14.452: Economic Growth
Problem Set 1
Due date: November 6, 2009 in Recitation.
Exercise 1:
growth model where the aggregate production function is
F
(
K;L;Z
) =
L
K
±
Z
1
±
;
where
Z
+
± <
1
,
capital depreciates at the rate
²
, and there is an exogenous saving rate of
s
.
1. First suppose that there is no population growth. Find the steadystate
capitallabor ratio and the steadystate output level. Prove that the steady
state is unique and globally stable.
2. Now suppose that there is population growth at the rate
n
, that is,
_
L=L
=
n
. What happens to the capitallabor ratio and output level as
t
! 1
?
What happens to returns to land and the wage rate as
t
! 1
?
3. Would you expect the population growth rate
n
or the saving rate
s
to
change over time in this economy? If so, how?
Exercise 2:
Consider the discretetime Solow growth model with constant
population growth at the rate
n
, no technological change and depreciation rate
of capital equal to
²
. Assume that the saving rate is a function of the capital
labor ratio, thus given by
s
(
k
)
.
1. Suppose that
f
(
k
) =
Ak
and
s
(
k
) =
s
0
k
1
1
. Show that if
A
+
²
n
= 2
,
then for any
k
(0)
2
(0
;As
0
=
(1 +
n
))
, the economy immediately settles
into an asymptotic cycle and continuously ±uctuates between
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 Spring '09
 Economics, The Land, Exogenous growth model

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