Question

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 effective worker

• the growth rate of output per effective worker

• the growth rate of output per worker

• the growth rate of output

• the growth rate of consumption

b. Suppose that the rate of technological progress speed up to 2% per year. Recompute the answers to part (a). Explain.

Answer #1

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=...

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 an economy is described by the following production
function:
Y = K1/2 (EL)1/2
The savings rate in the economy is 0.40, population is growing
at a rate of 0.01, technological progress is growing at a rate of
0.01, and the depreciation rate is 0.02.
What is the steady state level of output per effective
worker?

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 an economy is described by the following production
function:
Y = K1/2 (EL)1/2
The savings rate in the economy is 0.40, population is growing
at a rate of 0.01, technological progress is growing at a rate of
0.01, and the depreciation rate is 0.02.
What is the steady state level of investment per effective
worker?

Answer the following questions using the basic Solow growth
model, without population growth or technological progress.
(a) Draw a diagram with per worker output, y, consumption, c,
saving, s and investment, i, on the vertical axis and capital per
worker, k, on the horizontal condition. On this diagram, clearly
indicate steady-state values for c, i, and y. Briefly outline the
condition that holds in the steady- state (i.e. what is the
relationship between investment and the depreciation of
capital?).
(b)...

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...

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...

Question 1
Production is given by:
? 1−? ?≡?(?,?)=?? ?
where ??+1 = (1 + ?)?? and ??(0,1)
Show that F exhibits a constant return to scale technology.
Express output as a function of the capital labor ratio ?? = ??
∕ ??.
Find the dynamical system (describing the evolution of ?? over
time) under the assumption
that the saving rate is ? ?(0,1) and the depreciation rate is ?
∈ (0,1].
What is the growth rate of ??, ???≡(??+1...

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...

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