Suppose that a firm\'s production function is q 10L0.5K0.5 Its marginal product
ID: 1106337 • Letter: S
Question
Suppose that a firm's production function is q 10L0.5K0.5 Its marginal product functions are: MPL-5K0.50.5-0.50L MPK" 5L0.5/K0.5-0.50K 84 7 and 42- The cost of a unit of labor, w, is $50 and the cost of a unit of capital, r, is $50. Isoquants for output of 140 and 280 are illustrated in the figure to the right. Initially, the firm is producing 140 units of output and has determined that the cost-minimizing quantities of abor and capital are 14 and 14, respectively. 280 Suppose now that the firm wants to increase output to 280 units. If capital is fixed in the short run, how much labor will the firm require? 14 28 42 56 70 84 98 112 L Units of labor The firm will now require units of labor. (Enter your response rounded to two decimal places.)Explanation / Answer
q = 10L0.5K0.5
When K = 14 (capital is fixed at 14 units in short run),
q = 10L0.5(14)0.5
10L0.5(14)0.5 = 280 [Since q = 280]
L0.5(14)0.5 = 280 / 10 = 28
L0.5 = 28 / (14)0.5
L0.5 = 28 / 3.7417
L0.5 = 7.48
L = 56.00
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