With 100% reserve, one cannot apply infinite geometric series and sequences
Not in a closed system, no. But the economy isnt a closed system. Lets say im SigmaBank, instead of Sigmajin. And i run the first national bank of steemsville. In steemsville, there is a 100% reserve, so i can't lend money on my deposit account balances. I have company B in my loan office and they want a 100000 steem loan. I want to write the loan. Im fucked, right? 100% reserve. My deposits are spoken for.
FOrtunately, I know complexring. Complex is rich as all hell and he has 300K steem on deposit. He has millions of dollars in steem that he cant possibly use all of. So i say to complex, "why don't you take 100K steem out of your bank account, and give it to me. Ill write you an IOU, lend it out, and well split the interest."
You know im good for it because im a fucking bank... its not like im going to run off. If you didnt trust me, you wouldnt have 300K steem on deposit in the first place.
So you give 100K and i loan it to company B, then i write you an IOU for 100K plusinterest and pay you back as they pay me. So you get the principle payments, plus half the interest payments, and I get half the interest. Yeah, you personally might not be down, but in the wider economic world, there are absolutely a huge number of rich people that are down.
Now lets say company B isnt using the whole 100K steem they borrowed, they can make the same deal with me that you did so i can write a loan to company C. The only difference between this scenario and the one you present is that the banks liabilities are now in the form of IOUs, not in the form of deposit liabilities.
But it gets even better... because you know that IOU i wrote you, you can actually sell that IOU to someone else. Its called a debt security... and as long as sigmabank hasnt fucked up its credit, youll be able to sell it for probably nearly full face value. So lets say the 100K steem was for a house, and the 30 year mortgage repayment was slated to be around 200K steem.... your IOU is for 100% of principle, and 50% of interest, or 150K... youll be able to usually get between 110 and 125K on it. Which, if i can find another borrower, you can just lend back to me.
Like your scenario, it depends on the idea that a company would be willing to borrow a lot of money, then leave most of it in the bank, so that the bank could loan it out again..... the only difference is now they are explicitly loaning it to the bank, rather than simply leaving it on deposit.
So ... how does this all relate to loaning money to a bank and the bank loaning it out to others with respect to money multiplication, as per the definition that it is any increased supply beyond the original amount borrowed from the central bank.
also note that the primary difference here is that you would consider your Steem as already part of the money supply, even though you arent actively using it. Whereas you consider central bank money as coming in from the outside.
But all youre showing at the end of the day is that if enough people are willing to borrow money, then leave borrowed money sitting in the bank, that the bank can make a killing lending out the same borrowed money over and over. The accounting is different with a 100% reserve, but it depends on the same thing... multiple companies being willing to let the bank hold money that they borrowed.
Further side note... this is why when the fed wants to decrease money supply, they don't hike up the reserve rate, they hike up fed interest rates... that way its more expensive for banks to borrow money, so they have to be more selective about who they lend it to (or they have to charge more interest) so the demand for loans decreases.
I can't reply to sigmajin because of nesting limits, but I don't think the Federal Reserve has the interest rate set next to nothing right now because they want to. Their quantitative easing plan was to make lending money cheaply to avoid a prolonged recession (or Great Depression 2.0) but now they can't raise rates again because the US government will not be able to pay up. Think of how much interest 20 trillion dollars will rack up with a higher rate.
@theabsolute yeah, they definitely want to... I dont think its wise, but its definitely policy. They spent most of the first half of this year banging the NIRP gong. Its dead now, but if trump wins, i doubt itll stay dead (and tbh i dont think hillary would necessarily be against it either)... right now, everyone is terrified of a recession... like if politicians thought it would help, or even thought that the electorate thought it would help, i could easily imagine them sacrificing people like in the shirley jackson short story. .
The ECB and japans central bank both have NIRP right now.