Suppose marginal utility from consumption is given by 1.2e0.4/(c0.7) and marginal utility from leisure is given by 1.6c0.3/(e0.6) and that an individual can work up to 20 hours per day at a wage of $19 per hour. A. What must be true about the wage in order for a given worker to be a participant? Give the mathematical condition which expresses this. Now write the two mathematical conditions which a participant's optimal choice must satisfy (write them in terms of c and e rather than Y and e). B. Write the mathematical formula for this worker's marginal rate of substitution between leisure and labour. For this utility function, write the reservation wage as a function in terms of non-labour income YN and time available T. If Yn=$245 then WR= . In this case will the individual choose to work? (Enter "1" for yes, "-1" for no. Enter "0" if the individual is indifferent.) If YN=$723 then WR= . In this case will the individual choose to work? (Enter "1" for yes, "-1" for no. Enter "0" if the individual is indifferent.) C. Suppose YN=$5957. Write the formula for this individual's potential income constraint. This individual will choose to work hours. So they will have hours of leisure and spend $ on consumption. D. Suppose YN=$30. Write the formula for this individual's potential income constraint. This individual will choose to work on consumption. hours, So they will have hours of leisure and spend $
Suppose marginal utility from consumption is given by 1.2e0.4/(c0.7) and marginal utility from leisure is given by 1.6c0.3/(e0.6) and that an individual can work up to 20 hours per day at a wage of $19 per hour. A. What must be true about the wage in order for a given worker to be a participant? Give the mathematical condition which expresses this. Now write the two mathematical conditions which a participant's optimal choice must satisfy (write them in terms of c and e rather than Y and e). B. Write the mathematical formula for this worker's marginal rate of substitution between leisure and labour. For this utility function, write the reservation wage as a function in terms of non-labour income YN and time available T. If Yn=$245 then WR= . In this case will the individual choose to work? (Enter "1" for yes, "-1" for no. Enter "0" if the individual is indifferent.) If YN=$723 then WR= . In this case will the individual choose to work? (Enter "1" for yes, "-1" for no. Enter "0" if the individual is indifferent.) C. Suppose YN=$5957. Write the formula for this individual's potential income constraint. This individual will choose to work hours. So they will have hours of leisure and spend $ on consumption. D. Suppose YN=$30. Write the formula for this individual's potential income constraint. This individual will choose to work on consumption. hours, So they will have hours of leisure and spend $
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
1
![Suppose marginal utility from consumption is given by 1.280.4/(c0.7) and marginal utility from leisure is given by 1.6c0.3/(e0.6) and that an individual can work up to 20
hours per day at a wage of $19 per hour.
A. What must be true about the wage in order for a given worker to be a participant? Give the mathematical condition which expresses this. Now write the two
mathematical conditions which a participant's optimal choice must satisfy (write them in terms of c and & rather than Y and e).
B. Write the mathematical formula for this worker's marginal rate of substitution between leisure and labour. For this utility function, write the reservation wage as
a function in terms of non-labour income YN and time available T. If YN=$245 then WR=
. In this case will the individual choose to work?
(Enter "1" for yes, "-1" for no. Enter "0" if the individual is indifferent.) If YN=$723 then WR=
In this case
will the individual choose to work?
(Enter "1" for yes, "-1" for no. Enter "0" if the individual is indifferent.)
C. Suppose YN=$5957. Write the formula for this individual's potential income constraint. This individual will choose to work
they will have
hours. So
hours of leisure and spend $
on consumption.
D. Suppose YN=$30. Write the formula for this individual's potential income constraint. This individual will choose to work
hours. So
they will have
hours of leisure and spend $
on consumption.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Febe5f36d-e0e7-47ef-9db8-23400c58645e%2Ff8904249-63d9-4802-b9d5-473e74ca4f1c%2F5825tu7_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose marginal utility from consumption is given by 1.280.4/(c0.7) and marginal utility from leisure is given by 1.6c0.3/(e0.6) and that an individual can work up to 20
hours per day at a wage of $19 per hour.
A. What must be true about the wage in order for a given worker to be a participant? Give the mathematical condition which expresses this. Now write the two
mathematical conditions which a participant's optimal choice must satisfy (write them in terms of c and & rather than Y and e).
B. Write the mathematical formula for this worker's marginal rate of substitution between leisure and labour. For this utility function, write the reservation wage as
a function in terms of non-labour income YN and time available T. If YN=$245 then WR=
. In this case will the individual choose to work?
(Enter "1" for yes, "-1" for no. Enter "0" if the individual is indifferent.) If YN=$723 then WR=
In this case
will the individual choose to work?
(Enter "1" for yes, "-1" for no. Enter "0" if the individual is indifferent.)
C. Suppose YN=$5957. Write the formula for this individual's potential income constraint. This individual will choose to work
they will have
hours. So
hours of leisure and spend $
on consumption.
D. Suppose YN=$30. Write the formula for this individual's potential income constraint. This individual will choose to work
hours. So
they will have
hours of leisure and spend $
on consumption.
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)
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