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>the bank can make $9m worth of loans provided that the recipients of the loans never get them of the bank

The bank can make $9m worth of loans (actually the bank can make any amount of loans, maybe even more), and some proportion of that may be transferred to other banks as reserves, and some other reserves will be transferred onto the banks balance sheet from unrelated transactions the bank makes. Then at the end of the day if the bank needs more reserves, it borrows them. The likely amount the bank needs to borrow based on the loans it makes and the cost of that reserve borrowing determines how many loans it will make. If it wouldn’t be profitable to make more, it’ll stop.

At no point does the bank only make 900k of loans so that it is fully covered in case all its loans are transferred out. The whole thesis of the paper is that that way of thinking is backwards.

Then you could just as well say that it can make $9m in loans, $99m in loans or $999m in loans as long as enough reserves are transferred onto the banks balance sheet from unrelated transactions the bank makes (including borrowing if required).

The amount of reserves can (and will) go up and down for an individual bank as it operates depending on their strategy.

10x the initial reserves has no particular meaning for an individual bank, only for the whole system (and the whole thesis of the paper is that even then the 10x number doesn't really matter).

Yes, couldn’t you say that?

To go back to your previous point

> For that bank with $1m in deposits and $1m in reserves before any lending that 10% requirement means that it can not let its reserves go below 100k (10% times $1m in deposits) so it can only lend up to $900k out

This just doesn’t make any sense. The whole point of the reserve requirement is to guard against the risk that depositors will withdraw enough money at once to deplete the reserves. The bank needs to meet the reserve requirement of deposits on its balance sheet, not a theoretical future balance sheet. You’re explaining it as if the reserve requirement applies after the theoretical worst possible bank run occurs.

Say the debtor moves all their money to another bank as per your example. Now the bank has 1m deposits and 100k reserves. Now those other depositors also move 100k to another bank, so the bank has no reserves. Uh oh - making that 900k loan actually allowed the banks reserves to drop below the requirement in this theoretical eventuality!

Does that mean the bank shouldn’t have made the loan? No, because the reserve requirement applies to their current balance sheet. When the bank had 1m deposits and 1m reserves, it could make 9m loans. At this point it has 10% reserved (designed to guard against the eventuality that those debtors all withdraw their money). If the bank makes 900k loans and they are withdrawn, it has 1m deposits and 0.1m reserves. It is now in exactly the same situation as the previous example (scaled down). The bank doesn’t need to wait for this unlikely event to happen to allow its reserves to drop to 10%, it can just make the extra loans in the first place.

>> For that bank with $1m in deposits and $1m in reserves before any lending that 10% requirement means that it can not let its reserves go below 100k

> This just doesn’t make any sense. The whole point of the reserve requirement is to guard against the risk that depositors will withdraw enough money at once to deplete the reserves. The bank needs to meet the reserve requirement of deposits on its balance sheet, not a theoretical future balance sheet.

What part doesn't make sense precisely?

A) The bank has $1m in deposits

B) It has to meet the reserve requirement (10%) for the deposits in its balance sheet ($1m)

C) The reserve requirement is $100k

D) The rest are excess reserves

The balance sheet looks like this:

    Assets                      Liabilities
    $100k Required reserves     $1m Deposits
    $900k Excess reserves

> Say the debtor moves all their money to another bank as per your example. Now the bank has 1m deposits and 100k reserves.

Sure, this is the balance sheet now:

    Assets                      Liabilities
    $100k Required reserves     $1m Deposits
    $900k Loans

> Now those other depositors also move 100k to another bank, so the bank has no reserves. Uh oh - making that 900k loan actually allowed the banks reserves to drop below the requirement in this theoretical eventuality!

That's the whole point of fractional reserve! You have enough reserves to cover a fraction of the deposits amount. If the bank has no excess reserves it will be in breach as soon as some depositor decides to get some of their money back and it will need to get more reserves to remain in compliance.

> The bank doesn’t need to wait for this unlikely event to happen to allow its reserves to drop to 10%, it can just make the extra loans in the first place.

The unlikely event that the people who take loans sends the money elsewhere? What would be unlikely is that they didn't.

> That's the whole point of fractional reserve! You have enough reserves to cover a fraction of the deposits amount.

Yes exactly, by making 9m loans, the bank has a fraction (10%) of reserves to cover the deposit amount (10m).

> The unlikely event that the people who take loans sends the money elsewhere? What would be unlikely is that they didn't.

You are assuming that 100% of deposits created by loans will be immediately withdrawn. The thing that doesn’t make sense is that you’re treating deposits created from debt as special. The bank needs reserves of 10% of all its deposits.

Why are you considering the eventuality that the loan holder buys something but not that the saver buys something? They are both equally irrelevant as they are eventualities factored into the 10% requirement.

Say there is only one current account holder at the bank with 1m savings. Then the bank gives that customer a 900k loan. Now the customer buys a house. Why do you assume the house will cost 900k? They might buy a 1.2m house, in which case the bank is stuffed, as it only has 1m reserves. There is nothing special about the 900k.

> Why are you considering the eventuality that the loan holder buys something but not that the saver buys something?

Because people take loans for something? It could be to invest, definitely not to keep it untouched in a current account.

Do you know of a single case of someone who took a loan for the sake of it, leaving the deposit created untouched at the lending bank, and paying interests for the privilege of having that deposit?

(The eventuality that the saver buys something is why banks keep reserves, with minimums set by regulators in some countries. To allow for a fraction of those depositors to buy something without the whole setup collapsing immediately.)

Edit: and for what it's worth, this "eventuality" is also seen as a basic scenario in the paper under discussion. That's what Figure 2 is about:

"The house buyer takes out a mortgage... ...and uses its new deposits to pay the house seller."

"The mortgage lender creates new deposits... ...which are transferred to the seller’s bank, along with reserves, which the buyer’s bank uses to settle the transaction. But settling all transactions in this way would be unsustainable: [...] the buyer’s bank will in practice seek to attract or retain new deposits (and reserves) [...] to accompany their new loans."

> couldn’t you say that?

Ok, then this is NOT how it works -> "if a bank has $1 million in deposits the bank can make $10 million in loans"

I can agree with either of the following formulations:

"if a bank has $1 million in deposits the bank can make $10 million in loans as long as the loans remain as deposits in the bank"

"if a bank has $1 million in deposits the bank can make loans for any amount that it wants as long is it can comply with the reserve requirements"

Yes then I think we’re in agreement and just talking around in circles! It seems the second statement is most meaningful in relation to how banks actually operate (based on my understanding of the paper). The example where 9m loans are made and none transferred out, and the example where 900k loans are made and 100% are transferred out are both extremes.