Fractional Reserve Banking Mechanics

To understand some future blog posts, you are going to have to understand some of the mechanics of the fractional reserve banking system.

I think I have come up with a simple enough example that allows you to see where the money goes among people, banks, cash, and debt.  In this simple example, we can even track the individual dollar bills.  I have chosen the numbers to make the math very simple.  It all still holds when you scale it up to large amounts of money and down to a more realistic reserve requirement.

Start with $16 in one dollar bills from the U.S. mint with serial number $#1 through $#16. We need 4 banks numbered B1 through B4. 5 People number P1 through P5.

For simplicity, let’s say the reserve rate is 50%. Let’s also say that dollar bills are not divisible.

P1 has 16 dollar bills that he deposits in bank B1. B1 keeps the dollars $#1 through $#8 as a reserve. It then lends $#9 through $#16 to person P2.

Person P2 has a debt of $8 and cash of $8 which he deposits in bank B2. Bank B2 keeps dollars $#9 through $#12 as reserve, and lends $#13 through $#16 to person P3.

Person P3 has a debt of $4 and cash of $4 which he deposits in bank B3. Bank B3 keeps dollars $#13 and $#14 as reserve, and lends $#15 and $#16 to person P4.

Person P4 has a debt of $2 and cash of $2 which he deposits in bank B4. Bank B4 keeps $#15 as reserve and lends $#16 to person P5.

Person P5 just keeps the dollar because banks do not accept accounts of $1 because they cannot lend out part of the indivisible dollar.

This can all be presented visually by a number of charts from a spread sheet.

In this example, at the end of 9 days as you follow the circulation of money through the system, you see that there appears to be $31 of cash in the system even though there are only $16 of U.S. Money created by the U.S. mint.

In other words the Fractional Reserve Banking system has just about doubled the amount of cash given a reserve rate of 50%. The multiplier on the amount of cash created goes up as the fraction of reserves required to be held goes down. If the reserve requirement were 10%, the multiplier would be close to 10.

Don’t be blinded to reality because this example has most people leaving their cash in the bank. If people took some money out of the bank to buy something, the money would end up being deposited somewhere, the effect would be the same, just the math and keeping track would be more complicated.

The power of this scheme becomes really obvious when you consider that a bank is taking deposits from large numbers of people. The bank holds only a fraction of that money in reserve. Under ordinary circumstances, not all depositors will want to turn all their deposits into cash all at the same time. If the normal number of depositors want take cash out of the bank, the reserves accumulated from all the depositors is enough to cover the request. No depositor has to be concerned that the bank is only holding a fractional reserve.

When some extraordinary circumstance arises where a bank’s customers want more cash than the bank is holding in reserve, the Federal Reserve Bank can supply the cash necessary to keep alive the fiction that the bank had the depositor’s money all the time. Even in some extraordinary circumstances, the money the depositors took from one bank will find itself deposited in another bank and the system can remain stable.

In the extraordinary extraordinary circumstance, where the request for withdrawal is more systemic than just a single bank, the Fed can just create enough U.S. Money and feed it to the banks to stabilize the system, as it did in the financial crash of the mid 2000s.

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