The Keynesian model in the
three sector economy can be
derived from equation nos.5
Since investment is inversely related to interest rate, a fall in the
interest rate will increase the investment demand. As a result, there
will be multiple expansions of income and output which is related to
the value of multiplier.
Derivation of IS Curve:
The IS curve is derived in the following diagram
FIGURE 8.2: DERIVATION OF THE IS CURVE
1
Y
1 c 1 t
1
Multipler
1 MPC 1 tax
Y
c 1 t Y
A
bi
Y 1 c 1 t
A bi
2
A bi
1
A bi
Y
AD
1
A c 1 t Y bi
1
E
2
E
2
Y
1
Y
0
1
E
2
E
1
Y
2
Y
0
IS
Income / Output
Income / Output
1
i
2
i
2
A c 1 t Y bi
AggregateDemand
InterestRate
In the upper panel of the diagram, a fall in the interest rate
from i
1
to i
2
has caused an upward shift of the Aggregate Demand
curve and the equilibrium
income increased form Y
1
to Y
2
. This is
brought down in the lower panel of the diagram which shows the
income and interest relationship.
In lower panel Y
1
is corresponds
to higher interest rate of i
1
and Y
2
corresponds to i
2
. The equilibrium
point E
1
and E
2
corresponds to equilibrium points in upper panel.
The IS curve connects such points of equilibrium.
Therefore, IS curve represents those combination of income
and interest rates which keeps goods market in equilibrium.
The Slope of the IS Curve:
The IS curve is steeper of flatter, according to the value of
MPC and
b (investment responsiveness
to change in rate of
interest). The IS curve will be flatter if the value of
MPC and
b are
higher. A higher value of MPC and lower value of rate of interest
rate make the Aggregate Demand steeper and therefore IS curve is
flatter. A higher value of ‗
b‟ cause a greater shift in the Aggregate
Demand in the upper panel and hence the IS curve will be flatter.
The Shift in the IS Curve
The shift in the IS curve
is caused by an increase in
autonomous components of Aggregate Demand such as
private
sector investment or
government expenditure on goods and
services, after holding the interest rate constant. This is shown in
following diagram.
