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 $25 and the per-unit wage, w, is $15, then the average total cost of using 81 units of capital and 9 units of labor is A)$5. B)$75. C)$80. D)there is insufficient information to determine the average total costs.

Question

Quizplus · Accepted Answer

To find the average total cost, we need to first calculate the total cost, which is the sum of the cost of capital and labor.

Cost of capital = rK = $25 x 81 = $2,025 
Cost of labor = wL = $15 x 9 = $135

Total cost = $2,025 + $135 = $2,160

Next, we need to find the quantity produced using these inputs.

Q = K^1S^1U^1P^0.5S^1S^1P^0L^1S^1U^1P^0.5S^1S^1P^0 
Q = (81)^1 x (1)^1 x (1)^1 x (1)^0.5 x (1)^1 x (1)^1 x (9)^1 x (1)^1 x (1)^1 x (1)^0.5 x (1)^1 x (1)^1 
Q = 9 x 3 = 27

Average total cost = total cost / quantity produced 
Average total cost = $2,160 / 27 = $80

Therefore, the answer is (C) $80.

Suppose That Production for Good X Is Characterized by the Following