Monopoly, is it a problem?

  If such status is gained by competition in the free-market then the
  "monopoly" -- the successful business -- is good. If such status is gained 
  by using the government, or Mafia, to force one's competition out of 
  business, then the monopoly is evil.

Some more modern, mathematically-heavy theory phrases this as more or less an issue of feedback behavior: in a properly functioning market, the market is determined by something outside the market mechanisms themselves (idealized as "real" supply and demand), but in a malfunctioning market, the market mechanisms themselves feed back into the market, so it's mostly determined, self-referentially, by itself.

Of course monopolies are not intrinsically evil. I can’t really see what that has to do with the question as to whether states should prevent companies from becoming monopolists, though.

This seems dated in our modern world.

Of course you can force your competition out of business if you're big enough. It's even easier if you're willing to use some dirty tricks. It's also sometimes impossible to compete in some modern industries like software. I can't simply sell a cheaper version of Windows -- only Microsoft can sell Windows. It's not as simple as going to the shoppe to pick from different brands of top hat. They're basically the same thing so they can compete against each other directly. Capitalism is great for soft drinks and tennis shoes but I'm not convinced it's the best choice for everything.

http://www.debunkingeconomics.com/extracts.htm#4

>"The historical record gives many reasons to be critical of monopolies. Some of today’s most respectable names accumulated fortunes in the 19th century by grossly unethical means, and held on to their economic wealth by the abuse of the many forms of power that wealth can confer. This record of 19th century corporate lawlessness is the major explanation for America’s distinctive anti-trust laws, which enable the judiciary in this bastion of capitalism to dismantle corporations that have acquired the position of ultimate market power.

>Economists have reduced this plethora of reasons to be critical of monopolies to just one: the size of a monopolist relative to the size of the market. According to economists, monopolies are worse than the alternative of competitive markets simply because the absence of competitors allows a monopoly to set price above marginal cost. Perfectly competitive industries, on the other hand, set price equal to marginal cost. Economists argue that monopolies are therefore necessarily bad, and that small, competitive firms are necessarily good, because monopolies produce a lower output for a higher price, thus restricting the supply of their products and exploiting consumers by over-pricing. However, the ‘proof’ of this argument makes the fundamental mathematical mistake of equating a very small quantity to zero. When this mistake is corrected, the economic argument against monopolies collapses, as does the economic theory of competition..."