14 CIRCULAR 905, U. S. DEPARTMENT OF AGRICULTURE 
beyond 1,000 pounds per acre result in decreases in output of grain, 
that is, beyond this point forage and grain are competitive. 
Forage-grain substitution rates for rotations may be related to the 
feed-substitution rates for livestock to determine the crop rotation and 
livestock ration which results in the largest production of livestock 
from a given acreage. If a grain-forage combination is to yield the 
largest output of a livestock product from a given acreage of land, two 
conditions must be met: The rate at which forage replaces grain in the 
crop rotation is equal to the rate at which forage substitutes for grain 
in the livestock ration; and the proportion of forage in the rotation is 
equal to the proportion of forage in the livestock ration. It can easily 
be demonstrated that only this set of forage-grain combinations will 
result in the maximum output of livestock from a given acreage. 
Any decrease in the proportion of forage in the ration results in an 
increase in the replacement value of a pound of forage in terms of 
grain; but the reduction in the proportion of forage in the crop ro- 
tation decreases the substitution value of forage. Thus, in lowering 
the proportion of forage, the value of forage relative to grain as a feed 
increases, whereas the relative cost of forage decreases, making it 
profitable to substitute forage for grain. Movement in the opposite 
direction causes the substitution value of forage in the ration to de. 
crease, whereas the cost of forage in terms of grain sacrificed increases, 
making it profitable to substitute grain for forage. For any forage- 
grain combinations for which rotation substitution rates are equal to 
the livestock ration substitution rates, any increase in either forage or 
grain involves a reduction in output of the other. It follows that the 
proportion of forage in the feed combination produced must be equal 
to the proportion of forage in the feed fed to livestock, if the livestock 
product from a given land area is to be a maximum. If the forage- 
grain ratios differ, a portion of one of the feeds is not fed—and the 
unused feed is produced at the expense of a reduction in the yield of 
the other feed. 
A decision as to the forage-grain combination that will maximize 
the output of livestock from a given acreage may be illustrated for 
dairy cows by using the feed-combinations data for dairy cows in 
table 2 and the rotation data in table 6. Comparison of tables 6 and 
2 shows that the substitution rate between forage and grain in the crop 
rotation is the same as that in the dairy ration at several forage-grain 
combinations. Similarly, the proportion of forage in the crop rota- 
tion is the same as the proportion of forage in the dairy ration at 
many different feed combinations. However, in only one set of 
forage-grain combinations are both the substitution rates and the 
forage-grain proportions equal. This set of combinations is a crop 
rotation that produces between 1,800 and 2,000 pounds of forage and 
a dairy ration that includes between 5,000 and 5,500 pounds of forage. 
The specific set of feed combinations for which both forage-grain 
substitution rates and forage-grain ratios are equal is a dairy ration 
that consists of 5,120 pounds of forage and 5,973 pounds of grain per 
cow and a crop rotation that yields 1,807 pounds of forage and 2,108 
pounds of grain per acre. Each of these feed combinations contains 
46.15 percent of forage; in each case 1 pound of forage substitutes for 
1.46 pounds of grain. 
