Show your work whenever possible. A firm has the following production function. Q=K.√L the rent (cost of capital) is $100 and wage (cost of labor) is $20. In the short run, the firm uses K=2. Please answer the following questions. - Please derive the total cost as functions of Q in the short run. (Hint: first derive the use of labor as a function of Q.) - If the market price is $30, please determine the short-run profit-maximizing output and profit. - Please derive the total cost as functions of Q in the long run. (Hint: consider first condition in the cost-minimization problem, and then derive the use of K and Las a function of Q.)
Show your work whenever possible. A firm has the following production function. Q=K.√L the rent (cost of capital) is $100 and wage (cost of labor) is $20. In the short run, the firm uses K=2. Please answer the following questions. - Please derive the total cost as functions of Q in the short run. (Hint: first derive the use of labor as a function of Q.) - If the market price is $30, please determine the short-run profit-maximizing output and profit. - Please derive the total cost as functions of Q in the long run. (Hint: consider first condition in the cost-minimization problem, and then derive the use of K and Las a function of Q.)
Chapter10: Cost Functions
Section: Chapter Questions
Problem 10.3P
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Transcribed Image Text:Show your work whenever possible.
A firm has the following production function.
Q=K.√L
the rent (cost of capital) is $100 and wage (cost
of labor) is $20. In the short run, the firm uses
K=2. Please answer the following questions.
- Please derive the total cost as functions of Q in
the short run. (Hint: first derive the use of labor
as a function of Q.)
- If the market price is $30, please determine the
short-run profit-maximizing output and profit.
- Please derive the total cost as functions of Q in
the long run. (Hint: consider first condition in the
cost-minimization problem, and then derive the
use of K and Las a function of Q.)
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