Suppose that production for good X is characterized by the following production function,Q = K^0.5L^0.5,where K is the fixed input in the short run.If the per-unit rental rate of capital,r,is $86.80 and the per-unit wage,w,is $20,then the average total cost of using 25 units of capital and 49 units of labor is: A) $5. B) $75. C) $90. D) There is insufficient information to determine the average total costs.

Question

Quizplus · Accepted Answer

The formula for the average total cost (ATC) is:
ATC = Total Cost / Quantity
To calculate the total cost, we need to multiply the inputs with their respective prices and then add them up. Using the given values, we get:

Total Cost = rK + wL
Total Cost = 86.80 x 25 + 20 x 49
Total Cost = 2170 + 980
Total Cost = $3150

Now, we can calculate the ATC:
ATC = Total Cost / Quantity
ATC = $3150 / (25 x 1 x 49^0.5)   [Using the given production function]
ATC = $90.29 (rounded off to two decimal places)

Therefore, the average total cost of using 25 units of capital and 49 units of labor is $90.29, which is closest to option (C), $90.

Suppose That Production for Good X Is Characterized by the Following