ECONOMIC USE OF FORAGES IN LIVESTOCK PRODUCTION 5 
Thus if forage substitutes for grain at a constant rate it pays farm- 
ers to feed either-all grain or all forage, depending on the price of 
each. But a constant rate of substitution is inconsistent with the 
feeding practices of livestock farmers. Farmers generally feed a 
combination of grain and forage to beef cows, feeder cattle, dairy 
cows, and sheep. On many farms hogs also are fed forage in some 
form. Furthermore, studies of animal nutrition indicate that grain 
fed in small quantities to livestock consuming rations made up largely 
of forage stimulates production more than when the ration includes a 
smaller proportion of forage. Finally, the substitution of forage for 
grain is limited by the capacity of an animal’s stomach. We may 
therefore expect that a diminishing rather than a constant rate of sub- 
stitution exists between forage and grain in livestock feeding. 
If forage substitutes for grain at a diminishing rate, some combi- 
nation of forage and grain is usually more profitable than either 
extreme of all grain or all forage in the ration. Returning to the 
example of forage and grain requirements for production of 100 
pounds of milk, let us suppose the amount of forage in the ration is 
increased from 100 to 106 pounds. ‘The previous increase of 6 pounds 
in the amount of forage fed resulted in a saving of 8 pounds of grain. 
But if forage substitutes for grain at a diminishing rate somewhat 
less than a 3-pound reduction in grain requirements would be ex- 
pected as a result of this last 6-pound increase in forage. In substi- 
tuting more forage eventually a point would be reached at which the 
value of the grain saved would be no greater than the value of the 
forage added. This is the forage-grain combination which mini- 
mizes the feed cost of producing 100 pounds of milk. 
Derivation of feed-substitution rates is a difficult and complex 
problem. Rates of substitution may vary with (1) the type and 
quality of grain and forages, (2) the production ability of the live- 
stock, and (38) the general management conditions under which live- 
stock are produced. Thus a multitude of situations exist for which 
substitution rates might be derived. After reviewing a wide range 
of experimental data, those from several experiments were analyzed 
to derive estimates of forage-grain replacement rates. These esti- 
mates of substitution rates between forage and grain in feeding milk 
cows, feeder cattle, hogs, and sheep under specified conditions are 
discussed in the following sections. 
FORAGE-GRAIN SUBSTITUTION RELATIONSHIPS IN MILK PRODUCTION 
Estimates of the various combinations of grain and forage that will 
produce 8,500 pounds of 4-percent fat-corrected milk per cow are 
shown in table 2. They are based on part of an experiment by the 
United States Department of Agriculture in cooperation with 10 
State agricultural experiment stations, which included several hun- 
dred cows of several breeds and involved many kinds and qualities 
of feed (S). Data for 30 cows of the heavy breeds (Holsteins and 
Brown Swiss) in the series II experiments (grain ration varied with 
free choice of hay) that receive comparable feeds (legume hay, corn 
silage, and grain) with an expected production capacity of 300 to 400 
pounds of butterfat (when fed the standard Haecker ration) were 
