Marginal revenue

In microeconomics, 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.^[1] 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:

.

For a firm facing perfectly competitive markets, price does not change with quantity sold (), so marginal revenue is equal to price. For a monopoly, the price received will decline with quantity sold (), so marginal revenue is less than price. This means that the profit-maximizing quantity, for which marginal revenue is equal to marginal cost 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 [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. ^[2]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 + Q^2[3]. 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.

References

See also

• Cost curves