Problem 2: Growth Models Solow Growth Model: Assume there is an imaginary country where output is produced according to the following constant returns to scale production function that lies at the heart of the standard Solow growth model: Y = 10K0.5 L0.5 Also assume that the savings rate is 13% (s = 0.13), the population grows at a rate of 2% per year (n = 0.02), and capital depreciates at a rate of 2% per year (d = .02). (a) Which of the following is an expression of the production function in per-capita terms y expressed as a function of capital per worker k: i. Y = k0.5 ii. Y = 10k0.5| iii. y = k0.5 iv. y = 10k0.5 (b) What is the steady state level of capital per worker? (c) What is the steady state level of output per worker? (d) Suppose that the populist leader of our imaginary country increases the savings rate from 13% to 15%, i.e., (s = 0.15), what is the new steady state level of capital per worker? [Note: Assume that the other parameters n and d remain unchanged.] (e) [TRUE or FALSE] Other things constant, a technological change (i.e., increased productivity) in the Solow model increases the steady state level of capital and output per worker. i. True ii. False (f) As discussed in the video lecture, which of the following are true statements about another growth model - the Quantitative Theory of Credit? [Multiple select] i. Credit creation drives nominal GDP growth and asset price inflation. ii. Banks are only financial intermediaries between borrowers and lenders. iii. Empirically, in the 20th century, the velocity of money is usually constant over time when money is defined as M0, M1.. M5. iv. A large ratio of Cr/C can lead to bank crashes and recession.
Problem 2: Growth Models Solow Growth Model: Assume there is an imaginary country where output is produced according to the following constant returns to scale production function that lies at the heart of the standard Solow growth model: Y = 10K0.5 L0.5 Also assume that the savings rate is 13% (s = 0.13), the population grows at a rate of 2% per year (n = 0.02), and capital depreciates at a rate of 2% per year (d = .02). (a) Which of the following is an expression of the production function in per-capita terms y expressed as a function of capital per worker k: i. Y = k0.5 ii. Y = 10k0.5| iii. y = k0.5 iv. y = 10k0.5 (b) What is the steady state level of capital per worker? (c) What is the steady state level of output per worker? (d) Suppose that the populist leader of our imaginary country increases the savings rate from 13% to 15%, i.e., (s = 0.15), what is the new steady state level of capital per worker? [Note: Assume that the other parameters n and d remain unchanged.] (e) [TRUE or FALSE] Other things constant, a technological change (i.e., increased productivity) in the Solow model increases the steady state level of capital and output per worker. i. True ii. False (f) As discussed in the video lecture, which of the following are true statements about another growth model - the Quantitative Theory of Credit? [Multiple select] i. Credit creation drives nominal GDP growth and asset price inflation. ii. Banks are only financial intermediaries between borrowers and lenders. iii. Empirically, in the 20th century, the velocity of money is usually constant over time when money is defined as M0, M1.. M5. iv. A large ratio of Cr/C can lead to bank crashes and recession.
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![Problem 2: Growth Models
Solow Growth Model: Assume there is an imaginary country where output is produced according to the
following constant returns to scale production function that lies at the heart of the standard Solow growth
model:
Y = 10K0.5 L0.5
Also assume that the savings rate is 13% (s = 0.13), the population grows at a rate of 2% per year (n
0.02), and capital depreciates at a rate of 2% per year (d = .02).
(a) Which of the following is an expression of the production function in per-capita terms y expressed as
a function of capital per worker k:
i. Y = k0.5
ii. Y = 10k0.5|
iii. y = k0.5
iv. y = 10k0.5
(b) What is the steady state level of capital per worker?
(c) What is the steady state level of output per worker?
(d) Suppose that the populist leader of our imaginary country increases the savings rate from 13% to 15%,
i.e., (s = 0.15), what is the new steady state level of capital per worker? [Note: Assume that the other
parameters n and d remain unchanged.]
(e) [TRUE or FALSE] Other things constant, a technological change (i.e., increased productivity) in the
Solow model increases the steady state level of capital and output per worker.
i. True
ii. False
(f) As discussed in the video lecture, which of the following are true statements about another growth
model - the Quantitative Theory of Credit? [Multiple select]
i. Credit creation drives nominal GDP growth and asset price inflation.
ii. Banks are only financial intermediaries between borrowers and lenders.
iii. Empirically, in the 20th century, the velocity of money is usually constant over time when money
is defined as M0, M1...M5.
iv. A large ratio of Cr/C can lead to bank crashes and recession.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ed5a4b1-5b75-4e1a-af8e-7dfe45088af1%2Fc254c48d-d713-4339-afb8-8848fcf04539%2F5i1owad_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 2: Growth Models
Solow Growth Model: Assume there is an imaginary country where output is produced according to the
following constant returns to scale production function that lies at the heart of the standard Solow growth
model:
Y = 10K0.5 L0.5
Also assume that the savings rate is 13% (s = 0.13), the population grows at a rate of 2% per year (n
0.02), and capital depreciates at a rate of 2% per year (d = .02).
(a) Which of the following is an expression of the production function in per-capita terms y expressed as
a function of capital per worker k:
i. Y = k0.5
ii. Y = 10k0.5|
iii. y = k0.5
iv. y = 10k0.5
(b) What is the steady state level of capital per worker?
(c) What is the steady state level of output per worker?
(d) Suppose that the populist leader of our imaginary country increases the savings rate from 13% to 15%,
i.e., (s = 0.15), what is the new steady state level of capital per worker? [Note: Assume that the other
parameters n and d remain unchanged.]
(e) [TRUE or FALSE] Other things constant, a technological change (i.e., increased productivity) in the
Solow model increases the steady state level of capital and output per worker.
i. True
ii. False
(f) As discussed in the video lecture, which of the following are true statements about another growth
model - the Quantitative Theory of Credit? [Multiple select]
i. Credit creation drives nominal GDP growth and asset price inflation.
ii. Banks are only financial intermediaries between borrowers and lenders.
iii. Empirically, in the 20th century, the velocity of money is usually constant over time when money
is defined as M0, M1...M5.
iv. A large ratio of Cr/C can lead to bank crashes and recession.
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