32 
BULLETIN 1411, U. S. DEPARTMENT OF AGRICULTURE 
Total retail value, total distribution expense, and percentage margin for each 
of the three illustrative commodities are 
Total 
retail 
value 
R-W 
Total 
distribution 
expense 
R-W 
R 
Margin 
Northern cabbage 
Barreled apples. .. 
California oranges 
$2, 370, 000 
17,940,000 
22, 420, 000 
$1, 380, 000 
8, 710, 000 
9, 150, 000 
Per cent 
58 
49- 
41 
In each case a change in R is accompanied bv a relativelv smaller change in 
R-W; thus 
While R for apples is 7.5 times R for cabbage, 
yet R-W " " " only 6.3 " R-W " " ; 
and R for oranges is 1.3 times R for apples, 
but R-W " " " only 1.1 " R-W " " . 
Now the percentage margin for each commodity is a quotient derived by divid- 
ing the figure in the second column by that in the first column. The decline in 
the margin for apples (49) from that for cabbage (58), results from the fact that 
R-W for apples is only 6.3 times R-W for cabbage, whereas R for apples is 7.5 
times R for cabbage. The margin for apples is therefore -=-^ times 58, which is 
49 per cent. Similarly, the decline in the margin for oranges (41) from that for 
apples (49), results from the fact that R-W for oranges is only 1.1 times R-W for 
apples, whereas R for oranges is 1.3 times R for apples. The margin for oranges 
is therefore - 1 -- times 49, which is 41 per cent. Throughout the 14-commodity 
series, it may be demonstrated similarly that the inverse association between 
percentage margins and total retail value results from the fact that total retail 
value increases from one article to another more rapidly than does the total 
distribution expense. 
It remains still to explain why increases in total retail values are accompanied 
by relatively smaller increases in distribution expense. The total retail value of 
any commodity may be conceived of as the product of (1) retail price per pound 
and (2) total number of pounds sold annually. The total distribution expense 
may be regarded either as the product of price spread per pound and total 
number of pounds, or as the difference between total wholesale value and total 
retail value. If for any commodity, r represents the retail price per pound, w the 
wholesale price per pound, and P the total number of pounds sold in the metro- 
politan area in 1923, then the total retail value R is equivalent to r times P; the 
total wholesale value is equivalent to w times P; and the total distribution expense 
R-W is rP minus wP. The percentage margin is therefore p — By can- 
r — w 
celling out the P's in this fraction, the percentage margin becomes This 
means that for any commodity in the series the percentage margin is the 
same, whether based on total values or on values per pound. The conclusion is, 
therefore, that percentage margins are independent of physical volume as a 
separate factor. Any influence exerted by physical volume is expressed already 
in the prices themselves. 
The analysis shows that a difference in physical volumes of two given com- 
modities affects R-W and R identically. The' reason why R-W fails to increase 
as rapidly as R, within the series of articles, is that r-w does not increase as 
rapidly as r. In other words, price-spread per pound does not increase pro- 
portionally with retail price per pound. Calculations from the per pound figures 
for the three illustrative commodities shows it to be true that an increase in 
retail price is accompanied by a relatively smaller gain in price-spread, thus: 
