Question II - Solow Model with Population or Technology Growth Consider the Solow growth model with population growth and technology growth. Suppose that x = 0.1 and that n = 0.02, i.e., At = (1+0.1) At-1, and Lt = (1 +0.02) Lt-1. 1 Output is created by a Cobb-Douglas production function combining Labor, Lt, and capital, Kt, such that output Yt is given by Recall that efficient units of labor are given by Y₁ = A+ KL-a ล Assume that 8 = 0.1, s = 0.2, and a = 0.3. 1-a 1. What is the growth rate x = (1 + x) ¹/(1-a) – 1 - 2. Using the answer to the previous question, what is capital per efficiency units in steady state? Ess = | S itn tử + nữ 1-a Replace the numbers for s, d, ã and a to find the value of capital per efficient worker in steady state. 3. Take the production function (2) and divide by efficient worker, t = Y₁/Lt. You would find: yt = kg. What is output per-efficient worker if capital per-efficient worker is at its steady-state value? 4. If capital per-efficient worker is at its steady state value, does output per efficient worker grow over time? By how much? 5. Suppose that the savings rate in this economy increases to s = 0.3. What happens to steady-state level of capital per-efficient worker? Is it higher, lower, the same? 6. Continue assuming that the savings rate in this economy increases to s = 0.3. What happens to steady-state level of output per-efficient worker? Is it higher, lower, the same? 7. Recompute the growth rate of output per worker gyat the steady state with the higher savings rate s = 0.3. Is it higher, lower, the same? Use your results to comment on how does the savings rate affect the growth rate of output per capita in this model. ?
Question II - Solow Model with Population or Technology Growth Consider the Solow growth model with population growth and technology growth. Suppose that x = 0.1 and that n = 0.02, i.e., At = (1+0.1) At-1, and Lt = (1 +0.02) Lt-1. 1 Output is created by a Cobb-Douglas production function combining Labor, Lt, and capital, Kt, such that output Yt is given by Recall that efficient units of labor are given by Y₁ = A+ KL-a ล Assume that 8 = 0.1, s = 0.2, and a = 0.3. 1-a 1. What is the growth rate x = (1 + x) ¹/(1-a) – 1 - 2. Using the answer to the previous question, what is capital per efficiency units in steady state? Ess = | S itn tử + nữ 1-a Replace the numbers for s, d, ã and a to find the value of capital per efficient worker in steady state. 3. Take the production function (2) and divide by efficient worker, t = Y₁/Lt. You would find: yt = kg. What is output per-efficient worker if capital per-efficient worker is at its steady-state value? 4. If capital per-efficient worker is at its steady state value, does output per efficient worker grow over time? By how much? 5. Suppose that the savings rate in this economy increases to s = 0.3. What happens to steady-state level of capital per-efficient worker? Is it higher, lower, the same? 6. Continue assuming that the savings rate in this economy increases to s = 0.3. What happens to steady-state level of output per-efficient worker? Is it higher, lower, the same? 7. Recompute the growth rate of output per worker gyat the steady state with the higher savings rate s = 0.3. Is it higher, lower, the same? Use your results to comment on how does the savings rate affect the growth rate of output per capita in this model. ?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Question II - Solow Model with Population or Technology Growth
Consider the Solow growth model with population growth and technology growth. Suppose that x = 0.1 and that
n = 0.02, i.e.,
At = (1+0.1) At-1, and Lt = (1 +0.02) Lt-1.
1
Output is created by a Cobb-Douglas production function combining Labor, Lt, and capital, Kt, such that output
Yt is given by
Recall that efficient units of labor are given by
Y₁ = A+ KL-a
ล
Assume that 8 = 0.1, s = 0.2, and a = 0.3.
1-a
1. What is the growth rate x = (1 + x) ¹/(1-a) – 1
-
2. Using the answer to the previous question, what is capital per efficiency units in steady state?
Ess = |
S
itn tử + nữ
1-a
Replace the numbers for s, d, ã and a to find the value of capital per efficient worker in steady state.
3. Take the production function (2) and divide by efficient worker, t = Y₁/Lt. You would find:
yt = kg.
What is output per-efficient worker if capital per-efficient worker is at its steady-state value?
4. If capital per-efficient worker is at its steady state value, does output per efficient worker grow over time? By
how much?
5. Suppose that the savings rate in this economy increases to s = 0.3. What happens to steady-state level of
capital per-efficient worker? Is it higher, lower, the same?
6. Continue assuming that the savings rate in this economy increases to s = 0.3. What happens to steady-state
level of output per-efficient worker? Is it higher, lower, the same?
7. Recompute the growth rate of output per worker gyat the steady state with the higher savings rate s = 0.3. Is
it higher, lower, the same? Use your results to comment on how does the savings rate affect the growth rate of
output per capita in this model. ?
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