Suppose that the hourly wage is Dollars 10 and the price of each unit of capital

Question

Suppose that the hourly wage is Dollars 10 and the price of each unit of capital is Dollars 20. The price of output is constant at Dollars 40 per unit. The production function is f(L,K) = L1/2 K1/4, where L is labor and K is capital, so that marginal product of each input is, respectively, MP L = 1/2L-1/2 K1/4 MP K = 1/4L1/2 K-3/4 If the current capital stock is fixed at 1,600 units, how much labor should the firm employ to maximize its profit in the short run? What is the long run labor demand in the long run?

Explanation / Answer

price = MR = $40
FOC : w = (1/2)(1600/L)^(1/2) * 40 = 800/L^1/2
L = 10,000
1600^(1/2) * 8000^(1/4) = 378.29 output

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