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

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Quizplus · Accepted Answer

Average Fixed Cost (AFC) is calculated as the total fixed costs divided by the quantity produced. In this scenario, the fixed input is capital (K), and we are told that 9 units of capital are used, with a per-unit rental rate of $15. Therefore, the total fixed cost is 9 units * $15/unit = $135. The production function does not explicitly provide the quantity produced (Q), but for calculating AFC, we only need to know the total fixed costs and the quantity. Since the quantity isn't given, we assume it's related to the inputs. However, for AFC, we divide the total fixed costs by the quantity produced. Without the quantity, we directly calculate AFC based on the information given about fixed costs and the units of capital. The mistake here is assuming we need to calculate based on quantity, but we actually need the formula for AFC, which is total fixed costs divided by the number of units of capital when considering capital as the basis in this context. Thus, with $135 total fixed costs for the capital and considering the context might imply looking at the cost per unit of capital rather than per unit of output, the calculation provided was incorrect for determining AFC without the quantity of output. The correct approach to find AFC without the quantity of output would involve knowing how AFC is traditionally calculated, which is not applicable here due to the lack of output quantity, leading to a misunderstanding in the explanation. Therefore, without the quantity of output, we cannot accurately calculate AFC as traditionally defined, pointing towards a misinterpretation in the initial explanation.

Suppose That Production for Good X Is Characterized by the Following