Question

An economy has the following Cobb-Douglas production function:

Y = K^{a}(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 state, does the saving rate need to increase or decrease?

b. Suppose the change in the saving rate you described in part the previous question occurs. During the transition to the Golden Rule steady state, will the growth rate of output per worker be higher or lower than the rate you derived in the previous steady state?

c. Suppose the change in the saving rate you described in part the previous question occurs. After the economy reaches its new steady state, will the growth rate of output per worker be higher or lower than the rate you derived in the previous steady state?

Answer #1

An economy has a Cobb–Douglas production function:
Y=Kα(LE)1−αY=Kα(LE)1−α
The economy has a capital share of 0.30, a saving rate of 42
percent, a depreciation rate of 5.00 percent, a rate of population
growth of 2.50 percent, and a rate of labor-augmenting
technological change of 4.0 percent. It is in steady state.
Solve for capital per effective worker (k∗)(k∗), output per
effective worker (y∗)(y∗), and the marginal product of capital.
k∗=k∗=
y∗=y∗=
marginal product of capital =

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...

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...

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=...

In a country called Nubaria, the capital share of GDP is 40
percent; the average growth in output is 4 percent per year; the
depreciation rate is 5 percent per year; and the capital-output
ratio is 2.5. Suppose the production function is Cobb-Douglas and
Nubaria is in a steady state.
What is the saving rate in the initial steady state?
What is the marginal product of capital in the initial steady
state? What is the economic interpretation of this number?...

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...

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,...

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

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...

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...

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