Absolutely fascinating Freakonomics…in which a little scamp of an aspiring economist runs right through the old saw about losing the penny like BJ McKay going through billboards. Turns out losing the penny alone doesn’t really help overall efficiency that much if we assume:
1. Some combination of coins must reach every integer value in [0,99].
2. Probability of a transaction resulting in value v is uniform from [0,99].
You could split some obvious hairs about (2), but (1) seems to me to be the real sticking point on getting rid of the penny: people see it as just another chance for everything to go up in price; everyone assumes they’ll always come out behind on any rounding scheme. And, let’s face it: everyone probably would.
So, what was the most efficient system? Prepare to be Obamazed:
The penny, 3-cent piece, 11-cent piece, 37-cent piece, and (1,3,11,38) are tied at 4.10 coins per transaction.
Now who could possibly argue with that arrangement? I DEMAND it be implemented. But, forseeing the loser, stick-in-the-mud attidudes that he’d receive once he announced that all payments to Death Panels are henceforth mandated to be rendered in 38-cent coins, the little scamp sorted down to some more reasonable options (among others):
(1,4,15,40) is the first “reasonable looking” combination, with 4.14 coins per transaction.
(1,3,10,35) also does well, with 4.16 coins per transaction.
[or, restricting ourselves to multiples of 5]
(1,5,15,35) at 4.50 coins.
(1,5,10,30) at 4.60 coins.
Fantastic. But, perhaps unsurprisingly, given the “lose the penny!” nature of conventional wisdom, what would you assume is the least worthwhile coin?
Why, it’s the dime, of course.
…losing the dime entirely only costs us ~0.8 coins per transaction in efficiency; it does the least good of the existing coins.
So: a two pronged attack is in order. We couple a bill that removes dimes from circulation whilst putting the serene visage of Reagan or Lord Jesus on the obverse…
Lemkin 