Wikipedia:Reference desk/Archives/Mathematics/2024 January 30

= January 30 =

How to disprove the claim that interest in banking will cause harm to at least one citizen?
A similar claim was used by one interest free banking supporter to denounce interest in banking:


 * 1) In a new country, there are 10 rulers and 10 subjects.
 * 2) The country's bank has 1,000,000 ¤
 * 3) Each subject has to buy a house so each subject loans 100,000 ¤ in the interest rate of 1%
 * 4) After one month, each subject has to pay the rulers 110,000 ¤ so the rules will get 1,100,000 ¤, thus earning 100,000 ¤.
 * 5) Given that the 100,000 that the subjects have to pay does not exist in the monetary system, they will have to borrow money one from each other to pay it thus their debt never ends and at least one of them won't be able to pay it, as in the musical chairs game.

How to disprove the claim that interest in banking will cause harm to at least one citizen?

Thanks. 2A10:8012:3:DE50:BDE7:2606:BEB6:CFDA (talk) 13:27, 30 January 2024 (UTC)
 * See Leverage (finance). They loan out more than they get. NadVolum (talk) 16:38, 30 January 2024 (UTC)


 * Is this a mathematical question? What is true in one contrived situation may be false in another situation. To make the question even more contrived, consider a frigid country with just two people, one a king who runs a real estate company and a bank, the other a peon. The homeless peon rents a hut from Regal Estates Ltd. for shelter, for 100,000 ¤ per month, to be paid in advance. For this he takes a loan from the Royal Bank. At the end of the month he needs to repay the bank 110,000 ¤ but he doesn't have any money. Does this prove that charging rent for shelter will cause harm to at least one citizen? No, it doesn't. Does this prove anything at all, except that life is sometimes unfair for fictional peons? No, so there is nothing to be disproved. --Lambiam 17:07, 30 January 2024 (UTC)
 * User:Lambiam, I don't get your argument, how could the peon pay the interest-debt? and, do you approve the stance that at least one of the 10 subjects will be misfortunate? 2A10:8012:3:DE50:EDB4:DDED:F594:D4D5 (talk) 22:02, 30 January 2024 (UTC)
 * I said he doesn't have any money, so there is no way for him to pay the amount due. Your scenario is not very detailed but appears to assume an invariant total amount of money in the economy, so if you equate fortune with the amount of money one possesses, it is a zero-sum game. Either no one gains (but it appears that the rich are getting richer) or someone loses. --Lambiam 22:40, 30 January 2024 (UTC)


 * Not economically aware so this may be a silly question on my part, but doesn't this normally happen in conjunction with the country printing out more money? GalacticShoe (talk) 17:11, 30 January 2024 (UTC)
 * There should be a reason to distribute the money fairly, how would that be done in such a situation? Also, the rules could also delete the debt.
 * Well I mean, yes, in this particular situation the rulers could delete the debt, and in fact it would make sense to given that there's only 10 people. But as other people have mentioned this is sort of a contrived scenario. We're to assume that for some reason the rulers arbitrarily decide to have interest and increase the amount owed despite there being no incentive for it, which is oversimplified from the real world. That being said, if the rulers wanted for some strange reason to have interest but also print out money for people to pay off their debt, they could print out exactly enough money to cover each person's debt to make it fair. GalacticShoe (talk) 02:13, 31 January 2024 (UTC)
 * The ruler's incentive is to become richer in a "fair" way which in their understanding is banking interest. The rulers may say to the subjects "we demand this interest money so you should give us a reason to print it and give it to you". 2A10:8012:3:DE50:EDB4:DDED:F594:D4D5 (talk) 06:59, 31 January 2024 (UTC)
 * If you assume a ruler who is interested in extorting money from the populace then this might make more sense, but you still only have 10 people who are put into arbitrary debt over some amount of money that has no intrinsic value, so that they are supposedly motivated to work to generate more money despite the fact that said money is not backed by anything. This might work as a simplification for an actual economy if you had more people, a more complicated system, a money system actually backed by some real value, etc. etc. but in this case it really sounds like the 10 people have no incentive to do anything of the sort. GalacticShoe (talk) 07:25, 31 January 2024 (UTC)
 * Well, I think that we should be able to create some general yet minimal model of the current common interest based banking of humanity. Perhaps the two people example, ruler (king) and subject (peon) is better, but then the peon has no other person to borrow money from unlike the ten subjects borrowing one from each other. 2A10:8012:3:DE50:EDB4:DDED:F594:D4D5 (talk) 07:49, 31 January 2024 (UTC)


