Question

Suppose that XYZ Company hires labor and capital in competitive input markets. Assume that labor costs $200 per day and that a unit of capital costs $150 per day. At the current level of production, labor's marginal product is 40 units of output produced per day and capital's marginal product is 30 units of output per day.
a) Given the information provided, is the firm minimizing the cost of current production? Explain why or why not.
b) If the daily wages were to increase, explain the long run adjustments that the firm would likely make in response to the wage increase.

Answer 1

Answer:

a) Yes, the firm is minimizing the cost of current production. This is because MRPL / w = MRPC / r = 0.20.

b) The long run adjustments that the firm would likely make in response to the wage increase is to use more labor and less capital until MRPL / w = MRPC / r, which is the condition for the cost minimization of a firm.

Explanation:

a) Given the information provided, is the firm minimizing the cost of current production? Explain why or why not.

The condition for the cost minimization of a firm is as follows:

MRPL / w = MRPC / r ……………………………. (1)

Where:

MRPL = Labor's marginal product = 40

w = Cost of labour = $200

MRPC = Capital's marginal product = 30

r = Cost of capital = 150

Therefore, we have:

MRPL / w = 40 / 200 = 0.20

MRPC / r = 30 / 150 = 0.20

Since MRPL / w = MRPC / r = 0.20, this implies that these conditions are consistent with equation (1). Therefore, the firm is minimizing the cost of current production.

b) If the daily wages were to increase, explain the long run adjustments that the firm would likely make in response to the wage increase.

If the daily wages were to increase, the MRPL / w in equation (1) in part a above will fall and we will have:

MRPL / w < MRPC / r …………………… (2)

Since equation (2) is no longer consistent with equation (1), the firm is NOT minimizing the cost of current production.

Therefore, the long run adjustments that the firm would likely make in response to the wage increase is to use more labor and less capital until MRPL / w = MRPC / r, which is the condition for the cost minimization of a firm.