6 CIRCULAR 905, U. S. DEPARTMENT OF AGRICULTURE 
used in making the estimates in table 2.2. It is likely that the quan- 
tity of feed required to produce 8,500 pounds of milk would differ 
for cows of different producing ability fed similar kinds and qualities 
of feeds and for cows of a given production capacity fed different 
kinds and qualities of grain and forage. 
Table 2 shows, first, that a wide range of combinations of grain 
and forage will give the same production of milk. With 5,000 pounds 
of forage and 6,154 pounds of grain, 8,500 pounds of milk were pro- 
duced; the same amount was obtained from 11,000 pounds of hay 
and only 2,281 pounds of grain. It is likely that combinations be- 
yond each of these extremes are also possible, but this experiment 
did not include cows producing outside this range of feed com- 
binations. | 
A second relationship apparent from the data in table 2 is that 
forage substitutes for grain at a diminishing rate. Each succeeding 
increase in the quantity of forage fed reduces the quantity of grain 
required by something less than the preceding increase in forage. 
For example, when 5,500 pounds of forage are fed, 5,459 pounds of 
grain are needed to produce 8,500 pounds of milk per cow, whereas 
when the quantity of forage fed is increased to 6,000 pounds, only 
4,892 pounds of grain are needed—a reduction of 567 pounds of 
grain. If the quantity of forage is increased by another 500 pounds 
(to 6,500 pounds), an even smaller quantity of grain (4,423 pounds) 
is needed to yield 8,500 pounds of milk, and the quantity of grain 
saved (469 pounds) is smaller than that resulting from the previous 
500-pound increase in forage. Each additional 500-pound increase 
in the quantity of forage results in progressively smaller replace- 
ments of grain, until finally, as the quantity of forage is increased 
from 10,500 pounds to 11,000 pounds, the amount of grain replaced 
is only 188 pounds. The average quantity of grain saved per added 
pound of forage for each 500-pound increment in forage in the ration 
1s Shown in column 3 of table 2. This column shows that the rate at 
which forage substitutes for grain in the dairy ration declines from 
an average of 1.39 pounds of grain replaced per pound of hay added 
when hay is increased from 5,000 to 5,500 pounds to only 0.28 pound 
of grain saved per pound of hay added when the quantity of forage 
is increased from 10,500 to 11,000 pounds. 
FORAGE-GRAIN SUBSTITUTION IN PORK PRODUCTION 
A study by the United States Department of Agriculture (3) pro- 
vided the data for the estimates of feed-substitution rates in produc- 
*The Jensen-Woodward study was directly related to levels of total feed for 
dairy cows and only indirectly to combinations of grain and forage in the ra- 
tion. Higher levels of total feed were possible, however, only as levels of grain 
feeding were increased and the cow reduced her consumption of forage. Thus 
the resulting data included an element of feed substitution as well as the rela- 
tionship between total feed fed and the production of milk. Within the range 
on the “production surface” used in the present analysis, considerable varia- 
tion appeared in the combinations of grain and hay in the ration. But we can- 
not be certain that mingling of the two relationships (factor-factor and factor- 
product) has been entirely eliminated in the present analysis. Additional ex- 
periments are needed wherein an attempt is made to isolate feed-combination 
relationships for certain outputs per cow separately from the total feed-input 
milk-output relationships. 
