Pricing by the Piece against Pricing by Weight: Buyer Selection, Fairness, and a Two-Size Grading Rule for Apples

A vendor who sells apples by the piece charges the same for fruit of different weights. A vendor who sells by weight charges in proportion to what each buyer takes. This paper compares the two methods for apples with a stated weight distribution, a stated price per kilogram, and a stated pattern of buyer choice. When fruit is allocated at random, the methods return almost the same revenue. When buyers choose the largest fruit, piece pricing transfers a substantial sum from vendor to buyer: the vendor receives $109.50 for fruit that would return $124.49 by weight in a day, a loss of $14.99, or 9.99 cents per apple sold. The same piece price charges different buyers between $3.07 and $5.74 per kilogram. Splitting stock into two sizes at the median weight and pricing each size separately reduces the loss to $9.34 per day, but grading labour costs $6.00 per day, so the net benefit is −$0.35 per day. From this the paper derives a grading rule: grade into two sizes only when the coefficient of variation of fruit weight exceeds a break-even value set by labour cost, the residual loss after grading, and the value at stake. For the stated terms that value is 0.2428, about a standard deviation of 43.7 grams at a mean of 180 grams. The stated apples, with a coefficient of variation of 0.2286, fall just below the line, so grading them on these terms does not pay.