According to data obtained by the U.S. Department of Agriculture, the relationsh

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

5,717

1,800

7,950

2,400

8,379

3,000

9,571

(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?

Amount of Grain (Pounds)

Amount of Milk (Pounds)

1,200

5,717

1,800

7,950

2,400

8,379

3,000

9,571

Explanation / Answer

a. Average product of grain = amount of milk / amount of grain

b. Marginal product = change in milk produced / change in grain fed

c)

From table in part b we can see that as the amount of grain fed is increasing marginal product is decreasing thus we can say that production function exhibits diminishing marginal returns.

Amount of grain Average Product of grain 1200 4.76 1800 4.42 2400 3.49 3000 3.19

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