Revenue concepts are central to understanding firm behaviour in different market structures. This topic explores how firms generate income and how revenue varies with price, output, and market conditions.
Introduction to Revenue
Revenue is the income a firm receives from selling its goods or services. Understanding how revenue behaves is crucial for analysing a firm's pricing decisions, market strategy, and overall profitability. The three most important revenue measures in economics are Total Revenue (TR), Average Revenue (AR), and Marginal Revenue (MR). Each plays a unique role in determining how firms operate in competitive and non-competitive markets.
Total Revenue (TR)
Definition
Total Revenue (TR) is the total amount of money a firm earns from selling its output over a given period of time.
Formula
TR = Price × Quantity Sold
This formula indicates that total revenue depends directly on the price a firm charges and the quantity of goods it sells. It provides an essential measure of how much income a firm is generating before subtracting any costs.
Example
If a firm sells 150 units of a product at a price of £4 each, the total revenue would be:
TR = 4 × 150 = £600
Total revenue is a useful measure for determining whether a business is generating enough income to cover its costs and potentially make a profit.
Average Revenue (AR)
Definition
Average Revenue (AR) is the revenue earned per unit of output sold. It represents the average amount of money the firm receives for each item sold.
Formula
AR = TR ÷ Quantity Sold
Since TR is equal to Price × Quantity, and AR is TR divided by Quantity, AR is equal to the price of the product in both perfect and imperfect market structures.
Example
If a firm earns £600 by selling 150 units:
AR = 600 ÷ 150 = £4
Therefore, the average revenue per unit sold is £4, which is the same as the price.
Marginal Revenue (MR)
Definition
Marginal Revenue (MR) is the additional revenue a firm receives from selling one more unit of a good or service.
Formula
MR = Change in Total Revenue ÷ Change in Quantity Sold
MR = ΔTR ÷ ΔQ
Marginal revenue is crucial for decision-making. It tells a firm how much extra revenue it will earn if it increases output by one unit.
Example
If TR increases from £600 to £640 when output increases from 150 to 160 units:
MR = (640 - 600) ÷ (160 - 150) = 40 ÷ 10 = £4
This means each of the additional 10 units sold adds £4 to total revenue.
Revenue Curves Under Different Market Structures
The behaviour of AR and MR curves depends on the type of market structure in which a firm operates.
Perfect Competition
In perfect competition, firms are price takers. They cannot influence the market price and must accept it as given.
The demand curve is perfectly elastic (horizontal).
Firms can sell as much output as they want at the prevailing market price.
AR = MR = Price at all levels of output.
Revenue Curves
AR and MR curves are horizontal straight lines at the market price level.
The TR curve is a straight upward-sloping line starting from the origin, showing a constant increase in total revenue as output increases.
Imperfect Competition
In imperfect competition, such as monopoly or monopolistic competition, firms are price makers.
The firm faces a downward-sloping demand curve.
To sell more output, it must lower the price.
As a result:
AR falls with increased output.
MR falls faster than AR and is always below AR.
Revenue Curves
The AR curve is downward sloping, representing the firm's demand curve.
The MR curve lies below the AR curve, also downward sloping but steeper.
The TR curve increases at a decreasing rate, reaches a maximum point, and then begins to fall when MR becomes negative.
Relationships Among TR, AR, and MR
Understanding the relationship among these three revenue concepts is essential for analysing firm behaviour.
In perfect competition:
Price = AR = MR
The firm faces a horizontal demand curve.
In imperfect competition:
AR and MR diverge.
AR = Price
MR falls at a faster rate than AR because the firm must lower the price on all units sold to sell additional units.
Key Revenue Points
When MR is positive, TR is increasing.
When MR is zero, TR is at its maximum.
When MR is negative, TR is decreasing.
This relationship can be visualised on a graph, where the MR curve intersects the x-axis when TR reaches its peak.
Price Elasticity of Demand and Revenue
Understanding PED
Price Elasticity of Demand (PED) measures the responsiveness of quantity demanded to a change in price.
PED > 1: Demand is elastic.
