Question: Consider the following production function: Q = 3K 1 3L 1 3 , with marginal products given by MPL = K 1 3 L 2

Consider the following production function: Q = 3K 1 3L 1 3 , with marginal products given by MPL = K 1 3 L 2 3 and MPK = L 1 3 K 2 3 . Define the unit prices of L and K as w and r, respectively. Finally, assume that the firm takes the price of its product, p, as given and maximizes profits.

(a) [4 marks] Imagine capital is fixed at K0 = 1 in the short run. What is the short-run cost function of the firm? Explain briefly.

(b) [7 marks] What is the long-run cost function of the firm?

(d) [6 marks] What is the profit function of the firm?

(e) [5 marks] Now suppose that set-up costs are 1. What is the shut down rule of the firm when r = w = 1?

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