The story (picked up from Daniel Davies at http://d-squareddigest.blogspot.com) goes that the way one argued with Milton Friedman was to listen until he got to the part of his argument where he said "let's assume x" and then say "no, let's not!" That is, the part of the argument doing all the work tended to be hiding in some premise that economists consider innocuous but is in no way representative of the world.

So here, premise (2): "probability of a transaction resulting in value v is uniform." No! Not true! In reality, people price a disproportionate number of transactions to make easy change with the coins we have, be easily divisible, be .01 less than a larger number of dollars, and so on. The discovery that cash transactions had a uniform distribution of change would actually be quite weird.

But worse is the smuggling in of an unconsidered definition of the good in the form of the efficiency metric -- fewest coins per transaction. Even granting the uniform distribution, making change out of your pocket is still solving the subset-sum problem in your head, which is of course NP-complete. The existing setup of coins, including the first three powers of 5, makes this problem very easy while almost all the proposed "better" solutions actually make this aspect of the problem harder rather than easier. Who cares if I have to handle a few extra tenths of a coin per transaction if it means I don't have to spend two minutes puzzling out how to make change?

I suppose the lesson, as usual, is that business logic is lived experience, not theory.