Question

If the production function is given by Yt=A(KtLt) 0.5 where Y is the output, A is the technology, L refers to the labor stock, and K is the capital stock. Suppose that the saving rate (s) equals 0.6 and the depreciation rate (δ) is 0.3

a. Write the output and capital accumulation equations in terms of the capital per worker?

b. Find the steady state capital, output, investment, and consumption?

c. What would happen to the steady state capital if the saving rate increases to 0.8 and the depreciation rate increases to 0.4?

Answer #1

Consider an economy described by the production function:
Y = F(K, L) = K0.3L0.7.
Assume that the depreciation rate is 5 percent per year.
Make a table showing steady-state capital per worker, output per
worker, and consumption per worker for saving rates of 0 percent,
10 percent, 20 percent, 30 percent, and so on. Round your answers
to two decimal places. (You might find it easiest to use a computer
spreadsheet then transfer your answers to this table.)
Steady State...

I have been given a production function which states Yt=
Kt^0.25N^0.75
Im told the number of workers is N constant, the saving rate is
s and the deprecation of physical capital is δ .
How do I go about explaining the evolution of physical stock
over time?
How do I show the the steady state levels of capital per worker
and output per worker in terms of the saving rate and depreciation
rate?
Thank you

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...

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...

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=...

Production Function: Yt = 10Kt^0.4 Lt^0.6 Consumption Function:
Ct = 0.7Yt Depreciation rate: 10% (i.e. δ= 0.1) Population growth
rate: 3% (i.e. n= 0.03) With this production function, it can be
shown that MPK= 4Kt^-0.6Lt^0.6 = 4kt^-0.6 and MPL= 6Kt^0.4 Lt^-0.4=
7k^t0.4
What kind of policies would an economist recommend in order to
reach the golden rule capital stock? (Hint: think about saving
rate)

Find steady-state output per worker: plug the expression for
steady state capital into the production function and simplify
EQUATIONS
steady state capital per worker: kt = (sA/δ + n)^1/1-α
0 = sAkt^α - (δ + n)kt (at steady state)
production function: Yt= AKt^αNt^(1−α)

Suppose that the economy’s production function is given by
Y = K1/3N2/3
and that both, the savings rate s and the depreciation rate δ
are equal to 0.10.
a. What is the steady-state level of capital
per worker?
b. What is the steady-state level of output per
worker?
Suppose that the economy is in steady state and that, in period
t the depreciation rate increases permanently from 0.10 to
0.20.
c. What will be the new steady-state levels of
capital...

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...

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...

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