Yes, they can do exactly that. He who controls the market dictates the price and product.
Fair-market being what it is, we wouldn't expect said company to stay in business very long if they got greedy and jacked the price up 1000% or so -- people simply wouldn't buy that product.
The government steps in and regulates (either by completely taking over or splitting up the monopoly [ex: AT&T to SBC and back again]) when this happens -- and when it involves a service that the people seemingly cannot do without or would hurt the economy in a drastic way (gasoline, telecom, credit, etc.).
I know that being a monopoly is not illegal in the US -- it's how one becomes a monopoly that could be illegal (price-fixing between companies, anti-competetive practices, etc.). This poll stemmed from a discussion on another site that threw around the idea that Apple has some kind of "monopoly" on the App Store (which they do, but "monopoly" isn't really the term) and therefore someone should step in and force them to open it up... or something like that.
I think the poster of that argument somehow misunderstood the basic definition of "monopoly" and thought that monopolies were inherently illegal. I think a lot of people have this misconception largely due to the whole Microsoft shenanigan, which wasn't about Microsoft having a monopoly on different things so much, but exactly how they got to that point.
Basically, the person just didn't like Apple's vertical-integration style of the App Store and the fact that the iPhone/iPod touch/iPad is a closed platform... no different from your Ford's engine-control computer, or your Sony DVD player, or your microwave oven, or... but you don't hear people complaining that they can't load a different menuing system on their VCR, or they can't change what "power level 10" does on their microwave.
The closed-platform is working for Apple in a huge way, and these confused people don't have to like it, but that doesn't make it illegal. The level of sense of entitlement is mind-boggling sometimes these days. Plus it makes me wonder why they bought an iPhone to begin with... in the words of a very intelligent man somewhere, "Don't go running your head into a wall over and over again then come around here bitching about your headache."