The situation is called **monopoly**. The company has **monopoly**. 

[Investopedia][1]

>A monopoly is a situation in which a single company or group owns all or nearly all of the market for a given type of product or service. By definition, monopoly is characterized by an absence of competition

>According to a strict academic definition, a monopoly is a market containing a single firm. 


  [1]: http://www.investopedia.com/terms/m/monopoly.asp