Marginal revenue

In microeconomics

Microeconomics

Microeconomics is a branch of economics that studies how households and firms make decisions to allocate limited resources, typically in markets where goods or services are being bought and sold...

, Marginal Revenue (MR) is the extra revenue that an additional unit of product will bring. It is the additional income from selling one more unit of a good; sometimes equal to price. It can also be described as the change in total revenue/change in number of units sold.

More formally, marginal revenue is equal to the change in total revenue over the change in quantity when the change in quantity is equal to one unit (or the change in output in the bracket where the change in revenue has occurred)

This can also be represented as a derivative.

In microeconomics

Microeconomics

Microeconomics is a branch of economics that studies how households and firms make decisions to allocate limited resources, typically in markets where goods or services are being bought and sold...

, Marginal Revenue (MR) is the extra revenue that an additional unit of product will bring. It is the additional income from selling one more unit of a good; sometimes equal to price. It can also be described as the change in total revenue/change in number of units sold.

More formally, marginal revenue is equal to the change in total revenue over the change in quantity when the change in quantity is equal to one unit (or the change in output in the bracket where the change in revenue has occurred)

This can also be represented as a derivative. (Total revenue) = (Price Demanded) times (Quantity) or
. Thus, by the product rule

Product rule

In calculus, the product rule is a formula used to find the derivatives of products of functions.It may be stated thus:or in the Leibniz notation thus:.- Discovery by Leibniz :...

:

.

For a firm facing perfectly competitive markets, price does not change with quantity sold , so marginal revenue is equal to price. For a monopoly

Monopoly

In economics, a monopoly exists when a specific individual or an enterprise has sufficient control over a particular product or service to determine significantly the terms on which other individuals shall have access to it...

, the price received will decline with quantity sold , so marginal revenue is less than price. This means that the profit-maximizing

Profit maximization

In economics, profit maximisation is the process by which a firm determines the price and output level that returns the greatest profit. There are several approaches to this problem...

 quantity, for which marginal revenue is equal to marginal cost

Marginal cost

In economics and finance, marginal cost is the change in total cost that arises when the quantity produced changes by one unit. It is the cost of producing one more unit of a good. Mathematically, the marginal cost function is expressed as the first derivative of the total cost function with...

 will be lower for a monopoly than for a competitive firm, while the profit-maximizing price will be higher. When marginal revenue is positive, Price elasticity of demand

Price elasticity of demand

Price elasticity of demand is defined as the responsiveness of the quantity demanded of a good to a change in its price.In other words, it is percentage change in quantity demanded by the percentage change in price of the same commodity...

[PED] is elastic, and when it is negative, PED is inelastic. When marginal revenue is equal to zero, price elasticity of demand is equal to -1.

Maximizing profits using MR

regardless of market structure firm maximized profit by producing where MR = MC. There are exceptions. If variable costs are zero or nominal the firm should seek to maximize revenue rather than follow the profit-max rule (MR = MC). For examples of pure pricing circumstance see Samuelson $ Marks, Managerial Economics 4th ed. (Wiley 2003) at 100.

Example

Assume the inverse demand function has the form P = 120 - .5Q. Total revenue equals price times quantity. Multiplying the inverse demand function by Q to derive the total revenue function gives: TR = (120 - 0.5Q) x Q = 120Q - 0.5Q². The marginal revenue function is the first derivative of the total revenue function or MR = 120 - Q. Note that the MR function has the same y-intercept as the inverse demand function, the x-intercept of the MR function is one-half the value of the inverse demand function and the slope of the MR function is twice that of the inverse demand function. This relationship holds true for all linear demand equations. The importance of being able to quickly calculate MR is that the profit maximizing conditions for firms regardless of market structure is to produce where marginal revenue equals marginal cost. To derive MC you take the first derivative of the total cost function. then equate MR to MC and solve for Q. Thus assume that the firm's cost function is C = 420 +60Q + Q2. The first derivative of the cost function is MC = 60 +2Q. Equating MR and MC gives: 120 - Q = 60 +2Q. Solving for Q - Q = 20. to find the profit maximizing price simply plug Q into the price equation: P = 120 -.5Q = 120 = .5(20) = 120 - 10 = 110.