Chapter 13 Homework Solutions
1. If the Fed sells $2 million of bonds to the First National Bank, what happens to
reserves and the monetary base? Use T-accounts to explain your answer.
If we assume that First National Bank pays for the bonds out of reserves, then there will
be a $2 million decrease in reserves at First National Bank and a $2 million increase in
securities. At the Fed, there is a decline of $2 million in reserve liabilities and a $2
million decline in securities (assets).
Reserves
Securities
First National Bank
Assets
-$2 million
+$2 million
Securities
Assets
-$2 million
Liabilities
Federal Reserve
Reserves
Liabilities
-$2 million
The monetary base is defined as currency in circulation plus reserves. The $2 million
drop in reserves means that the monetary base fell by $2 million.
2. If the Fed sells $2 million of bonds to Irving the Investor, who pays for the bonds with
a briefcase filled with currency, what happens to reserves and the monetary base? Use Taccounts to explain your answer.
This transaction causes currency in circulation to fall by $2 million. Since the entire
transaction was carried out in cash, there is no change in bank reserves. The monetary
base still falls by $2 million, though.
Irving the Investor
Currency
Securities
Assets
-$2 million
+$2 million
Securities
Assets
-$2 million
Liabilities
Federal Reserve
Currency
Liabilities
-$2 million
7. Suppose that the Fed buys $1 million of bonds from the First National Bank. If the
First National Bank and all other banks use the resulting increase in reserves to purchase
securities only and not make loans, what will happen to checkable deposits?
This is a somewhat tricky question in that you are not told who First National Bank
purchases securities from. The Fed’s purchase causes reserves in the banking system to
rise by $1 million. First National then uses this $1 million to purchase securities
(presumably from someone other than the Fed!) Suppose they buy the security from an
individual. This means that there is now $1 million more currency in circulation.
Suppose that $1 million is deposited in the bank. The bank then places a required
fraction of this $1 million in reserves (based on the reserve requirement) and uses the
remainder to purchase a security. With a 10% reserve requirement, the bank will buy
$900,000 worth of securities. The person who sold these securities will now have
$900,000 to deposit in the bank. They do so and total deposits are now $1 million at the
first bank and $900,000 at the second bank = $1,900,000. The second bank places 10%
of the $900,000 in reserve and uses the remaining $810,000 to buy securities from
another individual. That individual deposits the proceeds from her sale into her bank
and the process continues. Evenutally through the process of multiple deposit creation,
the total value of deposits created will be $1 million * (1/rr) = $1 million * (1/0.1) = $10
million.
8. If the Fed buys $1 million in bonds from the First National Bank, but an additional
10% of any deposit is held as excess reserves, what is the total increase in checkable
deposits?
Assuming that there is a 10% reserve ratio, then holding 10% excess reserves will lead to
20% of total deposits being held in reserve. The simple money multiplier becomes 1/0.2
= 5. As a result, multiple deposit creation will turn $1 million of reserves into $5 million
of deposits.
12. If the required reserve ratio on checkable deposits increases to 20%, how much
multiple deposit creation will take place when reserves are increased by $100?
Recall that reserves are related to deposits by the following formula:
ΔD = (1/rr)* ΔR, where rr is the reserve requirement.
ΔD =(1/0.2)*100 = $500
15. If you decide to hold $100 less cash than usual and therefore deposit $100 in cash in
the bank, what effect will this have on checkable deposits in the banking system if the
rest of the public keeps its holdings of currency constant?
According to the situation outlined above, there will be a $100 increase in reserves.
Through the process of multiple deposit creation, we will see a $100/rr increase in
deposits. If rr = 10%, then deposits will rise by $1000. If rr was 5%, deposits would rise
by $2000. If rr was 20%, deposits would only rise by $500.