Suppose that production for good X is characterized by the following production function,Q = 4K^0.5L^0.5,where K is the fixed input in the short run.If the per-unit rental rate of capital,r,is $12 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) $6.25. B) $9.14. C) $10.07. D) There is insufficient information to determine the average total costs.

Question

Quizplus · Accepted Answer

The average total cost (ATC) can be calculated by dividing the total cost by the quantity produced. The total cost includes both the cost of capital (K) and the cost of labor (L). Given that the rental rate of capital (r) is $12 and the wage (w) is $20, the total cost (TC) for 25 units of capital and 49 units of labor is TC = 25 * $12 + 49 * $20. The quantity produced (Q) is not directly given, but the production function is not needed to calculate ATC without Q. However, without the output quantity, we cannot directly calculate ATC, but we can calculate the total cost. The mistake here is that we actually do need either the production function to be applicable or the output quantity to calculate ATC correctly. Given the information, we cannot calculate ATC without knowing how many units of good X are produced or without a clearer production function. Therefore, the correct answer should be that there is insufficient information to determine the average total costs, but the explanation mistakenly attempted to calculate without acknowledging the necessity of the production quantity or a clearer function.

Suppose That Production for Good X Is Characterized by the Following