"Cash for clunkers" and bad math

Last year, in the journal Science, two Duke University business professors demonstrated just how misleading the fuel-efficiency measurement Miles Per Gallon (MPG) can be. Now Congress has underscored the professors' findings by failing to take into account the complexities of MPG when writing the new "cash for clunkers" bill. This has produced some economic incentives that are slightly askew.

The problem, as Richard Larrick and Jack Soll explained in their Science article, is that MPG (unlike, say, height) is a non-linear measurement. It can be confusing to work with, especially off the top of your head. Did you realize, for example, that you save significantly more gas moving out of a car that gets 12 MPG into one that gets 14 MPG than you would shifting from a 22-MPG into a 24-MPG vehicle? (Take out a pen and do the math: assuming 10,000 miles driven in each case. the former move saves 119 gallons, the latter a mere 38.)

Now consider the incentives Congress plans to provide SUV drivers. They will qualify for cash payments if their old vehicles get fewer than 18 miles per gallon and they buy more-efficient ones. They get $3,500 if the new car or truck gets 2 MPG more than their old vehicle, $4,500 if they increase MPG by 5. (Their old trucks must be junked, too.)

As a result of those rules, a driver improving from 18 MPG to 23 MPG will get $1,000 more from the Feds than one who boosts her MPG from 12 to 16. But over 10,000 miles, the latter driver will actually save more fuel: 208 gallons versus 121 gallons.

Larrick and Soll have proposed making "Gallons Per 10,000 Miles" the fuel-efficiency metric of choice. That would allow much more straightforward comparisons among cars and trucks: no pen-and-paper needed, and even Senators could do the math.