To affect the total money supply, you can use a simple formula.
Change in total money supply divided by money multiplier equals the change in necessary reserves.
The money multiplier is the inverse of the reserve ratio, so to calculate that, divide 1 by the reserve ratio.
1 / 0.25 = 4, which is the money multiplier. If you plug that value into the above equation, it looks like so:
100 billion (change in total money supply) / 4 (money multiplier) = 25 billion (change in necessary reserves).
In order to increase the total supply of money in circulation, the reserve will need to increase its funding by $25 billion. In the open market, the Fed can buy government securities total $25 billion, which would infuse that liquid cash into the market and deposit it into banks, giving them enough available capital to cover the increase in total money supply.
A reserve ratio of 0.25 means that banks have to keep 25% of all deposits. A high reserve ratio normally means that the government wants to control money supply by limiting the amount given out as loans. In this case, we can calculate the effect of the reserve ratio on the money supply using the money multiplier.
The formula for money multiplier is as follows: (1/reserve ratio), or in this case, 1/0.25, which is equal to 4.
Since we have the money multiplier, we can use it to estimate the amount of money in circulation. The formula is as follows:
Change in total Money supply / Money Multiplier = Change in the reserves or monetary base.
$100 billion / 4 = $25 billion. So, $25 billion is the change in the monetary base.
This means that if the money supply is to increase by $100 billion, the amount of money in circulation has to increase by $25 billion. Therefore, the Fed should take part in open market operations and buy bonds worth $25 billion. The money will be injected right back into the economy, and it will lead to a $100 billion increase in total money supply due to the effects of the money multiplier.
In order to determine what the Fed needs to do, we must first determine what the money multiplier is. The formula for finding the money multiplier is
Money multiplier = 1 / required reserve ratio.
In the scenario that you have given us, the required reserve ratio is .25. When we plug this into the money multiplier equation, we get
Money multiplier = 1 / .25 = 4.
This means that every new dollar that gets deposited in a bank can create a $4 increase in the overall money supply.
We also know that the Fed wants to create $100 billion in new money supply. We need to use the formula
Change in money supply = change in deposits x money multiplier.
Given that the money multiplier is 4, we can calculate that there needs to be a $25 billion increase in deposits.
So how does the Fed go about doing this? It cannot simply order people to deposit more money. Therefore, it needs to buy government securities. It needs to buy $25 billion in government securities. This money will be deposited in banks and the money multiplier will cause it to create a $100 billion increase in the money supply.