Faculty of Arts and Science
DECEMBER EXAMINATIONS 2009
ECO 325H1 F
Duration: 2 hours
NO AIDS ALLOWED
NOTE TO STUDENT:
Enter your name and student number on each examination book
that you use. There are
four questions
on this test for a
TOTAL OF 200 MARKS
. Count the
exam pages to ensure you have all 4 pages. Read each question carefully and note the number
of points allocated to each part. Good Luck.
1.
(Total 40 points) Assume that
Y
t
K
t
A
t
L
t
1
−
,where 0
1,
Y
t
is total
output at time
t
,
K
t
is total capital at time
t
,
A
t
is the amount of knowledge at time
t
,and
L
t
is the amount of labour at time
t
. Use the Solow model to answer the following
questions.
a.
(8 points)Using the Solow model find the steady state values for
k
,
y
and
c
(i.e.,
k
∗
,
y
∗
and
c
∗
) as functions of the savings rate,
s
, the growth rate of labour,
n
, the rate of
depreciation,
, the growth rate of knowledge,
g
,and
.What is the golden rule level of
capital,
k
G
as a function of
s
,
n
,
,
g
and
?
b.
(8 points) Prove that the elasticity of total output with respect to total capital is equal to
the elasticity of output per unit of effective labour with respect to capital per unit of
effective labour.
c.
Assume that there is a permanent increase in
s
.
i.
(8 points) Show what happens to the steady state levels of
k
,
c
,and
y
, and the level
of
k
G
using a diagram.
ii.
(8 points) Find and determine the signs of:
∂
k
∗
∂
s
,
∂
c
∗
∂
s
,
∂
y
∗
∂
s
,and
∂
k
G
∂
s
d.
(8 points) If
s
0.6,
decreases from 1% to 2%,
a
decreases from
1
2
to
1
3
,
n
1%
and
g
1%, how much time will it take for
k
and
y
to move half way to their new
balanced growth path? (Note: You only need to provide the final equation for each
variable. You do not need to evaluate it.)
(Continued on next page)