PED = 1: Demand is unit elastic.
PED < 1: Demand is inelastic.
Link Between PED and TR
The elasticity of demand directly affects how changes in price influence total revenue:
Elastic Demand (PED > 1):
A decrease in price causes a more than proportionate increase in quantity demanded.
TR increases.
Inelastic Demand (PED < 1):
A decrease in price causes a less than proportionate increase in quantity demanded.
TR decreases.
Unit Elastic Demand (PED = 1):
A change in price causes a proportionate change in quantity demanded.
TR remains constant and is maximised at this point.
Connection to MR
When demand is elastic, MR is positive.
When demand is unit elastic, MR is zero.
When demand is inelastic, MR is negative.
These relationships help firms understand where on the demand curve they should operate to maximise revenue or profit.
Worked Examples
Example 1: Calculating TR, AR, and MR
Suppose a firm faces the following demand:
Price at Q1 = £10, Quantity = 1, TR = 10, AR = 10
Price at Q2 = £9, Quantity = 2, TR = 18, AR = 9, MR = 8
Price at Q3 = £8, Quantity = 3, TR = 24, AR = 8, MR = 6
Price at Q4 = £7, Quantity = 4, TR = 28, AR = 7, MR = 4
Price at Q5 = £6, Quantity = 5, TR = 30, AR = 6, MR = 2
Price at Q6 = £5, Quantity = 6, TR = 30, AR = 5, MR = 0
Price at Q7 = £4, Quantity = 7, TR = 28, AR = 4, MR = -2
Interpretation
TR rises initially, peaks at 5-6 units, and then falls.
AR equals price at each output level.
MR declines and becomes negative as output increases.
At Q = 6, MR = 0 and TR is maximised.
PED = 1 at the point where MR = 0.
This shows the importance of MR in determining when TR is at its peak and helps explain a firm's incentive to operate where MR is still positive.
Example 2: PED and Revenue Change
Suppose price decreases from £10 to £8 and quantity demanded rises from 100 to 140 units.
Step-by-step Calculation
Change in quantity = 140 - 100 = 40
Percentage change in quantity = 40 ÷ 100 = 0.4 or 40%
Change in price = 10 - 8 = 2
Percentage change in price = 2 ÷ 10 = 0.2 or 20%
PED = 40% ÷ 20% = 2
Since PED > 1, demand is elastic. Lowering the price increases TR:
Initial TR = 10 × 100 = £1000
New TR = 8 × 140 = £1120
Thus, TR rises by £120, illustrating the gain from a price reduction when demand is elastic.
Graphical Diagrams to Include
Although not drawn here, the following diagrams are essential for a complete understanding:
Perfect Competition Revenue Curves:
Horizontal AR and MR lines at market price.
Straight upward-sloping TR curve from the origin.
Imperfect Competition Revenue Curves:
Downward-sloping AR and steeper MR curves.
TR curve that rises, peaks, then falls.
PED and TR Relationship:
Demand curve divided into elastic, unitary, and inelastic regions.
MR curve showing corresponding positive, zero, and negative values.
Application in Business Decision-Making
Understanding these concepts helps firms answer important questions such as:
Should we reduce the price to boost sales?
Will more output increase or reduce total revenue?
Are we operating in the elastic or inelastic part of our demand curve?
What is the impact of a price change on overall revenue?
These revenue concepts also prepare the foundation for analysing profit maximisation, cost structures, and long-run production decisions in later subtopics. Firms must be aware of how revenue behaves in order to achieve their goals and compete effectively.
FAQ
Marginal revenue (MR) falls faster than average revenue (AR) in imperfect competition because a firm must reduce the price on all units sold to sell an extra unit. This results in MR reflecting not just the revenue gained from selling the additional unit, but also the revenue lost on the previous units due to the price cut. For instance, if a firm reduces its price from £10 to £9 to sell one more unit, it gains £9 from the new unit but loses £1 on every previous unit sold. If the firm had sold five units before, the total revenue loss on those five units would be £5, meaning the marginal revenue from selling the sixth unit is £9 - £5 = £4. This causes MR to fall more steeply than AR, which simply reflects the price per unit. The steeper decline of MR is a key indicator of market power and is only observed in imperfect competition.
