If a profit-maximizing monopolist's marginal cost is $8 and its marginal revenue is $12, what should it do to increase profits?

The monopolist should increase output to maximize profit because the condition for profit maximization occurs where marginal revenue equals marginal cost. In this scenario, the marginal revenue is higher than the marginal cost ($12 compared to $8). This indicates that the monopolist can increase its profit by producing and selling more units.

When marginal revenue exceeds marginal cost, each additional unit produced adds more to revenue than to costs, which means that producing more will increase total profit. By increasing output, the monopolist can take advantage of this profit opportunity, capturing additional consumer surplus and increasing overall profits.

In contrast, increasing the price or reducing the output would not be advisable, as these actions could lead to a decrease in total revenue, since it would prevent the monopolist from selling more units where they could gain profit from the positive difference between marginal revenue and marginal cost. Thus, the correct approach is to reduce the price to increase output, leveraging the ability to sell more units at a lower price, which maximizes profit given the existing conditions of marginal revenue and marginal cost.