Question

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.
- Solve for the steady state level of capital, k*.
- What is the growth of rate of k* and y* in the steady state?
- Calculate the growth rate of GDP per capita and aggregate GDP in the steady state. Show all your calculations.

Answer #1

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...

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...

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...

Which of the following statements about the Solow growth model
is FALSE?
A. The higher steady-state capital per capita, the higher the
output/income per capita.
B. The higher output/income per capita, the higher consumption
per capita.
C. Golden-rule capital per capita must be a steady state, but
not all steady-state is also a golden-rule.
D. Golden-rule capital per capita can be achieved by setting
the saving rate at the appropriate level.

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...

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...

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,...

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...

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?

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