.

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