What is the justification for it being a problem if loans are not paid back?

As far as I could understand, the loan system applied by banks which is based on a fractional reserve system works as follows:

Assumptions:

1. The bank has initially 1000$. 2. The fractional reserve is currently 10%. 3. For simplicity, we assume that all deposits are made only on this bank, instead of having multiple banks. It has been argued in many places that, for the overall view of the money system, that this is a justfied assumption. The following happens now: 1) Guy A makes a loan for 900\$. The bank keeps 100\$(more than 10%, thus ok). Total loans owned by bank: 900$
Total deposits owned by bank: 100$ 2) Guy A pays guy A', which deposits the money on the bank again. Total loans owned by bank: 900$
Total deposits owned by bank: 1000$ 3) Guy B makes a loan for 800\$. The bank keeps 100$as a new reserve (more than 10%, thus ok). Total loans owned by bank: 1700$
Total deposits owned by bank: 200$ 4) Guy B pays guy B', which deposits the money on the bank again. Total loans owned by bank: 1700$
Total deposits owned by bank: 1000$ This repeats itself a couple of times, until we arrive at: Total loans owned by bank: 5000$
Total deposits owned by bank: 1000$ From the deposits, 500\$ are reserves of the bank, which belong to the bank, and 500\$are money which is owned by the last guy that got money from another guy. Ok, so this is, as far as I understood, the beginning of the "loan process with a fractional reserve system", with a couple of loans. The bank has still enough reserves, so it did everything ok. Now let's assume that Guy A comes to the bank and says "Hi, I'm sorry, I can't give you the money back, I'm broke". Currently, the following thing happens: The bank says "ok, so you must give us your security to cover our loss" (for example the car). Question: Why does this happen, what is the justification for taking the car from Guy A? Since the bank never lost anything...? - 4 Answers It appears that the OP confuses money with property rights A) It writes "deposits owned by the bank" which is simply wrong, since deposits are liquid assets belonging to the persons that deposited them. The bank leases the funds from them and then sublets them to the debtors. B) Looking also at an OP's comment to another answer, indeed the bank may create the money, but it creates the money as a medium of exchange and representative of value -it does not keep the property rights on the money itself it creates. C) Finally we should not forget that the bank is a distinct legal entity from its own shareholders. Stopping at the four explicit amounts the OP gave (after person$B$pays person$B'$and person$B'$deposits the money in the bank), the bank's balance sheet is as follows: \begin{array} {| r | r | r |} \hline \hline \text {ASSETS} & \text {USD} & \text{LIABILITIES} & \text{USD}\\ \hline \text{Loans} & 1,700 & \text{Shareholders Capital} & 1,000\\ \text{Cash} & 1,000 & \text {Deposits} & 1,700\\ \hline \text {TOTAL ASSETS} & 2,700 & \text{TOTAL LIABILITIES} & 2,700\\ \hline \end{array} A Balance Sheet is just an inventory at a specific point in time, of Cash and Rights to Collect in the future ("Assets") and Obligations to Pay (also in the future) ("Liabilities"). It is important to understand the "Liabilities" (obligations to pay) side. The initial USD$1,000$with which the bank started, represent an "obligation to pay" for the bank towards its own shareholders. Second the bank is obliged to pay at any time USD$1,700$total to persons$A'$and$B'$that deposited their wealth to the bank. The fact that the depositing transaction could happen because the bank in a previous instance has created the money, does not give the bank a property right on that money, just because it was its "creator". That the bank has at the moment$1,000$in Cash as when it started doing business, relates to the bank's "liquidity" situation. This is not unimportant, and in fact it is an index of financial health on its own right. But it has to do only with the short term horizon. For the long-term horizon though, it is property rights that matter. And so it is not the only financial criterion for the economic health of a bank. So assume that person$A$comes in and say "I cannot pay my loan of USD$900$". Certainly, in the short-term, this won't affect the liquidity of the bank -it will still have the USD$1,000$that it now has. But if the bank writes-off the debt, it will do so against the Shareholders capital invested. So after the write-off the balance sheet will be \begin{array} {| r | r | r |} \hline \hline \text {ASSETS} & \text {USD} & \text{LIABILITIES} & \text{USD}\\ \hline \text{Loans} & 800 & \text{Shareholders Capital} & 100\\ \text{Cash} & 1,000 & \text {Deposits} & 1,700\\ \hline \text {TOTAL ASSETS} & 1,800 & \text{TOTAL LIABILITIES} & 1,800\\ \hline \end{array} Assume things with debtor$B$go smoothly, the bank will eventually (in the long-term) collect his loan, and it will be able to give to persons$A'$and$B'$their deposits back... so where is the problem? Well, the problem is that it will give to its shareholders only USD$100$back instead of the initial USD$1,000$investment. And who might care? First, we live in societies built upon the principle of private property rights. The shareholders have a right to defend their property rights, and the bank acting as their representative attempts to defend them by not simply writing-off the debt (but demanding another asset -the car- in its place), even if such a write-off may affect the property rights only of the shareholders, and not of the people that keep their wealth to the bank as deposits. But again, does this creates a problem to the economy now? In terms of actual existing liquidity the answer is no. But the Present is affected by what we project for the Future. After the write-off, the future of the shareholders and of the bank looks worse, because their current wealth is less. And this will affect negatively what the bank and the shareholders will and can do in terms of their involvement in the economic activity now. So to the question "who cares?" the second answer is "the whole economy". - I can understand how examining the question in this 'closed' form could lead to fallacious reasoning. So, let's consider this: Any person who has deposited money at that bank is allowed to come withdraw their money and the bank must be able to service that request. What if all the$(N')$customers come to collect simultaneously? You're also incorrectly calculating the deposits held by the bank - which (I think) you seem to treat as an asset when in reality deposits are liabilities for bank. If I make a deposit to the bank, the bank loans it to person B, person B pays person B' and person B' deposits the total of the payment into the same bank (let's assume the deposit and loan are 1000 dollars for simplicity) then the bank now has 2,000 dollars in deposits. Also consider why banks need the money flowing in from loans. Remember, banks must service interest on deposits (which total more than 1000 here...do you see why now?), for operating costs and to build reserves to meet obligations. "Why must the bank take the car from guy A..." because the bank gave him money and he failed to repay that money. The bank must be able to balance liabilities and assets. Deposits are liabilities. Loans are assets. So what happens to the balance sheet when it loses some significant portion of its assets? - Ok so assume that everything works out well, there is no problem with not paying back. But, everybody wants to withdraw the money. This doesn't even work in this "good setting", as the bank technically has only 1000\$. So this problem has nothing to do with what I tried to describe. –  stolz Jan 16 at 16:27
The amount of required reserves a bank would have on hand would be significantly different without your mistaken calculation of deposits. And the ability to protect against bank runs goes much much much deeper than your question. I gave you an answer that I thought was roughly equivalent with your understanding of the situation. Asking how a bank can protect against a bank run is much different than "why must loans be repaid." –  mathtastic Jan 16 at 16:32
But you're right regarding maybe some unclarity with my wording, what I tried to describe with "loans owned by bank" is the sum of the deposits from the guys. –  stolz Jan 16 at 16:33
I tried to more directly address the question. I reread what I wrote and I think I assumed the conclusion might follow. The simple idea is that banks have balance sheets and, I am assuming you've done some amount of financial accounting, you know that liabilities must balance with assets. –  mathtastic Jan 16 at 16:36
But still I don't see the point in this loan system: The bank can give out more loans that they own ( = fractional reserve). They earn more money because of that (compared to a private person giving out loans, who could only lend the exact amount he has), and they are enabled to lend more money, by essiantially "creating new money". So what is the justification, of when someone can not repay them, that they must give them something else? They didn't lose anything, they created the money and then lent it, so what is the loss? –  stolz Jan 16 at 16:36

