Question 3 Part (c)

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Question 3 A rm's production function is Q = min(L,4K ). The price of labor is w and the price of capital is r. a) From the production function given above to the production function Q = min(4L, K), is it a technological progress? (No explanation is needed.) b) From now on, assume the production function is still Q = min(L,4K ). Derive the demand function for labor and capital respectively. How does the demand for capital change with the price of labor? c) Derive the long-run total cost function. Draw the long-run expansion path. Label your graph clearly. d) Suppose capital is xed at K = 3 in the short run. Derive the short-run total cost function. For simplicity, assume the xed cost is sunk in the short run. At what output level is K = 3 a cost-minimizing choice of capital in the long run