Question

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 developed country has a saving rate of 28 percent and a
population growth rate of 1 percent per year. A less developed
country has a saving rate of 10 percent and a population growth
rate of 4 percent per year. In both countries, *g* = 0.02
and S = 0.04. Find the steady state value of output per effective
worker, y^steady state for each country. Illustrate your answer
with a graph showing steady state capital per effective worker,
output per effective worker and consumption per effective
worker.

Answer #1

Assume that an economy described by the Solow model has the
production function Y = K 0.4 ( L E ) 0.6, where all the variables
are defined as in class. The saving rate is 30%, the capital
depreciation rate is 3%, the population growth rate is 2%, and the
rate of change in labor effectiveness (E) is 1%.
For this country, what is f(k)? How did you define lower case
k?
Write down the equation of motion for k....

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...

2. Consider a numerical example using the Solow growth model:
The production technology is Y=F(K,N)=K0.5N0.5 and people consume
after saving a proportion of income, C=(1-s)Y. The capital per
worker, k=K/N, evolves by (1+n)k’=szf(k)+(1-d)k.
(a) Describe the steady state k* as a function of other
variables
(b) Suppose that there are two countries with the same steady
state capital per worker k* and zero growth rate of
population(n=0), but differ by saving rate, s and depreciation
rate, d. So we assume...

Consider a numerical example using the Solow growth model: The
production technology is Y=F(K,N)=K0.5N0.5 and people consume after
saving a proportion of income, C=(1-s)Y. The capital per worker,
k=K/N, evolves by (1+n)k’=szf(k)+(1-d)k.
(a) Describe the steady state k* as a function of other
variables.
(b) Suppose that there are two countries with the same steady
state capital per worker k* and zero growth rate of
population(n=0), but differ by saving rate, s and depreciation
rate, d. So we assume that...

Portugal has the following per-worker production function:
y=3k^0.05
Depreciation rate is 0.08, population growth rate is 0.02.
Saving is S=0.2Y, where S is national saving and Y is national
output.
(a) what are the steady state value of capital-labour ratio,
output per worker and consumption per worker?
(b) Suppose that national saving increases to 0.4, what are the
steady state value of capital-labour ratio, output per worker and
consumption per worker?
(c) Suppose depreciation rate increases to 0.20, what are...

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...

Solow Growth Model Question: Consider an economy where output
(Y) is produced according to function Y=F(K,L). L is number of
workers and Y is the capital stock. Production function F(K,L) has
constant returns to scale and diminishing marginal returns to
capital and labor individually. Economy works under assumption that
technology is constant over time. The economy is in the
steady-state capital per worker. Draw graph. Next scenario is that
the rate of depreciation of capital increases due to climate change...

Question 1
Growth Suppose that the economy’s production function is: ?? =
?? 0.35(???? ) 0.65 and that the saving rate (s) is equal to 10%
and that the rate of depreciation (?) is equal to 2%. Further,
suppose that the number of workers grows at 5% per year and that
the rate of technological progress is 1% per year.
a. Find the steady-state values of:
• capital stock per effective worker
• output per effective worker
• consumption per...

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...

Suppose Richland has the production function YR=ARLR1/2KR1/2,
while Poorland has the production function YP=APLP1/2KP1/2. Assume
that total factor productivity (A) is fixed – i.e. not growing --
in each country, but that L and K are evolving as described in the
standard Solow model with population growth (i.e. their saving
rates are given by sR and sP, their depreciation rates are given by
dR and dP, and their population growth rates are given by nR and
nP.)
a) Write down...

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