Marginal revenue

In microeconomics, marginal revenue (R') is the additional revenue that will be generated by increasing product sales by one unit. It can also be described as the unit revenue the last item sold has generated for the firm. In a perfectly competitive market, the additional revenue generated by selling an additional unit of a good is equal to the price the firm is able to charge the buyer of the good. This is because a firm in a competitive market will always get the same price for every unit it sells regardless of the number of units the firm sells since the firm's sales can never impact the industry's price. However, a monopoly determines the entire industry's sales. As a result, it will have to lower the price of all units sold to increase sales by 1 unit. Therefore, the Marginal Revenue generated is always less (lower) than the price the firm is able to charge for the unit sold since each reduction in price causes unit revenue to decline on every good the firm sells. The marginal revenue (the increase in total revenue) is the price the firm gets on the additional unit sold, less the revenue lost by reducing the price on all other units that were sold prior to the decrease in price.

Marginal revenue is equal to the ratio of the change in revenue for some change in quantity sold to that change in quantity sold. This can also be represented as a derivative when the change in quantity sold becomes arbitrarily small. More formally, define the revenue function to be the following

By the product rule, marginal revenue is then given by

For a firm facing perfect competition, price does not change with quantity sold (${\displaystyle P'(q)=0}$), so marginal revenue is equal to price. For a monopoly, the price decreases with quantity sold (${\displaystyle P'(q)<0}$), so marginal revenue is less than price (for positive ${\displaystyle q}$).

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