4 CIRCULAR 905, U. S. DEPARTMENT OF AGRICULTURE 
forage in livestock production is not limited by availability of capital 
must consider how much to expand production of forage into the com- 
petitive areas as well as the problem of how to utilize the forage. Here 
substitution relationships become significant in deciding upon both 
the best ration for a particular type of livestock and the rotation that. 
will allow a maximum value of livestock products from a given quan- 
tity of land and other resources. 
Although they may be extremely limited as to capital, many farm- 
ers must operate in the competitive area. ‘This may be true for some 
because under their soil situations the grain-forage relationship is 
competitive throughout all combinations. For many it may be true 
because they remain on a particular farm only a short time. In a 
single year the relationship between forage and grain is competitive 
and, therefore, the complementary aspects of forage-grain combina- 
tions have no significance unless the individual remains on the farm 
long enough for the indirect benefits of the rotation to be realized. 
Further discussion of optimum combinations of forage and grain from 
the viewpoint of both production and utilization follows an examina- 
tion of the rates at which forage substitutes for grain in livestock- 
feeding rations. 
LIVESTOCK SUBSTITUTION RELATIONSHIPS 
A given quantity of a livestock product (100 pounds of milk, pork, 
or beef) can be produced with many combinations of grains and for- 
ages. Beef or milk can be produced with forages alone and pork or 
poultry products can be produced with grains alone. However, grain 
and forages can be substituted for each other so that 100 pounds of 
livestock product can be produced with many combinations of the two 
feeds. The lowest-cost combination among these combinations de- 
pends upon (1) the rate at which forage substitutes for grain in pro- 
ducing a given quantity of livestock product and (2) the price or cost 
of forage relative to that of grain. 
For example, suppose that 100 pounds of milk can be produced with 
40 pounds of corn and 94 pounds of alfalfa hay. Suppose further 
that the same quantity of milk can be produced with only 37 pounds 
of corn if 100 pounds of hay are included in the ration. In these two 
examples the addition of 6 pounds of forage reduces the grain re- 
quirement by 3 pounds. That is, the additional 6 pounds of hay are 
equivalent to 8 pounds of grain in producing milk. If hay is worth 
a cent a pound ($20 per ton) and corn is worth 2.5 cents a pound 
($1.40 per bushel), the additional 6 pounds of hay fed would be worth 
only 6 cents, whereas the 3 pounds of corn saved would be worth 7.5 
cents. Obviously it would pay to make the substitution. 
Will it pay to substitute still more forage for grain? The answer 
depends on the nature of the substitution relationship—whether 
forage substitutes for grain at a constant or at a diminishing rate. 
If the rate is constant, each additional 6 pounds of hay will replace 
another 8 pounds of grain. Obviously, with hay at a cent a pound 
and grain at 2.5 cents a pound it would be profitable to replace all of 
the grain in the ration with forage. If the price of hay rose in rela- 
tion to that of grain, so that 6 pounds of hay were more expensive 
than 3 pounds of grain, it would not pay to include any hay in the 
dairy ration. 
