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Homework Assignment #3
Economics 215
Intermediate Macroeconomics
Assigned: Tuesday, April 25, 2000
Due: Thursday, May 4, 2000
1. The Cost of Money Holding. Consider a two period model of the economy.
a. In period 1, the price of goods, P1 = 1. In period 2, the price level is P2 =
1.25. Calculate the net inflation rate P̂2 in period 2. If the real interest rate
is r = 0, what is the nominal interest rate.
ˆ
P2  .25 1  i  1.25
b. Consider a consumer who lives during period 1 and period 2. The
consumer pays no taxes. The consumer will earn income in each period by
selling Q1 = 200 goods in period 1 and Q2 = 100 goods in period 2. Thus,
the income from selling goods in period 1 is P1Q1 = 200. The income
from selling goods in period 2 is P2Q2 = 1.25100=125. At the end of
period 1, the consumer will store any income not spent on consumption in
the form of money M that pays no interest or bonds that pay interest, 1+i.
This wealth plus second period income can be spent on consumption in
period 2. This implies that the budget constraints of the consumer are:
M  B  P1Q1  P1C1
P2 C 2  P2 Q2  M  (1  i)  B
Use the prices in section a to show that these two equations imply that
i M1
C1  C2  300 

1  i P1
M
M
B
B
M  B  P1Q1  P1C1  1   Q1  C1 
 Q1  C1  1
P1 P1
P1
P1
P2 C 2  P2 Q2  M  (1  i )  B 

P2 C 2
PQ
P2
1 M (1  i ) B 1
 2 2 

,

1  i P1 1  i P1 1  i  P1 1  i P1 1  r 1  i P1
C2
Q2
1 M B



1  r  1  r  1  i  P1 P1
C2
Q2
M
1 M


 Q1  C1  1 ,1  r  1
1  r  1  r  1  i  P1
P1
 1
M
 i M
C1  C 2  Q1  Q2  
 1
 C1  C 2  300  

 1  i   P1
 1  i  P1
c. Assume that the consumer smoothes consumption perfectly C  C1  C 2 .
Solve for consumption, C in each period under the following
circumstances,
M1
 0 , C1 = C2 = 150
P1
M
ii. Money holdings are proportional to real output  1  f (Q1 )  .5  Q1
P1
i
 .2 C1+C2 = 300 - .2*.5*200=280C1 + C2 = 140
1 i
i. The consumer holds zero money: 
2. Money Creation and the Price Level
a. In Korea, the currency supply is 500 won (i.e. CU = 500). The currency to
demand deposit ratio is cd = .2 and the reserve to deposit ratio is .2. Solve
for reserves, R; demand deposits, D; high-powered money, Mh; and M1 =
CU+D. D=2500, M1 = 3000, R = 500, Mh = 1000.
b. In Korea, the money demand curve is a function of the output level and
MD
Q
the interest rate. 
 f (Q, i)  .5  . If Q = 500 and money supply is
P
i
equal to M1 from the previous section, what is the price level that sets
money supply equal to money demand when i = .1. What is the price level
that sets money supply equal to money demand when i = .25. Explain with
1 paragraph and 1 graph why the price level is higher in the second case
(when i = .25). i = .1 P = 1.2, i = .25P = 3.
The purpose for holding money is that it is a useful and convenient tool for
conducting transactions. An increase in the nominal interest rate will increase
the opportunity cost of holding wealth in the form of money rather than bonds.
A higher interest rate will provide incentives to households to undertake more
inconvenience (in the form of more frequent trips to the bank) in order to
avoid holding money. Thus, the given stock of money will circulate more
quickly increasing the speed with which money chases goods. Given a stock
of goods, this will increase the price level. At the higher price level, nominal
GDP will be greater making people willing to hold the supply of money at the
higher interest rate. See Figure 1 at end for graph.
c. Assume that an increase in financial technology allows banks to hold
fewer reserves, so that rd falls from .2 to .1. Holding the level of highpowered money constant, solve for the new supply of M1. Using the
money demand curve in section b, solve for the price level when i = .25.
Explain in 1 paragraph and using 1 graph why a drop in reserve ratios
increases the price level. The money multiplier at the original reserve ratio
was (1.2/.4) = 3. The money multiplier at the new reserve ratio is (1.2/.3)
= 4. Holding high powered money constant at 1000, the new money
supply is 4000. The new price level is 4.
As the fraction of deposits banks must hold in the form of reserves falls, they
may make that money money available in the form of loans. Thus, this extra
money which had formerly been locked up in the banks vault would be
available for spending on goods. This would increase the supply of money
available for purchasing goods and will lead to a jump in prices. See Figure 2
for graph.
3. Depreciation Rate. Two countries, Albania and Zimbabwe, have money demand
functions such that the demand for money is the ratio of nominal GDP to velocity
GDP P  Q
M 

V
V
Recall that the growth rate of a ratio is the difference between the growth rate of
the numerator and denominator so the growth rate of money is the growth rate of
GDP divided by the growth rate of velocity: gM = gGDP – gV. Recall, also that the
growth rate of a product of two variables is the sum of the growth rates of the two
variables so the growth rate of GDP is gGDP = gQ + P̂ .
a. Assume that velocity is the constant in both countries (gV = 0) and that the
money growth rate in both countries is always 10% (i.e. gM = .1). The
growth rate of output in Albania is always 2% (gQ = .02) while the growth
rate of output in Zimbabwe is 4%. Solve for the inflation rate in both
countries. Albania’s inflation rate is gM – gQ = 8% while the inflation in
Zimbabwe is 6%
b. The nominal interest rate in Albania is 20% (1+iA= 1.2). Assume that
purchasing power parity holds and that uncovered interest parity holds.
Treating Albania as the home country, solve for the growth rate of the
exchange rate, the nominal interest rate in Zimbabwe, and the real interest
rate in Albania. The real interest rate in Albania is 1.12%. The nominal
interest rate in Zimbabwe is 1.18%. The depreciation rate is 2%.
MD’
FIGURE 1
P
MS
MD
M
FIGURE 2
P
MS
MD
M