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

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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.
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]
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]
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