Marginal Revenue Explained, With Formula and Example

What Is Marginal Revenue?

Marginal revenue is the change in total revenue divided by the change in total output quantity. It is the increase in revenue that results from the sale of one additional unit of output.

While marginal revenue can remain constant over a certain level of output, it follows from the law of diminishing returns and will eventually slow down as the output level increases. In economic theory, perfectly competitive firms continue producing output until marginal revenue equals marginal cost.

Understanding Marginal Revenue

Marginal revenue is a financial and economic calculation that determines how much revenue a company earns for each additional unit sold. As the price of a good is often tied to market supply and demand, a company’s marginal revenue often varies based on how many units it has already sold.

Marginal revenue is useful in several contexts. Companies use historical marginal revenue data to analyze customer demand for products in the market. They also use the information to set the most effective and efficient prices. Lastly, companies rely on marginal revenue to better understand forecasts; this information is used to determine future production schedules, such as material requirements planning.

How to Calculate Marginal Revenue

A company calculates marginal revenue by dividing the change in total revenue by the change in total output quantity. Ideally, the change in measurements captures the change from a single quantity to the next available quantity (i.e., the difference between the one hundredth and one hundred-first units sold). However, the formula above can still be used to capture the average marginal revenue across a series of units (i.e., the difference between the hundredth and one hundred-fifteenth units sold).

The formula for marginal revenue can be expressed as:

$\begin{aligned}\text{Marginal Revenue}&=\frac{\text{Change in Revenue}}{\text{Change in Quantity}}\\\\[-9pt]MR&=\frac{\Delta TR}{\Delta Q}\end{aligned}$Marginal RevenueMR​=Change in QuantityChange in Revenue​=ΔQΔTR​​

For example, imagine a company sold its first 100 items in one week for a total of $1,000. Marginal revenue disregards the previous average price of $10 as it only analyzes the incremental change. So, if it next sold a total of 115 units for $1,100 the next week, the marginal revenue for units 101 through 115 is $100, or $6.67 per unit ($100 ÷ 15).

Marginal Revenue Curve

Like other related concepts, marginal revenue can be graphically depicted. It is most often represented as a downward-sloping straight line on a chart capturing price on the y-axis and quantity on the x-axis.

The marginal revenue curve is often downward sloping because there is often an economically inverse relationship between price and quantity. As a company decreases the price of its product, more units will likely be demanded; as the price increases, demand often decreases.

For this reason, a company must often decrease its price to increase its market share. By decreasing its price, the company will receive less marginal revenue for each additional unit sold. At some point, the market demand for additional units will drive the product price so low that it becomes unprofitable to manufacture additional units.

In the graph below, marginal revenue is depicted by one of the blue lines. The quantity in which marginal revenue and marginal cost intersect is the optimal quantity to sell; the associated price point is noted as bullet E (where quantity per period and demand intersect).

Average Revenue Curve

Marginal revenue can be analyzed by comparing marginal revenue at varying units against average revenue. Average revenue is simply the total amount of revenue received divided by the total quantity of goods sold.

In a perfect competition, marginal revenue is most often equal to average revenue. This is because collective market forces make each participant a price-taker. For example, the market may dictate that it is not profitable to sell a good below $10. However, charging more than $10 per unit puts a company at a disadvantage to other companies selling at that price.

In an imperfect competition, marginal revenue and average revenue will vary. This is because a firm must eventually lower its price to sell additional units. Both marginal and average revenue tend to be downward sloping, with marginal revenue often being the steeper of the two lines. Consider an example where a company sells one good for $100. If it prices its second good at $90, its marginal revenue will be $90. However, its average revenue will be $100 + $90 / 2 units sold = $95.

The following graph is the theoretical average revenue and marginal revenue curve for an agricultural chemical producer in a monopolistic industry. Both marginal revenue and average revenue decrease as the firm lowers prices to sell more quantities, though marginal revenue decreases faster than average revenue.

Example of Marginal Revenue

To assist with calculating marginal revenue, a revenue schedule outlines the total revenue earned, as well as the incremental revenue for each unit. The first column of a revenue schedule lists the projected quantities demanded in increasing order, and the second column lists the corresponding market price. The product of these two columns results in projected total revenues in column three.

The difference between the total projected revenue of one quantity demanded and the total projected revenue from the line below it is the marginal revenue of producing at the quantity demanded on the second line. For example, 10 units sold at $9 each, resulting in total revenues of $90; 11 units sold at $8.50, resulting in total revenues of $93.50. This indicates the marginal revenue of the 11th unit is $3.50 ($93.50 – $90).