Question

Assuming the following Cobb-Douglas production function is given for a closed economy without government.

i. Where returns to capital = 0.5; and rate of
depreciation of physical capital

Determine the steady-state level of capital per worker. What is the
savings rate at which the steady-state level of capital is
achieved?
[6marks]

ii Prove that the steady-state level of output is the ratio of the saving rate to the rate of depreciation [6 marks]

iii. Assuming that , what will be the effect of the savings rate on output per worker? [8 marks]

Answer #1

A closed economy has the following Cobb-Douglas production
function: F(KL) = K2/5 (EL)3/5, where the notation is as in class.
The depreciation rate is 1.5% and the saving rate is 20%. The
economy is in steady state, where the population decreases at a
rate 1% and capital K increases at a rate 1%. (a) Find the growth
rates of the following variables (i) labor efficiency, E (ii) the
number of workers per machine, L/K (iii) the average productivity
of capital,...

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...

A closed economy (NX = 0) without government (G = T = 0) has a
production function Y = K^1/4 ^L 3/4 . Capital depreciates at a
rate of 3 percent per year. Workers spend 76 percent of their
income each year. Investment adds up to the capital stock which is
available for production next year. Assume that capital per worker
is 5.0625 at the beginning of 2017 and the number of workers stays
the same each year.
(a) Find...

In a solow-type economy with Cobb-Douglas production, assume
that the population growth rate depends on the current level of
output per worker, y, so that n=my, where m is a positive constant.
For simplicity, assume d=0
a) Find an expression for the growth rate of the capital-labor
ratio, k̇ / k
b) Find expressions for the steady states of y and k
c) Find an expression for the growth rate of Y in steady state

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...

Assume that the production function in an economy is given by
y=k1/2, where y and k are the per-worker levels of output and
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
achieve the golden-rule steady state level of k?

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...

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 two countries: Country A and Country B. Each country
has the following Cobb-Douglas type production function:
Country A: Y = (K0.5)(EL)0.5 Country B: Y =
(K0.7)(EL)0.3
Unfortunately, your knowledge of Country A is a bit limited.
You have pieces of information, but you don’t know the entire
picture.
o Savings rate (s): unknown for Country A and 14.29% for
Country B
o Steady-state value of capital per effective worker: unknown
for both countries, but you have
heard that Country...

Consider an economy described by the production function:
Y = F(K, L) = K0.3L0.7.
Assume that the depreciation rate is 5 percent per year.
Make a table showing steady-state capital per worker, output per
worker, and consumption per worker for saving rates of 0 percent,
10 percent, 20 percent, 30 percent, and so on. Round your answers
to two decimal places. (You might find it easiest to use a computer
spreadsheet then transfer your answers to this table.)
Steady State...

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