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PROBLEMS
1.
Suppose the following data apply:
Total Bank
Reserves
Total Bank
Deposits
Cash Held by
the Public
$6 billion
Stocks held by public
$140 billion
$100 billion
Gross Domestic
Product
Interest rate
$5 trillion
Bonds Held by
the Public
$220 billion
Required reserve
ratio
0.05
LO: 2
a.
b.
c.
d.
$10 billion
How large is the money supply as measured by M1?
How much excess reserves are there?
What is the money multiplier?
What is the available lending capacity?
AACSB: Analytic
a.
b.
c.
d.
2.
6 percent
BT: Application
The basic money supply (M1) is transaction account balances and
cash. Assuming that the total bank deposits are in transactions
accounts the money supply is $110 billion.
If the required reserve ratio is 0.05, then banks are required to
keep $5 billion in reserve ($100 billion X 0.05). Since banks have
total reserves of $6 billion, there is $1 billion in excess reserves.
The money multiplier is calculated as 1/(required reserve ratio).
Thus, the money multiplier is 1/0.05 = 20.
Since there are $1 billion in excess reserves and the money
multiplier is 20, there is $20 billion in available lending capacity.
Assume that the following data describe the condition of the commercial banking
system:
Total Reserves:
$100 billion
Transactions deposits:
$800 billion
Cash held by public:
$100 billion
Reserve requirement:
0.125
a.
b.
c.
d.
e.
f.
How large is the money supply (M1)?
Are the banks fully utilizing their lending capacity? Explain.
What would happen to the money supply initially if the public deposited
another $50 billion in cash in transactions accounts? Explain.
What would the lending capacity of the banking system be after such a
portfolio switch?
How large would the money supply be if the banks fully utilized their
lending capacity?
What three steps could the Fed take to offset the potential growth in M1?
LO: 2
3.
LO: 3
AACSB: Analytic
BT: Application
a.
The money supply (M1) is $900 billion ($100 cash plus $800
Transactions Deposits).
b.
In this situation banks are fully utilizing their lending capacity.
$100 billion of reserves are required at the required reserve ratio
of 0.125. This is calculated as $800 billion in deposits x 0.125.
Thus, there are no excess reserves; ER=0 when fully utilizing
lending capacity.
c.
Assuming this $50 billion cash is not new money in the system,
i.e., it is part of the $100 billion in cash currently being held, then
there will be no change in M1.
d.
After the additional deposit of $50 billion in cash, now required
reserves are $850 billion x 0.125=106.25, and total reserves will
initially be $150 billion. Now, therefore, there are excess reserves
of $150 billion – 106.25 billion = $43.75 billion. The lending
capacity of the banking system is now $43.75*8 = $350 billion.
The money multiplier is 1/RR= 1/0.125=8.
e.
Assuming the lending capacity of $350 billion is fully used, the
money supply will rise to $1,250 billion. This consists of the
current $850 billion in transactions deposits, $50 billion in cash
remaining after the deposit was made, plus $350 billion in new
money created through the lending process.
f.
To offset the potential growth in M1 illustrated in ‘e’, the Fed
could increase the reserve requirement, raise the discount rate, or
sell bonds in the open market.
Suppose the Federal Reserve decided to purchase $10 billion worth of
government securities in the open market.
a.
How will M1 be affected initially?
b.
How will the lending capacity of the banking system be affected if the
reserve requirement is 20 percent?
c.
How will banks induce investors to utilize this expanded lending capacity?
AACSB: Analytic
BT: Application
When the Fed purchases $10 billion of securities on the open market:
a.
b.
c.
M1 will increase by $10 billion, assuming that the sellers of the
securities hold the proceeds as cash or deposit them in a
transactions account, e.g., checking account.
Lending capacity will increase by $40 billion. (A money
multiplier of 5 x excess reserves of $8 billion.)
As the money supply increases, interest rates go down and
investors will want to borrow more funds.
4.
LO: 4
Suppose the economy is initially in equilibrium at an output level of 100 and
price level of 100. The Fed then manages to shift aggregate demand rightward by
20.
a.
Illustrate the initial equilibrium (E1) and the shift of AD.
b.
Show what happens to output and prices if the aggregate supply curve is
(1) horizontal, (2) vertical, and (3) upward sloping.
AACSB: Analytic
BT: Application
When the economy is at an equilibrium output of 100 and a price level is
100, the impact of a shift in AD rightward by 20 is illustrated below:
(a)
Initial equilibrium is E1.
(b)
Output and price changes vary according to the shape of the AS
curve.
1
1
Aggregate
supply
P1
P5
Aggregate supply
P4
AD1
0
0
0
E1
AD2
AD5
0
1
QF
0
AD4
0
E1
R ATE O F OU T PUT
RATE OF OUTPUT
1
A gg re ga te
su pply
P7
P6
A D7
AD6
0
0
0
E1
Q7
1
R AT E O F O U TP U T
5.
LO: 3
Illustrate the effects on bank reserve of an open-market sale. (See Figure 14.5)
AACSB: Analytic
BT: Application
An open market sale of government securities by the Federal Reserve would
have exactly the opposite effect of the change illustrated in Figure 14.5:
1
Step 1, FMOC sells government bond to the public, who pays by check.
Step 2, Funds are withdrawn from buyer’s private bank.
Step 3, Private bank’s account at Regional Federal Reserve Bank is debited.
6. How did the money multiplier change when China increased its reserve requirement?
(see Headline p. 299)
LO: 2
AACSB: Analytic
BT: Application
When the reserve requirement increased from 10.5 percent to 11 percent, the
money multiplier decreased from 9.5 to 9.1.