Question

Assume that banks do not hold excess reserves and that households do not hold currency, so the only form of money is demand deposits. To simplify the analysis, suppose the banking system has total reserves of $500. Determine the money multiplier and the money supply for each reserve requirement listed in the following table.

Reserve Requirement	Simple Money Multiplier	Money Supply
(Percent)		(Dollars)
5
10

A lower reserve requirement is associated with a   money supply.

Suppose the Federal Reserve wants to increase the money supply by $200. Again, you can assume that banks do not hold excess reserves and that households do not hold currency. If the reserve requirement is 10%, the Fed will use open-market operations to   

worth of U.S. government bonds.

Now, suppose that, rather than immediately lending out all excess reserves, banks begin holding some excess reserves due to uncertain economic conditions. Specifically, banks increase the percentage of deposits held as reserves from 10% to 25%. This increase in the reserve ratio causes the money multiplier to   to   . Under these conditions, the Fed would need to   

worth of U.S. government bonds in order to increase the money supply by $200.

Which of the following statements help to explain why, in the real world, the Fed cannot precisely control the money supply? Check all that apply.

The Fed cannot control the amount of money that households choose to hold as currency.

The Fed cannot prevent banks from lending out required reserves.

The Fed cannot control whether and to what extent banks hold excess reserves.

Answer 1

Simple money multiplier is calculated as follows -

Simple money multiplier = 1/Reserve requirement

Money supply is calculated as follows -

Money supply = Total reserves * Simple money multiplier

Following is the complete table -

Reserve requirement	Simple money multiplier	Money supply
5	20	10,000
10	10	5,000

A lower reserve requirement is associated with larger money supply.

When Fed wants to increase money supply, it buys the government bonds.

When the reserve requirement is 10. The money multiplier is 10.

Amount of bonds to buy = Desired increase in money supply/Simple money multiplier

Amount of bonds to buy = $200/10 = $20

The Fed will use open market operations to buy $20 worth of US government bonds.

New reserve ratio = 25%

Money multiplier = 1/0.25 = 4

Thus,

This increase in the reserve ratio causes the money multiplier to decrease to 4.

Amount of bonds to buy = Desired increase in money supply/new money multiplier

Amount of bonds to buy = $200/4 = $50

Thus,

Under these conditions, the Fed would need to buy $50 worth of US government bonds in order to increase the money supply by $200.

The following are the required statements -

1. The Fed cannot control the amount of money that households choose to hold as currency.

2. The Fed cannot control whether and to what extent banks hold excess reserves.