# Background

I've done some research to get an understanding into the issue I want to ask about. Regrettably, I found out general descriptions of the mechanism and/or evidently biased explanations, which I've got no means to question. Please excuse me if I refer to a concept in a less than optimal terminology. I'm a bright guy but definitely not a scholar of economics.

Please note that I'm not asking for how fractional banking works in mathematical terms. I'm questioning the sanity of it. Well, not questioning - rather not grasping how it differs from hiding the lack of funds.

Alice owns X units of currency but doesn't use them. Bob comes by and asks to borrow it for a period of one unit of time. As a reward, he promises to return 5% higher amount. Carol comes by and makes the same request with the difference that he promises 10% return on the investment.

Alice considers the chances of the money being paid back in full including the interest as corresponding to the pay-off (e.g. Bob pays up 1.05 X with the probability of 95% and in any other case he's good for nada, zero, ziltch). Alice regards the offers and realizes that there are three options (partial investment of X units isn't of interests).

1. Keep the money in the mattress (0 risk, 0% gain).
2. Present the money to Bob (5% risk, 5% gain).
3. Present the money to Carol (10% risk, 10% gain).

Here, Alice might ask himself if the inflation forces him to invest into anything, if there's any slightest difference in correlation (5% gain but 5.01% risk) etc. But that's not the aim of the question.

The mechanics of the above is obvious to me. The bigger the risk (time the money invested), the bigger the gain. If at loss, only the amount being risked is lost. I.e. only the money risked to get the gain is being risked to getting lost. This part I view as sane and self-controlled.

# The banking approach

Suppose there's this typical bank, Bank of Scandinavia. As far I've understood the regulations, it's allowed to lend more money than it actually possesses, as long as it doesn't go bananas. The government of Scandinavia decided that the bananas level starts at 50%, meaning that if BS owns 10 X units, they can lend out 20 X without being considered unstable.

This part puzzles me, because the gain of the bank is being generated based on equal parts of the money risked to getting lost and some money that doesn't even exists.

It's my understanding that the stimulation of the economy is far greater using this approach. I also hear that the wealth created this way is sustainable, at least if we keep the bananas level fairly modest.

As far my research went to its conclusion (and by that I mean that I got tired of googling and watching suspected cartoons on YouTube claiming to reveal the ugly truth), I've learned that some governments set the bananas level to 10% (meaning that BS could lend out 100 X). In fact, during a period, there was the level of 3% in US and it was frown upon as too restrictive.

# Main question

Is it correct to regard the lending set-up as unhealthy, bound to implode and cause mayhem (at an extremely low risk, which in practice guarantees that such won't take place)?

Or is there a regulatory system covering either the tiny-whiney risky part or, alternatively, a means to recreate and pay back the part of the lost money that wasn't really there? Are there other gains to this set-up except boosting the economy (at incrementally larger risk)?

There are two ways I can think of interpreting this question.

My first thought is that a single bank doesn't lend out more money than it has, but the banking system does. So let's say someone deposits 100 dollars in Bank A and the reserve requirement is 10%. Then Bank A can lend out 90 dollars. Let's say that money is deposited in Bank B eventually. That bank can then lend out 81 dollars. This money then gets deposited in Bank C eventually, and it can lend out 72.9 dollars. This process continues, and if you take the sum of all this lending, you get that the money supply is now:

$$\sum_{n=0}^\infty 0.9^n(100) = \frac{100}{0.1} = 1000$$

So the banking system can lend out 1000 dollars without being considered unstable under this 10% reserve requirement. Notice how it kind of looks like we are double counting the money that is in the economy, and that's the point of fractional reserve banking. There isn't actually 1000 dollars, but there is credit worth that much floating around in the system.

The second way you could argue though is that individual banks in fact can lend more money than they have in their account. It creates an electronic record crediting the borrower's deposit with the sum of credit. So here, the limitation is still the reserve requirement. Say Bank A gets a deposit of 100 dollars. It can then lend out 1000 dollars at a 10% reserve requirement. Since it doesn't have 1000 in cash, it gives out credit.

I think that the real economy will use a combination of these two methods to get its lending out, but regardless, the result is the same. A simple money multiplier.

Edit: To reiterate (read: copy-pasted) from the comments below, how can a bank lend out credit that isn't backed up by paper/physical money?