The problem in your reasoning is caused by the fact, that you decrease deposits every time bank makes a loan. It doesn't work like that. Deposits pile up and bank is obliged to pay them off. Your calculations suggest that when you come to a bank and ask for the money you have deposited, bank should answer "Oh, well, you know... We have lent it to some other guy, so, no, we won't pay you back anything". What you have called deposits is actually a sum of reserves and free cash. Deposits on each step of your procedure are respectively $0, 900, 900, 1700, 4000$.

To put it another way, the bank has not produced any actual cash. It has produced promises to pay off the money if they will be requested. This promises are trusted only while the amount of promises (total deposits, summed properly and not as you have done) exceed the amount of what is promised to the bank (loans) plus what it actually has on it's hand (and that is what you have written as deposits, cash plus reserves). As soon, as the later is lower then the former (due to decrese in loans that are to be paid to the bank) no one will trust the bank and it's promises are worth nothing. Then everyone who had a deposit in the bank won't get his money back and all of those "money" you have referred to will disappear. That's why you have to return money to the bank. Otherwise you are robbing the depositors.

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You seem to be confused between Reserves and Deposits.

If you don't read anything else just remember:

Reserves + Loans = Deposits

One way to think about it is to treat loans and reserves as the banks' assets and deposits as its liabilities.

If the bank has 1000 at the start it means it has 1000 in deposits. It makes 900 in loans and keeps 100 in reserves. Loans: 900 | Deposits: 1000 | Reserves: 100

If someone else deposits 900 into the bank and the bank loans out 90% of 900 = 810 then we have Loans: 1710 | Deposits: 1900 | Reserves: 190

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