Question

Suppose that the economy is initially in steady state and that some
of the nation’s capital stock is destroyed because of a natural
disaster or a war.

A. Determine the long-run effects of this on the quantity of
capital per worker and on output per worker.

B. In the short run, does aggregate output grow at a rate
higher or lower than the growth rate of the labour force

C. After world war 2 , growth in real GDP in Germany and Japan
was very high. How do your results in parts (a) and (b) shed light
on the historical experience?

Answer #1

Suppose that the economy is initially in a steady state and that
some of the nation’s capital stock is destroyed because of the
natural disaster or a war.
(a) (10 points) Determine the long-run effects of this on the
quantity of capital per worker, output per worker, and their growth
rates.
(b) (10 points) In the short run, does the aggregate output grow
at a rate higher or lower than the growth rate of the labor
force?
(c) (5 points)...

4. How would each of the following changes affect the steady
state values of capital per worker and output per worker? a. A
large fraction of the physical capital stock is destroyed in a war.
b. A negative supply shock sharply reduces productivity.

Suppose an economy is initially in a steady state with capital
per worker below the Golden Rule level. If the saving rate
increases to a rate consistent with the Golden Rule, then in the
transition to the new steady state consumption per worker will:
a. always exceed the initial level.
b. first rise above then fall below the initial level.
c. always be lower than the initial level.
d. first fall below then rise above the initial level.

Suppose that a closed economy is in a steady state equilibrium
in the long-run. If there is a decrease in the depreciation rate of
this economy, discuss what will happen to the steady state
equilibrium, output per worker and capital per worker in this
economy. Graphically show and explain the developments by clearly
labeling your graphs.

2. The Solow-Swan Model
a) Consider an economy that is initially in a steady state
equilibrium. Assume that in this equilibrium it has a saving rate
of 50 per cent and a depreciation rate of 2 per cent. Further
assume that the population is constant and that the level of output
produced can be represented by the following production function: Y
= AKαL 1−α where A = 1 and α = 0.5. Use the Solow-Swan model to
determine the level...

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...

Assume the economy has achieved the balanced growth steady
state. Explain what factors determine the rates of growth of each
of the following variables when balanced growth is achieved: output
per effective worker, capital per effective worker, output per
worker, output, and consumption per worker.

Suppose an economy described by the Solow model is in a steady
state with population growth n of 1.8 percent per year and
techno- logical progress g of 1.8 percent per year.Total
output and total capital grow at 3.6 percent per year. Suppose
further that the capital share of output is 1/3. If you used the
growth- accounting equation to divide output growth into three
sources—capital, labor, and total factor productivity—how much
would you attribute to each source?

US Steady State and Golden Rule: In the US, the
capital share of GDP is 45%, the average annual growth rate of GDP
is 4%, the depreciation rate is 5% per year, and the capital-output
ratio is estimated to be 3. Assuming, a constant returns production
function (i.e., Cobb-Douglas) and that the US is in a steady state,
answer the following:
a) Find the savings rate.
b) Find the MPk
c) Find the MPk if US moved to the Golden...

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...

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