ECONOMIC USE OF FORAGES IN LIVESTOCK PRODUCTION 11 
animal. With grain (corn) at 2 cents a pound ($1.12 per bushel) 
and forage (hay) at a cent a pound ($20 per ton) and with the sub- 
stitution rates shown in table 2, the least-cost feed combination for 
producing 8,500 pounds of milk is one that includes 8,000 to 8,500 
pounds of forage and 3,406 to 3,156 pounds of grain. The rate of 
substitution (1 pound of grain for each 2 pounds of forage) is just 
equal to the inverse of their price ratios (grain at 2 cents a pound to 
forage at 1 cent per pound). At this combination, the value of the 
erain saved is just equal to the value of the forage added. ‘That is, 
each pound of hay added is equal in value to the 0.5 pound of grain 
saved. The total feed cost of producing 8,500 pounds of milk with 
this feed combination is $148.12. Any other feed combination would 
cost more. 
In producing pork a similar price relationship (grain at 2 cents 
a pound and hay at 1 cent a pound) means that it is not profitable to 
feed any forage because, as shown in table 3, each of the first 5 pounds 
of hay fed saves only 0.48 pound of grain. That is, it takes 5 cents 
worth of hay to save 4.8 cents worth of grain. If, however, the price 
of hay declines in relation to that of grain it may be profitable to feed 
considerable quantities of forage. For example, with corn at 2.25 
cents a pound ($1.26 a bushel) and hay at 75 cents a pound ($15 a ton), 
a feed combination that contains 20 pounds of forage and 319 pounds 
of grain will produce 100 pounds of pork at least cost. At this level 
of forage feeding, 1 pound of hay replaces 0.36 pound of grain; or 
75 cents worth of hay saves 81 cents worth of grain. But by addin 
another 5 pounds of forage only 72 cents worth of grain (0.32 pond) 
would be saved for each 75 cents worth of hay added. 
According to table 4, it does not pay to feed large quantities of 
forage in producing choice beef unless forage is cheap as compared 
to grain. With grain at 2.25 cents a pound ($1.26 a bushel) and 
hay at 75 cents a pound ($15 a ton) the least-cost feed combination in 
producing 100 pounds of choice beef on yearling steers would be the 
one that includes 600 pounds of forage and 882.7 pounds of grain. 
The forage-grain combination that minimizes the feed cost by put- 
ting 25 pounds of choice or prime finish on feeder lambs, when grain 
costs 2.25 cents a pound and forage costs 75 cents a pound, is the one 
that contains 90 pounds of forage and 108.3 pounds of grain. It 
would pay to feed considerable quantities of hay, even if prices of grain 
were low in relation to prices of hay. With corn at 2 cents a pound 
and hay at a cent a pound, it would be profitable to feed 60 pounds 
of forage to 120.1 pounds of grain. 
Many farmers produce both the grain and forage they feed. Others 
produce forage on their own farms and buy grain. However, the - 
*Feed substitution rates and hence least-cost feed combinations vary with 
levels of output per animal. Consequently the highest profit per animal is 
accomplished by (a@) obtaining the lowest cost (feed and other resources) 
combination for each level of production and (0) extending the level of pro- 
duction so far as the value of the additional product is greater than the cost 
of the additional feed and other resources used to produce it. Thus the most 
profitable level of production per animal depends on the rate at which resources 
are transformed into a particular livestock product (for example, the number 
of pounds of feed required to produce 100 pounds of milk as production per cow 
is extended to higher levels) and the price of the product relative to the price of 
feed and other factors used in its production. 
