In

microeconomicsMicroeconomics is a branch of economics that studies the behavior of how the individual modern household and firms make decisions to allocate limited resources. Typically, it applies to 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 revenueTotal revenue is the total receipts of a firm from the sale of any given quantity of a product.It can be calculated as the selling price of the firm's product times the quantity sold, i.e...

divided by the change in the number of units sold.

## Definition

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. This can also be represented as a derivative when the units of output are arbitrarily small. (Total revenue) = (Price that can be charged consistent with selling a given quantity) times (Quantity) or

. Thus, by the

product ruleIn calculus, the product rule is a formula used to find the derivatives of products of two or more functions. It may be stated thus:'=f'\cdot g+f\cdot g' \,\! or in the Leibniz notation thus:...

:

For a firm facing perfectly competitive markets, price does not change with quantity sold (

), so marginal revenue is equal to price. For a

monopolyA monopoly exists when a specific person or enterprise is the only supplier of a particular commodity...

, the price received will decline with quantity sold (

), so marginal revenue is less than price. This means that the

profit-maximizingIn economics, profit maximization 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 costIn economics and finance, marginal cost is the change in total cost that arises when the quantity produced changes by one unit. That is, it is the cost of producing one more unit of a good...

(MC) will be lower for a monopoly than for a competitive firm, while the profit-maximizing price will be higher. When demand is

elasticPrice elasticity of demand is a measure used in economics to show the responsiveness, or elasticity, of the quantity demanded of a good or service to a change in its price. More precisely, it gives the percentage change in quantity demanded in response to a one percent change in price...

, marginal revenue is positive, and when demand is inelastic, marginal revenue is negative. When the price elasticity of demand is equal to 1, marginal revenue is equal to zero.

## Marginal revenue curve

The marginal revenue curve is affected by the same factors as the demand curve - changes in income, change in the prices of complements and substitutes, change in populations. These factors can cause the MR curve to shift and rotate.

## Relationship between marginal revenue and elasticity

The relationship between marginal revenue and the elasticity of demand by the firm's customers can be derived as follows:

- MR = dTR/dQ
- MR = P+Q(dP/dQ)
- MR = P[1 + (dP/dQ) (Q/P)]
- MR = P(1 + 1/PED)

where PED is the price elasticity of demand. If demand is inelastic (PED < 1) then MR will be negative, because to sell a marginal (infinitesimal) unit the firm would have to lower the selling price so much that it would lose more revenue on the pre-existing units than it would gain on the incremental unit. If demand is elastic (PED > 1) MR will be positive, because the additional unit would not drive down the price by so much. If the firm is a perfect competitor, so that it is so small in the market that its quantity produced and sold has no effect on the price, then the price elasticity of demand is negative infinity, and marginal revenue simply equals the (market-determined) price.

## Marginal revenue and rule of thumb pricing

Profit maximization requires that a firm produce where marginal revenue equals marginal costs. Firm managers are unlikely to have complete information concerning their marginal revenue function or their marginal costs. Fortunately the profit maximization conditions can be expressed in a “more easily applicable form” or rule of thumb.

- MR = MC
- MR = P(1 + 1/PED)
- MC = P(1 + 1/PED)
- MC = P + P/PED/ P = - 1/PED

Markup is the difference between price and marginal cost. The formula states that markup as a percentage of price equals the negative of the inverse of elasticity of demand.Alternatively, the relationship can be expressed as:

- P = MC/(1 + 1/PED)

Thus if PED is - 2 and MC is $5.00 then price is $10.00.

(P - MC)/ P = - 1/PED is called the Lerner index after economist Abba Lerner. The Lerner index is a measure of market power - the ability of a firm to charge a price that exceeds marginal cost. The index varies from zero to 1. The greater the difference between price and marginal cost the closer the index value is to 1. The Lerner index increases as demand becomes less elastic.