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METU
Department of Economics
Econ 202 Macroeconomic Theory
Spring 2010
Answers of Problem Set 3
Q.1
Assume the following ISLM model:
C = 80 + 2/3Y
d
;
M
d
= 1/2Y + 400 – 20i;
T = 1/4Y + 20;
I = 250 – 5i;
TR = 80
P = 1;
G = 130;
M
s
= 500
a)
Derive the IS curve.
Y = 80 + 2/3(Y  1/4Y – 20 + 80) + 250 – 5i + 130 = 500 + 1/2Y – 5i
Y = 500 + 1/2Y – 5i
Y = 2(500 – 5i) = 1000 – 10i
b)
Derive the LM curve.
500 = 1/2Y + 400 – 20i
Y = 200 + 40i
c)
Calculate the equilibrium value of income.
1000 – 10i = 200 + 40i
i
eq
= 16 and Y
eq
= 840
d)
What is the value of the government spending multiplier when interest rates are assumed to be
constant?
Multiplier = [1/1c(1t)] = 1/[2/3(13/4)] = 2
e)
Calculate the equilibrium values of investment, tax revenues, and real money demand.
I = 250 – 5*16 = 170;
T = (1/4)*840 – 20 = 190;
= 500
f)
How much of I will be crowded out if the government increases its expenditure by ∆G = 100?
∆IS = 2*100 = 200 then,
1200 – 10i = 200 + 40i
→
= 20 and
= 1000
Since ∆i = 4, ∆I = 4*5 = 20
Check: I = 250 – 5*20 = 150
g)
What is the value of the government spending multiplier when interest rates are allowed to vary?
Multiplier = ∆Y/∆G = 160/100 = 1.6 (the multiplier is reduced)
Q.2
ܥ=ܥ
+ܿ
ଵ
ሺܻ−ܶሻ; ܫ=ܾ
−ܾ
ଵ
݅; ሺܯ/ܲሻ
ௗ
=݉
ଵ
ܻ−݉
ଶ
݅; ܩܽ݊݀ܶܽݎ݁ܿ݊ݏݐܽ݊ݐ.
a)
How should the parameters b1, m1, and m2 be interpreted?
is the sensitivity of investment to changes in the interest rate.
is the sensitivity of real
money demand to changes in income, and
is the sensitivity of real money demand to changes
in the interest rate.
b)
Use the ISLM model to graphically determine the effectiveness of fiscal versus monetary
policy when investment is very sensitive to changes in i, and money demand is very insensitive
to changes in i.
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IS relation is:
=
−
ሾ
++−
ሿ=
−
ሾ
+
−
+−
ሿ
Notice that when
is larger (investment more sensitive to changes in i, the IS curve is flatter.
LM relation is
:
/=
−
. When
is smaller (real money demand less sensitive to
changes in i, the LM curve is steeper.
c)
Now suppose that the government imposes a tax,
ݐ
ଵ
, on income, so that the following is true:
ܶ=ݐ
+ݐ
ଵ
ܻǡ Ͳ൏ݐ
ଵ
൏ͳ
. If money demand is very insensitive to changes in the interest rate, is a
decrease in the income tax rate an effective way to stimulate the economy?
Q.3
Suppose the goods market is described as follows:
Goods Market:
ܥ=ܽ+ܾሺܻ−ܶሻǡ ܽͲǡͲ൏ܾ൏ͳ
.
ܫ=݁−݂݅ǡ ݁ǡ݂Ͳ
.
ܩ=ܩ
ǡ ܩ
Ͳ
ܶ=݄ܻǡ Ͳ൏݄൏ͳ
.
Money Market:
ሺܪ
௦
/ܲሻ݅ݏ
ሺܯ/ܲሻ
ௗ
=ݑܻ−ݒ݅݅ݏݐ݄݁ݎ݈݁ܽ݉݊݁ݕ݀݁݉ܽ݊݀
=
−ሺ−
ሻ
ሾ
+
−
+−
ሿ
IS relation is now:
Lowering the income tax rate increases the multiplier.
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 Spring '10
 tunc
 Macroeconomics, Interest Rates, ISLM Model, Monetary Policy, lm curve

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