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 unit sold however the formula can still be used to capture the average marginal revenue across a series of units i e the difference between the 100th and 115th unit sold the formula for marginal revenue can be expressed as marginal revenue change in revenuechange in quantitymr tr q 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 q tr 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 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 positive marginal revenue is informative but does not convey enough information to a company for smarter decision making marginal transaction information should include expenses to garner the most insight marginal revenue curvelike 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 university of minnesotaaverage revenue curvemarginal 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 the economics of food and agriculture marketsexample of marginal revenueto 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 marginal revenue vs marginal costany benefits gained from adding the additional unit of activity are marginal benefits one such benefit occurs when marginal revenue exceeds marginal cost resulting in a profit from new items sold if the sale of one additional unit yields marginal revenue of 100 and marginal expenses of 80 the company will receive a marginal profit of 20 for the additional item sold a company experiences the best results when production and sales continue until marginal revenue equals marginal cost beyond that point the cost of producing an additional unit will exceed the revenue generated if the company sells one additional unit for 100 but incurs a marginal cost of 105 the company will lose 5 in the process of selling that extra unit 