In the country Simplifia, there is a Federal Reserve System (Central Bank) and just two commercial banks, First National and Second National. The Fed issues the currency and sets the reserve requirements for the banks, which are 20% of deposits. There are no savings or time deposits, just checking accounts. There are many government bonds in existence, most of which are held by insurance companies, and there is an active bond market. The accounts of the Fed look like this:

[An asset is something owned or owed to; a liability is something owed by, i.e. owed to somebody else. Currency in circulation is a liability of the Fed because (look at a $ bill) it is value the Fed owes the holder]

ASSETS                                                         LIABILITIES         [$ billion]

Government bonds     900                                 Currency in circulation                 1,000

Gold                           200                                 Deposits of commercial banks*     300

Other (buildings etc)     250                                 Other and net worth                       50

Total:                         1,350                                                                                 1,350

* For the commercial banks, these count as reserves.

If the commercial banks keep on average $ 200 billion of currency in their cashiers' tills and vaults,

1. What are the total reserves of the commercial banks?

Commercial bank reserves are the total of "vault cash," the currency in their tills and vaults ($200 billion) plus their deposits with the Fed ($300 billion), so the answer is $500 billion.
 
 

2. What is the monetary base? [Monetary base = currency in circulation outside the banks plus bank reserves]

Currency in circulation outside the banks is $1000 billion minus the $200 billion in the banks, i.e. $800 billion;

Bank reserves are $500 billion; so the answer is $1,300 billion.
 
 

3. What is the maximum possible size of the money supply M1 [equals currency in the hands of the non-bank public plus checkable deposits]?

The reserve requirement is 20%, so each $1 of bank reserves can support $5 of checkable deposits. So the maximum possible value of checkable deposits is 5 times $500 billion, the size of bank reserves. [The deposit creation multiplier is 1 divided by the required reserve ratio, 20%]. So maximum possible checkable deposits are $2,500 billion; add the $800 billion currency in the hands of the non-bank public, and you have $3,300 billion as maximum possible size of the money supply.
 
 

4. If the Fed buys $20 billion worth of existing government bonds from a life insurance company,

a. What happens to its [the Fed's] balance sheet?

Assets?                                             Liabilities?

+$20 billion bonds                         +$20 billion deposits of commercial banks

                                                                            [when the Fed's check clears]
 
 

b. What happens to bank reserves?

+ $20 billion when the commercial bank that gets the Fed's check for the bonds is deposited and the bank adds it to its deposit with the Fed

c. What is the maximum possible change in the money supply M1 (plus or minus)?

$20 billion times 5, because reserves are up $20 billion and each $1 of reserves can support $5 of deposits -- so money supply at maximum could increase $100 billion.