Two cars are for sale on the used car lot.  Car A has 62,847 miles on it and is listed for \$7500.  Car B has 89,113 miles on it and is listed for \$5600.  Which car would you buy?

Did you think about it?  OK, now your answer is not really important, but without looking back again at the numbers, answer this question:  what was the third digit of the mileage reading of the two cars?  You probably don’t remember because you probably didn’t pay close attention.

Apparently this inattention has been priced into the used car market.  For example, used cars with 39,900 miles on the odometer sell for significantly more than cars with 40,000 miles but not much less than cars with 39,000 miles.  This is the starting point of a paper by Nicola Lacetera, Devin Pope, and Justin Syndor.  They go on to estimate a structural model of attentiveness through the magnitude of the price discontinuities.

In fact, as they observe, sellers seem to understand this effect very well.  Here is a graph showing the volume of used cars sold wholesale at different odometer readings.  There is a huge spike in volume at the right end of an interval and a huge drop on the other side.

Indeed you could imagine that this kind of effect manifests even in a world where most buyers have unlimited attentiveness. Everybody knows that the price drops at the 1,000 mile mark so used cars with 31,100 miles are leased to rental agencies until they reach the 31,900 mark.  The only used cars for sale with 31,100 miles on them are the lemons that the seller is willing to part with at the price that older cars are selling for.  Buyers know this so they treat all cars with between 31,000-31,999 miles as equivalent to the oldest car in that range.

(The next time you see zeros roll over on your odometer you will understand why that always feels like a watershed event.  Your car is only a mile older but it just took a discrete drop in value.)