Question I - Solow Model without Population or Technology Growth Consider the Solow growth model with no population growth and no technology growth, i.e., n = x = 0. Output is created by a Cobb-Douglas production function combining Labor, Lt, and capital, Kt, such that output Yt is given by Y₁ = A+ KL 1-α = = Recall that, without population growth, Lt Lo and assume that Lo 1. Furthermore, recall that, without technology growth, At Ao and assume that A0 = 1. The law of motion for capital per worker is = kt+1 = (1 − 6) kt + sAtko. (1) Assume that the savings rate is s = 0.2, the depreciation rate is 8 = 0.1, and that the capital share is a = 0.3. 1. Use equation (1) to solve for the steady state level of capital, kss, (hint, replace kss in that equation on both sides) kss = What is the steady state level of capital? (Replace the numbers in the expression) = 2. Suppose that this economy starts with ko 1. Does capital grow or fall over time? What is the maximum level of capital per capita this economy will ever have? 3. Suppose that this economy was at its steady state level of capital kss when it is hit by a war, such as the one in Ukraine. After the end of the war the economy must start anew with ko 0.9kss. Use equation (1) to compute kt for the next 4 years. By how much does the capital per work recover by the fourth year? . 4. How much would Ukraine's GDP be 4 years after the end of the war? =
Question I - Solow Model without Population or Technology Growth Consider the Solow growth model with no population growth and no technology growth, i.e., n = x = 0. Output is created by a Cobb-Douglas production function combining Labor, Lt, and capital, Kt, such that output Yt is given by Y₁ = A+ KL 1-α = = Recall that, without population growth, Lt Lo and assume that Lo 1. Furthermore, recall that, without technology growth, At Ao and assume that A0 = 1. The law of motion for capital per worker is = kt+1 = (1 − 6) kt + sAtko. (1) Assume that the savings rate is s = 0.2, the depreciation rate is 8 = 0.1, and that the capital share is a = 0.3. 1. Use equation (1) to solve for the steady state level of capital, kss, (hint, replace kss in that equation on both sides) kss = What is the steady state level of capital? (Replace the numbers in the expression) = 2. Suppose that this economy starts with ko 1. Does capital grow or fall over time? What is the maximum level of capital per capita this economy will ever have? 3. Suppose that this economy was at its steady state level of capital kss when it is hit by a war, such as the one in Ukraine. After the end of the war the economy must start anew with ko 0.9kss. Use equation (1) to compute kt for the next 4 years. By how much does the capital per work recover by the fourth year? . 4. How much would Ukraine's GDP be 4 years after the end of the war? =
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Question I - Solow Model without Population or Technology Growth
Consider the Solow growth model with no population growth and no technology growth, i.e., n = x = 0. Output is
created by a Cobb-Douglas production function combining Labor, Lt, and capital, Kt, such that output Yt is given
by
Y₁ = A+ KL
1-α
=
=
Recall that, without population growth, Lt Lo and assume that Lo 1. Furthermore, recall that, without
technology growth, At Ao and assume that A0 = 1. The law of motion for capital per worker is
=
kt+1 = (1 − 6) kt + sAtko.
(1)
Assume that the savings rate is s = 0.2, the depreciation rate is 8 = 0.1, and that the capital share is a = 0.3.
1. Use equation (1) to solve for the steady state level of capital, kss, (hint, replace kss in that equation on both
sides)
kss
=
What is the steady state level of capital? (Replace the numbers in the expression)
=
2. Suppose that this economy starts with ko 1. Does capital grow or fall over time? What is the maximum
level of capital per capita this economy will ever have?
3. Suppose that this economy was at its steady state level of capital kss when it is hit by a war, such as the one
in Ukraine. After the end of the war the economy must start anew with ko 0.9kss. Use equation (1) to
compute kt for the next 4 years. By how much does the capital per work recover by the fourth year? .
4. How much would Ukraine's GDP be 4 years after the end of the war?
=
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