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...

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...

A country is described by the Solow model with a production
function of y=k^(1/2). Suppose that k is equal to 400. The fraction
of output invested is 50%. The depreciation rate is 5%.
a. How does k change at this level?
b. What is the steady state level of k?
c. Suppose the level of k is 900. How does this change affect the
rate of change of k to the steady state?

1. If the technology (production function) and all the Solow
model parameters are same for two economies, they will eventually
converge to the same steady state levels of per-capita capital even
if they start at different levels of initial k.
True
False
2. If the technology (production function) and all the Solow
model parameters are same for two economies, more time taken will
be needed to reach steady state for the economy with high initial
level of per-capita capital?
True...

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=...

1. In the Solow model without exogenous technological change,
per capita income will grow in the long term as
long as the country has an initial level of capital below the
steady state level of capital (k o < k ⋅)
TRUE OR FALSE?
2. In the Solow model without exogenous technological change, per
capita income will grow in the short term as long
as the country has an initial level of capital below the steady
state level of capital...

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...

Consider an economy that is characterized by the Solow Model.
The (aggregate) production function is given by:
Y =
1.6K1/2L1/2
In this economy, workers consume 75% of income and save
the rest. The labour force is growing at 3% per year
while the annual rate of capital depreciation is 5%.
Initially, the economy is endowed with 4500 units of
capital and 200 workers.
Is the economy in its steady state? Yes/no,
explain. If the economy is not in its steady state,
explain what...

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...

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