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Hakan Yetkiner
http://www.hakanyetkiner.com
Izmir University of Economics
Department of Economics
ECON 202
MACROECONOMIC THEORY
Dr. Yetkiner
11 April 2013
Key to Exercise 04
IS-LM Model
1. Suppose that the following information is given for an economy:
̅,
̅
̅
̅
(
),
,
,
̅ , ve
.
̅
,
(a) Find the IS equation.
(b) Find the LM equation.
(c) Find the equilibrium income (GDP) and interest rate.
Let us start solving the problem from IS equation:
̅
(̅
)
(
(
̅
̅
(
))
̅
(
))
̅
̅
̅ . We need to expresses interest rate in terms of
̅
̅
where ̅
in the equation above to find the IS equation:
̅
(
(
))
LM equation is obtained through the money market equilibrium:
̅
̅
̅
̅
Equilibrium income and interest rate are found through equating these two
equations:
̅
(
̅
(
̅
̅
̅
))
(
̅
(
))
1
Hakan Yetkiner
http://www.hakanyetkiner.com
̅
̅ ̅
[
(
(
))
Izmir University of Economics
Department of Economics
]
̅ ̅̅̅ ̅
[
(
(
))
]
If we use this result in any equation above, we find the equilibrium :
̅
̅ ̅̅̅ ̅
̅
[(
(
[
))
]
]
After finding equilibrium
values, one can easily calculate multiplier effect
of several exogenous components. For example, let us find out the multiplier
effect of government spending on GDP. To this end, we need to take partial
derivative of
with respect to ̅ :
̅
̅
(
(
[
))
]
.
Please find the following multipliers as an exercise:
̅
,
,
̅
̅
.
2. Suppose that the following information is given for an economy:
),
( )(
( ) ,
,
( )
(
) ,
ve
.
(a) Find the IS equation.
(b) Find the LM equation.
(c) Find the equilibrium income (GDP) and interest rate.
(a) IS equation can be found through income-expenditure equality:
(
){
( ){
(
)
[
(
(
) ]}
) }
2
,
Hakan Yetkiner
http://www.hakanyetkiner.com
(
(
)
Izmir University of Economics
Department of Economics
)
Hence, IS equation is
(b) LM equation is found through money market equilibrium:
( )
( )
(
)
(c) Equilibrium income and interest rate are found by equating IS and LM
equations:
As an exercise, now try to find the impacts of
and :
̅
,
̅
,
̅
.
3
̅
and
̅
on