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In economics, a firm is a monopoly when, because of the lack of any viable competition, it is able to become the sole producer of the industry's product. In a normal competitive situation, the price the firm gets for its product is exactly the same as the Marginal cost of producing the product. Because the monopoly firm does not have to worry about losing customers to competitors, it can set a price that is significantly higher the Marginal (Economic) cost of producing (the last unit of) the product. Therefore, a monopoly Situation usually allows the firm to set a monopoly price which is higher than the price that would be found in a more competitive industry., and to generate an economic profit over and above the normal profit that is typically found in a perfectly competitive industry. The economic profit obtained by a monopoly firm is referred to as monopoly profit. The existence of a monopoly, and therefore the existence of a monopoly price and monopoly profit, depend on the existence of barriers to entry: these stop other firms from entering into the industry and sapping away profits.
In a perfectly competitive market, firms are said to be price takers: since a customer can buy widgets from one producer as easily as another, any widget producer on the market faces a horizontal demand curve at the equilibrium price: if the firm tries to sell widgets above the equilibrium price, customers will simply buy their widgets elsewhere and the firm will lose all of their business. (In most actual markets, of course, a situation in which exactly comparable goods are available just as easily from one firm as from another does not exist ? though this situation does seem to exist in Commodity markets, the theory of perfect competition is usually a useful idealized model rather than a naturalistic description).
By contrast, lack of competition in a market creates a downward sloping demand curve for a monopolist or oligopolist: although they will lose some business by raising prices, they will not lose it all, and it may be more profitable in most situations to sell at a higher price. Though monopolists are constrained by consumer demand, they are not price takers. The monopolist can either have a target level of output that will ensure the monopoly price for the given consumer demand it faces in the industry, or it can set the monopoly price at the onset and adjust output to ensure no excess inventories occur as a result of the output level. Essentially, they can set their own price and accept a level of output determined by the market, or they can set their output quantity and accept the price determined by the market. The price and output are co-determined by consumer demand and the firm's production cost structure.
A firm with monopoly power setting prices will typically set price at the profit maximizing level. The most profitable price that they can set (what will become the monopoly price) is where the optimum output level (where marginal cost (MC) equals marginal revenue (MR) as seen on the diagram below) meets the demand curve. Under normal market conditions for a monopolist, this price will be higher than the marginal cost of producing the product, thereby indicating the price paid by the consumer, which is equal to the marginal benefit for the consumer, is above the firm's marginal cost. In the chart below the shaded area represents the profits of the monopolist. The lower half represents the normal profits that would go to a competitive firm (ignoring output losses). The upper half represent the additional economic profit going to the monopolist.
In the absence of barriers to entry and collusion in a market, the existence of a monopoly, and therefore monopoly profit, cannot persist in the long run. (Note that a barrier can be caused by increasing returns to scale — a bigger firm can produce more cheaply. If the most efficient size firm serves the whole market, we have a "natural monopoly," and no other firms will "rush" to enter.) Normally, when economic profit exists within an industry, economic agents rush to form new firms in the industry in an effort to obtain at least a portion of the existing economic profit. As new firms enter the industry, they increase the supply of the product available in the Market, and these new firms are forced to charge a lower price to entice consumers to buy the additional supply these new firms are supplying (they compete for customers). Since consumers will flock toward the lowest price (in search of a bargain), older firms within the industry actually face losing their existing customers to the new firms entering the industry, and are therefore forced to lower their prices to match the lower prices set by the new firms. New firms will continue to enter the industry until the price of the product is lowered to the point that it is the same as the average economic cost of producing the product, and all of the economic profit disappears. When this happens, economic agents outside of the industry find no advantage to entering the industry, supply of the product stops increasing, and the price charged for the product stabilizes. Essentially, a competitive situation always leads to an equilibrium solution".
Normally, a firm that introduces a brand new product can initially secure a monopoly for a short while. At this stage, the initial price the consumer must pay for the product is high, and the demand for, as well as the available of the product in the market, will be limited. In the long run, however, when the profitability of the product is well established, the number of firms that produce this product will increase until the available supply of the product eventually becomes relatively large, the price of the product shrinks down to the level of the average "Economic cost" of producing the product. When this finally occurs, all monopoly associated with producing and selling the product disappears, and the initial monopoly turns into a (perfectly) competitive industry.
When consumers have full information about the prices available in the market and the quality of the products sold by the various firms, there cannot be a persistent Monopolistic situation in the absence of barriers to entry and collusion. However, these barriers can be created in various ways, and because of various situations. For example, the existence of patents will guarantee the patent owner a monopoly. When a natural resource is controlled by only one economic agent, that agent also enjoys a natural monopoly" (This is wrong. See the definition of a natural monopoly two paragraphs up. Beware, this entry is quite misleading because it misunderstands this concept.) since he/she can control supply of the resource to ensure a price that will yield an economic profit.[dubious ] The American firm Alcoa Aluminum is a historical example of such a monopoly; their control of "practically every source of bauxite in the United States" (bauxite is used to produced aluminum) was one key reason that "Alcoa was, for a long time, the sole producer of aluminum in the United States." 
Anti-Trust (Competition) Laws were created to prevent powerful firms from using their economic power to artificially create the barriers to entry they need to protect their monopoly profits. This includes the use of predatory pricing toward smaller competitors. In the United States, Microsoft Corporation was initially convicted of breaking the Anti-Trust Laws and engaging in anti-competitive behavior in order to form one such barrier in United States v. Microsoft; after a successful appeal on technical grounds, Microsoft agreed to a settlement with the Department of Justice in which they were faced with stringent oversight procedures and explicit requirements designed to prevent this predatory behavior. Microsoft was successfully convicted of similar anti-competitive behavior in the European Economic Community's second highest court, the Luxembourg-based Court of First Instance, in 2007. If firms in an industry collude they can also limit production, thereby restricting supply to ensure the price of the product remains high enough to ensure all of the firms in the industry achieve an economic profit.
The diagram to the right depicts an industry that initially starts out with a single firm that enjoys a monopoly and the initial monopoly profit that comes with it. Later, a second firm enters into the industry, lowering its price to obtain customers that usually do not purchase the product at the high monopoly price. As the initial monopoly firm loses customers, it is forced to lower its price to retain profitability. In the competition for sales to customers, the firms lower their prices even further, which increases the consumer demand for the product, and thereby entices the firms to raise production and which then increases the industry's total production and sales. Finally, the price and production in the industry stabilizes into its "competitive equilibrium"; the price paid by the consumers are just high enough to cover the average economic cost of producing the product, and the available quantity of the product doubles from its initial sales (under the monopoly).
If a government feels it is impractical to have a competitive market, it will sometimes try to regulate the monopoly by controlling the price the monopoly charges for its product. The old AT&T (regulated) monopoly, which existed before the courts ordered its breakup and tried to force competition in the market, had to get government approval to raise its prices. The government examined the monopoly's costs, and determined whether or not the monopoly should be able raise its price and if the government felt that the cost did not justify a higher price, it rejected the monopoly's application for a higher price. Though a regulated monopoly will not have a monopoly profit that is high as it would be in an unregulated situation, it still can have an economic profit that is still well above a competitive firm has in a truly competitive market.
The government examines the marginal cost associated with raising the production level up to its presently desirable quantity, and allows the regulated monopoly to charge a price that is no greater than this marginal cost. Though the monopoly's profit is lower than it is in an unregulated Situation, it can still make a positive economic profit.