Weighing Accuracy and Short Weight: What a Small Systematic Error Transfers Over a Market Season

A scale error that is barely visible in a single transaction becomes a large sum when it repeats, in the same direction, for a whole season. This paper models a market stall selling 250 kg of produce per day over 96 trading days, at an average price of $4.00 per kg, for a season total of 24,000 kg and honest revenue of $96,000. A systematic short weight of 1% transfers $960 from buyers to the vendor over the season, 2% transfers $1,920, and 5% transfers $4,800. Per transaction the same errors are only 17.9 g, 35.7 g, and 89.3 g on an average purchase of 1.786 kg, worth 7.1, 14.3, and 35.7 cents respectively, which explains why no individual buyer is likely to notice or contest them. The cost is symmetric in retail value for over-weight: a vendor whose scale gives 1%, 2%, or 5% too much gives away produce with a retail value of $960, $1,920, or $4,800 over the season, at a direct stock cost of $576, $1,152, or $2,880. Accuracy is therefore not a matter of fairness in the abstract only. It is a priced quantity, and the price of a small fixed bias, in either direction, is set by season throughput. The paper also computes how many test purchases are needed to distinguish a bias from random weighing variation, showing that a 2% bias can be separated from a 1.5% random standard deviation with about three test purchases, while a 1% bias needs about nine.