Question

**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 MP_{k}

c) Find the MP_{k} if US moved to the Golden Rule steady
state.

d) Find the Capital-Output ratio at the Golden Rule Steady State.

e) Find the saving rate at the Golden Rule Steady State.

Answer #1

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?...

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...

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...

1) if the share of GDP used for capital goods is 0.33, the
growth rate of productivity is 0.04, the growth rate of population
is 0, the depreciation rate is 0.04, the initial capital/output
ratio is 3.23, and the elasticity of GDP with respect to capital is
0.1, then what is the steady state value of the capital/output
ratio? Use 2 decimal places.
2) If the share of GDP used for capital goods is 0.17, the
growth rate of productivity...

If the share of GDP used for capital goods is 0.12, the growth
rate of productivity is 0.09, the growth rate of population is
0.02, the depreciation rate is 0.01, the initial capital/output
ratio is 2.01, and the elasticity of GDP with respect to capital is
0.3, then what is the steady state value of the capital/output
ratio? Use 2 decimal places.

If the share of GDP used for capital goods is 0.12, the growth
rate of productivity is 0, the growth rate of population is 0.01,
the depreciation rate is 0.01, the initial capital/output ratio is
4.6, and the elasticity of GDP with respect to capital is 0.2, then
what is the steady-state value of the capital/output ratio? Use 2
decimal places.

Which of the following statements about the Solow growth model
is FALSE?
A. The higher steady-state capital per capita, the higher the
output/income per capita.
B. The higher output/income per capita, the higher consumption
per capita.
C. Golden-rule capital per capita must be a steady state, but
not all steady-state is also a golden-rule.
D. Golden-rule capital per capita can be achieved by setting
the saving rate at the appropriate level.

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.

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 =

18）At the current steady state capital - labor ratio, assume
that the steady state level of per capita consumption, ( C N ) ∗,
is less than the golden rule level of steady state per capita
consumption. Given this information, we can be certain that:
A.An increase in the saving rate will cause an increase in the
steady state level of per capita consumption .
B.A decrease in the capital-labor ratio will cause a decrease in
the steady state level...

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