Question

Consider an economy that is characterized by the Solow Model. The (aggregate) production function is given by:

Y =
1.6K^{1/2}L^{1/2}

**In this economy, workers consume 75% of income and save
the rest. The labour force is growing at 3% per year
while the annual rate of capital depreciation is 5%.**

**Initially, the economy is endowed with 4500 units of
capital and 200 workers.**

**Is the economy in its steady state? Yes/no, explain. If the economy is not in its steady state, explain what happens to the capital-labour ratio and output per worker in the economy during very long-run transition. (5 points)**

**The economy is in its steady state as described above
(the steady state you solved for in part
a). **

**Suppose the level of total factor productivity permanently doubles (i.e. the A term in the production function rises from 1.6 to 3.2). Determine the new steady state levels of capital per worker, output per worker & consumption per worker. Compared to the initial steady state (from part a) have these 3 variables gone up, down, or stayed the same? If they changed calculate their percentage change from initial steady state levels to new steady state levels. Explain your answer with the aid of ONE appropriate diagram (that depicts the steady state locations from part a & b. Be sure to explain what happens to the variables during transition to steady state. (10 points)****Suppose instead of the A term doubling (i.e. the shock described in part b did NOT occur) the levels of BOTH capital and the number of workers doubles. Determine the new steady state levels of capital per worker, output per worker & consumption per worker. Compared to the initial steady state (from part a) have these 3 variables gone up, down, or stayed the same? If they changed calculate their percentage change from initial steady state levels to new steady state levels. (5 points)**

Answer #1

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...

Assume that an economy is described by the Solow growth model as
below:
Production Function: y=50K^0.4 (LE)^0.6
Depreciation rate: S
Population growth rate: n
Technological growth rate:g
Savings rate: s
a. What is the per effective worker production function?
b. Show that the per effective worker production function
derived in part a above exhibits diminishing marginal returns in
capital per effective worker
C.Solve for the steady state output per effective worker as a
function of s,n,g, and S
d. A...

QUESTION 1
Suppose an economy can be characterized by a Cobb-Douglas
production function with capital share of 1/3, and A =
200. The investment rate is 0.12 (12%), the annual rate of growth
of the labor force is 0.02 (2%), and the annual depreciation rate
of capital is 0.04 (4%). According to the Solow growth model, this
economy's steady state capital/labor ratio (capital per worker,
k) is
4,000
8,000
10,000
12,000
None of the above.
QUESTION 2
The steady state...

17. Solow growth The production function in your country is: Y =
K^0.5(LE)^0.5.
Your economy saves 24% of output each period, and 5% of the
capital stock depreciates each period. The population grows 2%
annually. Technology grows 1% annually. You begin with 1000 workers
and 1 unit of capital, and a tech- nology level equal to 1.
a) Write the production function in per-eective-worker terms, so
that per-effective-worker output (y = Y/LE ) is a function of
per-effective-worker capital (k=...

Question #1: The Basic Solow Model
Consider an economy in which the population grows at the rate of
1% per year. The per worker production function is y = k6, where y
is output per worker and k is capital per worker. The depreciation
rate of capital is 14% per year. Assume that households consume 90%
of their income and save the remaining 10% of their income.
(a) Calculate the following steady-state values of
(i) capital per worker
(ii) output...

Consider a version of the Solow model where population grows at
the constant rate ? > 0 and labour efficiency grows at rate ?.
Capital depreciates at rate ? each period and a fraction ? of
income is invested in physical capital every period. Assume that
the production function is given by:
?t =
?ta(?t?t
)1-a
Where ??(0,1), ?t is output, ?t is
capital, ?t is labour and ?t is labour
efficiency.
a. Show that the production function exhibits constant...

An economy has the following Cobb-Douglas production
function:
Y = Ka(LE)1-a
The economy has a capital share of 1/3, a saving rate of 24
percent, a depreciation rate of 3 percent, a rate of population
growth of 2 percent, and a rate of labor-augmenting technological
change of 1 percent. It is in steady state.
a. Does the economy have more or less capital than at the Golden
Rule steady state? How do you know? To achieve the Golden Rule
steady...

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
are equal to 0.10.
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
t the depreciation rate increases permanently from 0.10 to
0.20.
c. What will be the new steady-state levels of
capital...

Let’s solve the two sector model from page 281 of your
textbook.
The economy has two sectors, manufacturing firms and
research universities. The two sectors are described by the
production functions
Y = K1/2[(1-u)LE]1/2
?E = u E
where u is the fraction of labour force in universities
(assume u is exogenous).
Write the equation of motion of capital, ?K = sY - ?K,
in intensive form.
Write down the steady state condition and find the
steady state level of...

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]
a. Capital per worker, k:
b. Output per worker, y:
c. Total output, Y:

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