Question

Suppose Canada’s aggregate production function is given by the
following:

Y = K^1/3 *(AN)^2/3

Variables are deﬁned as they were in class. Suppose the savings
rate in Canada is 20% (s = 0.2), the depreciation rate is 5% (δ =
0.05), the population growth rate is 2% (gN = 0.02), and the growth
rate of technology is 4% (gA = 0.04).

a) Solve for the equilibrium level of capital per eﬀective worker (
K/AN ) and output per eﬀective worker ( Y/AN ). Solve for the
equilibrium growth rates of the following variables: A, N, K, Y , Y
N , K N , Y/AN , and K/AN . Use a table to summarize your
answers.

b) Suppose the savings rate increases to 25%. Solve for the new equilibrium level of capital per eﬀective worker ( K/AN ) and output per eﬀective worker ( Y/AN ). Solve for the new equilibrium growth rates of the following variables: A, N, K, Y , Y N , K N , Y/AN , and K/AN . Use a table to summarize your answers.

c) In this model does an increase in the savings rate lead to
sustained long-run growth? Explain.

Answer #1

c)

an increase in the savings rate increases output and capital per effective worker. However, in the long run, a higher savings rate does not have any impact on the steady-state growth rates. Hence, it does not lead to sustained long-run growth.

Suppose that output (Y ) in an economy is given by the following
aggregate production function: Yt = Kt + Nt
where Kt is capital and Nt is the population. Furthermore,
assume that capital depreciates at rate δ and that savings is a
constant proportion s of income. You may assume that δ > s.
Suppose that the population remains constant. Solve for the
steady-state level of capital per worker.
Now suppose that the population grows at rate n. Solve...

Consider the Solow growth model. The production function is
given by Y = K^αN^1−α, with α = 1/3. There are two countries: X and
Y. Country X has depreciation rate δ = 0.05, population growth n =
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capital per worker k0 = 1
Country Y has depreciation rate δ = 0.08, population growth n =
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Suppose that the economy’s production function is given by
Y = K1/3N2/3
and that both, the savings rate s and the depreciation rate δ
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a. What is the steady-state level of capital
per worker?
b. What is the steady-state level of output per
worker?
Suppose that the economy is in steady state and that, in period
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c. What will be the new steady-state levels of
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3- Growth Model
Suppose that the output (Y) in the economy is given by
the following aggregate production function.
Yt = Kt +Nt
where the Kt is capital and Nt is population.
Furthermore assume that the capital depreciate at the rate of ẟ and
That saving constant and proportion s of income you may assume that
ẟ>s
1-suppose that the population remains constant . solve
for the steady state level of capital per worker
2- now suppose that the population...

Consider an economy described by the following production
function: ? = ?(?, ?) = ?^1/3 ?^2/3
depreciation rate is 5 percent (? = 0.05)
the population grows at 2 percent (n = 0.02)
savings rate is 20 percent (s = 0.20)
f) At what rates do the following grow at in the steady state:
[3 points]
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capital, respectively. The savings rate is given by s=0.2 and the
rate of depreciation is 0.05. What is the optimal savings rate to
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Answer the following
Y = f(k) = ka, where a = 0.25
S = 0.3
δ = 0.2
n = 0.05
g= 0.02
a. Find the steady state capital per effective worker, output
per effective worker, investment per effective worker, and
consumption per effective worker.
b. Find the steady state growth rate of capital per worker,
output per worker, investment per worker, and consumption per
worker.
c. Find the steady state growth rate of capital, output,
investment, and consumption.
d....

Consider the following Cobb-Douglass production
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where Y is output, the constant z measures productivity, K is
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?=0.02.
a. What are the steady-state (numerical) values of ?, ?, and
??
b. What is the golden-rule (numerical) level of capital per
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c. If the government wants to achieve the golden rule level of
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(a) Show that F has constant returns to scale.
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(c) Solve for the steady-state level of capital per worker (in
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Consider an economy described by the production function:
Y = F(K, L) = K0.3L0.7.
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Make a table showing steady-state capital per worker, output per
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