Question

Consider two countries: Country A and Country B. Each country
has the following Cobb-Douglas type production function:

Country A: Y = (K0.5)(EL)0.5 Country B: Y =
(K0.7)(EL)0.3

Unfortunately, your knowledge of Country A is a bit limited.
You have pieces of information, but you don’t know the entire
picture.

o Savings rate (s): unknown for Country A and 14.29% for
Country B

o Steady-state value of capital per effective worker: unknown
for both countries, but you have

heard that Country A has four times the steady state value of
capital per effective worker

compared to Country B.

o Population growth rate (n): 1% for Country A and 3% for
Country B

o Technological progress rate (g): 2% for both Country A and
Country B o Depreciation rate (δ): 5% for both Country A and
Country B

a. Convert both countries’ production functions to an
effective per worker production functions.

b. What is the savings rate for Country A? Needless to say,
you will also need to utilize what you know about

Country B.

c. What is the current steady-state consumption per effective
worker for both countries?

d. Now, please find the level of capital per worker that is
associated with the Golden Rule Steady State (in

other words, find k*Gold) for both countries. Is either
country at the Golden Rule Steady State level of k?

e. Choose one of the two countries (entirely up to you) and
calculate the savings rate required to bring that country to the
Golden Rule Steady State.

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...

17. Solow growth The production function in your country is: Y =
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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=...

Country A and country B both have the production function.
?=?(?,?)=?^1/2*?^1/2
c. Assume that neither country experiences
population growth or technological progress and that 5 percent of
capital depreciates each year. Assume further that country A saves
12 percent of output each year and country B saves 24 percent of
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Consider the following Cobb-Douglass production
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where Y is output, the constant z measures productivity, K is
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?=0.02.
a. What are the steady-state (numerical) values of ?, ?, and
??
b. What is the golden-rule (numerical) level of capital per
worker?
c. If the government wants to achieve the golden rule level of
k, should savings increase, decrease or remain unchanged? Solve
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Let’s solve the two sector model from page 281 of your
textbook.
The economy has two sectors, manufacturing firms and
research universities. The two sectors are described by the
production functions
Y = K1/2[(1-u)LE]1/2
?E = u E
where u is the fraction of labour force in universities
(assume u is exogenous).
Write the equation of motion of capital, ?K = sY - ?K,
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Write down the steady state condition and find the
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A closed economy has the following Cobb-Douglas production
function: F(KL) = K2/5 (EL)3/5, where the notation is as in class.
The depreciation rate is 1.5% and the saving rate is 20%. The
economy is in steady state, where the population decreases at a
rate 1% and capital K increases at a rate 1%. (a) Find the growth
rates of the following variables (i) labor efficiency, E (ii) the
number of workers per machine, L/K (iii) the average productivity
of capital,...

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...

Notice this is a multiple answers question.
Suppose there are two very similar countries (call them G and H).
Both countries have the same population and both are experiencing
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and are identical in both countries). Both
countries depreciate capital at the same rate, the both have the
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technological progress happens at the same rate in both
countries.
Suppose that currently both countries...

Assuming the following Cobb-Douglas production
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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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[6 marks]
iii. Assuming that , what will be...

The economies of two countries, Thrifty and Profligate, have the
same production functions and depreciation rates. There is no
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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...

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