42 CIRCULAR 905, U. S. DEPARTMENT OF AGRICULTURE 
time. In addition, they have a direct value as a livestock feed. 
Farmers generally are aware of these benefits of forage in a farm 
organization, but problems of utilization make it difficult for many 
farmers to determine the profitability of further increases in produc- 
tion of forage. 
Three basic sets of relationships determine the forage-utilization 
system that is most profitable for an individual farmer. These rela- 
tionships are: (1) the rate at which forage substitutes for other feeds 
in the livestock ration and the rate at which forage substitutes for 
grain in the crop rotation; (2) capital and labor requirements; and 
(3) risk and uncertainty. 
RoTATION RELATIONSHIPS 
Forage may be either complementary or competitive with grain in 
crop production. It is complementary if an increased acreage of 
forage causes total production of grain from a given area to increase. 
Forage is competitive with grain if greater acreage and production of 
forage is achieved at the expense of a decrease in total production of 
grain. Data examined in the study upon which this report is based 
show that when forage makes up only a small proportion of the 
acreage in a rotation it is complementary with grain—increases in 
the proportion of forage in the rotation result in increases in output 
of grain. Additional increases in the proportion of forage result 
in smaller increases in production of grain until eventually forage and 
grain become competitive—further increases in the proportion of 
forage results in less total production of grain. 
The profitability of increasing production of forage beyond the 
point at which it becomes competitive with grain depends on the value 
of the increased forage relative to that of the grain which it replaces. 
On livestock farms the value of forage is influenced by its value as a 
livestock feed. Thus the relationships of grain to forage in the crop 
rotation and in the livestock ration are crucial to determination of the 
more profitable grain-forage combination. 
FEED SUBSTITUTION IN LIVESTOCK RATIONS 
Many livestock feeding experiments were examined in order to 
estimate the substitution rates between forage and grains as feeds. 
Only a few of these experiments provided data suitable for estimating 
the substitution rates. With the limited data, estimates were made of 
forage-grain substitution rates for dairy cows, feeder cattle, hogs, 
and sheep. Although more experimental work is needed before reli- 
able estimates of the relationships between forage and grain in feeding 
different kinds of livestock under various conditions can be estab- 
lished, the estimates provided in this study suggest the nature of 
the feed-substitution relationships and provide an approximation 
to the substitution coefficients under certain conditions. 
Forage was found to substitute for grain at a diminishing rate 
for each of the four kinds of livestock considered. For example, it 
was found that a cow will produce 8,500 pounds of 4-percent fat-cor- 
rected milk with 5,500 pounds of hay and 5,459 pounds of grain or 
with 4,933 pounds of grain and 5,959 pounds of hay—567 fewer 
