The miles per gallon illusion (Miles per gallon vs. gallons per mile)

Phillip Torrone | posted on July 3, 2008

Mpg Science08
Bunnie has an interesting write up about AAAS’s Science publication “The MPG Illusion” he writes…

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.

 
More @ Bunnie’s site. At first glance it seems counterintuitive, but here’s an interesting thought…

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).

 



2 COMMENTS SO FAR


posted by: Kyle on July 8th, 2008 at 1:03 am


Congratulations on your rediscovery of a little understood fact. This is what GM has been saying for years, which is why they have been working on hybridizing their large vehicles (buses, then Silverados, now Tundras, etc) rather than their cars.


posted by: Crystal on July 18th, 2008 at 11:02 pm


Some people really need to go back to school! A 10 mpg improvement from a vehicle that gets 18 mpg is the bigger percentage improvement, but you’ll go more miles and spend less money on gas if you buy the 50 mpg vehicle.

Think of it this way: on a math test with 100 possible points with typical scoring (90 to 100 = A; 80 to 89 = B; 70 to 79 = C; 60 to 69 = D, below 60 = F), a 40-point improvement in your score from 10 to 50 is a very large percentage improvement, but you still failed! A 10-point improvement from 50 to 60 is a smaller percentage, but then you’d at least pass!

Furthermore, if a certain person I know had bought a 50 mpg vehicle for a 100-mile daily commute, she would spend less than $8.50 a day on gas. Instead, she bought a different vehicle and spends more than $20 per day on gas. Now, if she’d listened to me in the first place and not bought a house 50 miles from work, she’d be in a MUCH better position, regardless of which car she chose. And she could have gotten a similar house in a better school district closer in for only a little extra money — certainly far less than $400 per month.

How much do you think she envies my 3 mile bike ride, which costs me less than 50 cents when I drive instead of bike?


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