Question 3 A rm’s production function is Q = min(L,6K ). The price of labor is w and the price of capital is r. a) Derive the demand function for

Need help with question 3 please. Cant seem to get an answer. Much appreciated.

Question 3 A firm’s production function is Q = min(L,6K ). The price of labor is w and theprice of capital is r. a) Derive the demand function for labor and capital respectively. How does the demand forlabor change with the price of labor? National University of Singapore EC2101 Nficroeconomic Analysis IDepartment of Economics Semester 2 AY 2018/2019 b) Derive the long-run total cost function. Draw the long-run expansion path. Label yourgraph clearly. c) Suppose capital is fixed at K = 2 in the short run. Derive the short-run total cost function.For simplicity, assume the fixed cost is sunk in the short run. At what output level is K = 2 acost-minimizing choice of capital in the long run? Question 4 A firm’s production function is given by Q = L(2K — 5) where K 2 2.5. The price of labor is w and the price of capital is r. a) Suppose capital is fixed at K = 3 in the short run. Derive the short-run total cost function.h) Suppose the firm can choose labor and capital freely. Derive the demand function for laborand capital respectively using the Lagrange multiplier method. Solve for the Lagrangemultiplier. c) Derive the long-run total cost function. When labor becomes more expensive, how doesthe total expenditure on labor change?

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