First, there's already a ceiling on the price from the current supply. The price can only go down.

Second, if it works out for them and they're able to start mining these, other people will start doing it, too.

As a nation with an army, they could do something like this.

As a private company--especially if this mineral becomes very necessary and expensive--would be a very big target for some sort of 'congressional oversight' to 'protect national interests' and prevent a harmful monopoly.

Diamonds would be a good example too, right? Platinum would be even better in this situation, I think, because it has more practical uses than diamonds.

They would still be constrained to degrees by their marginal costs (the price floor) v what the market will bear. Who knows what the actual costs will be the day they have a giant rock in orbit, although I expect they will fall rapidly with advancing privatization. I am sure they will take very conservative actions, but imagine the potential liabilities–might be a lot more than the value of the rock.

Its only worth the $8 trillion because they haven't any.

Imagine they release 100 tons / year.

The world supply of platinum has just gone from 100 to 200 tons / year.

Or they release 200 tons, and the world supply goes up to 300 tons / year.

At some point really low they'll make platinum as common as dirt and worth about as much.

* exaggeration to make point. Point stands.

eg, De Beers for diamonds.

They would be the De Beers of precious metals [1]. With that kind of wealth at stake, the monopoly wouldn't last long. You'd see competition from other private ventures, as well as from countries (Russia, China, ...).

[1] http://en.wikipedia.org/wiki/De_Beers#Diamond_monopoly