In the following figure, the price of capital (r) is $10 per unit. (show your wo

Question

In the following figure, the price of capital (r) is $10 per unit. (show your work)

a. How many units of capital should the firm use to minimize the cost of producing 800 units of output?

b. If the firm decides to maximize output by producing 1200 units of output, how many units of labor should it use?

c. Suppose the firm is currently producing 400 units of output and would like to expanding production to 800 units of output. In the short-run, what quantities of capital and labor would be used to produce 800 units of output?

d. Describe how the firm would move to the cost-minimizing levels of capital and labor needed to produce 800 units of output in the long run.

e. Will this firm experience economies of scale, constant returns to scale or diseconomies of scale in the long run? How do you know?

Explanation / Answer

a)

When Q=800, cost minimizing mix of inputs is achieved at the point of tangency of IC (Q=800) curve and the budget line.

Looking at the figure, this comes out to be (100 K, 120 L)

Thus, firm should use 100 units of capital.

b)

When Q=1200, cost minimizing mix of inputs is achieved at the point of tangency of IC (Q=1200) curve and the budget line.

Looking at the figure, this comes out to be (130 K, 200 L)

Thus, firm should use 200 units of labor.

c)

When Q=800, cost minimizing mix of inputs is achieved at the point of tangency of IC (Q=800) curve and the budget line.

Looking at the figure, this comes out to be (100 K, 120 L)

d)

It will increase employment of both labor (from 100 to 120 L) and capital (from 60 to 100 K)

e)

Constant returns to scale, since proportional increase in inputs leads to proportional increase in output.

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