Gold has base value derived from its industrial, ornamental uses. But its trading value is much larger. Similarly Bitcoin has a base value in the cost of mining 1 BTC. Right now it is around $800 or so. Because of the competition in mining, asic chips development, and More's law. The cost of mining 1 BTC is going up exponentially.
If BTC falls below the cost of mining people will stop mining and the network will adjust to the reduced difficulty, making the cost of mining drop.
A problem is that if too few people mine, the network becomes easy to compromise. That's a problem that bitcoin has, and other currencies (and things like gold and silver) do not.