The value of No Change Provided

Vending and parking machines often display the message "no change provided", and retain any payment above the required amount. This is mildly annoying, but we live with it. But it got me asking what the value of this policy is to the vendor. Here is an interactive dashboard that uses random sampling to estimate the value of retaining change across many small transactions.

To play with this model, click on the sliders, and see how the graphs change.

How the model works

The model simulates the attempts of 100 customers to pay the required amount using the coins in their pocket (you can change the number of samples using the slider; higher values make the updates more sluggish, but result in less variation between updates).

For each customer, it assumes that a typical customer has a certain number of coins in his or her pocket, say 8. For each sample, this number of coins are chosen at random from denominations (in pounds) of 2.00, 1.00, 0.50, 0.20, 0.10, 0.05, 0.02, or 0.01. Repeats are allowed (so there can be several coins of the same denomination in the pocket).

The customer then tries to find the combination of coins that is closest to the required fee. There may be an exact match, or the best combination may be slightly over the required fee. This is what interests us.

In addition, some customers will not have enough coins in their pocket to pay the required fee. The model assumes this is lost revenue, although in some situations the vendor allows for credit card or mobile payments.

The bar graph shows the total revenue from three possible sources:

1. The basic sales revenue, i.e., the price times quantity sold
2. The total of all change retained
3. The revenue lost for customers who did not have enough change to make the payment

The pie graph shows the number and percentage of customers who were able to pay the exact amount, paid extra, and didn't have enough change.

What the model tells us

Playing with the model tells us several things (mostly admittedly intuitive, but interesting to see demonstrated):

• In the beginning case of 8 coins and a fee of 1.10, about 20% of revenue comes from withholding change; this could constitute much of the profit for a vendor
• If you increase the number of coins, the fraction of people who could pay exactly increases, and vice versa
• Increasing the number of coins also reduces the number of people who are unable to pay
• Setting the fee to an even, rounded amount (such as 1.00 or 0.50) results in a much higher number of people able to pay exactly, compared to a price such as 1.05 or 1.15 or even 1.17; however, the increase in revenue is not significant
• Lower fees result in more people being able to pay, while higher price increases the number of people unable to pay

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