UNIVERSITY OF VIRGINIA
ECON 3020  003: INTERMEDIATE MACROECONOMICS
MIDTERM 1  Solution key
1.
(a)
From the Solow growth model we know that in the steady state capital is
given by:
K
=
sA
d
¶
1
1
¡
fi
L
Therefore
K
TL
K
OL
=
s
TL
A
TL
s
OL
A
OL
¶
1
1
¡
fi
=
0
:
15
£
4
0
:
3
£
1
¶
3
=
2
= 2
:
828
Now
Y
TL
Y
OL
=
A
TL
K
1
=
3
TL
A
OL
K
1
=
3
OL
=
A
TL
A
OL
K
TL
K
OL
¶
fi
= 5
:
656
The ratio of consumption is given by:
C
TL
C
OL
=
(1
¡
s
TL
)
Y
TL
(1
¡
s
OL
)
Y
OL
= 6
:
869
(b)
Capital for
OL
will increase by ¢. This will increase output. It will also
increase investment by
sY
0
¡
sY
and depreciation by
dK
0
¡
dK
=
d
¢.
However because of diminishing returns the increase in investment will be
smaller than the increase in deprecation. Therefore over time capital will
fall back to its steady state. So over the long run Obsolitia’s economy will
move to its original state.
The graph is a standard Solow graph.
2.
(35 points)
(a)
In this model
K
is flxed. Wages will be given by:
w
=
2
3
A
K
L
¶
1
=
3
Let
L
0
= 2
=
3
L
be the population after the plague. Similarly, let
w
0
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 Spring '08
 Staff
 Macroeconomics

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