Consider a countries Am- This question is about the Solow growth model f brosia and Burunda. Ambrosia's GDP per worker is 1.96 times that of Burunda. The ratio of investment to output is 0.35 in Ambrosia, and in Burunda it is 0.25. Labour supply is constant over time in both countries. So is total factor productivity (TFP). Assume both countries are in their respective steady states. Suppose output in each country i = A, B is produced according to Yit = A,KL-a where Y is output for country i at time t, A, is TFP for country i, Kit is capital stock in country i at time t, and L, is labor in country i. Capital is accumulated according to AKit+1=8iYit-dKit Assume that the depreciation rate and the capital share are same across two countries
Consider a countries Am- This question is about the Solow growth model f brosia and Burunda. Ambrosia's GDP per worker is 1.96 times that of Burunda. The ratio of investment to output is 0.35 in Ambrosia, and in Burunda it is 0.25. Labour supply is constant over time in both countries. So is total factor productivity (TFP). Assume both countries are in their respective steady states. Suppose output in each country i = A, B is produced according to Yit = A,KL-a where Y is output for country i at time t, A, is TFP for country i, Kit is capital stock in country i at time t, and L, is labor in country i. Capital is accumulated according to AKit+1=8iYit-dKit Assume that the depreciation rate and the capital share are same across two countries
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
![Consider a countries Am-
This question is about the Solow growth model S
brosia and Burunda. Ambrosia's GDP per worker is 1.96 times that of Burunda. The ratio
of investment to output is 0.35 in Ambrosia, and in Burunda it is 0.25. Labour supply is
constant over time in both countries. So is total factor productivity (TFP). Assume both
countries are in their respective steady states.
Suppose output in each country i = A, B is produced according to
Yt = A,KGLa
where Y; is output for country i at time t, A, is TFP for country i, Ką is capital stock in
country i at time t, and Li is labor in country i. Capital is accumulated according to
AKit+1 = 5;Yit – dK#
Assume that the depreciation rate and the capital share are same across two countries.
(a) Derive an expression for the steady state value of output per worker (Y/L) in each
country i in terms of AA, 5A, d and a for country A, and in terms of AB, SB, d and a
for country B.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc50dde5e-f221-4c49-9c14-7828fedb2c55%2F83737095-8a85-4e6d-a042-7d39d7cda1d7%2F50ddswi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider a countries Am-
This question is about the Solow growth model S
brosia and Burunda. Ambrosia's GDP per worker is 1.96 times that of Burunda. The ratio
of investment to output is 0.35 in Ambrosia, and in Burunda it is 0.25. Labour supply is
constant over time in both countries. So is total factor productivity (TFP). Assume both
countries are in their respective steady states.
Suppose output in each country i = A, B is produced according to
Yt = A,KGLa
where Y; is output for country i at time t, A, is TFP for country i, Ką is capital stock in
country i at time t, and Li is labor in country i. Capital is accumulated according to
AKit+1 = 5;Yit – dK#
Assume that the depreciation rate and the capital share are same across two countries.
(a) Derive an expression for the steady state value of output per worker (Y/L) in each
country i in terms of AA, 5A, d and a for country A, and in terms of AB, SB, d and a
for country B.
![(b) Suppose a = 1/3. What must be the ratio of TFP in country A to TFP in country
B (i.e. AA/AB) in order to fit the facts noted at the beginning of the question.
i jAssume that the depreciation rate and the capital share are same across two
couïtries.]
(c) Assume TFP is equal across the two countries. If Burunda increases its savings rate
to 0.35, what will be the ratio of output ner worker (Y/L) in Ambrosia relative to
Burunda in the new steady state? ( y [Assume that the depreciation rate and
the capital share are same across two countries.]
10
10
(d) Using a Solow diagram, show the effect of an increase in savings rate in country B on
capital per worker. r
[Hint: you do not necgr to plot variables for country A in your answer]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc50dde5e-f221-4c49-9c14-7828fedb2c55%2F83737095-8a85-4e6d-a042-7d39d7cda1d7%2F9vj4xii_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(b) Suppose a = 1/3. What must be the ratio of TFP in country A to TFP in country
B (i.e. AA/AB) in order to fit the facts noted at the beginning of the question.
i jAssume that the depreciation rate and the capital share are same across two
couïtries.]
(c) Assume TFP is equal across the two countries. If Burunda increases its savings rate
to 0.35, what will be the ratio of output ner worker (Y/L) in Ambrosia relative to
Burunda in the new steady state? ( y [Assume that the depreciation rate and
the capital share are same across two countries.]
10
10
(d) Using a Solow diagram, show the effect of an increase in savings rate in country B on
capital per worker. r
[Hint: you do not necgr to plot variables for country A in your answer]
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 4 steps with 14 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
![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