Today, at the market appears a lot of suppliers who try to win over customers with their product and services whit certain characteristics. Namely, at the market there are many competitors who offer a different, or even similar, or about the same product, where the customer is placed in indecisive situation. That is why the quality and price of products or services are of great importance. On the other hand, there are markets where there is no competition, respectively, markets where only one company is in focus, that is a monopoly. Properly that kind of situation in the market is the subject of this paper and will be explained through various subtitles and explanations to provide insight into the shape of the market on which operates a monopoly. Therefore, monopoly is, on the one hand, a positive way of determining the market, while on the other side is the problem, and with intention to solve monopoly the role of public authorities who are trying to suppress it are very important. In market competition, state seeks to set certain rules of the games in the markets with laws and regulations. This paper will explain the role of market monopoly, its appearance, forms and methods of monopoly price discrimination, and the importance of combating monopoly laws.