Consider an economy that has the following production function:

=


(

,

)
=

1
4

3
4
where

,

,

and

denote output, total factor productivity, capital stock and
labour employment respectively
(


=
1
for simplicity
)
.
Assume the depreciation
rate

=
0
.
1
5
,
saving rate

=
0
.
2
,
and population growth rate

=
0
.
0
5
.
a
)
Write down the production function in per worker terms.
b
)
Calculate capital, income and consumption per capita in the steady state.
Use a diagram to illustrate your answer.
(
2
marks
)
c
)
The economy is initially in the steady state that you calculated in part
(
b
)
.
Now suppose that there is a surge in the saving rate such that

=
0
.
3
.
i
)
Calculate capital, income and consumption per capital in the new steady
state.
(
1
mark
)
ii
)
Starting from year
0
with the initial steady state, use Excel to determine
the path of the change in capital, income and consumption per capita
until the new steady state is reached. You will need to attach this Excel
sheet with your answers.
(
Hint: you may want to retain as many decimal
places as possible in your calculation to reach your decision
)
.
(
1
mark
)
iii
)
How long is the transition between the two steady states?
(
1
mark
)
iv
)
Looking at your Excel results, explain how capital per worker reaches the
new steady state. Sketch the path of consumption per worker in the
transition to the new steady state. Comment on any policy dilemma
implied. Use an appropriate set of diagrams to support your answers.