See here:
https
/en.bitcoin.it/wiki/Help:FAQ#Where_does_the_value_of_Bitcoin_stem_from.3F_What_backs_up_Bitcoin.3F
Where does the value of Bitcoin stem from? What backs up Bitcoin?
Bitcoins have value because they are useful and because they are scarce. As they are accepted by more merchants, their value will stabilize. See the list of Bitcoin-accepting sites.
When we say that a currency is backed up by gold, we mean that there's a promise in place that you can exchange the currency for gold. Bitcoins, like dollars and euros, are not backed up by anything except the variety of merchants that accept them.
It's a common misconception that Bitcoins gain their value from the cost of electricity required to generate them. Cost doesn't equal value – hiring 1,000 men to shovel a big hole in the ground may be costly, but not valuable. Also, even though scarcity is a critical requirement for a useful currency, it alone doesn't make anything valuable. For example, your fingerprints are scarce, but that doesn't mean they have any exchange value.
Alternatively it needs to be added that while the law of supply and demand applies it does not guarantee value of Bitcoins in the future. If confidence in Bitcoins is lost then it will not matter that the supply can no longer be increased, the demand will fall off with all holders trying to get rid of their coins. An example of this can be seen in cases of state currencies, in cases when the state in question dissolves and so no new supply of the currency is available (the central authority managing the supply is gone), however the demand for the currency falls sharply because confidence in its purchasing power disappears. Of-course Bitcoins do not have such central authority managing the supply of the coins, but it does not prevent confidence from eroding due to other situations that are not necessarily predictable.
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