Let the consumer have the utility function a. Show that the utility maximizing demands are and b. Letting p1 = p2 = 1, use the inverse elasticity rule to show that the optimal tax rates are related by c. Setting w = 100, r1 = 0:75, and r2 = 0:5, find the tax rates required to achieve revenue of R = 0:5 and R = 10. d. Calculate the proportional reduction in demand for the two goods comparing the no-tax position with the position after imposition of the optimal taxes for both revenue levels. Comment on the results.
Let the consumer have the utility function a. Show that the utility maximizing demands are and b. Letting p1 = p2 = 1, use the inverse elasticity rule to show that the optimal tax rates are related by c. Setting w = 100, r1 = 0:75, and r2 = 0:5, find the tax rates required to achieve revenue of R = 0:5 and R = 10. d. Calculate the proportional reduction in demand for the two goods comparing the no-tax position with the position after imposition of the optimal taxes for both revenue levels. Comment on the results.
Economics (MindTap Course List)
13th Edition
ISBN:9781337617383
Author:Roger A. Arnold
Publisher:Roger A. Arnold
Chapter19: Elasticity
Section: Chapter Questions
Problem 13QP
Related questions
Question
Let the consumer have the utility function
a. Show that the utility maximizing demands are
and
b. Letting p1 = p2 = 1, use the inverse elasticity rule to show that the optimal tax rates are related by
c. Setting w = 100, r1 = 0:75, and r2 = 0:5, find the tax rates required to achieve revenue of R = 0:5 and R = 10.
d. Calculate the proportional reduction in demand for the two goods comparing the no-tax position with the position after imposition of the optimal taxes for both revenue levels. Comment on the results.
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.
Step 1: State the given information
VIEWStep 2: prove that the utility maximizing demands x1 and x2
VIEWStep 3: Use the inverse elasticity rule to show that the optimal tax rates
VIEWStep 4: Find the tax rates required to achieve the following revenue
VIEWStep 5: Calculate the proportional reduction in demand before and after tax
VIEWSolution
VIEWStep by step
Solved in 6 steps with 30 images
![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
![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)
![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)