Suppose that a firm\'s production function is: 1211 98- q-10L0·5K0.5 Its margina

Question

Suppose that a firm's production function is: 1211 98- q-10L0·5K0.5 Its marginal product functions are: MPL = 5K0.5/0.5 = 0.5g/L 70- and MPK" 5L0.5/K0.5 = 0.5g/K. The cost of a unit of labor, w, is $20 and the cost of a unit of capitalr, is $80. lsoquants for output of 140 and 280 are illustrated in the figure to the right. nitially, 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. q 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? 0 14 28 42 56 70 84 98 112 L Units of labor The firm will now require 20 units of labor. (Enter your response rounded to two decimal places.)

Explanation / Answer

q = 10L0.5K0.5

When K = 7 (capital being fixed in short run, at cost-minimizing level of capital at 7 units already found out),

q = 10L0.5(7)0.5

10L0.5(7)0.5 = 280 [Since q = 280]

L0.5(7)0.5 = 280 / 10 = 28

L0.5 = 28 / (7)0.5

L0.5 = 28 / 2.6458

L0.5 = 10.583

Squaring both sides,

L = 112.00

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