In a monopoly, the monopolist will earn economic profits as long as his price exceeds marginal costs. This profit is called “normal” profit and it can be calculated by subtracting the average total cost from price.
As long as there are no significant barriers to entry for competitors, these normal or excess profits attract new firms into the market until competition drives prices down to where they equal marginal cost and all of the economic profits have competed away. This is the long-form content.
The short-form is already written above. The difference between a monopoly and perfect competition is that in a perfectly competitive market, average total costs will be at their minimum because of firms having to compete with each other for customers; whereas, in a monopolistic market, there are no competitors driving prices down so the price can exceed marginal cost without incurring any losses from lower production volumes or anything else.
This profit may only last as long as excess capacity exists – once this has been exhausted, profits turn into normal profits (or losses). As soon as these normal profits have been competed away by new entrants, an equilibrium point will exist where all economic profits have gone but some small amount.