Suppose the money supply is currently 500 billion and the Fed wishes to increase it by 100 billion. Given a required reserve ratio of .25, what should it do?

Show how each of the following initially affects bank assets, liabilities, and reserves. Do not include the results of bank behavior resulting from the Fed’s actions. Assume a required reserve ratio of 0.05.

a. The Fed purchases $10 million worth of U.S. government bonds from a bank.
b. The Fed loans $5 million to a bank.
c. The Fed raises the required reserve ratio to 0.10.

To determine how the Fed can increase the money supply by 100 billion given a required reserve ratio of 0.25, we need to understand the process of money creation through the fractional reserve banking system.

1. Calculate the initial required reserves:
The required reserve ratio is given as 0.25, which means that banks are required to hold 25% (or 0.25) of their deposits as reserves. Therefore, the initial required reserves can be calculated by multiplying the current money supply by the reserve ratio:
Required Reserves = 500 billion * 0.25 = 125 billion

2. Determine the potential money creation:
The money creation process arises from the fact that banks can lend out a portion of their deposits, retaining only the required reserves. The lending process allows multiple rounds of deposit creation as each loan becomes a new deposit in another bank.

The formula to calculate potential money creation is:
Potential Money Creation = (1 / Reserve Ratio) * Initial Required Reserves

In this case, the reserve ratio is 0.25, so we can calculate the potential money creation as follows:
Potential Money Creation = (1 / 0.25) * 125 billion = 500 billion

This means that with an initial required reserve of 125 billion, the banking system can potentially create up to 500 billion in additional money supply.

3. Determine the necessary change in reserves:
To increase the money supply by 100 billion, the Fed needs to provide additional reserves to the banking system. This change in reserves is equal to the desired change in the money supply (100 billion) multiplied by the reserve ratio:

Change in Reserves = Desired Change in Money Supply * Reserve Ratio
Change in Reserves = 100 billion * 0.25 = 25 billion

Therefore, the Fed should increase the reserves in the banking system by 25 billion.

4. Implement the policy:
The Fed can increase the reserves in the banking system through various mechanisms, such as open market operations (buying government bonds), decreasing the discount rate (the interest rate charged to banks on loans from the central bank), or adjusting reserve requirements. The specific method chosen will depend on the monetary policy tools available and the objectives of the central bank.

By increasing the reserves in the banking system by 25 billion, the potential money creation by banks would be:
Potential Money Creation = (1 / 0.25) * (Initial Required Reserves + Change in Reserves)
Potential Money Creation = (1 / 0.25) * (125 billion + 25 billion) = 600 billion

As a result, the money supply would increase by 100 billion, reaching a new total of 600 billion.

I am not entirely sure of this but I will explain from what I know. The reserve ratio is the amount of money banks have to have on hand. For example, if a bank had 100 dollars, it is required to keep 25% of it if the ratio os .25. The other 75 can be lent. So 75 is in the money supply. This means that for a reserve ratio of .25, only 75% of the newly added funds go into the money supply. so if the fed wants to increase by 100 mil, it would need to inject .75X=100

X= 400/3 million dollars. Make sense?