Question

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 income per worker in the economy of the previous question is

4,000 |
||

8,000 |
||

10,000 |
||

12,000 |
||

None of the above. |

QUESTION 3

Suppose that the investment rate in the economy described in the previous questions was to increase. In the new steady state

income per worker would be higher. |
||

income per worker would remain unchanged. |
||

income per worker would be lower. |
||

we cannot say what will happen to income per worker. |

QUESTION 4

Which of the following statements concerning the increase in the investment rate of the previous question are implied by the Solow growth model?

The growth rate of income per worker in the new steady state will be higher. |
||

The growth rate of income per worker in the new steady state will remain unchanged. |
||

The growth rate of income per worker in the new steady state will be lower. |
||

The growth rate of income per worker during the transition to the new steady state will be higher than in the original steady state. |
||

The growth rate of income per worker during the transition to the new steady state will be lowerer than in the original steady state. |

QUESTION 5

Suppose that instead of the investment rate it is the population growth rate that increases. According to the Solow growth model in the new steady state

income per worker would be higher. |
||

income per worker would remain unchanged. |
||

income per worker would be lower. |
||

we cannot say what will happen to income per worker. |

QUESTION 6

Which of the following statements concerning the increase in the rate of growth of the labor force in the previous question are implied by the Solow growth model?

The growth rate of income per worker in the new steady state will be higher. |
||

The growth rate of income per worker in the new steady state will remain unchanged. |
||

The growth rate of income per worker in the new steady state will be lower. |
||

The growth rate of income per worker during the transition to the new steady state will be higher than in the original steady state. |
||

The growth rate of income per worker during the transition to the new steady state will be lower than in the original steady state. |

QUESTION 7

Which of the following statements concerning the simple Solow growth model with population growth are correct?

The model can account for most of the variation across countries in income per worker as the result of differences in steady state capital per worker and population growth rates. |
||

The model can account for less than half the variation across countries in income per worker as the result of differences in steady state capital per worker and population growth rates. |
||

The model can account for the variation across countries in growth rates of income per worker as a steady state phenomenon. |
||

The model cannot account for the variation across countries in growth rates of income per worker as a steady state phenomenon. |

Answer #1

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...

Consider an economy that is characterized by the Solow Model.
The (aggregate) production function is given by:
Y =
1.6K1/2L1/2
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...

Could you please answer these two questions?
1- If two economies are identical except for their population
growth rate, then the economy with the higher population growth
rate will have:
A. higher steady-state output per worker.
B. higher steady-state capital per worker.
C. lower steady-state depreciation rates.
D. lower steady-state capital per worker.
2- if the population growth rate decreases in an economy
described by the Solow growth model, the line representing
population growth and depreciation will.
A. Become steeper....

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...

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

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 =

The economies of two countries, Thrifty and Profligate, have the
same production functions and depreciation rates. There is no
population growth in either country. The economies of each country
can be described by the Solow growth model. The saving rate in
Thrifty is 0.3. The saving rate in Profligate is 0.05.
(a) Which country will have a higher level of steady-state
output per worker?
(b) Which country will have a higher growth rate of output per
worker in the steady...

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...

Suppose, in the Solow growth model, that learning by doing is
captured as a cost of installing new capital. In particular,
suppose that for each unit of investment, r units of goods are used
up as a cost to firms.
(a) Determine how r affects the steady state quantity of capita per
worker, and per capita income.
(b) Now suppose that r differs across countries. How
will these countries differ in the long run? Discuss.

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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