Exercise 11 Quest its marginal product functions are -5K0.5/0.5 = 0.5g/L and MPK
ID: 1105989 • Letter: E
Question
Exercise 11 Quest its marginal product functions are -5K0.5/0.5 = 0.5g/L and MPK-5L0.5/K0.5-0.50K The cost of a unit of labor, w, is $20 and the cost of a unit of capital, r, is $80. 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 labor and capital are 28 and 7, respectively. 42 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? The firm will now require 112.00 units of labor. (Enter your response rounded to two decimal places.) If the marginal rate of technical substitution is T, find the optimal level of capital and labor required to q 280 0 14 28 42 56 70 8498 112 L, Units of labor produce the 280 units of output. The optimal level of capital is units and the optimal level of labor isunits. (Enter your responses as integers.) Enter your answer in the edit fields and then click Check AnswerExplanation / Answer
Cost is minimized when MRTS = w/r = $20 / $80 = 1/4
K / L = 1/4
L = 4K
Substituting in production function,
10L0.5K0.5 = 280
L0.5K0.5 = 280 / 10 = 28
(4K)0.5K0.5 = 28
40.5K0.5K0.5 = 28
2 x K = 28
K = 28 / 2 = 14 units
L = 4K = 4 x 14 = 56 units
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