Question

Suppose that the reserve requirement for checking deposits is 12.5 percent and that banks do not hold any excess reserves.

If the Fed sells $2 million of government bonds, the economy’s reserves Increase/Decrease by________million, and the money supply will Increase/Decrease by_________million.

Now suppose the Fed lowers the reserve requirement to 10 percent, but banks choose to hold another 2.5 percent of deposits as excess reserves.

True or False: The money multiplier will remain unchanged.

a. True
b. False

True or False: As a result, the overall change in the money supply will remain unchanged.

a. True
b. False

Answer 1

The economy's reserves decrease by $2 million, and the money supply will also decrease due to the Fed's sale of $2 million of government bonds. The money multiplier remains unchanged after the Fed alters the reserve requirements and banks adjust their excess reserves, but the overall change in the money supply will decrease.

Step-by-step explanation:

When the Fed sells $2 million of government bonds, the economy's reserves decrease by $2 million because banks use their reserves to buy the bonds. Consequently, the money supply will decrease as a result of the reduced reserves available for banks to make loans.

If the Federal Reserve lowers the reserve requirement to 10 percent, and banks choose to hold an additional 2.5 percent of deposits as excess reserves, the money multiplier will indeed change. The money multiplier is calculated as 1 divided by the reserve ratio (required reserves plus excess reserves). In the first scenario with a reserve requirement of 12.5 percent and no excess reserves, the money multiplier is 1 / 0.125 = 8. After the change to a reserve requirement of 10 percent and 2.5 percent excess reserves, the new reserve ratio is 0.125 (10 percent + 2.5 percent), so the money multiplier remains 1 / 0.125 = 8, showing that the money multiplier will remain unchanged, which makes the first statement true.

However, even if the money multiplier remains the same, the actual change in money supply depends on the initial amount of reserves and how they are multiplied through the banking system. Since the initial reserves have decreased due to the sale of bonds, the overall change in the money supply will also decrease. This means the second statement is false.

Answer 2

1) If the Fed sells $2 million of government bonds, the economy’s reserves Decrease by $2 million, and the money supply will Decrease by $16 million.

2) The money multiplier will remain unchanged. True

3) As a result, the overall change in the money supply will remain unchanged. True

Step-by-step explanation:

1.) We have the reserve requirement for checking deposits as 12.5% with banks not holding any excess reserves.

To calculate Money Multiplier:

Money Multiplier =
`(1)/(required reserved ratio)` =
`(1)/(0.125)` = 8

If the Fed sells $2 million of bonds, reserves will decrease by $2 million and the money supply will decrease by 8 x $2 million = $16 million.

2) and 3) Now the Fed lowers the reserve requirement to 10 percent, but banks choose to hold another 2.5 percent of deposits as excess reserves.

To calculate Money Multiplier:

Money Multiplier =
`(1)/(required reserved ratio)` =
`(1)/(0.1+0.025)` = 8

Money multiplier is 8 same as in 1) Therefore the statements: "The money multiplier will remain unchanged" and "As a result, the overall change in the money supply will remain unchanged" are both True.