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.
Microeconomics A Contemporary Intro
10th Edition
ISBN:9781285635101
Author:MCEACHERN
Publisher:MCEACHERN
Chapter7: Production And Cost In The Firm
Section: Chapter Questions
Problem 18PAE
Related questions
Question
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e9f74db-68ca-409f-99ca-c3b15e89955c%2F468ef724-a1ed-4778-b6e6-20a7a48cd8ea%2Fo31xwew_processed.jpeg&w=3840&q=75)
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.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Economics (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781337617383/9781337617383_smallCoverImage.gif)
Economics (MindTap Course List)
Economics
ISBN:
9781337617383
Author:
Roger A. Arnold
Publisher:
Cengage Learning
![Economics (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781337617383/9781337617383_smallCoverImage.gif)
Economics (MindTap Course List)
Economics
ISBN:
9781337617383
Author:
Roger A. Arnold
Publisher:
Cengage Learning
![Microeconomics](https://www.bartleby.com/isbn_cover_images/9781337617406/9781337617406_smallCoverImage.gif)