Experts find key to saving fuel: say gallons per mile.
I'll summarize: d/dx 1/x = -1/x2.
Research has been done that shows that people believe that an improvement of 1 mpg will always save them the same amount of gas. But this is obviously false, as some simple arithmetic shows. Let's say I drive 12,000 miles a year. (Why 12,000? Because everything that follows will work out to be integers.) If I improve from 15 mpg to 16 mpg, I go from using 800 gallons of gas a year to 750, a 50-gallon reduction. But if I improve from 24 mpg to 25 mpg, I go from using 500 gallons of gas a year to 480, a 20-gallon reduction.
A driver driving m miles per year in a car getting x miles per gallon will of course use m/x gallons of gas; the derivative of this is -m/x2. So if you get x miles per gallon already, improving by one mile per gallon saves m/x2 gallons. (I'm assuming here that 1 is small compared to x.)
The article claims that this means people wanting to get better gas mileage, if they have multiple vehicles, should always target the least efficient vehicle -- but that's going too far. It might be cheaper to get a 1-mpg improvement for less fuel-efficient cars. There's no reason that the cost of a car should be linear in the number of miles per gallon it gets, all else being held constant.
Note that I'm also not saying the cost of a car should be linear in the number of gallons per mile it gets! In fact this would be impossible, because it would predict that cars that get zero gallons per mile could be made for a finite amount of money.
"Gallons per mile" is kind of an annoying unit, though, because all cars get less than 1. Perhaps "gallons per 100 miles" would be a good way to go, with most cars measuring between perhaps 3 and 6 on this scale. And people can picture driving 100 miles. (For example, if they have a ten-mile commute each way, it's five round-trips to work.) But on the other hand, there's a temptation to not have to deal with decimals, and there's a big difference between 4 gallons per 100 miles and 5 gallons per 100 miles. Perhaps "gallons per 1000 miles" works nicely; typical values are now 2-digit integers, and rounding to the nearest integer gives roughly the same precision as the current system.
(Readers from other countries: please spare me the "in my country we measure fuel economy in liters per 100 km" comments. I know this.)