 * Why do you say that the 100,000 does not exist in the monetary system? Where did it go? Surely the purchasers bought the houses from someone, and those sellers now have the money. Also: How do you determine whether it's better to be homeless, or housed but in debt? If it's a nonrecourse debt system, then the loans allowed the subjects to be housed for a month and then bankrupt, instead of homeless the entire time and equally bankrupt. --Amble (talk) 17:55, 30 January 2024 (UTC)
 * I didn't say it wen't anywhere or that they should consider homelessness. What if the rulers themselves built the houses? 2A10:8012:3:DE50:EDB4:DDED:F594:D4D5 (talk) 22:02, 30 January 2024 (UTC)
 * If the rulers sold the houses, then they have the money; it still exists in the system; and the premise of point 5 is false. The point about homelessness is that the argument is incomplete. Even if I take all the points as given, it needs to establish what is a harm, or how to balance costs and benefits. --Amble (talk) 22:34, 30 January 2024 (UTC)
 * While the rulers sold the houses the money was not existing in the monetary system, the rulers should print it or invent it. Harm in this case would be homelessness or infinite debt. 2A10:8012:3:DE50:EDB4:DDED:F594:D4D5 (talk) 22:51, 30 January 2024 (UTC)
 * Sure it exists. It starts in the bank, the bank lends it to the subjects, the subjects pay it to the sellers (who are not specified in the argument but may be the rulers). At every point it exists in the system. So point 5 has a false premise. And the argument itself needs to establish what constitutes a harm and what caused the harm. These are not things that can be waved away or taken for granted, they are serious work that the argument must do but hasn't attempted. --Amble (talk) 23:09, 30 January 2024 (UTC)
 * The argument claims that only 1,000,000 exists, nothing more. The sellers are indeed the rulers. I am sure that it is clear to you that generally, debt is a risk and may cause harm. Anyway, The rulers may say to the subjects "we demand this interest money and you should give us a reason to print it and give it to you". 2A10:8012:3:DE50:EDB4:DDED:F594:D4D5 (talk) 06:59, 31 January 2024 (UTC)


 * The concepts of credit, interest, and inflation in the sense of modern economies do not apply in your scenario of an static, zero-sum system with fixed capital.
 * Interest is a hedge against inflation and defaults. If someone defaults on a loan -- say in your government bank (more like royal coffers) scenario -- then that's a loss to the coffers. If the money supply is fixed and the economy is zero-sum, then in your scenario the amount of interest received would probably have to equal the amount of loans lost on default. There's no inflation.
 * In reality, your time, labor, land, assets, and credit thereof all have measurable and changing monetary value. You add money to the economy by working, creating, repairing, teaching, nurturing, helping, negotiating, etc. Every mutual agreeable transaction is a positive-sum addition to the economy. (Economics questions may be better addressed to Reference desk/Science in future, btw.) SamuelRiv (talk) 19:24, 30 January 2024 (UTC)
 * I talk only about interest, not about inflation, why isn't interest relevant if the subjects loan by interest? 2A10:8012:3:DE50:EDB4:DDED:F594:D4D5 (talk) 22:02, 30 January 2024 (UTC)
 * From what I'm gathering, if there's no value entering or leaving the system, then asking for interest doesn't make a lot of sense. If you only have a million ¤, and someone demands 1.1 million ¤, then where's that additional 0.1 million ¤ supposed to come from? If you just add that amount of ¤ arbitrarily into the economy, then the amount of value and worth is still the same, only now each ¤ is worth less. As mentioned earlier, even if someone outright demands that these 10 people generate enough "value" to cover that 0.1 million ¤, there's no real incentive to do so with this particularly small system. If you force them to do so by suggesting punitive measures for their "debt", then that's less about interest and more about the system itself forcing people to labor for value. GalacticShoe (talk) 07:32, 31 January 2024 (UTC)
 * The concepts of credit, interest, inflation - and leverage and crashes too have been around since at least the Romans . You can even see quantitive easing at work there! NadVolum (talk) 13:43, 31 January 2024 (UTC)
 * Let me try explaining again: the IP assumes a closed zero-sum system. They use this as a model to argue that concepts in economics essentially don't work. But real economic systems are not closed and not zero-sum.
 * Where does the missing 100k in value come from? From the loans themselves, and then from people doing work to pay loans. And btw, in a real economy, if the money supply doesn't expand with an expanding economy, the money deflates. (This is what you seen with a gold standard, if not enough is continuously mined.) SamuelRiv (talk) 14:02, 31 January 2024 (UTC)
 * UseR:SamuelRiv, the model only regards interest, not "concepts in economics". A real economy can be closed; imagine a planet with a single global state for example; "zero sum" can be a vague term here. Anyway, The missing 100k would have to be printed as payment for some work won't they? 2A10:8012:3:DE50:B96F:CC69:BBE8:B926 (talk) 22:02, 1 February 2024 (UTC)


 * I propose we close this protracted unfruitful discussion. It does not concern a defined mathematical problem; indeed, the issue appears to be lacking in definition in any sense of the term and it is unclear what, if anything, might lead to some form of closure. --Lambiam 14:07, 31 January 2024 (UTC)