# Formula for Calculating Marginal Revenue

by Will Gish

Microeconomics constitutes the field of economic study focusing on small financial units, such as a person, family or individual business. A number of specialized concepts arise from this field of study, including marginal revenue. You can use a few formulas for calculating marginal revenue. The formula most suited to your needs depends upon the information available to you. The market conditions surrounding revenue affect marginal revenue values, and the calculation thereof.

### In Theory

Marginal revenue constitutes the difference in total revenue incurred by the sale of one additional unit. Two formulas arise instantly from this definition. You can calculate marginal revenue by dividing the change in total revenue (TR) by the change in quantity (Q) sold, which is calculated as ΔTR/ ΔQ. The Greek letter Delta (Δ) represents the change in value in this case. So, for example, if revenue changes by \$16 after the sale of four additional units, marginal revenue equals 16/4, or four. Or, if you know the total revenue before the sale of a unit and the total revenue after the sale, you can simply subtract the former form the latter. For instance, if total revenue jumps from \$105 to \$113 from the sale of one unit, marginal revenue for that unit equals \$113 - \$105, or \$8.

### In Perfect Conditions

In perfect market conditions, marginal revenue equals the market price of an item. Perfect conditions occur when no reciprocal relationship exists between the price of an object and the quantity sold. For instance, if you sell 100 yams all at the price of \$5 each, the market price of the yam, which is \$5, equals marginal revenue. To determine marginal revenue in perfect market conditions, simply divide the number of items sold by the total revenue. This only works if all items you sell are the same. For instance, if you sell yams for \$5 each and mangoes for \$2 each and include both on marginal revenue, you cannot use this formula.

### Calculating Marginal Revenue

A common method of calculating marginal revenue in imperfect situations entails graphically representing shifting marginal revenue values. As per microeconomics theory, the more of an item you sell, the less you sell it for, because lower prices precipitate higher sales. Thus the more of something you sell, the lower the marginal revenue for each subsequent item. To graphically represent this, create a graph with the X-axis representing units sold and the Y-axis representing price. Use the ΔTR/ ΔQ formula or simple subtraction to calculate marginal revenue on each sale, and enter those coordinates on the graph. The resulting line segment allows you to track and calculate marginal revenue at all points and determine trends.

### Marginal Revenue vs. Average Revenue

Marginal revenue bears some distinct similarities to average revenue, leading some to confuse the methods for calculating each. Average revenue constitutes the average price of each item sold, or Total Revenue/Quantity. If average revenue goes down, marginal revenue is necessarily lower than average revenue. This occurs because the average price of each item adjusts for all items sold when price goes down, while marginal revenue simply records diminishing returns in the relationship between units sold and revenue. For instance, if you sell 100 items for \$6 each, but sell a 101st item for \$5, average revenue changes from \$6 (600/100) to \$5.99 (605/101) for each item, while marginal revenue simply records a change of \$5 on the last item. If price goes up, marginal revenue is higher than average revenue for the same reason.