Question: Question 4 A firm's production function is given by Q = ( L 2)( K 1)where L 2and K 1. The price of labor is!

Question 4A firm's production function is given byQ= (L2)(K1)whereL2andK1. The price of labor is!wand the price of capital isr.

a) Suppose capital is fixed atK= 4in the short run. Derive the short-run total cost function.

b) Suppose the firm can choose labor and capital freely. That is, consider the scenario in the long run. Derive the demand function for labor and capital respectively using the Lagrange multiplier method.

c) Derive the long-run total cost function. In the long run, ifw=r, is the total expenditure on labor the same as the total expenditure on capital? If not, which is higher?

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