Macroeconomic Policies
Exercise 1.
Consider an economy, where the aggregate production function Y=F(K,N) exhibits
Constant Return to Scale, positive and decreasing marginal productivity and unit
elasticity of substitution between factors. Admitting that the saving rate, the
population growth rate, technology and the rate of capital depreciation are all
constant and exogenous:
a) Describe in a graph the steady state of this economy. Is it a stationary steady
state? Why?
b) Consider the following production function Yt  AK t
0, 5
Nt
0, 5
and assume that
A=1, the saving rate is 20%, the capital depreciation rate is 8% and that the
population grows at 2% per year. Find our the steady state levels of output per
capita and capital per worker and the growth rate of output.
c) Describe in a graph the effects of the following changes on the long run level of
per capita output:
i. Introduction of more efficient management practices in
business;
ii. An earthquake that destroys part of the capital stock.
d) In light of the Solow model, is there a tendency for per capita output levels in
different countries to approach each other in the long term? Why?
Exercise 2.
Consider an economy, where the aggregate production function Y=F(K,N) exhibits
Constant Return to Scale, positive and decreasing marginal productivity and unit
elasticity of substitution between factors. Admitting that the saving rate, the
population growth rate, technology and the rate of capital depreciation are all
constant and exogenous:
a) Describe the effects of a rise in the saving rate in the time paths of the
following variables:
i. Capital per worker
ii. Per capita income;
iii. Per capita consumption.
b) Describe the effects of a rise in the level of technology on the time paths of
the following variables:
iv. Per capita output;
v. Capital per worker
Exercise 3.
In Country XXX the production function is given by Yt  AK t
0, 5
Nt
0, 5
, where A is the
level of technology.
a) Write down the main assumptions of the Solow Model.
b) Find out the expression that describes the dynamics of the capital-labor ratio.
c) Assume that A=2, the saving rate is 40%, the capital depreciation rate is 14%
and that the population grows at 6% per year. Find out the steady state levels
of output per capita and capital per worker and the growth rate of output.
Graph the equilibrium.
Exercise 4.
1
2
In country YYY the production function is given by: Yt  20 K t 3 N t 3 . In this economy,
25% of income is saved, the labor force growth rate is 2,5% and the capital
depreciation rate is 2,5%.
a) Describe the model and write down the production function in the intensive
form y=Y/N.
b) Compute the equilibrium value of capital and output per worker. Represent it
in a graph.
c) Country WWW has an identical economic structure to YYY, but was recently
affected by a hurricane, which reduced its capital stock. Discuss the dynamic
adjustment of this economy with the help of a graph.
d) Will per capita incomes of YYY and WWW converge? Why?
Exercise 5.
Consider an economy which is described by the following production function
05
0, 5
Yt  At K t N t . N is the constant number of 100 workers who save 20% of their
savings. Capital depreciation is 5%.
a) Assume that the level of technology is constant and equal to 2. Find out the
long-run capital stock.
b)
c) Now suppose that
At  4e 0, 025t
, find out the equilibrium levels of K/L (where L
is labour in efficiency units), Y/N and Y. Compute the growth rate of output.
d)
e) c) Imagine that the number of workers increases to 200. What will be the
evolution of output per efficiency unit and capital per efficiency unit after this
shock?
Exercise 6.
~
~
Consider the following production function: y t  A k t
0,5
a) Find out the expressions for the equilibrium level of income and capital.
b) Consider that the saving rate equals 14%, population grows 1% per year, the
capital depreciation rate equals 4% and At  2e 0, 01t . Find out the steady state
levels of income and capital per efficiency units.
c) Describe what happens to each variable if the saving rate rises.
d) Consider another economy (LDC) with a 10% saving rate, 4% population growth
and similar technological progress and capital depreciation as the previous
economy. Which policy actions could the less developed economy adopt in
order to improve its income level?
Exercise 7.
1
2
In country CCC the production is given by: Yt  At K t 3 N t 3 , where At  Ae 0,01t
describes the technological progress. Saving rate equals 12,5%, the labor force
grows 1% per year and the capital depreciation rate is 3% and A equals 2.
Compute the steady state levels of capital and output per efficiency unit and the
growth rate of per capita income.
Exercise 8.
Consider an economy X, which is described by the following production
1
2
t
1
2
t
function: Yt  At K N , where At  4e 0, 05t describes the technology and N is the
(constant) number or workers. Assume that the saving rate is 25% and capital
depreciation rate is 10%.
a) Find out the equilibrium values of K/L, Y/L and K/Y, where L is labour in
efficiency units.
b) Suppose that initially the K/L ratio equals 2 in this economy. What will be the
corresponding initial levels of Y/L, C/L and Y/N?
c) Starting from the position described in b), what is the expected evolution of
Y/L?
Exercise 9.
Consider an economy with the following production function: Y  AK 0,5 N 0,5 .
Where A is the constant level of technology equal to 2. The constant number of
workers save 40% of their income. The capital depreciation rate is 1%.
a) Find the steady state equilibrium of this economy.
USA registered an annualized GDP growth rate of 2,5% in the first quarter of 2010,
while China grew 11,9% and India 6%, proving a negative relationship between
wealth and growth.
b) Comment on this statement in light of the Solow model.
c) Assume that the production function takes the form Y=AK, where A is equal to
0,2. Mention the main implications this would have for the economy, in
comparison to a Coub Douglas production function and find the growth rate of
output per capita.
d) Does this extension of the model predict convergence?