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The production function for doors is given by: Q=(K^(a))(L^(1-a)). The wage is equal to 1 and the price of capital is equal to 5. Consider first the short-run decisions of the firm Microhard (simply fix the level of capital at K).
a) Write down the cost minimization problem that Microhard has to solve in the short run.
b) Find the contingent demand function for labor and the corresponding short-run total cost function.
c) Find the short run-average cost and the short-run marginal cost of labor. Now consider long-run decisions, where we are free to choose the optimal amount of labor and capital.
d) Write down the cost minimization problem that Microhard has to solve in the long run.
e) Find out the contingent demand function for labor and capital and the corresponding total cost function.
f) Find the long-run average cost and the long-run marginal cost of both inputs.
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