Do We Need a 37-Cent Coin?

Dubner thinks we should do away with the penny.

A young economist I know, Patrick DeJarnette, believes a much more radical change in currency is warranted. Here is what Patrick writes:

Late one night I was curious how efficient the “penny, nickel, dime, quarter” system was, so I wrote a little script to compare all possible 4-coin systems, with the following stipulations: 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]. In other words, you start with $10 and no coins. You buy something at the store. Afterward, the chance you have 43 cents in your pocket is equal to the probability that you have 29 or 99 cents in your pocket (in addition to any bills). Requirement (1) implies the penny is necessary, as you must have a combination of coins that reach value = 1 cent. With this in mind, the current combination of coins (penny, nickel, dime, quarter) results in an average of 4.70 coins per transaction. What’s a little surprising is how inefficient our current setup is! It’s only the 2,952-nd most efficient combination. There are effectively 152,096 different combinations of penny + three coins. In other words, it’s only in the 98th percentile for efficiency.

How can you tell that Patrick is a young economist from the preceding discussion? Because he finds that the current government solution for the coins we use is 98 percent efficient and thinks this is inefficient. The other day I was walking through the halls of the University of Chicago economics department and heard a faculty member say that the right rule of thumb for government spending is that it is worth only 10 cents on the dollar because of inefficiency.

Anyway, Patrick then tackles the question of which combinations of coins would be most efficient: