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RE: The Mathematics of Fractional Reserve Banking
I always appreciate original research, or just a new look on things. I even understand quite a bit of math myself. But this post is complete bullshit, there's absolutely zero connection between limits and fractional reserves. Sure, you can apply any formula to any phenomenon with enough substitutions, but that doesn't imply a meaningful relationship.
The fact that this post is scoring so well, can be both seen as a general inability to understand mathematical principles by normal people (which I don't mind at all) or as a "riding-the-whale" circlejerk of upvotes (which I am finding more and more annoying).
I disapprove of people misunderstanding mathematics.
I also disapprove of my complete lack of misunderstanding of economics.
Explain to me why you approve of the general population not understanding mathematics?
Or maybe I didn't understand your comment properly ... probably so. I am almost always incorrect.
I don't mind the general population not understanding advanced mathematics. Just as I expect people to don't mind I don't speak French fluently.
Infinite geometric series and sequences are not necessarily all that advanced. We've been studying, constructing, and observing such objects for at least 2 millennia and are relatively basic.
Neither is speaking French, if you speak French.
And what's so bad about trying to teach people the language that I happen to be the most fluent in?
Trying to teach anything is a noble cause and can only be encouraged. But it's important to understand not everybody needs French, and plenty of people dislike French enough to TL;DR anything related. It's this last option I think is the case for many upvoters of this post. And I know I sound jealous (I am, a bit) but I dislike the riding-the-whale voting on this platform.
I'm trying to create a math blog, and I just happened to explore a topic that both interests me as well as the general audience (many blockchain enthusiasts). Most people here dislike the banking system (hence, why they are cryptotoken users).
The purpose of this post was to illustrate money multiplication via reserve rates and demonstrate how infinite geometric series can be applied to my understanding of the system at that time.
My illustration may have been a poor example to what happens in the real world, but whether banks borrow from the central bank in order to meet RR before a loan is made or after a loan is made does not change the underlying principle of how money multiplication, via deposits in a bank.
So, yes, one could have instead simply used the (inverse of 1 - RR) - 1 and expressed this as the maximal money multiplier that could have occurred and stated that the actual MM is determined by numerous factors, including a ratio of how much of a particular loan is kept in cash, not used to pay off other businesses, and is therefore not deposited into a new bank account. And in fact, you'll note that I do state that is the maximal MM that can exist and indeed derive it from using the infinite geometric series model. Coincidence?
I could do a completely new post that explains this in light of all the new economics that I have learned from @sigmajin and yourself, if you think it would prove worthwhile.
I don't have the feeling I have anything I can learn you, tbh :)
As for the new article, please no, forvtwo reasons: 1) I don't want to be the cause, even partly, for anyone doing anything and 2) after this discussion, I think the OP+thread is a very complete assessment of the concept.
And maybe a 3) I'd much rather see you work on another blogpost, next in the series...
Meanwhile, check out my latest post I linked here somewhere. That'll give you an idea how bad I am at economics, lol. And there are some questions I'd like to see answered by more capable people...
Also, if you want to write an article (or 3) on the myths of the money multiplier effect, I'm all for learning more ...
I also think that when someone just comes in and says you are wrong and leaves it at that and doesn't explain your failings, you do both him and yourself a a great disservice.
Ok, let's try this: why do you need limits to describe something that can be expressed as a simple percentage?
Because it is a deeper analytical method of mathematics that can be used to understand the subject and in fact you need limits to really understand how an infinite geometric series really operates.
Yeah, the "loaners/sellers" wasn't meant as a quote or anything, it's just the simplified concepts my brain uses to try understand all this :)
Ok, I get your point. I'm not nearly as good in math as you, and much less in translating math to English. I was hoping to do what you suggested and write one (3?) articles about this. However, I can't get it working in my head... See this post, feedback highly appreciated. Same for our friend @sigmajin
https://steemit.com/steemit/@r4fken/fractional-reserve-banking-and-steemit-questions-for-experts
Yes, you need limits for infinite series. Not for percentages. It feels like a farfetched look-how-smart-i-am post.
Also, the assumption that loaners pay and sellers just deposit again is flawed.
I don't see how percentages would get point across of money multiplication as well as how this model (albeit, imperfectly) fits with an infinite geometric series.
This is an example I've used in my Calculus II courses numerous times when introducing infinite geometric series and sequence.
Can you provide an example of how percentages describe this phenomena?
In response to the loaners and sellers comment ... I never used the terminology of sellers and loaners, so it looks like you're interpreting that I said certain statements that I did not?
Maybe you could provide a quote or an example with some more meat on the bone to back up what you are claiming that I said.
OK. I think I see what you mean by loaners and sellers (although, as I said, that terminology was not used).
For all practical purposes of understanding the situation, assume that any loan that a bank gives to 1 contractor goes to one other business. In reality, the loan goes to pay for employees, business expenses to multiple businesses, stays on hand for petty cash, etc. However, at the end of the day, the vast majority of the capital winds up back in the banks.
Even if 80% is re-deposited back into banks, you still have money multiplication, just not at the extreme end if 100% was re-deposited. See @sigmajin's example where some of the cash was kept on hand from various businesses.
For the purpose of instruction, aggregating totals of payments of a business into a single entity (when the practical mathematics are the same) is easier to explain the mathematics of an infinite geometric series.