Rounding and Change: What Coin Denominations Cost a Produce Vendor over a Day and a Season, and the Arithmetic of Giving Produce Instead of Small Change

Cash prices at a market stall rarely fall exactly on the coins handed over, so somebody absorbs the difference. This paper computes what common rounding practices cost or gain a stated vendor over a day and over a season of 96 trading days, with 280 transactions per day of which 112 are in cash. Rounding each cash total to the nearest 5 cents is fair on average: mean gain in simulation is $0.006 per day and $0.60 per season, with a daily standard deviation of $0.148 and an approximate 95 percent season range from −$27.29 to $28.50. Rounding systematically one way is different. Always rounding down costs an average of 2 cents per cash transaction, $2.24 per day, and $215.04 per season. Always rounding up gains the same, at customers' expense. Price points carry a larger lever: moving every item price up to the next multiple of 25 cents adds a mean of 11.99 cents per item, or $0.384 per transaction at 3.2 items per transaction. The paper then prices giving produce instead of small change, and originates a rule: give produce only when its marginal cost is below the change owed while its retail value is above the change owed. A garnish costing 3 cents with retail value 12 cents, given in place of an average 4 cents owed, saves 1 cent per use; across a season it saves $19.35 against a cash cost of $77.41, while handing customers $232.24 of retail value. A whole extra apple, costing 41 cents in place of 5 cents owed, fails the rule by a wide margin.