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Answer to Question #12070 in Microeconomics for Temesgen

Question #12070
the production function of the firm is 411/2k1/2. the cost of labor is $40 per unit and the cost of using capital is $ 10 per unit determine the amount of labor and capital that should be used in order to minimize the cost to produce 40 units of output.
Expert's answer
The cost-minimizing combination of capital and labor is the one where
Marginal product of labor is 4K
The marginal product of capital is 4L
The marginal rate of technical substitution is
4K/4L= K/L
To determine the optimal capital-labor ratio set the marginal rate of technical substitution equal to the ratio of wage rate to rental rate of capital
Substitute for L in the production function and solve where K yields an output of 40 units
40 = 4*4K1/2*K1/2

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