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Suppose that we have perfectly competitive input markets (for both capital and labor) and output markets....

Suppose that we have perfectly competitive input markets (for both capital and labor) and output markets. Firm "Tropical Juice" produces orange juice which it sells at $6. The input price that the firm faces is an hourly wage of $5 and the rental rate of $2.

Furthermore, the firm currently has a capital stock of 2.

Find the labor demanded by the firm in the short run under the following production technologies.

a) f(k,l) = k0.1l0.9

b) f(k,l) = max{k, 4l(1/2)}

c) Given the answers in part a and b, rewrite both problems as a cost minimization problem and show the labor demanded for the optimal quantity produced is the same.

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