# Chapter 3: The IS

```Chapter 3: The IS-LM Model
Kornkarun Kungpanidchakul, Ph.D.
Macroeconomics
MS Finance
Chulalongkorn University, Spring 2008
Introduction
• The IS-LM model is developed by Sir John
Hicks and Alvin Hansen. It is widely used
to analyze the impact of the money market
and the interest rate on output.
The IS Curve
• The IS curve represents the locus of all
equilibriums in the output market. It is
determined by the following equations:
Q=C+I+G
(1)
C = C0+c(1-t)Q
(2)
I = I0 – br
(3)
G = G0
(4)
With t&gt;0 is a tax rate, r&gt;0 is the interest rate, c&gt;0 is
consumption propensity, C0,I0 and G0 are
constant.
The IS Curve
From (1) – (4), we have
1
1  c(1  t )
r  (C0  I 0  G0 ) 
Q
b
b
(5)
(5) defines the relationship between output and
interest rate in the equilibrium in the output
market.
The IS Curve
From (5), we have the IS curve as follows:
r
Q
The LM Curve
• The LM curve represents the locus of all
equilibriums in the money market. It can
be defined by:
Ms/P = MD/P
MD /P=kQ - hr
Ms = M0
with k,h &gt;0, M0 is constant.
(6)
(7)
(8)
The LM Curve
From (6)-(8) we have:
1 M 0 kQ
r

h P
h
(9)
The LM Curve
• From (9), we have the LM curve as follows:
r
Ms &gt;MD
Ms &lt; MD
Q
The equilibrium when price is fixed
r
LM
IS
Q
Qo
Qf
The equilibrium when price is fixed
r
• Suppose that the
central bank increases
the money supply.
LM1
• The immediate effect is
that the interest rate
drops to r1 at point B.
• At r1, there is excess
demand in the output
market. The economy
IS
Q point C with the higher
interest rate.
LM0
r0
A
C
r2
r1
B
Qo
Q1
The equilibrium when price is
flexible
• Price is rigid only in the short run.
• In the long run, price is flexible and output
is at the full employment level (QF).
• From (5), the interest rate is constant, r=rF
as well.
• Consider the equilibrium in the money
market: M0/P = kQF-hrF. An increase in the
money stock leads to price increase only.
There is no effect on real variables.
Liquidity Trap
• It is the situation in which the money demand is
perfectly elastic. Usually, liquidity trap occurs at
very low interest rate.
• An increase in money supply cannot change the
interest rate when there is a liquidity trap.
• When there is a liquidity trap, the fiscal policy is
more effective since there is no crowding out
effect.
```