12 CIRCULAR 905, U. S. DEPARTMENT OF AGRICULTURE 
same basic principles apply regardless of the source of feed. For 
example, if it costs the farmer 5 cents to produce a pound of hay ($10 
a ton) and 1.5 cents to produce a pound of corn (84 cents a bushel) the 
cost of 8 pounds of hay is equal to the cost of producing a pound of 
erain. The least-cost feed combination is then the one at which 3 
pounds of hay just replace 1 pound of grain. Table 2 shows that in 
producing 8,500 pounds of milk at a combination that includes about 
10,000 pounds of hay and 2,572 pounds of grain, about 3 pounds (2.94) _ 
of hay replace 1 pound of grain. The cost of this feed combination 
is $88.58. No other forage-grain combination will produce 8,500 
pounds of milk as cheaply. 
The same principles apply when labor and other costs are included 
in the calculations. It is then the total cost of feeding grain or hay 
which establishes the feed-cost relationships. The cost of feeding a 
pound of each feed in this case includes the price of the feed, plus a 
charge for other factors. 
FoRAGE-GRAIN PRODUCTION IN RELATION TO UTILIZATION 
Substitution relationships in feeding are also important in defining 
the maximum amount of livestock product that can be produced from’ 
a given area of land. It was pointed out earlier that even though 
none of the forage is utilized for feed, it is profitable to grow enough 
forage so that the total output of grain is as high as possible. So 
that it will pay to grow still more forage, the forage grown must be 
utilized—its value as feed must offset the value of the production of 
grain sacrificed. To maximize the output of livestock product ob- 
tained from a given area, the rate at which forage substitutes for 
grain in the crop rotation must be related to the rate at which the two 
crops substitute for each other in the livestock ration. 
If we assume, for example, that forage substitutes for grain in the 
crop rotation at the rate of 2 pounds of forage for 1 pound of grain— 
that is, 1 pound of grain is sacrificed for each 2-pound increase in 
forage—then the dairy ration which allows the maximum production 
of milk from a given area will include 8,500 pounds of hay and 8,156 
pounds of grain, on the basis of the feed requirements shown in table 
2. At this combination the amount of milk that can be produced 
with each pound of hay added is the same as the amount that could 
have been produced with the 2 pounds of grain given up. With the 
rotation substitution rates remaining the same and with a change 
in the ration to include 9,000 pounds of hay and 2,937 pounds of 
grain, an average of 2.27 pounds of hay would be needed to replace 
a pound of grain in producing 8,500 pounds of milk. Yet, as the 
rotation was shifted to include more forage, only 2 pounds of hay 
could be obtained for each pound of grain sacrificed. 
This example is useful only in explaining the interrelationship of 
substitution rates for crop rotations and for livestock rations. The 
response in yields of grain to increases in the proportion of forage 
in the rotation differs for different soil situations. On some soils 
(table 1) the crops may be complementary over a range; on other soils 
forage and grain may be competitive at all combinations. But for 
any type of soils, it appears likely that when acreage of forage is low 
an increase in forage acreage is more effective in improving yields of 