1. FDIC insurance from the central bank, but more to the point,

2. The bank isn't going to back up all the credit at the same time. Say in our above scenario (100 dollars, 10% req.) the bank lends out "air money" of 5 dollars to someone, who then spends the credit purchasing from a business. The business then claims on that credit, and the bank still had some reserve (10 dollars in cash) to pay the business. Meanwhile, the bank, because it lent out so much credit, is also collecting a lotttt of interest, and borrowers pay back that interest...in cash. That replenishes the reserve. So in an equilibrium money market, hopefully the rate at which the bank gets cash in interest is the same as the rate which they pay back the "air money" with that actual cash.

Take the car example from in the comments. That is, say you "promise both your friends a car, but you only have one car and both friends know this". Well, the analogy is a little stilted, not quite parallel to what a bank is like. If you were a bank, you would only lend (not give away forever) out the car if you were promised to get it back with some interest, (maybe more gas or something). Problems only happen if both friends want the car the same time.

• Perhaps I can finally get it right. Your answer summarizes what I've seen on the net but now I can ask my questions. In the first case it doesn't look life if we're double counting. We are indeed double counting. Aren't we? Suppose that instead of A-B-C-..., the chain goes A-A-A... The calculation remains the same but now it's obvious that something is fishy here. If we start with a total deposit of 100, we can't end up lending more than 100 without "air money", can we? And it can't be chalked to spreading the risk because each subsequent bank has in this case no own, real money. – Konrad Viltersten Dec 12 '15 at 19:11
• As for the second case, I think you're hitting my problem spot-on. How can a bank give credit if it doesn't back it up with own and real money? Of course, if we trust that the bank can cough up the dineros, then it works. But wait! It can only cough up 10% of the dough. The rest, it'll need to cover from "the next guy" who hasn't deposited his money yet. How can we trust that? It sounds like a Ponzi scheme. I understand that it seems to work but I still don't get how it can be rational to lend out something one doesn't have. – Konrad Viltersten Dec 12 '15 at 19:19
• Perhaps I'm too dumb but the way I see it, if two of my friends know that I've got only one car and I promise to give each of them a car, one of those friends will be disappointed. How does this differ from the example with banks? I must be missing something. But what? – Konrad Viltersten Dec 12 '15 at 19:23
• I think that in your reasoning you are missing basic arithmetic. Instead of worrying about the bank lending out imaginary money, on what basis can anybody repay more money than they borrowed? Where does the extra 5% or 10% interest lenders demand come from? In other words, the demand of returning more money than you borrowed creates money. – rocinante Dec 12 '15 at 20:20
• @KonradViltersten I think a bank can lend out credit that isn't backed up by money because of 1.) FDIC insurance from the central bank, but more to the point 2.) the bank isn't going to back up all the credit at the same time. Say in our above scenario (100 dollars, 10% req.) the bank lends out "air money" of 5 dollars to someone, who then spends the credit purchasing from a business. The business then claims on that credit, and the bank still had some reserve (10 dollars in cash) to pay the business. – Kitsune Cavalry Dec 13 '15 at 4:57

Yesterday I promised my wife that if she would do the dishes, I would sweep the floor.

Five minutes earlier, my promise didn't exist. I created it myself. Does that strike you as unhealthy or bound to implode and cause mayhem?

• No, it doesn't strike me as mayhem-prone at all. Now, supposing you're a busy gent and only have one hour of free time (8-9 PM), if you'd promise her to also walk the dog (both the sweeping and dogging takes precisely one hour - then I'd say is fishy (and depending on the marital relation, potentially risking mayhem). – Konrad Viltersten Dec 13 '15 at 16:38
• Making a promise isn't bad. Making a promise for something that's already being promised to something else, can't be divided nor simultaneously used is. And if we cover the shortage of promised resources by hoping we won't be asked to present them, then we have a Ponzi scheme. Or at least that's how I figure. Please advise if I'm mistaken. – Konrad Viltersten Dec 13 '15 at 16:38
• Last week I promised my 200 students that I would be available to all of them at my office hour. In the course of an hour I can actually meet with about 12. Six showed up. If all 200 had showed up, there would have been mayhem. Was I running a Ponzi scheme? – Steven Landsburg Dec 13 '15 at 16:43
• No, you were not. Although I wonder if it's a representative case. If you, as a professor, agree to a salary obliging you to provide attention to each pupil's needs but then cynically bet on most of them not needing it... That's a Ponzi scheme, I'd say. You're paid under the assumption of full availability but you're unable to provide it, unless not all actors entitled, will request it. (I love the examples of yours - they make it easier to formulate the doubts, so to speak. +1) – Konrad Viltersten Dec 13 '15 at 17:06
• I'm glad the examples. help. They are intended to focus your doubts, not to dismiss them. Thank you for taking them in that spirit. – Steven Landsburg Dec 13 '15 at 17:11