Bitcoins are no different from any other commodity in this regard. We say that the price of a car is $45,000, but that doesn't guarantee that you can sell one for $45,000 unless you can find someone willing to buy one for $45,000. When we say some particular number is the price, we mean that's basically the number that buyers and sellers both agree that it is worth. But it's not a guarantee that you'll be able to buy or sell at that price.
Bitcoin exchanges report the prices at which Bitcoins change hands when they do change hands. They also report the price at which people are willing to buy (typically slightly less) and the price at which people are willing to sell (typically slightly more). If you try to buy or sell a large quantity, this will change the price. For example, if the last trade was at $250 and someone is willing to buy 10 bitcoins for $240, and you sell them 10 bitcoins, the price would move to $240. And now there wouldn't be anyone left willing to buy at $240, so the new buy price might drop to $235.
I'm not sure why you would connect this to a Ponzi scheme. Ponzis don't work this way at all -- they pretend to be investing but actually a central operator pays out of a fixed pool. Bitcoins behave more like stock, they are bought and sold at some agreed value based on the value of the underlying assets. Bitcoins have underlying value because they can be securely exchanged, allowing them to function like a currency.
While some people buy Bitcoins hoping they can sell them at a higher price, other people buy them strictly as a means of exchange. They exchange the Bitcoins for goods and the recipient may exchange the Bitcoins back to some other currency. The Bitcoins provide value because they allow the exchange to take place in a neutral currency, with high security, and at high speed, something that might otherwise be impossible. This capability makes Bitcoins have value beyond speculation.
In an sense nobody sets the price and in a sense everybody does. Anyone who wants to buy a Bitcoin can set the price they're willing to pay however they please. Anyone who wants to sell a Bitcoin can set the price they're willing to take however they please. As a result of trades in a free market, discovering the value is not difficult. If the highest price buyers are willing to pay is $250, and the lowest price sellers are willing to take is $251, the fair value is right in-between. (Assuming a perfect market, which we don't quite have.)
This is how many markets, including stock markets, work.
13You can't count "money in the system" based on the total purchase price of the asset and expect it to remain unchanged. By this logic, every capital market is a Ponzi scheme. – Nate Eldredge – 2015-05-04T07:41:17.217
2
closely related: Is Bitcoin a scam?
– Murch – 2015-05-04T09:17:19.0402It is part of the FAQ – Peter Mortensen – 2015-05-04T17:42:58.837
1It's not a strict ponzi scheme, but it does appear slanted toward giving early adopters and easy way to make a ton of money at the expense of those buying in late. – Almo – 2015-05-05T01:35:54.123
It is likely a ponzi because there is not a single exchange posting public records of their bank account holdings, that are verifiable with the bank. The money is (mostly) gone. – BAR – 2015-05-05T06:08:55.033
2@Almo Umm, that is true of all deflationary currencies. This only feels weird because for a hundred years, we've been using currencies that are only ever inflationary (by design!) - i.e. buying earlier means a net loss. And it's not really relevent to the question anyway, since that's not what a Ponzi scheme is, even in part. The investment return is just related to the risk - the initial adopters had much higher risks of wasting their investment than you have today - this is reflected in the demand going up while supply doesn't really change much -> increased real value. – Luaan – 2015-05-05T09:06:57.867
@Almo: And the same is true for successful startups, yet they wouldn't be classified as ponzis either. – Murch – 2015-05-08T09:10:00.977
But the sole purpose of a Ponzi is to give early adopters the advantage, with no mathematical possibility for late adopters to profit. It's all in the intent. Without knowing the BTC founders' intent, we can't say if their interest really was in the idea of the open "currency" (BTC is a lousy currency, it functions more as a commodity), or if they figured they had hit on a way to funnel a lot of money into their pockets. I can think of mining difficulty curves that would generate much fairer distribution over the lifetime of the network. – Almo – 2015-05-08T13:21:38.433
Well, as long as the coins mined by Satoshi remain untouched, I like to assume good intent. And then, "Hindsight can be merciless. People of any given era often look back in time and wonder how their predecessors could have been so dimwitted." -James Balog – Murch – 2015-05-11T22:29:12.800
1The question just makes no sense. What does "$1000 in the system" mean? When you buy a Bitcoin, the money goes to the person who sold you the Bitcoin who can then do whatever they want with it. It isn't in any system. Buying a Bitcoin is not like buying a share in a company. – David Schwartz – 2015-12-24T20:38:51.780