Why is a firm's average revenue equal to their marginal revenue in perfect competition?

Some important conditions of perfect competition are that all firms sell an identical (homogeneous) product, there is a large number of buyers and sellers, and no one buyer or seller can influence the ruling market price. A firm’s average revenue is their total revenue (price x quantity) divided by their total quantity sold, which is simply equal to the price at every level of output. This is illustrated by the firm’s demand curve, which shows the quantity demanded by consumers at any given level of output. The firm’s marginal revenue is the extra revenue they earn from selling an additional unit of output.

In perfect competition, price is determined by the intersection of market supply and market demand, and no one firm or consumer can influence the ruling market price of £5, for example. This means that demand is perfectly elastic at the price of £5, because consumers would not be willing to pay any other price. Firm A would not be able to charge a price of £8, because another firm is selling an identical product for £5. Firm A also would not charge £3, because they will receive less revenue than if they sold at £5. Therefore, every unit sold by the firm is sold at the ruling market price of £5. This means that the additional revenue the firm earns for an extra unit sold is equal to £5, which is the same as the average revenue the firm earns for each unit sold. Therefore, in perfect competition, average revenue is equal to marginal revenue, as a single price, the ruling market price, is charged for all units sold by firms.