Here’s an interesting question.

Suppose you had a household with two cars, and each car needs to be driven 10,000 miles per year. One car consumes 34 MPG, and the other car consumes 18 MPG. Since gas is expensive, you want to replace one car. Because of utility constraints, you have two choices:

Replace the 34 MPG car with a 50 MPG car — a 16 MPG improvement

Replace the 18 MPG car with a 28 MPG car — a 10 MPG improvement

Which car replacement would save you the most gas?

Normally, I consider myself not bad with quantitative comparisons like this, yet initially I picked the answer of replacing the 34 MPG car with the 50 MPG car based on the superior 16 MPG improvement. Another seemingly more analytical approach also leads to the same conclusion: 50 + 18 MPG giving a 34 MPG household average seems more efficient than 34 + 28 MPG giving a 31 MPG household average.

This very interesting article in Science, “The MPG Illusion” by Richard P. Larrick and Jack B. Soll at the Fuqua School of Business in Duke University (Vol 320, June 20, 2008, p. 1593), points out the mathematically obvious truth that gas used per mile is inversely proportional to miles per gallon, which means that you have a steeper slope at lower MPG ratings, and diminishing returns at higher MPG ratings.

(The above image is taken from the article, available here with subscription).

When you run the numbers, replacing the 34 MPG car with a 50 MPG (a 16 MPG improvement) car saves you 94.1 gallons per 10,000 miles, whereas replacing the 18 MPG car with a 28 MPG (a 10 MPG improvement) car saves you 198.4 gallons per 10,000 miles — more than double the savings.

Or, to give an even more clear-cut example, replacing a 5,000 MPG car with a 10,000 MPG car saves you just one gallon of gas, whereas replacing a 1 MPG car with a 2 MPG car saves you 5,000 gallons of gas, using a fixed mileage of 10,000 miles driven for comparison.

There are some important policy implications of this. Relatively small MPG improvements in the most gas-hungry vehicles pay off greater than larger improvements in already efficient cars (hence, it does make sense to offer tax breaks for modest improvements in SUVs versus tax breaks for hybrids, which typically replacing already gas-efficient sedans). Also, personal driving habits, especially for gas-hungry cars, can often times add or subtract a few MPG to a car’s efficiency on average. For example, a car that may get 25 MPG “average highway” will degrade to under 15 MPG if you gun it out of stoplights in city traffic. That’s a huge increase in gas consumed per distance driven, especially for the less efficient cars, whereas for more efficient cars it doesn’t hurt as much to goose the engine a bit.

Apparently the thinking that gas savings is linear with MPG is not uncommon. A survey of college students revealed that a majority of them shares this misconception. I’m not sure what the sociological term is for such a massively accepted factual inaccuracy, but it seems like a textbook case for how common wisdom can fail the common person. It’s also a good example of why you don’t want to put policies to a vote — people just don’t have the time to run the numbers, and simple numbers can be so simply deceptive, even with the best intentions. Good democracies are probably more about the people directly controlling principles (“conserve oil”), rather than the policies (“reward car makers that achieve the greatest fleet MPG delta”). Of course, that doesn’t address the problem of creating accountability between principles, policies, and politicians that make the policies to execute the principles.