# Answer to Question #57137 in Microeconomics for asif

Question #57137

a) Derive the expansion path for a firm with the production function Q=10K^0.6 L^0.4 and input prices r = 10 and w = 5.

b) The firm is currently using fifty units of capital and forty units of labor. Is this an efficient input combination?

b) The firm is currently using fifty units of capital and forty units of labor. Is this an efficient input combination?

Expert's answer

a) Derive the expansion path for a firm with the production function Q=10K^0.6 L^0.4 and input prices r = 10 and w = 5.

Expansion path is a curve in a graph with quantities of two inputs, typically capital and labor, plotted on the axes. in our case the expansion path is the same as the production function Q = 10K^0.6 L^0.4.

b) The firm is currently using fifty units of capital and forty units of labor. This input combination is efficient, if the total output Q is maximized, so Q = 10K^0.6 L^0.4 = max, Q' = 0, 6L^0.4/K^0.4 = 0, 4K^0.6/L^0.6.

Expansion path is a curve in a graph with quantities of two inputs, typically capital and labor, plotted on the axes. in our case the expansion path is the same as the production function Q = 10K^0.6 L^0.4.

b) The firm is currently using fifty units of capital and forty units of labor. This input combination is efficient, if the total output Q is maximized, so Q = 10K^0.6 L^0.4 = max, Q' = 0, 6L^0.4/K^0.4 = 0, 4K^0.6/L^0.6.

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