Why does a monopoly equate marginal revenue and marginal cost?

We should start by understanding what marginal revenue and marginal costs are. The marginal revenue is simply the marginal change in revenue after a rise in quantity (fall in price), we can think of it as the derivative of the total revenue curve. Similarly, the marginal cost is the marginal change in the cost of production after a rise in quantity (fall in price). If the marginal revenue is below the marginal cost then increasing output by a small amount will lead to a rise in revenue that is smaller than the rise in costs - reducing profit - the monopoly should instead lower the quantity. If the marginal revenue is greater than the marginal cost then an increase in quantity will increase revenue by more than costs and increase profit - they should increase the quantity. Therefore when the marginal revenue equals the marginal cost, there is no reason for the monopoly to increase or decrease the quantity and profits will be maximised.We can also think of the monopolies problem logically / mathematically:Show step by step the monopoly maximisation problem if the student is interested, usually not required at A-Level, but potentially useful for interviews When a monopolist increases the quantity it sells it has to reduce the price in order to sell the extra good, and incurs more costs to produce it. How does the price fall affect the revenue of the monopolist? Well firstly they gain an extra sale at the new lower price, a gain at the margin. But the lower price reduces the revenue on all of the other units sold - this is called a loss on the 'infra-margin' . The monopoly must balance this revenue effect with the increase in costs to maximise its profits.Graph: Step by step, demand curve, marginal revenue curve, marginal cost curve, average total cost curve and profits. Second graph: Dead weight welfare loss. ................Extensions to this problem and area of the course: perfect competition, price discrimination, benefits and costs of monopoly power (dynamic and static efficiency), regulation, natural monopolies, durable goods monopolies and the Coase conjecture.