Side IS-LM Model (Part 1): Money, Interest rate & Income in the Short Run
IS-curve
= + + + = 0
IS curve shows the relationship b/w Investment and
Saving
() = ( )
- Private household can be determined
when tax and consumption is subtracted from
aggregate output.
= () +( )
- National Saving can be determined as the summation of private household saving and total tax income
of nation excluding the government spending.
Thus, when savings of private household and nation are combined,
= =
1. Investment function
I=I0-bi
I0
I
i
=
Here,
=
= ( )
: () , .
=
= (
)
, =
=
LM
IS
Y*
i*
i
Y
2. Derivation of IS curve
(
0
=
0
+
+
0
Derivation
= + +
, =
0
+
=
0
=
0
= (
0
+ ) +(
0
) +
0
= (
0
+
0
+
0
) + =
+
Thus, the equation of AD can be displayed as below.
=
+
=
0
(1 )
Thus, the equation of I S-curve can be displayed as below.
( ) +
With AD-equation;
( ) () ( )
I t means that the investment increases up by decreasing interest rate, so the aggregate demand is
correspondingly increased. Considering the I S-curve and its equation, the interest rate for equilibrium will be
decreased as the aggregate demand is increased.
IS-curve slopes down;
( ) ()
Slope of IS-curve is flat when output is responsive to change in interest rate.
- Investment is responsive to interest rate.
- The multiplier is large.
AD
Y
E1
E2
i
Y
E1
E2
i1
i2
Y1 Y2
AD
AD'
IS
3. Slope of the IS-curve
Recall the equation of IS-curve.
( ) +
- Slope of IS-curve is flatter when
I is sensitive to i, which means b is larger.
When b is large I (investment) is increased, the slope of IS-curve will be flatter.
( ) + ,
( <
)
Y
i1
i2
Y1 Y2
IS
IS'
i
Multiplier (c) is large, which means c is large.
( ) + ,
( <
)
Where, due to larger c, the term of (i-c) became smaller, so the slope will be flatter.
- Recall the equation of AD for decrease of investment interest rate,
=
+
=
+ ( ) = ,
+ - +
- Recall the equation of AD for increase of output,
=
+
( ) =
( ) = ,
- +
=
( )
AD
Y
E1
E2
i
Y
E1
E2
i1
i2
Y1 Y2
AD
AD'
IS
dY
IS'
- IS-curve will be flatter, the larger are b & c.
- IS-curve is shifted caused by exogenous increases in aggregate demand, such as
Higher consumer confidence =
0
Higher business confidence = I
0
Higher government spending = G
0
This increase in autonomous spending shifts the AD curve up.
& This shifts the IS-curve right.
( ) +
4. Introducing Money
- Money supply (M) exogenously set by the central bank.
- Demand for money (real balances) (L) is negative function of (nominal) interest rate (i).
=
When interest rates rise, opportunity cost of holding money rises, so people hold less of it.
Positive function of income (Y)
When income rise, money demand rises as transaction demand rises.
i
L
k dY
L1 L2
i1
L1=kY1-hi1
L2=kY2-hi2
- A change in i causes a movement along the L curve.
- A change in Y causes shift in L-curve.
5. Money market equilibrium
- Money market is in equilibrium when the demand for real balances = real money supply
= /
i
L
i*
L=kY-hi
M/P
L*
( /)
- When income (Y) rises (
), money demand curve (L)
- When money demand rises from
to
, interest rate rises from
to
.
i
L
i1
M/P
i2
L1=kY1-hi
L2=kY2-hi
E1
E2
i LM
E1
E2
i1
i2
Y
- A change in Y results in a movement along the LM-curve.
- A higher Y results in higher i.
Slope of LM Curve
- Recall the equation of LM curve,
( /) =
Slope of the LM-curve: /
LM curve steeper the higher is k and the lower is h
Higher k means transaction demand for money is sensitive to Y.
Lower h means demand for money not sensitive to i.
- A large shift in a steeply sloped L curve implies a steep LM curve (Y relative less sensitive to i)
6. What cause LM curve to shift?
i
L
i1
M/P
i2
E1
E2
L1=kY1-hi
M'/P
- For the given price level (P), if the money supply rises, the real money supply curve shifts to right
hand side. It means the equilibrium will be formed at the lower interest for money demand.
i
L
i1
M/P
i2
E1
E2
L1=kY1-hi
M'/P
i
LM
i1
i2
Y
LM'
E1
E2
Y1
- The intercept of LM is
- LM curve shifts down, when real money supply .
M
P
/ rises.
- The size of shift depends on h, the sensitivity of money demand to interest rate.
- The smaller is h, the larger is shift in LM-curve.
IS-LM equilibrium
i
LM
i*
Y
IS
Y*
E
- The point of E is the equilibrium of goods market and service market.
- Along the IS-curve, demands of consumption, investment, and income are satisfied.
- Along the LM-curve, money demand is equal to money supply.
IS-LM equilibrium
- Equilibrium Y and I will change when either the LM or the IS curve shifts.
- An increase
Slide 22 of IS-LM part 1
