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Suppose that a firm uses capital (K) and labor (L) to produce widgets, and that the...

Suppose that a firm uses capital (K) and labor (L) to produce widgets, and that the production function for widgets is given by

Q = K 1/3L1/2

Assume that r = $4 and w = $4, where r is the price of capital and w is the wage rate. Finally, suppose that the price of widgets, p, is $8.

a) Suppose that K = 64 in the short run. Given that w = 4, how many workers should this firm hire?

b) Now find the optimal quantity of labor and capital in the long-run (i.e. capital is no longer fixed).

c) Finally, suppose that the price of labor increases so that w = 6. What are the firm’s new optimal quantities of labor and capital (in the long run)? Given your findings, would you say that capital and labor are substitutes or complements? Explain.

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