Marginal Revenue
Marginal revenue is the additional revenue a firm receives from selling one more unit of output. It is a central concept in the theory of the firm, because profit maximisation requires that marginal revenue equal marginal cost. Marginal revenue differs from price for firms facing a downward-sloping demand curve, since selling an additional unit requires lowering the price on all units sold, so that marginal revenue is less than price.
Calculation
Marginal revenue is the change in total revenue divided by the change in quantity. For a firm facing a linear demand curve, marginal revenue declines twice as fast as price, so the marginal revenue curve lies below the demand curve and has twice the slope. For a perfectly competitive firm, which faces a horizontal demand curve at the market price, marginal revenue equals price.
The relationship between marginal revenue and the elasticity of demand is important. Marginal revenue equals price times one minus the reciprocal of the absolute value of the price elasticity of demand. When demand is elastic, marginal revenue is positive; when demand is unit elastic, marginal revenue is zero; and when demand is inelastic, marginal revenue is negative. A profit-maximising firm therefore never operates where demand is inelastic, because it could raise price and increase both revenue and profit.
Profit maximisation
A firm maximises profit by producing the quantity at which marginal revenue equals marginal cost, provided that price exceeds average variable cost in the short run and that the firm covers all costs in the long run. At this output, the firm sets the price on the demand curve, earning a profit equal to the difference between price and average cost multiplied by quantity.
The equality of marginal revenue and marginal cost applies across market structures. For a competitive firm, it reduces to price equals marginal cost, which yields the efficient outcome. For a monopolist, marginal revenue is below price, so the monopolist produces less and charges more than a competitive market, generating a deadweight loss.
Market structures
Marginal revenue analysis distinguishes market structures by the shape of the demand curve facing the firm. Under perfect competition, the demand curve is horizontal, marginal revenue equals price, and firms cannot influence price. Under monopoly, the demand curve is the market demand curve, marginal revenue lies below price, and the firm has market power. Under monopolistic competition, the demand curve is downward sloping but relatively elastic because of product differentiation. Under oligopoly, the demand curve depends on the anticipated reactions of rivals, making marginal revenue more complex to determine.
The elasticity of demand determines the markup over marginal cost. The Lerner index, the ratio of price minus marginal cost to price, equals the reciprocal of the elasticity of demand, providing a measure of market power.
Applications
Marginal revenue analysis is used in pricing, capacity planning, and competitive strategy. Firms set prices with reference to the elasticity of demand, charging higher markups where demand is less elastic. Pricing strategies such as price discrimination, bundling, and two-part tariffs are designed to capture more consumer surplus by segmenting markets with different elasticities.
Marginal revenue is also central to antitrust analysis, since the ability to price above marginal cost indicates market power and potential consumer harm. Estimating marginal revenue and marginal cost in practice is challenging, requiring demand estimation and cost analysis, and is an important area of applied industrial organisation.
Marginal revenue and pricing strategy
Marginal revenue analysis underpins pricing strategy. Firms set prices with reference to the elasticity of demand, charging higher markups where demand is less elastic. This principle explains why firms charge more to customers with few alternatives, such as travellers booking late, and less to price-sensitive customers, such as those buying in advance. It also underlies practices such as price discrimination and yield management, in which capacity is allocated across customer segments to maximise revenue.
The markup over marginal cost depends on the structure of competition. In markets with many close substitutes, elasticity is high and markups are low; in markets with few substitutes or with switching costs, elasticity is low and markups are high. Digital markets illustrate both tendencies, with intense competition in some segments and strong lock-in in others. Understanding these dynamics is essential for predicting how prices respond to entry, merger, or regulation.
Marginal revenue in multi-product firms
Most firms sell multiple products, and marginal revenue analysis extends to product lines. When products are substitutes, sales of one cannibalise sales of another, so the marginal revenue of an additional sale is lower than the price. When products are complements, sales reinforce one another, raising the value of each. Firms account for these interactions when setting prices and product ranges, and they may use bundling, tying, and loss-leader pricing to maximise profit.
The analysis of multi-product pricing is complex, requiring estimates of cross-price elasticities and of the structure of demand. It is important for competition policy, because practices such as tying can foreclose markets and harm consumers, and for merger review, because combining firms with overlapping product lines can raise prices.
Limitations and empirical challenges
Estimating marginal revenue and marginal cost in practice is difficult. Marginal cost is not directly observed and must be inferred from accounting data or estimated econometrically. Marginal revenue depends on the elasticity of demand, which varies by customer, time, and market conditions and must be estimated from data. Measurement error and model misspecification can lead to misleading conclusions.
These challenges have motivated advances in demand estimation, including the use of scanner data, discrete choice models, and experimental methods. They have also shaped the practice of competition policy, which increasingly relies on quantitative evidence, including merger simulation and estimates of upward pricing pressure, to assess the likely effects of transactions.