Cognitive Daily

Suppose you’re running a small organization with five motor vehicles used by your staff and you want to replace them with more fuel-efficient versions, both to save money and reduce your organization’s carbon footprint. Each vehicle travels 10,000 miles a year. Based on your budget and the requirements for each vehicle, you can do the following, but you can only afford to replace one car every six months:

Replace a 16-MPG car with a 20-MPG car
Replace a 22-MPG car with a 24-MPG car
Replace a 18-MPG car with a 28-MPG car
Replace a 34-MPG car with a 50-MPG car
Replace a 42-MPG car with a 48-MPG car

What order should you replace them in in order to save the most money and make the fastest reduction in your carbon footprint? Let’s make this a poll:

Richard Larrick and Jack Soll asked their students a similar question. They wanted to know if miles-per-gallon was the best way to help the students calculate an improvement in efficiency. While it’s obvious that each car will improve mileage, it’s not as clear exactly how much money, gas, and carbon emissions will be saved. That’s because the relationship between a car’s fuel efficiency measured in miles-per-gallon and its fuel consumption isn’t linear:

As miles per gallon increases, the number of gallons of gas used to travel a specific distance decreases by smaller and smaller increments. If you start with a vehicle that gets 10 MPG, to save 200 gallons a year you’d only have to increase to a 12.5 MPG car. But if your car gets 25 MPG, then to save 200 gallons you’d need to increase to 50 MPG.

So how did the students respond?

They responded exactly as you’d expect if there was a linear relationship between miles-per-gallon and actual savings. Sixty percent of the 77 respondents said the cars should be purchased in 4, 3, 5, 1, 2 order: the cars with the biggest miles-per-gallon increase should be replaced first. In fact, the most efficient replacement order is 3, 1, 4, 2, 5. Only 1 respondent got it right.

So do people do better when they’re given a better way of understanding the savings? Larrick and Soll suggest that reporting fuel efficiency in terms of gallons per mile (or per hundred miles, so you’re not working with fractions) makes it easier for people to make comparisons between cars. If a car gets 15 MPG, that’s 6.67 gallons per hundred miles (GPM). A 19 MPG car uses 5.26 GPM. A 34 MPG car uses 2.94 GPM, and a 44 MPG car uses 2.27 GPM. So improving your mileage from 15 to 19 MPG saves 1.41 gallons every 100 miles (this is calculated by simple subtraction: 6.67 – 5.26 GPM). Improving from 34 to 44 MPG only saves 0.67 gallons: less than half as much.

In an online survey, the researchers asked respondents whether it would be better to replace a 15 MPG car with a 19 MPG version or a 34 MPG car with a 44 MPG version. As you might expect, respondents overwhelmingly (and incorrectly) chose the second option. But in a separate survey, when asked whether to replace a 6.67 GPM car with a 5.26 GPM car or a 2.94 GPM car with a 2.27 GPM car, respondents correctly chose the first option.

Larrick and Soll say this is clear evidence that cars should be rated in GPM rather than MPG. They say that people would be more likely to replace truly inefficient cars (like those which only get, say 12 MPG). While people might think it’s not worth the trouble to upgrade from a 12 MPG car to an 18 MPG car, the actual savings would be over 277 gallons a year (assuming 10,000 miles per year), versus just 133 gallons a year saved by improving from 30 MPG to 50 MPG.

Larrick, R., & Soll, J. (2008). ECONOMICS: The MPG Illusion Science, 320 (5883), 1593-1594 DOI: 10.1126/science.1154983

Comments

#1 Koka Thomason
March 19, 2009

I’ve heard about this recently on NPR, and even after reading your blog above, I still don’t get it. I have a college degree, I’m decent at math, and I have above-average intelligence. But I still don’t get it. Maybe I’m just sleep-deprived?
#2 Ron
March 19, 2009

Here in Germany, “mileage” is conventionally measured in Liters per Hundred Kilometers, which is effectively what your authors are suggesting. So, to test their hypothesis (that people would then make more rational choices), we could look to see if people in countries that measure the “right way” make more rational choices. I suspect they don’t; It has to do with so many other factors… but my suspicions are irrelevant. This must be something that can be verified. Right?
#3 Dave UH
March 19, 2009

Woot, got it right without even calculating it out. And it seems as though many of the readers of this post also got it right. Must be a smart crowd.
#4 AaronB
March 19, 2009

Koka :

You may be looking at the problem backwards. Simply -

if your car gets 10 miles per gallon it will cost you 10 gallons to go 100 miles.

if your car gets 20 miles per gallon it will cost you 5 gallons to go 100 miles, a savings of 5 gallons.

if your car gets 30 miles per gallon it will cost you 3 1/3rd gallons to go 100 miles, a savings of only 1 2/3rds gallons over going from 20 to 30 miles per gallon.

