36 BULLETIN" 1411, U. S. DEPARTMENT OF AGRICULTURE 
vailing size of sale. Variation in percentage margins is therefore the result of 
wrongly using the dollar's worth, with its variable service requirements, as the unit 
of distribution. When the individual retail sale is taken as a new distribution 
unit, the actual margin per sale is nearly uniform for all commodities, and no 
appreciable differences remain to be explained. 
LIMITATIONS OF PERCENTAGE DIFFERENTIALS FOR COMPARING 
PRICES 
Use of percentages for analyzing price differences incurs certain mathematical 
difficulties which may vitiate their meaning. This made it necessary to abandon 
the original plan of making detailed comparisons of margins as percentages of 
retail prices and to analyze the actual prices and price differences in their stead. 
The margin concept assumes a constant money expenditure by the consumer, 
representing a dollar's worth of goods under given price conditions. Any varia- 
tion in retail price involves, therefore, a change in the quantity of goods secured 
for $1. The margin represents in cents of the consumer's dollar the spread 
between wholesale and retail prices for a variable quantity of goods, whose volume 
changes with any change in the selling price. Use of differentials between per- 
centage margins to measure the relative efficiency of a given money outlay is 
therefore logically unsound. 
The difficulty in interpreting percentage differentials may be illustrated by 
making a comparison of percentage margins in two types of retail stores. The 
general margin in independent credit-delivery stores for the whole commodity 
series is 47 per cent of the mean retail price, while in cash-and-carry stores it is 
only 42 per cent of the retail price. This is equivalent to saying that of a dollar's 
outlay by the consumer in a credit-delivery store, 47 cents are required to cover 
handling expenses, leaving 53 cents to pay for the goods in the wholesale market; 
whereas of the dollar spent in a cash-and-carry store only 42 cents is required for 
handling and 58 cents is left to pay for goods in the wholesale market. 
Thus the apparent difference in handling cost of 5 cents on a dollar's worth of 
goods, actually turns out to be quite otherwise than a difference of 5 per cent of 
the retail price. Out of the dollar expended by the consumer, 58 cents of the 
cash-and-carry customer's money is used to buy goods in the wholesale market, 
whereas only 53 cents of the credit-delivery customer's money may be so used. 
Hence the cash-and-carry customer will obtain ff times the quantity of goods 
received by the credit-delivery customer. For an identical quantity of goods, 
therefore, the cash-and-carry customer would pay only -ff of the other's outlay. 
The latter fraction, for the cash-and-carry store, is 91.4 per cent of the amount 
required for the same quantity of goods in the credit-delivery store. The actual 
differential between prices in the two store types is therefore 100-91.4, or 8.6 
per cent, of the credit-delivery price, instead of the apparent 5 per cent. If it 
were desired to express the differential in terms of the cash-and-carry price, 
then the corresponding inverted fraction, ff , would be used, which is 109.4 
per cent. This indicates that the selling price for a given quantity of goods in a 
credit-delivery store is 9.4 per cent higher than that for the same quantity in a 
cash-and-carry store. 
The difficulty here illustrated exists wherever comparisons of percentages 
derived from varying or noncomparable bases are attempted. Any effort to 
make accurate price comparisons by comparing percentage margins is therefore 
likely to be misleading and to confuse the real differences. 
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