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METU, Department of Economics
ECON 202 Section 1
Spring 2016-2017
Instructor: Hasan Cömert
T.A.: Güney Düzçay
PROBLEM SET 3 & ANSWERS
1- Suppose that a person’s yearly income is $60,000. Also, suppose that this person’s
money demand function is given by
MD=$Y(0.35-i)
MS=15,000
a. What is this person’s demand for money when the interest rate is 5% and 10%?
b. Explain relationship betwee

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1
METU, Department of Economics ECON 202 Section 1 Spring 2016-2017 Instructor:
Hasan Cömert
T.A.:
Güney Düzçay
PROBLEM SET 3 & ANSWERS 1-
Suppose that a person’s yearly income is $60,000. Also, suppose that this person’s
money demand function is given by M
D
=$Y(0.35-i) M
S
=15,000
a.
What is this person’s demand for money whe
n the interest rate is 5% and 10%?
b.
Explain relationship between i and M
D
.
c.
Graph M
S
and M
D
and calculate the equilibrium i.
d.
Suppose that there is an increase in M
S
by 3000. What happens to money market equilibrium? (Solve & graph).
e.
Describe how the Central Bank changes i in the economy.
Answer: a)
i=0.05, M
D
=$Y(0.35-i)= $60,000(0.35-0.05)=$18,000 i=0.10, M
D
=$Y(0.35-i)= $60,000(0.35-0.10)=$15,000
b)
Money demand decreases when the interest rate increases because bonds, which pay interest, become more attractive. That is, the higher interest rate means the higher opportunity cost of holding money. So, people demand less money (hold less).
M
D
= M
D
(Y,i) There is positive relation with Y and negative relation with i.
c)
At equilibrium: M
S
= M
D
15,000=60,000(0.35-i) i=0.1=10%
d)
Equilibrium: M
S
= M
D
18,000=60,000(0.35-i) i=0.05=5%
e)
The CB can increase the interest rate by decreasing M
S
. OMO (open market operation is the basic tool to affect the interest rate.
M
Sold
M
Snew
i
18,000 15,000 21,000 M
2
2-
a. Consider the basic economy in which money consists of currency and checkable deposits. Suppose that people get worried about the possibility of bank runs and decide to hold a higher proportion of money in the form of currency. If the central bank keeps the money supply constant, what will happen to the interest rate? Explain. b. Suppose that banks doubled the number of locations of ATMs, making them more convenient to use for their customers. What would happen to the demand for central bank money? Explain. c. People in many countries that have suffered from high inflation in the past have learned that their domestic currency may quickly become worthless, so they might have seen US dollars as a safe asset. What would happen to US money demand and interest rate, supposing that the Fed does not adjust its money supply, if the degree of civil unrest increased in the rest of the world?
Answers:
a.
This scenario implies that the demand for currency increases and the demand for checkable deposits decreases exactly at the same amount. However, due to a decrease in the demand for deposits, there will only be a small decrease in the demand for reserves (only in proportion to required reserve ratio). Thus, the demand for central bank money increases. Since the central bank keeps the money supply constant, the interest rate will increase.
b.
When the number of ATMs doubled, people will hold less cash at their hands. This is the opposite of the case in part a. The demand for central bank money will decrease. c.
This scenario implies that the demand for US dollars increase. Since the money supply is constant, then the interest rate in the US will increase.
3-
Consumption and investment are given as C= 4000 + 0.20Y; I = 2400
–
4000i. As usual, Y is output and i is the interest rate. Government purchases, G, are 2000. a.
What value of the interest rate clears the goods market when Y = 10,000? What value of the interest rate clears the goods market when Y= 10,200? b.
Government purchases rise to 2400. What value of the interest rate clears the goods market when Y = 10,000? How is the IS curve affected by the increase in G ?
Answer:
a.
Using the equation that goods supplied equals goods demanded gives
Y
C
I
G
(4000
0.2
Y
)
(2400
4000
i
)
2000
8400
4000
i
0.2
Y
. So 0.8
Y
8400
4000
i
, or 4000i
8400
0.8
Y
. When
Y
10,000, 4000i
8400
(0.8
10,000)
400,
3
so
i
0.10. When
Y
10,200, 4000i
8400
(0.8
10,200)
240, so
i
0.06.
b.
When
G
2400, using the equation that goods supplied equals goods demanded gives:
Y
C
I
G
(4000
0.2
Y
)
(2400
4000
i
)
2400
8800
4000
i
0.2
Y
. So 0.8
Y
8800
4000
i
, or 4000i
8800
0.8
Y
.
At
Y
10,000, this is 4000
i
8800
(0.8
10,000)
800, so
i
0.20. The market-clearing real interest rate increases from 0.10 to 0.20. Thus the
IS
curve shifts up and to the right
4-
In a particular economy the real money demand function is:
M
d
/
P
= 2800 + 0.1Y - 10,000i. Assume that M = 6000, P = 2.0. a.
What is the interest rate i, that clears the asset market when Y = 8000? When Y = 9000? Graph the LM curve. b. Repeat Part (a) for M = 6600. How does the LM curve in this case compare with the LM curve in Part (a)?
Answer:
(a)
M
d
/
P
2800
0.1
Y
10,000
i
Setting
M
/
P
M
d
/
P
: 6000/2
2800
0.1
Y
10,000
i
10,00
0i
200
0.1
Y
r
0.02
(
Y
/100,000). When
Y
8000,
r
0.06. When
Y
9000,
r
0.07. These points are plotted as line
LM
a
in Figure below.
4
(b)
M
6600, so
M
/
P
3300. Setting money supply equal to money demand: 3300
2800
0.1
Y
–
10,000
r
10,000
r
–
500
0.1
Y
r
–
0.05
(
Y
/100,000). When
Y
8000,
r
0.03. When
Y
9000,
r
0.04. The
LM
curve is shifted down and to the right from
LM
a
to
LM
b
in Figure, since the same level of
Y
gives a lower interest rate at equilibrium.
5-
Consider the following stylized economy. Good Market Financial Market Goods Demand: Z = C + I + G Money Supply:
= 1600
Consumption: C = 200 + 0.25 Y
D
Money Demand :
= 2 8000
Investment: I = 150 + 0.25Y
–
1000i Government Expenditure: G = 250 Tax Revenue: T = 200
a.
Derive the IS relation.
b.
Derive the LM relation.
c.
Solve for the equilibrium interest rate, equilibrium output, equilibrium private consumption and equilibrium investment.
d.
Now suppose that the money supply increases to M/P=1840 through open market operations. Solve for output, interest rate, consumption and investment and describe in graph.
e.
Set M/P to its initial value of 1600. Now suppose that government spending increases to G=400. What happens to the equilibrium Y, i, C and I when the government expenditure increases?

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