But if Bit coin can only be created by very expensive computer searches, what happens if the Fed wanted to pump , say, $100 Billion into the economy (or a Bitcoin equivalent ) ? It can't just print Bitcoins in the same way it prints Dollar bills.
I said before that this was a "non-sensical question error" and, in retrospect, I apologise for appearing to be patronising but... well, it was, and still is, non-sensical.
Let me make a couple of observations which might better explain why:
(a) Bitcoin is distributed. No one controls it[1]. Generation of Bitcoins is limited by its algorithm. It is important to understand that this is both a goal and a strength.
(b) QE with Bitcoin is therefore not only impossible but irrelevant (and "non-sensical").
(c) You seem to be implicitly assuming that there must be some kind of central authority. The world does not have to work that way. Bitcoin doesn't work that way.
(d) Indeed, many people take the view that statist meddlings like QE are a bug to be fixed and that distributed currencies like Bitcoin are the feature (or one of the features) that fixes the bug.
In short, in an economy that makes heavy use of cryptocurrencies there would be no notion of either central control of the currency or of QE[2].
You mention above that the price of shares in not related to the value of a company.
It was Mikefule who wrote that, not me. He wrote "the price of shares in big companies goes up and down with little or no link to the true value of the company" and he was correct. You can see this day to day where the value of shares in big companies goes up and down daily with little or no direct link to the underlying, fundamental value of the company itself. There is some link between share price and a company's value, of course, in that successful companies tend in general to have higher market capitalisation than poorly performing companies, but the market can get it wrong too.
I was under the impression that the share price was related to some multiple of the company value at the time of the IPO.
(a) The share price at IPO is whatever the company's shareholders think they can get away with!
(b) Indeed, as you say, a common basis for valuing a company at IPO is to base it on a multiple of turnover whilst factoring in of assets or balance sheet value. But assets are not necessarily a fixed thing. Intangible assets, such as "goodwill" (that is is to say how customers, the "market", and even suppliers in some cases feel about the company) is hugely open to interpretation.
(c) Important: Whatever basis is used to value a company at IPO, it is valid only at the moment of IPO. As of that moment onwards, a company's share price varies according to what people are willing to buy and sell at. Thus the company's value will go up and down with no relation to what the price was at the moment of IPO.
(d) And the price that people are willing to buy or sell shares at is, as Mikefule said, not necessarily directly related to the underlying value of the company (as best this can be calculated at any one time!).
Anyway, I am now thoroughly confused.
Life in the 21st Century tends to do that, I think.
I think it can help to free oneself of implicitly held assumptions, such as that there must always be some kind of central authority. Bitcoin is, right now, a highly successful functional anarchy, for example.
I still have the feeling that a lot of people are going to get burned by this.
Oh, I'm sure. But that's life. One might even say that "new" == "a lot of people are going to get burned".
Progress (and I think this is definitely positive progress) is like that. People get burned. So be it (perhaps sadly).
If it's going to be the way to go, why haven't billionairs bought them all up at the current price ? That way they would own the economy.
(a) Billionaires own the economy anyway. We all work for them, whether we know it or not[3].
(b) If someone has made billions using more conventional means then they are often very cautious indeed (small-c conservative) about new ideas. They don't really need them to get rich or even to get richer, afterall. They already know how to get richer.
(c) All that said, what makes you think billionaires aren't involved? Rather than buying Bitcoins, a good business for billionaires would have been (and still is to a great extent) in funding Bitcoin mining on as large a scale as possible. This is increasingly expensive and energy-intensive to run and yet, if Bitcoin is to survive, it will have an assured future. Being the person (or one of the persons) that people have to pay to validate Bitcoin transactions would surely be an excellent business model for billionaires.
Footnotes:-
1: There are "core developers" for Bitcoin but they only have de facto control, not de jure. In other words, if you dislike the way they do things then you (and people who think like you) can fork Bitcoin and do it your own way. This has happened numerous times for the protocol itself and at least twice for live Bitcoin. If no one likes your fork it will die. If enough people like it then it will prosper.
2: As an aside, bear in mind that QE was only needed because conventional banks had been operating on a fundamentally dishonest and/or incompetent business basis (despite so-called state 'regulation'!). If distributed and decentralised cryptocurrencies were more ubiquitous, there might well be far less opportunity for governments to bail out badly run private businesses such as banks.
3: As another aside, both billionaires and very big businesses have what is in effect a de facto symbiotic relationship with governments.