As you see, even though the increase is linear, the savings is not. Hence it is more efficient to replace a 16MPG car with a 20MPG than it is to replace a 20MPG car with a 24MPG car, all other variables being equal.
#5 Dave X
March 19, 2009

I like the GPM measure better, and personally like keeping track of my car’s milage as cents/mile (11.3c/mile last fill-up).

If you multiply the GPM (gal/100mi) numbers by the price of gas, you get the cents per mile, which makes it easy to think about how much each optional trip costs you.

Koka, one way to think about it is that you consume travel in miles. So, you need to do a division or inverse to turn the more-is-better MPG measure into something like cost, where the less-is-better GPM measure is already inverted, and so it corresponds directly to cost.

Or more math-wise, cost is directly proportional to GPM, while cost is inversely proportional to MPG.
#6 Dave X
March 19, 2009

In regards to Dave UH’s comment, I should say that when I took the poll, I didn’t do the math either, I thought one of the low MPG cars should be one of the first options, and then eliminated the options from there. Option 3 stands out as the only one starting with the two sub-20MPG cars.
#7 OmegaMom
March 19, 2009

I’m with Dave X; I took the only one that had the two low MPG cars first.
#8 Christopher Lord
March 19, 2009

We’re also big on the system of measuring in l/100km in Canada.

I adore it. It’s very easy to compute how much gas I need to buy for a trip, or for reasoning about fuel economy.

my current car hovers around 6.8l/100k.

When I run into MPG or GPM on the web, i can convert to l/100km with google: just punch in “6.8 l per 100 km in mpg” or “34.6 mpg in l/100km” and it does the conversions. once converted, you too can reason about your fuel consumption without reference to rods, fathoms, quarts, and stones (whatever those are).
#9 Chas
March 19, 2009

I found the correct answer by dividing miles per year by mpg before and after, figuring the gallons saved and sorting based on most gallons saved over 10,000 miles (any distance per year would result in same answer).
#10 Cristian M
March 19, 2009

@Chas: You just converted it from MPG into GPM, but used the 10,000 miles as a reference, and not the 100 miles proposed above.

@Ron: I’m from Europe, and using the l/100 km is really convenient. It lets you easily estimate you costs/savings, and thus your car choice. Of course that would be limited to the cars which are appealing to you, but none the less, would help you make an informed decision.

In the end, the whole change from one system to the other is not so amazing, but it would help those which are not car fanatics, or strong in math to get clearer about the facts.
#11 Alex
March 19, 2009

“In the end, the whole change from one system to the other is not so amazing, but it would help those which are not car fanatics, or strong in math to get clearer about the facts.”
That group probably accounts for a fair chunk of the population. Also, if you converted from MPG to L/100km, it helps the car fanatics who are good at maths and use metric units.
#12 Stephen Downes
March 19, 2009

So what have we learned? We’ve learned that economics students are poor at mathematical reasoning.
#13 Ken LaBelle
March 20, 2009

A strong argument for using the gallons/mile (or gallon/1000 miles), is that it makes much more obvious the answer to the question “what saves more gas, switching from a 10 mpg car to a 15 mpg car or switching from a 25 mpg vehicle to one that gets 100 mpg?” Switching from 10 to 15 mpg saves you 33.4 gallons per 1000 miles. Switch from 25 mpg to 100 mpg and you save only 30 gallons. To save the same 33.4 gallons, you would have to get 150 mpg.
#14 Craig Overend
March 20, 2009

To improve fuel econbomy, forget MPG
#15 Joel
March 20, 2009

I’d be curious to know how many of us would have gotten this right had it not been for the recent NPR report… I can’t say for sure I would have.
#16 Stephanie Chasteen
March 20, 2009

I’m with Koka — it took me quite a while to understand this argument (and I’m a physicist). I think the only way is to sit down with pen and paper and run a few numbers and convince yourself of the logic.

I wrote quite a long blog post on this when the study was first published,
http://blog.sciencegeekgirl.com/2008/08/06/myth-doubling-your-mileage-will-cut-your-driving-costs-in-half-or-news-from-geek-dad/
Lots of great comments there, and ways to think about the argument and what it means.
#17 Cody
March 20, 2009

It’s not that hard to understand as long as you ignore the absolute values and think of the switch in terms of percentages. A switch from 10 MPG to 15 MPG is a 50% increase in efficiency, whereas a switch from 30 MPG to 35 MPG is only a 16.7% increase.
#18 Kelly
March 20, 2009

Cody,
You are so right — thinking about percentages helps make it much more clear!
#19 Tatil
March 20, 2009

Nope, percentages are still misleading. 20MPG to 40MPG and 10MPG to 20MPG are both 100% improvements, but the latter would save you twice as much gas for the same distance traveled.
#20 Tony Jeremiah
March 20, 2009

That’s because the relationship between a car’s fuel efficiency measured in miles-per-gallon and its fuel consumption isn’t linear:

The linear assumption seems a reasonable one to make without relevant background knowledge. Therefore, the ‘error’ is logically intuitive without the relevant data indicating the relationship is non-linear.

