Marginal revenue (MR) is the change in total revenue that arises when the quantity sold changes by one unit. Since perfect competition is a in which no producer or consumer has the to influence . Therefore, in this form of market marginal revenue always equals the average revenue because the demand (D) is perfectly elastic. As a consequence the price equals average revenue and marginal revenue, P=MR=AR.
Profit maximization always leads the marginal cost (MC) to equal marginal revenue (MR). Moreover, perfect competition wipes out abnormal profits. In fact, if these are positive new firms will enter and compete by selling their products at a lower price. If they are negative, less efficient firms will go out of business and only the most innovative firms will survive with a better technology and a lower AC curve. In this situation, the abnormal profits will be zero and it will go back and the equilibrium is shown in the graph below, where P=MC=MR=AR=AC.
In monopoly there is only one producer, so it represents the industry. In this market form there are no competitors as there are barriers that block other firms to enter in the business. As a consequence the firm usually gets positive abnormal profits. As we can see from the diagram below, the MR curve is below the AR curve (demand). The monopolist maximises profit by producing by the level of output where marginal cost (MC) is marginal revenue (MR). If the firm produces a product which has a small demand then the demand curve will be lower than that shown in the diagram. In that case, the firm makes losses and it might close or change business, because it is not able to cover the costs (P <AC). In the particular case where the AC curve crosses the demand curve at the point of equilibrium, the monopolist does not earn abnormal profits (P=AC).
In the monopolistic market the price usually differs from marginal cost (MC) and average cost (AC) therefore we have MC=MR that are different from MR and AC.
The equilibrium described above is only theoretical because the monopolist may fear that the barrier to entry are not high enough to keep out other possible firms, which are attracted by his very high profit. In order to prevent this, the monopolist may expand the output beyond the point of the maximum profit and reduce the profit level to discourage potential competitors.
Both these forms of market are only theoretical, because it is not possible to have a 100% monopoly and a perfect competition.