IS-LM analysis: deriving the IS
curve
Extension Class Presentation
Ruth Tarrant
Consumption (C)
Consumption functions
45⁰ line Income = consumption
C = a + bY
a = y-intercept =
autonomous
consumption (i.e. the
level of consumption
when income is zero)
b = slope of the line =
marginal propensity to
consume
Yo
Income (Y)
At Yo, we say there is equilibrium, as consumption = income
Transferring this to Aggregate
Demand
AD
45⁰ line
AD
1. At Yo, the goods market
in the economy is in
equilibrium: AD = Y
2. In equilibrium, injections
= withdrawals
3. So, we can assume that
Savings = Investment
Yo
Income
Developing the IS curve
• An IS (Investments = Savings) curve shows the
different combinations of income (Y) and
interest rates (r) at which the goods market is
in equilibrium
Aggregate
Demand
45⁰ line
AD1
Income
Interest
Rate
Y0
Assume that the rate of interest in the
economy is r0. At this rate of interest,
aggregate demand is shown as AD1. So,
when the rate of interest is r0, the goods
market of the economy is in equilibrium at
y0 .
r0
We can now plot a point on the bottom
diagram, at the intersection of r0 and y0.
At this point we know that the goods
market in the economy is in equilibrium
Y0
Income
Aggregate
Demand
45⁰ line
AD2
AD1
Now suppose that interest rates are
lowered, to r1. Lower interest rates
boost consumer spending and
investment, and so AD rises.
We draw a new AD curve at AD2. At
this higher level of AD, the economy’s
goods market equilibrium is achieved
at Y1.
Y1
Income
Interest
Rate
Y0
Now we plot a point at the
intersection of Y1 and r1 to indicate the
point at which the goods market is in
equilibrium.
r0
r1
Y0
Y1
Income
Aggregate
Demand
45⁰ line
AD2
AD1
Y0
Y1
Income
We can repeat this process for all interest
rates, and then plot all of the relevant points
on the bottom diagram.
Interest
Rate
If we join the dots, we create an IS curve.
r0
r1
IS
Y0
Y1
Income
The slope of the IS curve
• Why might the IS curve be steep? Shallow?
• The slope of the IS curve depends on the
sensitivity of AD to interest rate changes
– If changes in interest rates only lead to a small
change in AD, the IS curve will be steep
– If changes in interest rates lead to a large change
in AD, the IS curve will be shallow
Shifts in the IS curve
• Remember, the IS curve shows the effect of
interest rates in shifting AD and the resultant
level of income
• If anything else changes, the IS curve will shift
Shifts in the IS curve
• What would happen to the IS curve if:
– Government spending increased?
– Consumer confidence fell?
– Business optimism about future profits improved?