Econ 102 Winter 2012
Lecture Note 4.5  Solutions to LN 4
Solutions
1. True or False (and explain): In a Solow model with
g
= 0, wages will always increase at the same rate
as population growth.
False.
In the Solow model without technological growth (when
g
=
0
), the wage will
be:
w
t
= (1

α
)
Ak
α
t
which is not growing, even if
n >
0
.
2. True or False (and explain): In the Solow model without growth, steady state consumption increases
in the level of technology (
A
).
True.
The expression for steady state capital is
k
ss
=
(
sA
δ
)
1
1

α
In steady state,
c
ss
= (1

s
)
y
ss
= (1

s
)
Ak
α
ss
= (1

s
)
A
(
sA
δ
)
α
1

α
"Increases in the level of technology" means that
A
and
C
t
are directly proportional (not
inversely related)  it does not mean that
C
t
has to be growing.
3. Just like the problem from the previous notes, write down the Solow model equations (either the three
equation version or the two equation version) in aggregate (not per capita) and per capita terms for:
(a) The Solow model with only population growth
Y
t
=
AK
α
t
L
1

α
t
I
t
=
sY
t
K
t
+1
=
K
t
+
I
t

δK
t
(b) The Solow model with population growth and technological growth
1
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Y
t
=
K
α
t
(
A
t
L
t
)
1

α
I
t
=
sY
t
K
t
+1
=
K
t
+
I
t

δK
t
(c) (Harder) The Solow model with only
TECHNOLOGICAL growth
(in the notes I wrote only
population growth) (for this model  also in question 7 and 8d  follow the derivation for the model
with both technological and population growth but set
n
= 0)
Y
t
=
K
α
t
(
A
t
L
t
)
1

α
I
t
=
sY
t
K
t
+1
=
K
t
+
I
t

δK
t
4. For each of the above models, graph the steady state. Describe in words what happens if the economy
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 Spring '11
 d
 Thermodynamics, Kt Kt

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