Why does a firm with a monopoly set price to be equal to marginal cost?

First, is important to note that a firm that has a monopoly has the ability to set its own price since there is no other competitors in the market. In addition, in economics, we typically assume that all firms are trying to maximise their profits. By setting price equal to marginal cost they do this.To see why consider the scenarios where the marginal cost is greater than the price. This means that the cost of producing the last unit is greater than the price, and is therefore making a loss, reducing profit. In the alternate case, if it is less than the price, by producing additional units, profits can be increased. Hence, it is optimal for them to set price equal to marginal cost.