Larrick and Soll suggest that reporting fuel efficiency in terms of gallons per mile (or per hundred miles, so you’re not working with fractions) makes it easier for people to make comparisons between cars.

This makes sense since GPM takes into account the non-linear relationship (which when one looks at the above graph, clearly involves the diminishing return principle).

Probably just providing the graph alone would help participants determine the most fuel efficient choices, since one can look at the graph and figure out the gallons being consumed for each fuel efficiency (i.e., mpg) rating:

3. 320 (28 mpg) – 550 (18 mpg) = -230 gallons used
1. 500 (20 mpg) – 700 (16 mpg) = -200 gallons used
4. 200 (50 mpg) – 310 (34 mpg) = -110 gallons used
2. 400 (24 mpg) – 425 (22 mpg) = -25 gallons used
5. 230 (48 mpg) – 250 (42 mpg) = -20 gallons used

What makes these calculations not so straightforward are other factors affecting fuel efficiency calculations such as vehicle age (replacing a really old car might be more effective than replacing one that’s fairly new given that cars become less fuel efficient with age, and presumably new ones are more fuel efficient with better technology); weather and road conditions (heavy traffic and winter conditions reduce fuel efficiency); and probably most important, is the somewhat random fluctuation of gas prices (and usually not in a downward direction).

If you purchase the most fuel efficient vehicle but then the gas prices skyrocket soon after purchasing it, that would seem to reduce the effect of saving money by purchasing a fuel efficient vehicle. Of course, one would have to do a cost-benefit analysis to see what the cost saving loss would be due to changing gas prices.

On the other hand, skyrocketing gas prices should have the effect of making people drive less, and thus reducing the carbon footprint.
#21 Will
March 22, 2009

I’m on the same page as some of the others. I thought more about the frequency of cars on the road in the 16-20 mpg range and thought it would be most beneficial to replace those right away, then move on to the others. But the gpm math makes a lot of sense. I had heard about it before, but it was confusing to me until I read this post. Thanks!
#22 Fil Tribble
March 23, 2009

I didn’t read all of these replies, but when we switched from a big VW Toureg to a little Toyota Yaris, we estimated that we saved one US dollar every 6.5 miles or so. I relished driving the little car all summer, knowing that it was like money in the bank. Of course, when the price of gas went down, so did that figure, but I’m just fine with that for our household.

On a related resource-conscious note:
A friend once made a similar comparison to the use of shampoo when he had his hair cut — having it cut, cut his use of shampoo in half or better, and he calculated the savings (though I forget the figure). It turned out that the savings in shampoo paid for a haircut once every 2 months for him.
#23 Epinephrine
March 23, 2009

In Canada we use L/100km. Avoids the issue with MPGs
#24 NB
March 24, 2009

I had studied this in detail last year. One issue that is peripheral to the psychological issue (but that matters greatly from a practical viewpoint) is that of vehicle use. These are statements made from industry data–not just guesses.

1) The less efficient the vehicle, the more it gets driven.
2) The less efficient the vehicle, the less discretionary the mileage is.

To make sense of this, think about the work trucks used by plumbers vs the cars owned by college kids. Efficiency and amount of use have a strong negative correlation.

I mention this because it highlights that this is NOT strictly an academic point–to reduce overall oil use, we need automakers to focus on improving the lowest-efficiency vehicles NOT the flashy highest-efficiency vehicles.
#25 uffe hellum
March 24, 2009

To reduce consumption we don’t need to talk to the auto industry at all. We need to increase the fuel price and let the smartest people save money.

Example: If we (gradually over five years) reduce income tax with 10% ($3000 per American) and increase fuel tax with $10/gal ($3000 per American), then the most stubborn gain nothing, but the smartest people start using their bike and isolating their house.

These smart people pay less tax after the reform, but that’s OK, because we can start exporting oil, just like smart nations have been doing for decades.

This is really expensive for poor people living in the forest in a badly isolated house with an old truck. Currently I, the tax payer, subsidizes their crazy behavior. If they had to pay their own bill, I think we’d see fewer old pickups…