Temple University
Economics 52
Production Theory
Based on data obtained by the U.S. Department of Agriculture, the relationship between a cow's total output of milk and the amount of grain it is fed is as follows:
Number of pounds of grain |
Milk Production |
Marginal Product |
Average Product |
2 |
75 |
-- |
37.5 |
3 |
90 |
15 |
30 |
4 |
110 |
20 |
27.5 |
5 |
130 |
20 |
26 |
6 |
135 |
5 |
22.5 |
7 |
136.5 |
1.5 |
19.5 |
a. Fill in the blanks in the table.
b. Does this production function exhibit diminishing marginal returns
to the variable input?
Yes or No, with
the 5th pound of grain.
c. Suppose that the farmer is able to sell raw milk for $.50 per gallon. He pays $2.50 per pound of feed. How much feed will he buy for each cow? The concept is that we will keep buying additional pounds of grain as long as the revenue that we gain from that additional grain exceeds the cost of buying the grain. The third column of the table shows the change in output for an additional pound of grain. We can sell each of these addional gallons for $.50. Let's make a table for this:
| lbs. of grain | 2 | 3 | 4 | 5 | 6 | 7 |
| Marginal Product | - | 15 | 20 | 20 | 5 | 1.5 |
| Marginal Product x $.50 | - | $7.50 | $10 | $10 | $2.50 | $.75 |
The fifth pound of grain adds $10 to revenue and only $2.50 to cost, So we should buy more grain. The sixth pound of grain adds 5 gallons of milk to our output or $2.50 to our revenue and It cost us $2.50 to buy that 6th lbs. of grain, so we shouldn't buy any more.