Eco 202
Problem Set 10
Name_______________________________
27 July 2012
C&T chapter 15
1. a. Suppose that banks have decided they need to keep a reserve ratio of 10%—this guarantees
that they’ll have enough cash in ATM machines to keep depositors happy, and enough electronic
deposits at the Federal Reserve so that they can redeem checks presented by other banks. What
is the money multiplier in this case?
The money multiplier is 1/(reserve ratio). In this case, that’s 1/0.10 = 10.
b. If depositors start visiting the ATM a lot more often, will banks want to have a higher reserve
ratio or a lower reserve ratio? Will this increase the money multiplier or lower it?
If people start visiting the ATM more often, then banks will want to keep more reserves. This
will raise the reserve ratio, which will lower the money multiplier.
2. If the Federal Reserve wants to lower interest rates via open market operations, should it buy
bonds or should it sell bonds?
The Fed should buy bonds to raise the reserve supply and push rates down. Buying bonds raises
the demand for bonds, which raises the price of bonds, thus lowering the interest rate on bonds.
This is worth practicing: Even many experts in the field slip up from time to time.
3. Practice with money multipliers. Think of the “money supply” (MS) as equal to either M1 or
M2.
a. RR = 5%, Change in reserves = $10 billion. MM = ______ ; Change in MS = _________
b. RR = _______, Change in reserves = −$1,000. MM = 5 ; Change in MS = _________
c. RR = 100%, Change in reserves = $10 billion. MM = ______ ; Change in MS = ________
3. a. MM = 1/0.05 = 20. Change in MS = 20 × $10 billion = $200 billion
b. RR = 1/0.2 = 5. Change in MS = 5 × −$1,000 = −$5,000
c. MM = 1/1 = 1. Change in MS = 1 × $10 billion = $10 billion. Some monetarists and other
monetary reformers have supported a mandatory 100% reserve requirement, in order to give the
Fed better control over aggregate demand.
4. In the previous question, one example assumed that banks kept a 100% reserve ratio. Some
economists have recommended that all banks be required by law to keep 100% of their deposits
in the bank vault, at the Federal Reserve, or invested in ultrasafe investments such as short-term
U.S. Treasury bills.
a. If this happened, what would be money multiplier be equal to?
With 100% reserves, the money multiplier would equal 1.
b. If this happened, would the interest rate on bank deposits probably go up or down?
With 100% reserves, the interest rate on bank deposits would probably go down: Banks earn
interest by investing in businesses and splitting some of the proceeds with depositors. If they
weren’t allowed to do this, they’d have fewer profits to split with depositors. This would push
down the interest rate on deposits. Banks might even charge depositors for protecting their cash.
c. If this happened, would people be more likely or less likely to invest their savings in bank
alternatives, such as bonds, mutual funds, or their cousin’s lawn-mowing business?
With 100% reserves, the lower interest rate would push people to save in bank alternatives: They
would buy more money market mutual funds, buy government and corporate bonds, or perhaps
even invest in local businesses directly. In short, they would replicate some of the activities of
modern banks.
5. The main interest rate that the Federal Reserve tries to control is the Federal Funds rate, the
interest rate that banks charge on short-term (usually overnight) loans to other banks. Let’s see
how much interest a bank can earn if it lends money at the Federal Funds rate. Virginia
Community Bank has $2,000,000 of extra cash sitting in its account at the Federal Reserve Bank
of Richmond. It gets a call from Bank of America asking to borrow the whole $2,000,000 for
24 hours. (This is typical: It’s usually the smaller banks lending money overnight to the bigger
banks.)
a. If the annual interest rate on federal funds is 4%, what is the one-day interest rate on federal
funds? (Note that interest rates, like GDP growth rates, are usually reported as “per year,” just as
speeds are reported as miles “per hour.”)
We can get an approximate daily rate by dividing by 365. Thus, 4.00/365 = 0.011% per day.
b. How many dollars of interest will Virginia Community Bank earn for lending this money for
one day?
$2 million × 0.011% = $220. This might pay the daily salary of two tellers or one loan officer.
c. If Virginia Community Bank lent this amount every day at the same rate for an entire year,
how much interest would it earn?
Unsurprisingly, this is 4% of $2 million: $80,000.
6. Let’s use the model of the supply and demand for bank reserves to explain how the Federal
Reserve can change aggregate demand in the short run. Remember that the Federal Reserve
controls the supply of bank reserves, but private banks create demand for bank reserves.
a. After a meeting, the Federal Reserve’s Open Market Committee votes to cut interest rates
from 2% to 1.5%. How will they make this happen: Will they increase the supply of reserves or
decrease the supply?
To cut the rate, the Fed will increase the supply of reserves through open market purchases.
b. As a result of your answer to part a, will banks usually lend more money in response, or will
they lend less money? Will this tend to increase the nation’s money supply, lower it, or will it
have no net effect on the money supply?
The rise in reserves will encourage banks to lend more money, which will increase the money
supply.
c. Will this typically increase aggregate demand or lower it?
This increase in the money supply will raise aggregate demand.
7. We mentioned that the central bank can influence a short-run real interest rate—this is
because in the short run the inflation rate is relatively constant but the central bank can adjust the
nominal rate on short-term loans. Recall that after investing in a T-bill, the real rate that investors
receive is
Real interest rate = Nominal interest rate
Inflation
a. If inflation is 3% and the Fed wants the real rate on short-term loans to be 2%, what should it
set the nominal Fed Funds rate equal to?
The nominal Fed Funds rate should be set to 5% according to the Fisher equation of Chapter 12.
b. If inflation is 3%, and the Fed wants to encourage borrowing by cutting the real rate on shortterm loans to 21%, what should it set the nominal Fed Funds rate equal to?
The nominal Fed Funds rate should be set to 2%.
c. If inflation is 6%, and the Fed wants to discourage borrowing by raising the real rate on
short-term loans to 4%, what should it set the nominal Fed Funds rate equal to?
The nominal Fed Funds rate should be set to 10%.