Superb paper (minus all the modelling) in Bank of Canada series by Heng Chen, Kim P. Huynh and Oz Shy.
They look at this simple problem. When do people prefer to pay via notes/coins and when via card? When you expect to get a lot of coins in return you pay via card. If not, then via cash/coins:
To empirically estimate the burden of holding coins, we exploit thresholds of transaction values at $5, $10, $15, $20 and $25. This is because our model provides a theoretical underpinning for discontinuity in the cash payment, where the probability of paying with cash conditional on transaction value is discontinuous at thresholds, due to the denomination structure of banknotes.
As an illustrative example, we assume that consumers receive change in the most efficient manner as to minimize the number of coins. That is, the change is composed of coins with the highest possible denomination so that a cash payment of $4.95 with one $10 banknote would result in one nickel (0.05) and a $5 note.
A cash purchase of $5.05 would result in receiving six coins as change: two two-dollar (2.00), one fifty-cent (0.50), one quarter (0.25), and two dimes (0.10).
Since consumers care about weights of their wallets and dislike change in the form of coins, the probability of using cash is higher to the left of $5 and lower to the right, provided that other factors affecting payment choices are varying smoothly with respect to transaction values around $5.
Thus, cash payment discontinuities are driven by discontinuous numbers of coins received as change around thresholds, which are induced by the denomination structure.
Actually, card payment on the so called right of $5 is also due to most purchase counters lacking change as well. So it is both demand and supply push factors at work..