A plant's production function is Q = 2KL. For this production function, MPx = 2L and MPL = 2K. The price of labor, w, is $4 and of capital, r, is $6 per unit. a) In the short run, the plant's capital is fixed at K = 5. Find the amount of labor it must employ to produce Q = 300 units of output. b) How much money is the firm losing by not having the ability to choose its level of capital optimally? Hint: Solve the long run cost minimization problem (where the firm can choose its level of both capital and labor) and compare the cost of the solution with the cost of the inputs used in the answer to part a.
A plant's production function is Q = 2KL. For this production function, MPx = 2L and MPL = 2K. The price of labor, w, is $4 and of capital, r, is $6 per unit. a) In the short run, the plant's capital is fixed at K = 5. Find the amount of labor it must employ to produce Q = 300 units of output. b) How much money is the firm losing by not having the ability to choose its level of capital optimally? Hint: Solve the long run cost minimization problem (where the firm can choose its level of both capital and labor) and compare the cost of the solution with the cost of the inputs used in the answer to part a.
Chapter10: Cost Functions
Section: Chapter Questions
Problem 10.3P
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Transcribed Image Text:A plant's production function is Q = 2KL. For this production function, MPx = 2L and MPL = 2K.
The price of labor, w, is $4 and of capital, r, is $6 per unit.
a) In the short run, the plant's capital is fixed at K = 5. Find the amount of labor it must
employ to produce Q = 300 units of output.
b) How much money is the firm losing by not having the ability to choose its level of capital
optimally? Hint: Solve the long run cost minimization problem (where the firm can
choose its level of both capital and labor) and compare the cost of the solution with the
cost of the inputs used in the answer to part a.
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