Yes, marginal revenue can be negative in imperfect competition. This occurs when the additional unit sold decreases total revenue. In practical terms, it means the price reduction necessary to sell one more unit causes such a large drop in revenue from existing sales that it outweighs the gain from the new unit sold. At this point, increasing output further leads to a fall in total revenue, which is economically irrational for a profit-maximising firm. The total revenue curve, which initially rises, reaches a maximum when MR equals zero and begins to fall when MR becomes negative. Selling in a region where MR is negative implies that the firm is operating in the inelastic portion of its demand curve, where consumers are less responsive to price changes. Rational firms avoid producing in this region because they would reduce their overall earnings with every additional unit sold. Therefore, a negative MR is a signal to reduce output.
In perfect competition, firms are price takers with no market power. The market sets the price, and each firm can sell any quantity at that price. Consequently, average revenue (AR) and marginal revenue (MR) are equal and constant, and both are horizontal lines on a diagram. There is no need to reduce price to increase sales, so MR does not fall with increased output. In contrast, a monopoly faces a downward-sloping demand curve. To increase output, it must lower the price for all units sold, causing marginal revenue to fall faster than average revenue. The monopoly has full control over its price-output decisions, meaning AR and MR diverge, and MR is always less than AR. Unlike competitive firms, a monopolist's total revenue curve rises, peaks, and then falls. These differences reflect the contrasting degrees of market power and the pricing flexibility between the two market structures, fundamentally affecting how firms decide on output and pricing.
A firm can estimate whether it is operating in the elastic or inelastic portion of its demand curve by observing the relationship between changes in price and changes in total revenue (TR). If a price decrease leads to an increase in TR, demand is elastic at that point. Conversely, if a price decrease leads to a fall in TR, demand is inelastic. Another method involves calculating price elasticity of demand (PED) using the formula: percentage change in quantity demanded divided by the percentage change in price. If the result is greater than one, the firm is in the elastic range; less than one indicates inelastic demand. Additionally, firms can analyse historical sales data or conduct market experiments to determine how sensitive consumers are to price changes. Knowing whether demand is elastic or inelastic helps firms decide whether to adjust prices to maximise TR, avoid negative marginal revenue, and improve overall pricing strategy.
Understanding the relationship between revenue and price elasticity is crucial because it directly influences a firm's pricing strategy and its ability to increase total revenue (TR). If a firm knows its product has elastic demand (PED > 1), it can reduce prices to boost sales volume and ultimately raise TR. However, if demand is inelastic (PED < 1), reducing prices will decrease TR, as the additional sales won’t compensate for the lower price. Misjudging this relationship can lead to poor pricing decisions, loss of revenue, or even long-term damage to profitability. Furthermore, recognising where TR is maximised (when PED = 1) enables firms to position their price close to the point of unitary elasticity for optimal revenue. This understanding also helps in evaluating promotional strategies, determining whether to use discounts or premium pricing, and forecasting how market changes might affect earnings. Essentially, it allows firms to align pricing decisions with consumer behaviour and maximise revenue efficiency.
Practice Questions
Using a diagram, explain the relationship between marginal revenue (MR), average revenue (AR), and total revenue (TR) for a firm in imperfect competition.
Using a diagram, explain the relationship between marginal revenue (MR), average revenue (AR), and total revenue (TR) for a firm in imperfect competition.
Explain how price elasticity of demand (PED) affects a firm’s total revenue when it changes price.
If demand is price elastic (PED > 1), lowering the price leads to a more than proportionate increase in quantity demanded, increasing total revenue. If demand is price inelastic (PED < 1), lowering the price causes a less than proportionate increase in quantity demanded, decreasing total revenue. When PED equals 1, total revenue is maximised, and any change in price leaves it unchanged. This relationship allows firms to adjust prices strategically depending on whether they want to increase total revenue, taking into account where on the demand curve they currently operate.
