A consumer has a utility function U (x, y) = xy³. a. Find MRS. b. Find Marshallian demand for x and y. c. Find Indirect Utility. d. Find the Expenditure Function.
A consumer has a utility function U (x, y) = xy³. a. Find MRS. b. Find Marshallian demand for x and y. c. Find Indirect Utility. d. Find the Expenditure Function.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Please explain into details. Thank you!
![1. Theory of the Consumer
A consumer has a utility function U (x, y) = xy³.
a. Find MRS.
b. Find Marshallian demand for x and y.
c. Find Indirect Utility.
d. Find the Expenditure Function.
e. Find Compensated (Hicksian) Demand for x using the expenditure function and
Marshallian demand for x.
f. Find Compensated (Hicksian) Demand for x using expenditure minimization, and
show that it is the same.
g. Write out the Slutsky Equation for good x, evaluate the terms, and show that both
sides of the equation are equal.
For the following parts, set PÅ = Py = 1 and I = 1. Then impose a tax on x of size t = 1.
h. How much revenue is collected?
i. Suppose the government collected the same revenue by taxing income (I) directly.
How much better off would the consumer be?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F362a762f-914f-42d1-b0fa-542c2b1764ea%2F2b75ad03-953e-4afa-9f26-b9b0cbeaafc3%2Frqgfnar_processed.png&w=3840&q=75)
Transcribed Image Text:1. Theory of the Consumer
A consumer has a utility function U (x, y) = xy³.
a. Find MRS.
b. Find Marshallian demand for x and y.
c. Find Indirect Utility.
d. Find the Expenditure Function.
e. Find Compensated (Hicksian) Demand for x using the expenditure function and
Marshallian demand for x.
f. Find Compensated (Hicksian) Demand for x using expenditure minimization, and
show that it is the same.
g. Write out the Slutsky Equation for good x, evaluate the terms, and show that both
sides of the equation are equal.
For the following parts, set PÅ = Py = 1 and I = 1. Then impose a tax on x of size t = 1.
h. How much revenue is collected?
i. Suppose the government collected the same revenue by taxing income (I) directly.
How much better off would the consumer be?
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 6 steps with 47 images
![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
Please solve from Part E to Part I. Kindly explain in detail, please. Thank you!
![## 1. Theory of the Consumer
### A consumer has a utility function \( U(x,y) = xy^3 \).
**a. Find MRS.**
**b. Find Marshallian demand for \( x \) and \( y \).**
**c. Find Indirect Utility.**
**d. Find the Expenditure Function.**
**e. Find Compensated (Hicksian) Demand for \( x \) using the expenditure function and Marshallian demand for \( x \).**
**f. Find Compensated (Hicksian) Demand for \( x \) using expenditure minimization, and show that it is the same.**
**g. Write out the Slutsky Equation for good \( x \), evaluate the terms, and show that both sides of the equation are equal.**
For the following parts, set \( p_x = p_y = 1 \) and \( I = 1 \). Then impose a tax on \( x \) of size \( t = 1 \).
**h. How much revenue is collected?**
**i. Suppose the government collected the same revenue by taxing income (I) directly. How much better off would the consumer be?**](https://content.bartleby.com/qna-images/question/362a762f-914f-42d1-b0fa-542c2b1764ea/d5f57d52-6dc4-4e46-9d8d-7fd8ff40fbe7/r7ifchqo_thumbnail.png)
Transcribed Image Text:## 1. Theory of the Consumer
### A consumer has a utility function \( U(x,y) = xy^3 \).
**a. Find MRS.**
**b. Find Marshallian demand for \( x \) and \( y \).**
**c. Find Indirect Utility.**
**d. Find the Expenditure Function.**
**e. Find Compensated (Hicksian) Demand for \( x \) using the expenditure function and Marshallian demand for \( x \).**
**f. Find Compensated (Hicksian) Demand for \( x \) using expenditure minimization, and show that it is the same.**
**g. Write out the Slutsky Equation for good \( x \), evaluate the terms, and show that both sides of the equation are equal.**
For the following parts, set \( p_x = p_y = 1 \) and \( I = 1 \). Then impose a tax on \( x \) of size \( t = 1 \).
**h. How much revenue is collected?**
**i. Suppose the government collected the same revenue by taxing income (I) directly. How much better off would the consumer be?**
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