I'm almost done reading Thinking, Fast and Slow by Daniel Kahneman. Soon I will post some key points the book makes. Meanwhile the following is an entertaining question he posed.
Consider two car owners who seek to reduce their costs:
Adam switches from a gas guzzler of 12 mpg to a slightly less voracious guzzler that runs at 14 mpg.
The environmentally virtuous Beth switches from a 30 mpg car to one that runs at 40 mpg.
Suppose both drivers travel equal distances over a year. Who will save more gas by switching?
I will give the answer as a comment in a couple days.
The following is Kahneman's answer but not his exact words. The key to the solution is not mpg but its inverse, gpm. Assuming each drives the same number of miles (> 0) in a year, Adam will save more gas, despite his mpg change being smaller -- both absolute and as a percent -- than Beth's. Assume each drives 10,000 miles.
ReplyDeleteAdam: 10000/12 - 10000/14 = 833 - 714 = 119 (rounded)
Beth: 10000/30 - 10000/40 = 333 - 250 = 83 (rounded)
The following is a more general proof with M = mileage (> 0).
Adam: M/12 - M/14 = (7M - 6M)/84 = M/84
Beth: M/30 - M/40 = (4M - 3M)/120 = M/120