Tuesday, August 4, 2009

Off-Topic: The Cash for Clunkers Program

I'm not given to political commentary, and I'm not going to take a partisan stance. It's just that while waiting for my daughters' ballet, I asked myself, "How much value are we getting from Cash for Clunkers?" And I was surprised that I had not seen any articles running the numbers on this one.

Computations follow.

Let's take a better-case scenario. Assume that a clunker gets 10 mpg and is traded in for a 30 mpg mid-sized car. Assume further that the CfC program causes Joe Schmoe to trade his clunker in early by four years. Assume further that Joe drives 30,000 miles in one year.

On these assumptions, Joe's gasoline usage for four years with the clunker would be

4 yr * 30,000 gal/yr * 1 gal / 10 miles = 12,000 gallons.

With the new car, his gas usage would be

4 yr * 30,000 gal/yr * 1 gal / 30 miles = 4,000 gallons.

This means that Joe is saving 8,000 gallons of gasoline because of this program.

Assume further that gasoline's density is 0.77 kg/L and assume that gasoline is 100% isooctane, C8H18. Changing these assumptions could move my numbers in the direction of worse-case by a few percent.

A quick use of the periodic table can show that 1 kg of gasoline (isooctane) creates 2.444 kg of CO2.

Thus we calculate:

8000 gallons saved * 3.75 L / gal * 0.77 kg gas / L * 2.444 kg CO2 / kg gas = 56,456 kg CO2 = 62 tons CO2.

So we are paying $4,500 for 62 tons CO2 saved, or $72.50 / ton. We compare this to the cost of a "certified carbon offset", which Wiki pegs at $1 - $30 / ton.