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 fixed 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 fixed costs.

Question

Quizplus · Accepted Answer

The average fixed cost (AFC) is calculated by dividing the total fixed costs by the quantity produced. In this case, the fixed input is capital (K), and we are given that 81 units of capital are used at a per-unit rental rate of $25. Therefore, the total fixed cost is 81 units * $25/unit = $2025. However, to calculate the average fixed cost, we need the quantity produced (Q), which is not provided in the question. Despite this, the question asks specifically for the average fixed cost of using the capital, not in relation to the quantity produced. Thus, without needing to calculate Q, we can directly calculate the average fixed cost per unit of capital, which is simply the cost per unit of capital since it's fixed. This interpretation might be misleading because typically AFC is calculated per unit of output, not per unit of input. Given the information and typical understanding of AFC, there seems to be a misunderstanding in how AFC is being asked for, leading to the conclusion that there might be insufficient information or a misinterpretation in the question's phrasing. However, interpreting the question as asking for the cost per unit of capital, it's $25, which doesn't match any of the provided options directly in terms of calculating traditional AFC. The mistake in my explanation is assuming the question asks for AFC in the traditional sense per unit of output, but it's actually asking for the total fixed cost divided by the number of units of capital, which still wouldn't directly lead to any of the given answers without considering the quantity produced. Given the confusion and typical calculation methods for AFC, the correct approach based on the standard formula cannot be applied without knowing the quantity produced, leading to a reconsideration of the provided options.

Suppose That Production for Good X Is Characterized by the Following