Homework 4 (Due October 4)
1. (The Solow model with exogenous technological progress.) The tech
nology level at
t
is given by
A
t
=(1+
g
)
t
A
0
,where
g
≥
0
. To keep the case
simple, let us assume
n
=0
. Now the transitional equation is simply
k
t
+1
=
s
·
A
t
·
(
k
t
)
β
+(1
−
δ
)
k
t
.
(1)
That is, we simply replace the constant
A
intheprev
ioustrans
it
iona
lequa
tion with
A
t
.
Regarding the steady state, by de
f
nition (see PPT4), if the economy is
in the steady state at
t
,then
y
t
+1
k
t
+1
=
y
t
k
t
.
(2)
Substituting
y
t
=
A
t
k
β
t
and
y
t
+1
=
A
t
+1
k
β
t
+1
into Equation (2) and doing
some algebra, we have
k
t
+1
k
t
=(1+
g
)
1
1
−
β
.
(3)
(If we apply
g
=0
to Equation (3), then we get
k
t
+1
=
k
t
, as in the previous
study.)
To see how to use the new transitional equation (Equation (1)) and the
new steadystate relationship between
k
t
+1
and
k
t
(Equation (3)), let us do
some exercises. Let
A
0
=1
,
g
=0
.
01
,
β
=0
.
5
,and
δ
=0
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 Fall '07
 MBIEKOP
 Macroeconomics, Steady State, Endogenous growth theory, Yt, transitional equation

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