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Economia V; Instructor: Marco Del Negro
Problem set 5
Solutions
Page 214 Prob 2
1)
|
20 Y ago |
today |
%change |
Y |
1000 |
1300 |
30 |
K |
2500 |
3250 |
30 |
N |
500 |
575 |
15 |
:
capital growth contributed 9%
:
labor growth contributed 10.5
(productivity growth) 10.5
b)
=30%-(0.5)(30%)-(0.5)(15%)=7.5%
:
capital growth contributed 15%
:
labor growth contributed 7.5%
2a) In the steady state:
Kt+1=Kt
if
goes down, the growth rate goes down.
b) The steady state is:
if
falls k* goes up. By the production function y goes up then c goes up.
) See figure.
) Golden Rule
taking derivatives to maximize:
Since the solution is:
if
goes down kgold goes up.
3a) The destruction of some of a country´s capital stock in war would have no effect on the steady state because
there has been no change in s, f(k),
or
.
Instead, k is reduced temporarily,
but eventually returns to the old pre war steady state.
b) Immigration raise
from
to
.
The rise in
lowers the steady state k, and lowers the steady state consumption per worker.
c) The rise in energy prices reduces the productivity of capital per worker.
This causes sf(k) to shift down. Therefore a decline in the steady state consumption per worker falls for 2 reasons:
1) Each unit of capital has a lower productivity.
2) Steady state k is reduced.
d) A temporary rise in s has no effect on the steady state equilibrium.
e) The increase in the size of the labor force does not affect the growth rate of the labor force.
So there is no impact on the steady state capital to labor ratio or on consumption per worker.
However, because a larger fraction of the population is working, consumption per person increases.
4) Increase in the depreciation rate
.
Since
If
goes up, kgold goes down as well as consumption.
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Marco Del Negro
2000-03-28