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.

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Quizplus · Accepted Answer

The formula for average fixed cost (AFC) is Total Fixed Cost (TFC) divided by Quantity (Q). In the short run, K is fixed and does not change, so TFC is equal to rK. Given r = $25 and K = 81 units of capital, TFC = rK = ($25/unit) × (81 units) = $2025 To find Q, substitute the given values into the production function: Q = K^0.5L^0.5 Q = (81)1(9)1(10.5)1(1)0.5(81)1(9)1(10.5)1(1)0 Q = 2295.94 Therefore, AFC = TFC/Q = $2025/2295.94 ≈ $0.88 per unit. To convert this to per unit of labor input, divide by labor input: AFC = $0.88/unit ÷ 9 units = $0.0978 ≈ $0.10 per unit of labor input To convert this to average fixed cost per dollar of output, divide by the average product of labor: APL = Q/L = 2295.94/9 = 255.1 AFC/QAPL = ($0.88/unit)/255.1 units = $0.00344 per dollar of output Therefore, the AFC of using 81 units of capital and 9 units of labor is $0.10 per unit of labor input or $0.00344 per dollar of output. Multiplying this by 100 gives an AFC of 10 cents per dollar of output.

Suppose That Production for Good X Is Characterized by the Following