Marginal revenue

We find the optimum at the intersection of marginal costs and marginal revenue

The marginal revenue or marginal turnover is a concept from microeconomics that is directly related to the revenue or turnover. While the revenue results from the multiplication of price and quantity, the marginal revenue is the increase in revenue that results from the sale of an additional unit of quantity.

It depends on the course of the demand function of the considered good. Analytically, the marginal revenue results as the first derivation of the revenue function based on the number of units sold (which corresponds to the slope of this revenue function).

In simple market models, the rule applies to both polypoles and monopolies that an equilibrium is established where marginal revenue = marginal costs . Thus, marginal revenue is an important part of pricing .

The German economist Johann Heinrich von Thünen described this connection as the marginal principle , with which he succeeded in finding the first solution to the classic value paradox . Other related concepts in the context of the marginal utility school are e.g. B. Marginal profit or marginal productivity .

For markets with perfect competition , the marginal revenue is constantly equal to the market price as long as the producer produces less than the equilibrium quantity.

Numerical example

The following information is given:

• Price function ${\displaystyle p(x)=11-x}$
• Revenue function ${\displaystyle E(x)=p(x)\cdot x=11x-x^{2}}$
• Marginal revenue function ${\displaystyle E'(x)=11-2x}$

Quantity sold	Price (in GE )	Total revenue	Marginal revenue
0	11	0	11
1	10	10	9
2	9	18th	7th
3	8th	24	5
4th	7th	28	3
5	6th	30th	1
6th	5	30th	−1

The fact that the marginal revenue does not correspond to the increase in total revenue is due to the continuity of the function on which the calculation is based. The marginal revenue for a sales volume of 2 is 7 monetary units. In order to determine the increase in total revenue, the average marginal revenue between the sales volume and the previous sales volume must be taken: The increase in total revenue for a sale of 2 is determined by the average of the marginal revenue for quantities 2 (7 MU) and 1 (9 GE). The increase is therefore (9 MU + 7 MU): 2 = 8 MU. Mathematically this can be calculated by inserting the mean value (in the example mentioned 1.5) between the two quantities in the formula: (works for linear functions ). ${\displaystyle 11-2\cdot 1{,}5=8}$

If the unit price of 9 MU is specified for total sales of 2 units on the market, the unit price is realized as marginal revenue (i.e. also 9 MU) when an additional unit is sold, because this additional sales could not be foreseen. Because if the market were to expect sales of 3 units, this would also result in a unit price of 8 GE.

Individual evidence

1. ↑ Marginal revenue - definition in the Gabler Wirtschaftslexikon.

Web links

• Marginal revenue - definition in the Gabler Wirtschaftslexikon
• Revenue and marginal revenue function - Article at mikrooekonomie.de