Marginal revenue

The marginal revenue and marginal revenue is a term from microeconomics, which is directly related to the revenue or sales. While the proceeds obtained by multiplying price and quantity, the marginal revenue is the one growth of revenue resulting from the sale of an additional unit of measure.

It depends on the shape of the demand function of the considered good. Analytical results in the marginal revenue as the first derivative of the revenue function according to the number of units sold (which corresponds to the slope of the revenue function ).

In simple market models applies to both Polypole as well as monopolies, the rule that an equilibrium where marginal revenue = marginal cost is. Thus, the marginal revenue is an important part of pricing.

This relationship is called the German economist Johann Heinrich von Thünen as marginal principle, which he succeeded in the first solution of the classical value paradox. Other related concepts in the context of the marginal utility school are eg limit profit or marginal productivity.

Numerical example

Given the following information:

• Price function p ( x ) = 11 - x
• Revenue function E ( x ) = p ( x) * x = 11x - x ²
• Marginal revenue function E '(x ) = 11 - 2x

The fact that the marginal revenue is not equal to the increase in revenues is due to the continuity of the function, which is the basis for calculation. Thus, the marginal revenue is at a rate of nearly 2 at 7 monetary units. To determine the increase in total revenue, the average marginal revenue between the sales amount and the previous paragraph, the amount that needs to be taken: for example, the increase in total revenue determined at sales of 2 by the average of the marginal revenue in the amount of 2 (7 GE ) and 1 (9 GE). The increase is thus (9 7 GE GE): 2 = 8 GE. Mathematically, the calculated by multiplying the mean value ( in the example 1.5 ) is inserted between the two quantities in the formula: 11 - 2 * 1.5 = 8 (works with linear functions).

If a total sales of 2 units on the market, the unit price of EUR 9 GE is given, then (also 9 GE so ) is realized by selling an additional unit, the unit price as marginal revenue, because this additional paragraph was not foreseeable. Because the market would expect sales of 3 pieces, it would result in a price of 8 GE.