Question 4 Consider the production function Y = ƒ (L) = e¹¹ (L² − 8) where Y = units of output, L = units of labour (a) Calculate marginal product of labour f'(L). (b) Measuring L on X-axis and Y on the Y-axis, locate the stationary points, giving the exact L and Y coordinates. (c) Use the second derivatives test to classify the stationary points. (d) Find the equation of the normal to the curve at the positive L-intercept.
Question 4 Consider the production function Y = ƒ (L) = e¹¹ (L² − 8) where Y = units of output, L = units of labour (a) Calculate marginal product of labour f'(L). (b) Measuring L on X-axis and Y on the Y-axis, locate the stationary points, giving the exact L and Y coordinates. (c) Use the second derivatives test to classify the stationary points. (d) Find the equation of the normal to the curve at the positive L-intercept.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
I can't do this question. Please help. thank you!
![Question 4
Consider the production function Y = = f(L) = e¹ (L² − 8)
where Y = units of output, L = units of labour
(a) Calculate marginal product of labour f'(L).
(b) Measuring L on X-axis and Y on the Y-axis, locate the stationary points, giving the exact
L and Y coordinates.
(c) Use the second derivatives test to classify the stationary points.
(d) Find the equation of the normal to the curve at the positive L-intercept.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F377b406c-f666-4c6a-b576-22801b03459e%2F28d2b590-adfe-41a0-9c1d-23d1478160c3%2F2l9u27_processed.png&w=3840&q=75)
Transcribed Image Text:Question 4
Consider the production function Y = = f(L) = e¹ (L² − 8)
where Y = units of output, L = units of labour
(a) Calculate marginal product of labour f'(L).
(b) Measuring L on X-axis and Y on the Y-axis, locate the stationary points, giving the exact
L and Y coordinates.
(c) Use the second derivatives test to classify the stationary points.
(d) Find the equation of the normal to the curve at the positive L-intercept.
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 5 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question
'' Setting f'(L) = 0:
(2L + L2 - 8) * eL = 0
To find the exact L coordinates, we need to solve the equation (2L + L2 - 8) = 0. The solutions to this quadratic equation will give us the L values for the stationary points. ''
why didn't you do a quadratic equation with the eL, why is not (2L + L2 - 8 ) * eL = 0
Solution
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Recommended textbooks for you
![ENGR.ECONOMIC ANALYSIS](https://compass-isbn-assets.s3.amazonaws.com/isbn_cover_images/9780190931919/9780190931919_smallCoverImage.gif)
![Principles of Economics (12th Edition)](https://www.bartleby.com/isbn_cover_images/9780134078779/9780134078779_smallCoverImage.gif)
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
![Engineering Economy (17th Edition)](https://www.bartleby.com/isbn_cover_images/9780134870069/9780134870069_smallCoverImage.gif)
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
![ENGR.ECONOMIC ANALYSIS](https://compass-isbn-assets.s3.amazonaws.com/isbn_cover_images/9780190931919/9780190931919_smallCoverImage.gif)
![Principles of Economics (12th Edition)](https://www.bartleby.com/isbn_cover_images/9780134078779/9780134078779_smallCoverImage.gif)
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
![Engineering Economy (17th Edition)](https://www.bartleby.com/isbn_cover_images/9780134870069/9780134870069_smallCoverImage.gif)
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
![Principles of Economics (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305585126/9781305585126_smallCoverImage.gif)
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
![Managerial Economics: A Problem Solving Approach](https://www.bartleby.com/isbn_cover_images/9781337106665/9781337106665_smallCoverImage.gif)
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
![Managerial Economics & Business Strategy (Mcgraw-…](https://www.bartleby.com/isbn_cover_images/9781259290619/9781259290619_smallCoverImage.gif)
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education