Question

Consider an economy where the production function is ? = ? 2 + 100. The savings rate in the economy is ? = 0.02 and the depreciation rate is ? = 0.2.

a. The economy starts in year 1 with ? = 20 units of capital. Compute the economy’s output, investment and depreciation in year 1.

b. What will be the economy’s capital stock in year 2?

c. Compute the economy’s output, investment and depreciation in year 2

d. What will be the economy’s capital stock in year 3?

e. Compute investment and depreciation for the levels of capital shown on the table. Capital Investment Depreciation

? = 0

? = 10

? = 20

? = 30

? = 40

? = 50

f. Graph the investment and depreciation functions below.

What is the steady-state level of capital in this economy? You may use your diagram to explain – No math needed.

Answer #1

Assume that the production function in an economy is given by
y=k1/2, where y and k are the per-worker levels of output and
capital, respectively. The savings rate is given by s=0.2 and the
rate of depreciation is 0.05. What is the optimal savings rate to
achieve the golden-rule steady state level of k?

Consider an economy described by the following production
function: ? = ?(?, ?) = ?^1/3 ?^2/3
depreciation rate is 5 percent (? = 0.05)
the population grows at 2 percent (n = 0.02)
savings rate is 20 percent (s = 0.20)
f) At what rates do the following grow at in the steady state:
[3 points]
a. Capital per worker, k:
b. Output per worker, y:
c. Total output, Y:

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?

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?

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
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depreciation
[6 marks]
iii. Assuming that , what will be...

Use the Solow model to solve. Suppose, you are the chief
economic advisor to a small African country with an aggregate per
capita production function
of y=2k1/2. Population grows at a
rate of 1%. The savings rate is 12%, and the rate of depreciation
is 5%.
(a) On a graph, show the output, break-even investment, and
savings functions for this economy (as a function of capital per
worker). Denote steady-state capital per worker k* and
steady-state output per worker y*. Label...

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 Golden Rule level of capital per effective worker?
(Use two decimal places)

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(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
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. Let the production function be Y=AL^1/2*K^1/2 where Y is
output, K is capital, L is labor and A represents the level of
technology.
a. What happens to the marginal product of capital as the level
of capital increases?
b. If L=100, A=5, the savings rate is 1/2 and the depreciation
rate is 1/3, what will the steady-state levels of capital, output
and consumption be?

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...

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