Market Power
The first issue that must be decided in the case is that of market power, and monopoly. A common misconception is that monopolies must control the entire market for a given good. A monopoly requires only that you hold a controlling interest in the market, that is there is so little competition you can sell as much of your product as you like at any price you like, and not fear that you will be displaced by competitors who offer better services.
When classifying a firm as a monopolist, it is important to carefully define the market in question. If your choice is too narrow, you may wrongfully accuse someone of a monopoly. For example, a market defined as the market for a particular book will certainly have a monopoly, as only one publisher would have rights to that book. This would not give a realistic portrayal of the market, however, as the firm producing that book would have competition from other firms producing other books. By the same wisdom, you would not define a market that includes all modes of transportation, as this would protect a monopolist of automobiles on the ground that he faces competition from firms producing walking shoes.