Problem Set 2
MSU EC 410
Prof. Ahlin
due
2
/
1
9
/
1
5
1
.
Consider a country in which Y = 200 K
2/5
N
3/5
. Assume in this country they save 20% of
their income, population grows at 3% per year, and depreciation of capital occurs at 10% per
year. Use the Solow
model.
a.
Compare the effectiveness of i) a 50% increase in the savings rate (to 30%), ii) a 67% decline
in the population growth rate (to 1%), and iii) a 10% increase in productivity (to 220). That is,
for each, give the percent by which it increases lon
g
–
run average income (
y
*
)
and long
–
run
average consumption (
c
*
).
b.
Give one policy each that could be undertaken to accomplish i)
–
iii).
W
hich
policy has the
greatest impact
on long
–
run well
–
being
(assuming
each policy has
zero costs)
?
2
.
Imagine the fol
lowing goal of Lenin/Stalin at the beginning of the Soviet regime in Russia: to
overtake (i.e. equal) and surpass the world’s industrialized economies in terms of GDP per
capita. To achieve this goal, the main instrument of control is the fraction of nati
onal production
that is devoted to building the nation’s productive capacity: new machines, factories,
transportation equipment, and roads (i.e. investment as a share of GDP). The rest of national
production is used for consumer items like clothing and fo
od. The country begins with relatively
little capital, being mostly rural and non
–
industrialized. Assume each of the following:
·
GDP per capita starts in Russia at $300/year.
·
The world’s industrialized economies start with GDP per capita of $5000/year.
·
Po
pulation growth rates are 2% everywhere in the world.
·
All capital depreciates at 8% per year.
Assume the basic growth framework of Solow. Further assume
y
= 400
k
1/3
in Russia.
a.
Solve for Soviet long
–
run GDP per capita
(
y
*
)
as
a function of its savings rate.
For parts b.
–
d., assume long
–
run GDP per capita equals $10,000 in the industrialized countries,
and that they are saving 10% of income.
b.
What fraction of national output should be devoted by the Soviet Union to building n
ew
capital goods in order to overtake, i
.
e.
equal
, the industrialized nations’ GDP per capita in the
long
–
run? What fraction is left for consumer items?
c.
What fraction of national output should be devoted by the Soviet Union to building new
capital good
s in order to surpass, i
.
e.
double
, the industrialized nations’ GDP per capita in the
long
–
run? What fraction is left for consumer items?
d.
In the long run, what is the ratio of Soviet GDP per capita to GDP per capita in the
industrialized countries, a
nd what is the ratio of Soviet consumption per capita to consumption
per capita in industrialized countries if the Soviet Union achieves the goal of part b? of part c?
(That is, find four ratios.)
e.
Comparing the outcomes of part d. of this question to the same question answered using the
Harrod
–
Domar model (5e. from problem set 1), which model produces a more optimistic outlook
for achieving, by saving and investing at high rates, the Soviet goals of
overtaking and
surpassing industrialized countries’ living standards? Remember that living standards are best
measured by consumption here.
3.
a.
Use the Solow model to determine the a) instantaneous impact on GDP per capita, b)
instantaneous impact on
consumption per capita, c) impact on long
–
run GDP per capita, d)
impact on long
–
run consumption per capita, e) impact on long
–
run GDP per capita growth rate,
and f) impact on long
–
run GDP growth rate
of a
one
–
time and instantaneous increase in the
populat
ion N
t
, through wartime refugee immigration, say.
Assume the country begins at its
steady state value of
k
*
before this event occurs. Justify your answer by use of graph and/or
equation.
[Hint: this should not be considered a change in n, since the population continues to
grow at rate n after the one
–
time jump; it should be modeled as a one
–
time jump in N
t
.]
b.
Graph the path of
y
t
and
c
t
against time for the event analyzed in part a.
c.
U
se the Harrod
–
Domar model to determine the a) instantaneous impact on GDP per capita, b)
instantaneous impact on consumption per capita, c) impact on long
–
run GDP per capita growth
rate, and d) impact on long
–
run GDP growth rate of a
one
–
time and instantan
eous increase in the
population N, through wartime refugee immigration, say.
Justify your answer by use of graph
and/or equation.
d.
Graph the path of
y
t
and
c
t
(or ln
y
t
and ln
c
t
, which are typically linear) against time
for the
event analyzed in part c
.
4.
Discuss
whether, to what extent, and why the following are true or false. (Adapted from Ray
ch. 3, exercise 8.)
a.
The Harrod
–
Domar model predicts that a country’s long
–
run per capita growth rate
depends
on its rate of savings, whereas the Solow mod
el predicts that it does not.
b.
According to both the Harrod
–
Domar and Solow models, if total factor productivity (i.e. A) is
higher
in one country than in another, the country with the higher productivity will see faster
long
–
run growth in GDP per capita
.
c.
The Solow model predicts that a change in the population growth rate affects neither the
long
–
run growth rate of GDP nor the long
–
run growth rate of GDP per capita.
d.
In the Solow model, output per capita (
y
) goes down as capital per capita (
k
)
increases,
because of diminishing returns.
e.
Both the Solow and the Harrod
–
Domar model point to the inadequacy of GDP per capita (i.e.
y
) as a measure of well
–
being
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