fractional reserve banking

Banks create money by lending. Few understand this.

Alice and Bob are on a desert island. Alice has $100, which she deposits in the Desert Island Bank (DIB). The island also has a central bank which imposes a reserve requirement on commercial bank lending, meaning that the DIB is required to hold 10% of its assets in an account at the central bank. This leaves it with $90 available to lend.

Bob then takes out a $90 loan from the bank. Now:

• Alice's account has a balance of $100 (the amount she deposited)
• Bob's account has a balance of $90 (the loan he took out)

Adding up the balances, there is now $190 on the island. The loan created ninety dollars! Meanwhile the bank (DIB) now has $190 of liabilities (the account balances) and $190 of assets:

• $10 of reserves at the central bank
• the remaining $90 of Alice's deposit, and
• an IOU for $90 from Bob.

The bank must now increase its reserves to $19, leaving it with $81 available to lend to Charlie (who is also hungry for a loan). This action leads to $271 of accounts, and the bank must increase its reserves to $27.10. How long can the bank keep doing this? If it keeps lending, eventually the whole of Alice's original $100 deposit will be in reserve at the central bank, and it will constitute 10% of total bank assets, with $900 of IOUs constituting the rest. Bank lending has therefore multiplied the money supply by a factor of 10, from the original $100 to a total of $1000.

We say that the $100 is the base money supply, and $1000 the broad money supply. In general, the broad money supply is bounded by a multiple 1 / (1 - reserve requirement) of the base supply (this is just the sum of the geometric series described above).

Bank lending may create less than the $900 maximum that the reserve requirement would allow. For example, high interest rates may reduce the demand for loans. The central bank's power to set interest rates therefore allows it to (indirectly) influence the money supply. Apparently there is some empirical evidence that demand for loans, not reserve requirements, tends to be the constraint on lending in practice.

The bank's loans have created money, but they have not yet created any value. Suppose that all value on the island is in the form of widgets, of which there are currently 100; equating this with the base money supply implies an initial price of $1 per widget. If Bob does nothing with his $90 loan, then the only effect of the bank's lending is to increase the money supply to $190, implying an equilibrium per-widget price of $1.90. Then the lending would have simply resulted in inflation.

On the other hand, suppose that Bob uses his borrowed capital to manufacture 100 new widgets. Once Bob sells enough of the new widgets (perhaps to Alice) to pay back his loan, the money supply reverts to the base $100. But that money is now chasing a total of 200 widgets, implying a price of $0.50 / widget. Because the lending was a productive investment, increasing the amount of value on the island, prices ultimately fell: everyone on the island is now effectively wealthier.

Ideally, banks make just enough loans to fund all of the productive investments, but none of the unproductive ones. At the margin, this is determined by interest rates: someone with a productive investment opportunity will be willing to pay a higher interest rate than someone with a less productive opportunity, so lowering interest rates opens up lending to less productive investments. It's the job of the central bank to set a balance: too much lending and we get inflation, but too little and we miss out on opportunities for economic growth.

In response to the new value created by Bob's investment, the central bank may try to encourage DIB to extend new loans (e.g., by setting a low interest rate) so that the money supply increases to match the amount of value on the island. Hopefully, these new loans will lead to new productive investments, generating even more value and creating a virtuous cycle.