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Short-run factor demand

A price-taking firm (p = 100) chooses an amount of labor to employ that maximizes its profits. It has a fixed amount of capital (K= 100), and constant returns to scale CobbDouglass production function: q(L, K) = L ^(1/2) K ^(1/2). The wage rate and rental rate of capital are 10 (w = r = 10).

(a) Set up the profit function.

(b) Solve for the optimal level of labor IN THE SHORT RUN.

(c) With additional capital, would the optimal level of labor increase or decrease?

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Namita kumari
Namita kumariLv6
28 Sep 2019

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Long-run factor demand

A price-taking firm (p = 100) chooses amounts of labor and capital that maximize its profits. It has decreasing returns to scale Cobb-Douglass production function: q(L, K) = L ^(1/6) K ^(1/8). The wage rate and rental rate of capital are 10 (w = r = 10).

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(b) Provide the two profit maximization conditions for this case (no need to solve for L — , K— ).

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(a) Set up the profit function in terms of labor only.

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Another price taking firm chooses its inputs to maximize long-run profits. Labor and capital are substitutes in production and both exhibit decreasing returns to scale, q(L, K) = L^(1/2) + K^(1/2) . The output price is 100 and the price of each of the inputs is 10.

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(a) Set up the profit function in terms of labor only.

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