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 $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) $5.25. B) $22.50. C) $31.00. 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 per-unit rental rate of capital (r) is $86.80 and the per-unit wage (w) is $20, for 25 units of capital and 49 units of labor, the total cost (TC) is calculated as follows:TC = (r * K) + (w * L) = ($86.80 * 25) + ($20 * 49) = $2170 + $980 = $3150The production function is not directly used to calculate ATC in this scenario because the quantity produced (Q) is not given, and the function itself is not correctly formatted or relevant to the calculation needed. However, if we assume the quantity produced (Q) is such that the ATC calculation is relevant with the given costs, we proceed with the calculation based on costs alone.Without the quantity produced, we cannot directly calculate ATC from the information given. However, the question seems to aim at understanding the calculation of costs based on inputs. Since the actual calculation of ATC requires the quantity produced, and it is not provided or directly calculable from the given production function, the correct answer would typically be that there is insufficient information (D). However, based on the options provided and the approach to calculate total costs, it seems there might be an error in the question's premise regarding the calculation of average total costs without the quantity produced. Given the ambiguity and the error in the question's setup (incorrectly formatted production function and the lack of necessary information to calculate ATC), the most accurate guidance is to clarify the calculation method for ATC requires both total costs and the quantity produced, which is not provided or calculable with the given information.

Suppose That Production for Good X Is Characterized by the Following