Would it even be possible for m2 to remain stable under positive interest rates?

Question

Let's say bank A has 1 of assets and 10% reserve requirements. It lends to bank B 9 Then they lend back and forth so they both have 50 of assets and liabilities (or whatever they can).

Then those liabilities are 5% interest. Both of them are charging interest and principal which is 5% more than the total amount of money that exists. How is this possible?

I'm guessing that if there's other countries adding funds to the system it could work. But as a closed system how could you charge more interest than m2 is growing by? It seems like you would need constant monetary growth to sustain positive interest, but it's not even fast enough, and real interest rates are persistently positive. The real interest rate should always be zero, minus short term changes due to measurement problems, because there is no monetary growth available to sustain positive interest or any net gain to banks assets. The short term changes have to average to zero.

The only other answer I can imagine is that banks actually aren't functioning, and Eurodollars are maintaining these positive rates.

The accepted answer is sort of bizzare, it implies bank spending is necessary for interest to exist.

Answer 1

This is not an issue in real economy.

First of all you are mischaracterizing the problem. When someone charges 5% interest that is not 5% more than total amount of money that exists. That is 5% of money that already exists.

1. Money has a velocity. 1 US dollar or 1 euro can be use more than just single time.

Every time you pay an interest on long term loan, bank will not just keep that money as an art installation. They will spend it either to pay for costs of their operation or use it to pay profits. In turn bank employees, suppliers or shareholders will not keep the money as an art installation either. They will spend it for goods and services they desire.

2. Interest rates are not random numbers they are determined by money demand and money supply. Assuming we’ll functioning market interest rates are always set in a way to equilibrate quantity of money supplied to quantity of money demanded (see Mankiws Macroeconomic).

3. Prices in the economy are not random. Prices that people can charge for their goods and services etc depend on what is the quantity of money in the economy. Now In a simplistic way this relationship can be described by the equation of exchange (see Mankiw Macroeconomics pp82). The equation of the exchange is given by:

$$MV=PY$$

Where $M$ is total money supply, $V$ velocity of money (how often one bill is used in the economy), $P$ are aggregate prices and $Y$ real output. Hence, price level and velocity of money have to adjust to make it possible to purchase all goods and services in the economy otherwise the economy is not in an equilibrium.

4. Also, the extra money cannot come from other countries since only US is allowed to create US dollars. It’s not like Brazil can (legally) issue dollars

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Stylized example:

Consequently, suppose you take out 2y 100 loan with 10% simple interest. Also, not all money is created by banking sector, with a reserve requirement of 10% for 100 dollars of lending there has to be somewhere in the economy at least 10 dollars (or more) worth of high powered money (now reserve requirements has recently been abolished and replaced with capital requirements - see Fed explainer here, these are more complex than reserve requirements but in the end they still constrain banking lending in conceptually similar way so I will continue using reserve requirements for simplicity sake$. You will spend 100 dollars to produce 11 donuts each year that you sell for 10 dollars each.

Well the same 100 dollars that you spend on production (by paying suppliers, workers etc) won’t disappear from the economy. Those workers need to eat so they will purchase your donuts from their wages so you again have 100 dollars. Also with 100 dollars there had to be at least 10 dollars of high powered money so at the minimum so there is enough money to buy your 11 doughnuts for 10 dollars each, the holder of the 10 dollar high powered money will purchase it.

Now it is end of the year so you pay 10 dollars interest to the bank. Next you also work to be able to buy goods and services so you spend the 100 dollars on stuff you like and now the money is back in the economy. The interest of 10 dollars will also be back in the economy because bank will not keep that money as art installation but to pay for its costs or to pay dividends to the owners of the bank. In turns these people will spend their paychecks or dividends on goods and services.

Next year you produce again 11 donuts and the same thing will happen. People will purchase 10 donuts with 100 they have, bank owners (assuming original interest rate way all used for dividends) will now buy the last donut and you will get 110 dollars, exactly as much as you need to pay for interest and principal.

Sure the example above is extremely simplistic and cheesy but it just goes to show that even with interest there is no need for extra money.

Answer 2

Deposits are counted in M2 money supply.

On the books of a bank or bank sector a new loan +10 creates new deposits:

Loans +10, Deposits +10

When the loan is repaid with interest the borrower pays with deposits:

Loans -10, Interest Income +1, Deposits -11

Suppose the bank pays interest expense equal to interest income:

Interest Expense +1, Deposits +1

There is no net profit to the bank on the original loan and there is no net change in M2. The borrower had to attract +1 deposit from some other depositors in the bank sector and the bank redistributes the deposit ownership by paying expenses equal to the +1 interest income.

Suppose the bank books +1 equity as net interest income earned from the loan:

Net Interest Income -1, Equity + 1

The bank could hold the new equity as reserves which would not increase the M2 money supply. However when the bank invests the +1 interest income into new loans or the purchase of securities or into other bank assets and then it will further increase the M2 money supply as it did when it issued the original loan.

The source of deposits in M1/M2/M3/M4 and equity claims and/or credit market claims on the liability side of the bank balance sheet is the origination of loans and purchase of securities by the bank or bank sector on the asset side of the bank balance sheet.

If there is a run on the liabilities of a bank or bank sector it is forced to sell assets to the non-bank sector and reduce its balance sheet. Banks cannot profit when forced to sell assets or when facing a large default loss in the asset portfolio. Banks profit when there is a positive interest rate spread of assets over liabilities. This seems to be caused by the expansion of the bank sector when banks are expanding financial assets over time. Therefore the asset side of the bank or bank sector must be seen as the source of the increase of the liability side of the bank balance sheet. Money supply is the liability side.