Well, in fact, they can't. I am pretty sure, there are many regimes that you can consider dictaroship, and they haven't solved these problems.

Dictatorships can do a lot of nasty things, but they cannot solve such problems. They may _look_ like they are able to, and they may _pretend_ that they solved these problems(especially if problems aren't easily noticeable by an average citizen. Take heavy heroin abuse as an example), but no, they can't and won't solve them.