Bryan Cutsinger has been doing an excellent job of presenting economic problems to solve.
Sometimes, to do basic economics, you need to know basic math.
Here’s a statement from research scientist Carey King in “Why Energy Efficiency Might Not Cut Emissions As Much as You Think,” Wall Street Journal, November 11, 2024 (print edition):
The idea that more efficiency can spur more consumption rather than less is known as the Jevons Paradox. Named after the British economist William Stanley Jevons, who first described it in his 1865 book “The Coal Question,” the paradox challenges the intuitive belief that efficiency gains automatically lead to energy savings.
Critics who dismiss Jevons’s idea often focus on consumer behavior. For example, it is hard to imagine that a driver would drive 50% more miles if purchasing a car that uses 50% less fuel per mile. They might drive a little more, but it wouldn’t be enough to make a difference.
Implicit in King’s statement, given the context, is the idea that if mileage were to rise by 50%, fuel consumption would not change. Is that true?
Show your work.
Note: King, the Journal tells us, is a research scientist and assistant director at the Energy Institute at the University of Texas at Austin.
READER COMMENTS
Aaron W
Nov 13 2024 at 11:00pm
The inverse of 50% is not 150%, it’s 200%.
People make this mistake all the time in both directions. For example, 10% inflation does not reduce real incomes (all things being equal) by 10%, it reduces them by 1 – 1/1.1 ≈ 9%. Not that the distinction means much near 1, or to your subjective feeling of purchasing power. 🙂
David Henderson
Nov 13 2024 at 11:27pm
You nailed it.
Another example: When the Dow Jones falls by 20% and then rises by 20%, it doesn’t go back to where it was.
David Seltzer
Nov 14 2024 at 1:17pm
David wrote, “When the Dow Jones falls by 20% and then rises by 20%, it doesn’t go back to where it was.” Right. If a stock loses half its value, it would have to double to return to pre-loss price. E.g. 100-50 =50.
50 * (1+r) = 100
(1+r) = 100/50
(1+r) =2
(r) = 1
50*( 1+1) = 50*(2)
50*(2) =100
QED
steve
Nov 13 2024 at 11:14pm
Hard to imagine they would drive 50% or 100% more.
Steve
Rob Rawlings
Nov 13 2024 at 11:23pm
If fuel costs halved and people only drove 50% more then fuel consumption would fall (Fuel costs $1 a gallon. My original car gets 10 miles to the gallon and I drive 100 miles so I spend $10 on gas. My new car gets $20 miles to the gallon and I drive 150 miles so I now spend $7.50 on gas)
I’m not sure this is a math error rather than an implicit assumption about the demand for travel – he assumes that it is relatively inelastic to a price change.
David Henderson
Nov 13 2024 at 11:28pm
Yes.
It’s a math error.
Rob Rawlings
Nov 14 2024 at 1:43pm
Its a math error if King is thinking that fuel consumption would not change in his scenario – but that not 100% clear from the bit you quote – perhaps its clear in the full (pay-walled) article.
David Henderson
Nov 14 2024 at 2:24pm
That’s why I said it’s clear from context. Why would he choose 50% rather than, say, 30% or 70%?
Knut P. Heen
Nov 14 2024 at 5:41am
I teach this every year when I explain that a rebound after a stock market crash usually does not make up for the loss. 50 percent down and 50 percent up brings you to 75 percent of the original value.
That said, King’s statement does not change meaning if you substitute 50 percent more miles with 100 percent more miles. His statement is probably also true. It is therefore not obvious whether it actually is a mathematical error or just a word missing. “For example, it is hard to imagine that a driver even would drive 50% more miles if purchasing a car that uses 50% less fuel per mile.”
David Seltzer
Nov 14 2024 at 1:22pm
Knut, see my comment. You are right. If a stock loses 50% of its value, the rule of 72 tells us that an annual return of 10% compounded, would require about 7 years for that issue to double to its pre-loss price.
MarkW
Nov 14 2024 at 5:50am
Well, we’ve already run the experiment. Annual per capita vehicle miles travelled did rise historically up until the late 1990s, after which it is essentially flat (and we still haven’t quite gotten back to pre-pandemic levels). And fuel costs are unlikely to be the main factor at this point, given the very high cost of vehicles. A $50K vehicle (close to the average new vehicle transaction price) fully depreciated over 150,000 miles works out the 0.33 per mile. If that vehicle gets 25 mpg, at $3 / gallon, that’s 0.12 / mile in fuel. Add in insurance and maintenance, and fuel makes up a relatively minor (and declining) fraction of the overall cost of owning and using a car. I suspect the plateauing of vehicle miles per person, though, has less to do with costs, and more to do with people reaching the limits of how much they actually want to drive (just as historically, I’m sure daily food calories per person increased steadily and then plateaued and is unlikely to increase further).
rick shapiro
Nov 14 2024 at 8:10am
Jevons certainly does apply; but you need to focus not on the relatively inelastic miles per person, but on the fuel efficiency of the fleet of vehicles. Overall efficiency encourages people to buy larger and more powerful cars.
Matthias
Nov 16 2024 at 2:56am
Not only that. They also drive their existing cars faster: petrol used per metre driven goes up quickly when you drive faster. (Same goes for electricity, of course.)
If your vehicle is ‘magically’ more efficient, you might also not bother taking the snowboard rack off the roof of your car. Or you might use your Aircon even more, etc.
There’s lots of ways to use more fuel, even without driving more metres.
Craig
Nov 14 2024 at 8:53am
The one that gets me frequently is markup vs gross margin…..d’oh…..
Karl
Nov 14 2024 at 5:43pm
The statement is reasonable. If it’s hard to imagine that a driver will drive 50% more miles, then it’s even harder to imagine that they will drive 100% more miles. He was just making a stronger statement than mathematically necessary.
Of course, it was also a mistake.
Jim Glass
Nov 14 2024 at 11:27pm
Thus Warren Buffett’s first rule for making money from investing: don’t lose money.
Yet the Jevons Paradox is a real thing. When Henry Ford increased productivity to reduce the amount of labor used in building a car by 95%, demand for labor used in building cars exploded. There are lots of other examples. It depends on the elasticities.
Matthias
Nov 16 2024 at 3:09am
The first steam engines were so inefficient, that you could only really use them were coal was cheap and abundant: ie in coal mines to pump water out.
Subsequent efficiency improvements led to steam engines being much more useful everywhere else, thus also driving demand for coal.
Jing
Nov 15 2024 at 1:51am
It’s an indictment of my quantitative skills that it took me like 5 minutes of staring at the screen before I saw the issue.
David Henderson
Nov 15 2024 at 12:06pm
Good for you for admitting it.
Comments are closed.