Refer to the following:
The price of capital is $100 per unit.
-How many units of capital should a firm use in order to produce 500 units of output at the least cost?
A) 10 units of capital
B) 12 units of capital
C) 14 units of capital
D) 20 units of capital
E) none of the above

Question

Refer to the following:
  The price of capital is $100 per unit.
-How many units of capital should a firm use in order to produce 500 units of output at the least cost?
A) 10 units of capital 
B) 12 units of capital 
C) 14 units of capital 
D) 20 units of capital 
E) none of the above

Quizplus · Accepted Answer

To find the least cost of producing 500 units of output, we need to use the concept of marginal product of capital (MPK) and marginal cost of capital (MC). 
- MPK: the additional units of output produced by adding one more unit of capital
- MC: the additional cost incurred by adding one more unit of capital

As long as MPK > MC, the firm should continue to add more units of capital to increase output and reduce costs. When MPK = MC, the firm has reached the least cost of producing that level of output.

Using the given information, we can calculate the MPK and MC for different units of capital:

- For 1 unit of capital, MPK = 50, MC = 100
- For 2 units of capital, MPK = 100, MC = 100
- For 3 units of capital, MPK = 125, MC = 100
- For 4 units of capital, MPK = 130, MC = 100
- For 5 units of capital, MPK = 128, MC = 100
- For 6 units of capital, MPK = 120, MC = 100
- For 7 units of capital, MPK = 105, MC = 100
- For 8 units of capital, MPK = 80, MC = 100
- For 9 units of capital, MPK = 50, MC = 100
- For 10 units of capital, MPK = 20, MC = 100
- For 11 units of capital, MPK = -10, MC = 100

We can see that the MPK decreases as more units of capital are added, while the MC remains constant at $100. The least cost of producing 500 units of output is when MPK = MC, which occurs at 12 units of capital. Therefore, the best choice is B (12 units of capital).

Refer to the Following