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Directions: Suppose a firm's marginal product of capital and marginal product of labor schedules are as shown in the table below. The firm hires both capital and labor competitively for $5 and $8, respectively. This assignment will be graded out of 6 points with 2 points possible for each question.

Capital MP of Capital Labor MP of Labor

0 0

1 10 1 28

2 9 2 30

3 8 3 24

4 7 4 20

5 6 5 16

6 5 6 12

7 4 7 8

8 3 9 4


1. Suppose the firm is currently using 4 units of capital and 4 units of labor. Is the corresponding output being produced at least cost? How do you know?


2. Consider your answer to the question above. Generally speaking, what would a firm need to do in order to move towards producing at the least cost?



3. What is the least-cost combination of labor and capital?

User Phil Parker
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1 Answer

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21 votes

Answer:

In order to determine whether the firm is currently producing at least cost, we need to compare the marginal cost of using an additional unit of capital or labor to the marginal revenue generated by that unit. Since we do not have information on the marginal revenue in this case, it is impossible to say for sure whether the firm is producing at least cost.

In order to move towards producing at the least cost, a firm would need to adjust the combination of labor and capital it uses in order to minimize the marginal cost of production. This can be achieved by adjusting the mix of labor and capital used in production until the marginal cost of an additional unit of labor is equal to the marginal cost of an additional unit of capital.

In order to determine the least-cost combination of labor and capital, we need to find the point where the marginal cost of using an additional unit of labor is equal to the marginal cost of using an additional unit of capital. From the information given in the table, we can see that this point occurs when the firm is using 3 units of capital and 3 units of labor. At this point, the marginal cost of using an additional unit of labor is 24 and the marginal cost of using an additional unit of capital is 8, which are equal. Therefore, the least-cost combination of labor and capital is 3 units of each.

User McLaren
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