What does the value of bitcoins depend on? I've been looking up stuff about bitcoins for some time now and i have two question stuck in my mind:

How is the value of bitcoins so unstable?

And can there be bitcoin inflation?
The price is unstable because there's a fairly small free float (the quantity available for buying and selling with true currencies) compared to the level of transactions.

It's a Ponzi scheme, so demand is driven by Bitcoin marketing: it is in immediate financial interest of the holders of Bitcoin to drive up the price by "ramping" it: talking up the market price. The amount of attention that the media gives Bitcoin goes up and down - this affects demand, and that drives the price, as supply is fairly stable.

The originators of Bitcoin, and the original hoarders, have most to gain: it was easiest for them to create Bitcoins. It would be rational for them to slowly release their hoard into the market as price goes up.

It's also attracted a lot of gullible but evangelical supporters: for them, continuing to hold Bitcoin is a means of validating their beliefs, and even validating the identity they've built for themselves around it. That's why the free float tends to stay low.