Question

According to 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:

Amount of Grain (Pounds) - Amount of Milk (Pounds)

1,200 5,917

1,800 7,250

2,400 8,379

3,000 9,371

(This relationship assumes that forage input is fixed at 6,500 pounds of hay.)

a. Calculate the average product of grain when each amount is used.

b. Estimate the marginal product of grain when between 1,200 and 1,800 pounds are fed, when between 1,800 and 2,400 pounds are fed, and when between 2,400 and 3,000 pounds are fed.

c. Does this production function exhibit diminishing marginal returns? Why or why not?

Answer 1

Question:

Amount of Grain (Pounds)	Amount of Milk (Pounds)
1200	5917
1800	7250
2400	8379
3000	9371

a.

Average product of grain(AP) = Amount of milk(Qm) / Amount of grain(Qg)

• When Qm= 5917 and Qg= 1200. AP= 5917/1200= 4.93
• When Qm= 7250 and Qg= 1800. AP= 7250/1800= 4.03
• When Qm= 8379 and Qg= 2400. AP= 8379/2400= 3.49
• When Qm= 9371 and Qg= 3000. AP= 9371/3000= 3.12

b.

Marginal product(MP)= Change in Qm / Change in Qg

• When between 1,200 and 1,800 pounds are fed: MP= 1333/600= 2.22
• When between 1,800 and 2400 pounds are fed: MP=1129/600= 1.88
• When between 2400 and 3000 pounds are fed: MP= 992/600= 1.65

c.

The production function exhibits diminishing return if marginal product of a factor decreases as the amount of factor employed rises.

Here we can observe that MP is decreasing so this production function exhibit diminishing marginal returns