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A firm’s production function is Q! = min(4L ,5K ). The price of labor is w...

A firm’s production function is Q! = min(4L ,5K ). The price of labor is w and the price of capital is r.

a) Derive the demand function of labor and capital respectively. How does the demand of capital change with the price of capital?

b) Derive the long-run total cost function. Write down the equation of the long-run expansion path.

c) Suppose capital is fixed at K = 8 in the short run. Derive the short-run total cost function. At what output level is K = 8 a cost-minimizing choice of capital in the long run?

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