A monopoly has at least one of these five characteristics:

• Profit maximizer: monopolists will choose the price or output to maximise profits at where MC=MR. This output will be somewhere over the price range, where demand is price elastic. If the total revenue is higher than total costs, the monopolists will make abnormal profits.
• Price maker: Decides the price of the good or product to be sold, but does so by determining the quantity in order to demand the price desired by the firm.
• High barriers to entry: Other sellers are unable to enter the market of the monopoly.
• Single seller: In a monopoly, there is one seller of the good, who produces all the output.[6] Therefore, the whole market is being served by a single company, and for practical purposes, the company is the same as the industry.
• Price discrimination: A monopolist can change the price or quantity of the product. They sell higher quantities at a lower price in a very elastic market, and sell lower quantities at a higher price in a less elastic market.

Just so we have a definition of a monopoly.