$3,700,000,000 of debt is a bit more complicated than "simple economics." If someone wants to buy MGM, it needs to first come up with the capital to cover the outstanding debt that could be called in at a moment's notice. If you haven't looked around recently, the global economy is still more than mildly in the shitter at the present time. After the debt, there's still the value of the studio to be factored into any purchase price.
You seem to be under the impression that getting The Hobbit made will save MGM. First, the studio has to find the buckets of money just to get it made. Then, okay, both movies will make a few hundred million dollars domestically (which would be split with Warner Bros.). Overseas grosses would be diluted from all the sharing. This isn't a situation where a fantasy movie will magically save the studio. The Hobbit is a one-time moneymaking opportunity, not a bucket in the sky that will simply overturn and pour hundred-dollar bills all over the landscape. MGM is in bad shape and has been in bad shape for a very, very long time.