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A firm's production function is given by Q= (L - 2)(K - 1) where L≥ 2 and K ≥ 1. The price of labor is !w and the price of capital is r.
a) Suppose capital is fixed at K = 4 in 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, if w = r, is the total expenditure on labor the same as the total expenditure on capital? If not, which is higher?
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