Consider a pure exchange economy with two goods, x and y, and two consumers, A and B. Consumer A cares not only about her own consumption, but also benefits from B consuming good r. (For example, you can think of good x as art that, when consumed by B, A sometimes has the opportunity to see.) The consumers' utility functions are and u₁(x, y) = XAYA+XB up(x, y) = xBYB, respectively, where (A, YA) is the bundle consumed by A and (TB, YB) is the bundle consumed by B. The endowments are (2, 1) for consumer 1, and (1,1) for consumer 2. You may use without proof the fact that a consumer with utility u(x, y) = xªy has Marshallian demand x(p,w) = ((a+b)p₁¹ (a+b)p²) · aw (a) Find a Walrasian equilibrium. Assume as usual that each consumer chooses only her own bundle. (Note that the value of TB does not affect A's optimal choice.) (b) Is the allocation in the Walrasian equilibrium you found in part (a) Pareto optimal? Explain carefully.
Consider a pure exchange economy with two goods, x and y, and two consumers, A and B. Consumer A cares not only about her own consumption, but also benefits from B consuming good r. (For example, you can think of good x as art that, when consumed by B, A sometimes has the opportunity to see.) The consumers' utility functions are and u₁(x, y) = XAYA+XB up(x, y) = xBYB, respectively, where (A, YA) is the bundle consumed by A and (TB, YB) is the bundle consumed by B. The endowments are (2, 1) for consumer 1, and (1,1) for consumer 2. You may use without proof the fact that a consumer with utility u(x, y) = xªy has Marshallian demand x(p,w) = ((a+b)p₁¹ (a+b)p²) · aw (a) Find a Walrasian equilibrium. Assume as usual that each consumer chooses only her own bundle. (Note that the value of TB does not affect A's optimal choice.) (b) Is the allocation in the Walrasian equilibrium you found in part (a) Pareto optimal? Explain carefully.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
please only do: if you can teach explain each part
![Consider a pure exchange economy with two goods, x and y, and two consumers, A and B.
Consumer A cares not only about her own consumption, but also benefits from B consuming
good r. (For example, you can think of good x as art that, when consumed by B, A sometimes
has the opportunity to see.) The consumers' utility functions are
and
u₁(x, y) = TAYA+IB
3
uв(x, y): = I BYB,
respectively, where (XA, YA) is the bundle consumed by A and (TB, YB) is the bundle consumed
by B. The endowments are (2, 1) for consumer 1, and (1,1) for consumer 2. You may use
without proof the fact that a consumer with utility u(x, y) = xªy has Marshallian demand
x(p,w) = ((a+b)p₁' (a+b)p²).
(a) Find a Walrasian equilibrium. Assume as usual that each consumer chooses only her
own bundle. (Note that the value of в does not affect A's optimal choice.)
(b) Is the allocation in the Walrasian equilibrium you found in part (a) Pareto optimal?
Explain carefully.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa1ab2968-d288-4fd8-b87c-74963c459231%2F5e249ac8-2a80-49b0-92fe-d203d0deee98%2Frsmjfle_processed.png&w=3840&q=75)
Transcribed Image Text:Consider a pure exchange economy with two goods, x and y, and two consumers, A and B.
Consumer A cares not only about her own consumption, but also benefits from B consuming
good r. (For example, you can think of good x as art that, when consumed by B, A sometimes
has the opportunity to see.) The consumers' utility functions are
and
u₁(x, y) = TAYA+IB
3
uв(x, y): = I BYB,
respectively, where (XA, YA) is the bundle consumed by A and (TB, YB) is the bundle consumed
by B. The endowments are (2, 1) for consumer 1, and (1,1) for consumer 2. You may use
without proof the fact that a consumer with utility u(x, y) = xªy has Marshallian demand
x(p,w) = ((a+b)p₁' (a+b)p²).
(a) Find a Walrasian equilibrium. Assume as usual that each consumer chooses only her
own bundle. (Note that the value of в does not affect A's optimal choice.)
(b) Is the allocation in the Walrasian equilibrium you found in part (a) Pareto optimal?
Explain carefully.
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 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