The grandparent comment (i.e. by URspider94) is correct. What you write about banks is a common, but incorrect misconception about what banks do.
The truth of the matter is: Banks do not need deposits to make loans.
Quite the contrary: Banks make loaning decisions independent of the level of their deposits - and it is the loan that causes the deposit, rather than the other way around, because the money loaned by the bank eventually lands in somebody's deposit.
Think about it this way: A bank cannot force anybody to take out a loan. Instead, there is a demand for loans which banks satisfy (subject to checks of creditworthiness and available collateral). Whether person A spends $10 or puts it in a deposit does not change person B's demand for credit,[1] and therefore the amount lent by banks does not change either.
[1] Of course, this is not entirely true. There can be causal links, but their direction is totally uncertain. For example, person A deciding not to spend money could mean that person B's business begins to struggle and person B needs to take out a loan that they otherwise would not have had to take. In that case, saving does increase the level of loans, but in a way that most people would judge to be detrimental to the economy.
Conversely, person A deciding to spend the money could lead to person B's business projecting growth, which encourages person B to invest by taking out a loan. In this case, the loan level increases as well, and in a way that most people would judge to be beneficial.
Where do banks get the money that they loan out if not from deposits?
Reserve requirements dictate what percentage of deposits banks have to keep on hand rather than loan out, and its inverse, the money multiplier, determines how much the money supply is expanded by repeated application of the deposit->loan process. This seems to be the standard treatment: I checked Abel-Bernanke's and Mankiw's Macroeconomics textbooks and they both tell basically the same story.
The supply and demand for loanable funds are balanced through a price mechanism: the interest rate. If banks have lots of deposits and can't loan them all out, then they'll lower the interest rate that they charge until they can. If there's more demand for loans than can be covered by deposits, then banks will increase the interest rate that they charge until the two are balanced.
The banks emphatically do not get the money they loan out from deposits, because even though your bank makes loans, the money in your deposit is still there and available whenever you want.
Compare this to a private investment arrangement where after you invest (aka lend) your money, your money is gone (in exchange for the promise to get more back later, and/or certain other rights such as ownership in a company).
When banks lend out money, what they do is either give you an account with a positive balance (in this case, the money doesn't have to come from anywhere, because all the bank is doing is changing some rows in their databases) or they make a payment to another bank on your behalf. In the latter case, the money that you actually see as a bank customer again doesn't have to come from anywhere, because it gets created by the involved banks changing some rows in their databases. There is also settlement in reserves occuring behind the scenes, and if a bank's reserve position drops low, what I write elsewhere applies: As long as a bank is solvent, they can always get reserves either from another bank or, in the worst case, from the central bank.
As far as the money multiplier is concerned, there are two ways to look at it. The first is empirical: https://research.stlouisfed.org/fred2/series/MULT
How does a wildly varying money multiplier fit in with your story?
Also, there a countries where the reserve requirement is zero. The inverse of zero is not well-defined or infinity, depending on how you look at it. Yet those countries don't have an infinite money supply. How does that fit in with your story?
The second way is from first principles by actually looking at the laws. If you look into reserve requirements, you'll see that banks only have to satisfy them after the fact. That is, people in a bank's loan department first make loans, and then people in a different department of the bank go out and ensure that the bank satisfies the reserve requirements. They usually do so by lending and borrowing on the interbank market, but if they cannot borrow there, they can always get the required reserves from the central bank. See e.g. here: http://en.wikipedia.org/wiki/Discount_window
Finally, your last paragraph does show a potential causal pathway from increased savings to a higher demand for credit, via the interest rate. The import question is the relative strength of that pathway compared to others, such as the ones that I have described in my previous comment.
Obviously even economists end up disagreeing on that matter, given their political biases (though beware false prophets paid by wealthy people to spread lies and half-truths). Three final points on that particular matter:
(1) How sensitive to interest rates do you really think loan demand is? If a business sees growth in revenue, they are likely to invest and expand (which often involves taking loans) even in a high interest rate environment. On the other hand, if a business sees decreasing interest rates but also a fall in revenue, will they still take on loans in order to invest in a growth of their business? The answer can be yes occasionally, but it is more likely to be no. This is supported by surveys of business leaders.
This point is important, because in the face of high savings, businesses may see lower interest rates as a second-order effect, but they will also definitely see lower revenue as a first-order effect. When a large-scale shift of customer behavior towards savings happens, then businesses will see the fall in revenue first, long before banks lower their interest rates on loans.
(2) Empirically, some people have predicted for a long time, since the beginning of the financial crisis, that low interest rates would bring growth back via investment. And yet interest rates have been at the zero lower bound for some time with at best mixed results. (Again, the quantitative parts matter: Yes, low interest rates encourage demand for credit, but how strong is that effect compared to others that may go in the opposite direction?)
(3) The range in which interest rates actually vary by that mechanism is limited, because the central bank fixes the short term interest rate based on political considerations. (That's what e.g. the FOMC meetings in the US are all about. It's totally in your face, actually, but still many people refuse to really grok it ;-)) Obviously, the long term interest rate for loans taken by banks (which is some markup above that politically set rate) can vary, but the real story is control by the central bank.
[My comments are getting too long, so I stop here, even though there are more details to be talked about.]
> even though your bank makes loans, the money in your deposit is still there and available whenever you want
This is definitely not true. If everyone asks for their money at once, the money won't be there because most of it has been loaned out. That's a bank run.
> How does a wildly varying money multiplier fit in with your story?
Over three decades, it looks pretty stable to me. The multiplier also varies based on the amount people want to hold in cash (I'm getting this from Krugman's book), because that's how money leaks out of the deposit->loan cycle. That could easily vary a non-trivial amount over 30 years. The most recent period where the multiplier is less than one I will grant is weird. The Fed has started paying interest on reserves, and banks are more wary post-recession, so they've started accumulating a huge amount of excess reserves: https://research.stlouisfed.org/fred2/series/EXCSRESNS.
> there a countries where the reserve requirement is zero
Obviously, the ratio that matters is not the legal minimum reserve requirement, but the actual effective reserve ratio. A bank has to keep a certain amount of reserves to keep their business running. The legal requirement is just to make sure that the amount they keep on hand is prudent. There's also the aforementioned leakage of money out of the deposit->loan cycle via currency held by the public, which can reduce the money multiplier further.
The rest of your post gives some good reasons that the real world doesn't work quite like the mainstream theory. It sounds like you're explaining an endogenous money theory; do you have any suggested references for further reading?
The truth of the matter is: Banks do not need deposits to make loans.
Quite the contrary: Banks make loaning decisions independent of the level of their deposits - and it is the loan that causes the deposit, rather than the other way around, because the money loaned by the bank eventually lands in somebody's deposit.
Think about it this way: A bank cannot force anybody to take out a loan. Instead, there is a demand for loans which banks satisfy (subject to checks of creditworthiness and available collateral). Whether person A spends $10 or puts it in a deposit does not change person B's demand for credit,[1] and therefore the amount lent by banks does not change either.
[1] Of course, this is not entirely true. There can be causal links, but their direction is totally uncertain. For example, person A deciding not to spend money could mean that person B's business begins to struggle and person B needs to take out a loan that they otherwise would not have had to take. In that case, saving does increase the level of loans, but in a way that most people would judge to be detrimental to the economy.
Conversely, person A deciding to spend the money could lead to person B's business projecting growth, which encourages person B to invest by taking out a loan. In this case, the loan level increases as well, and in a way that most people would judge to be beneficial.
The economy is complicated.