Ayn Rand and Leonard Peikoff have answered that question several times. No individual, by obligation, is responsible for any other human being unless they're your children. Now then, what would happen to the mentally challenged people who have no loved one to take care of them? They'll depend on voluntary charity. Just because it is a free society, it does not mean that no one will be charitable. It would be bad if charity was an obligation but voluntarily it's ok. Now just because its not an obligation it wouldn't mean that nobody will do it. Along history it has been proved that voluntary charity exist even when government does it and in most cases private charity works more efficiently than the other.
I'm sure that in a free objectivist society there would be some people helping the ones in need because of mental disfunctions but they wouldn't be altruistic. There would be some kind of cost and profit of it somehow. But in short the answer is what I said at the beginning: nobody is responsible for the mentally challenged unless someone wants to do it. One may say that it isn't fair because they were born that way, it is also not fair to place the burden of their problem to other people who have done nothing wrong to them. That, in fact, would be slavery.
answered Jan 22 '13 at 17:02
Juan Diego dAnconia