THE MONEY MULTIPLIER 

The creation of money does not stop with First National Bank. Suppose the borrower from F national uses the $90 to buy something from someone who then deposits the currency in Second National Bank. Here is the T-account for Second National Bank:

SECOND NATIONAL BANK

SECOND NATIONAL BANK

After the deposit, this bank has liabilities of $90. If Second National also t keeps assets’ of $9 in reserve and makes $81 in loans. In this way additional $81 of money. I,~this $81 is eventually deposited in Third ‘National  reserve’ ratio of 10 percent, this bank keeps $8.1 0 in reserve and T-account for Third National Bank!

SECOND NATIONAL BANK

SECOND NATIONAL BANK

It turns out that even though this process of money creation can continue forever, it does not create an infinite amount of money. If you laboriously add the infinite sequence of numbers in the fore going example, you find the $100 of reserves generates $1,000 of money. The amount of money the banking system generates with each dollar of reserves is called the money multiplier. In this imaginary economy, where the $100 of reserves generates $1,000 of money, the money multiplier is 10. What determines the size of the money multiplier? It turns out that the answer is simple: The money multiplier is the reciprocal of the reserve ratio. If R is the reserve ratio for all banks in the economy, then each dollar of reserves generates dollars of money. In our example, R = 1/10, so the money multiplier is 10. This reciprocal formula for the money multiplier makes sense. If a bank. holds $1,000 in deposits, then a reserve ratio of 1/10 (10 percent) means that the bank. must hold $100 in reserves. The money multiplier
just turns this idea around: If the banking system as a whole holds a total of $100 in reserves, it can have only $1,000 in deposits. In other words, if R is the ratio of reserves to deposits at each bank. (that is, the reserve ratio), then the ratio of deposits to reserves in the banking system (that is, the money multiplier) must be 1/R.