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Calculating average and marginal product

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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 follow:

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?

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Solution Preview

Please refer attached file for better clarity of expressions.

(a) Calculate the average product of grain when each amount is used.
Amount of Grain (Pounds),G Amount of milk (Pounds), M Average Product=M/G
1200 5917 4.93
1800 ...

Solution Summary

Solution depicts the steps to calculate average and marginal product.

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Calculating marginal and average products, and Lerner Index

1. The following table shows data for a simple production function.

Capital(K) Labor(L) Total Product(TP) Average Product(AP) Marginal Product(MP)
Column 1 numbers = Capital ; Column 2 numbers = Labor; Column 3 numbers= Total Product
10 0 0
10 1 5
10 2 15
10 3 30
10 4 50
10 5 75
10 6 85
10 7 90
10 8 92
10 9 92
10 10 90

a. From the information in the table, calculate marginal and average products.
b. Graph the three functions on separate graphs (Total production, Marginal Products and Average Products).
c. For what range of output does this function have diminishing marginal returns?
d. At what output is average product maximized?

2. Suppose the demand curve for a monopolist is QD= 500 - P, and the marginal revenue function is MR = 500 - 2Q. The monopolist has a constant marginal and average total cost of $50 per unit.
a. Find the monopolist's profit-maximizing output and price.
b. Calculate the monopolist's profit.
c. What is the Lerner Index for this industry?

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