AQA Specification focus:
‘The difference between marginal, average and total revenue; why the average revenue curve is the firm’s demand curve; the relationship between average and marginal revenue; the relationship between marginal revenue and total revenue; students should be able to calculate marginal, average and total revenue from given data and draw and interpret revenue curves.’
Introduction to Revenue Measures
In economics, revenue is a key concept used to measure the financial performance of a firm. This subsubtopic explores three different revenue measures — marginal revenue, average revenue, and total revenue. Understanding the relationships between these measures, as well as their connection to the demand curve, is crucial for analysing how firms make pricing and production decisions.
Total Revenue (TR)
Total revenue is the total amount of money a firm receives from the sale of its goods and services. It is calculated by multiplying the price per unit by the quantity sold.
DEFINITION
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Total Revenue (TR): The total income a firm receives from selling its goods or services, calculated as the price per unit multiplied by the quantity sold.
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Formula:
TR = P × Q
Where:
P = Price per unit (in currency)
Q = Quantity sold (in units)
As the quantity of goods sold increases, total revenue will generally increase, assuming the price remains constant. In cases where the price changes, the relationship between price and quantity sold can lead to variations in total revenue.
Average Revenue (AR)
Average revenue refers to the revenue earned per unit of output. It is calculated by dividing the total revenue by the number of units sold.
DEFINITION
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Average Revenue (AR): The revenue earned per unit of output, calculated as total revenue divided by the quantity of output sold.
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Formula:
AR = TR ÷ Q
Where:
TR = Total revenue
Q = Quantity sold (in units)
In a competitive market, average revenue is often the same as the price per unit, since the firm cannot influence the price and must sell at the prevailing market price. Thus, for a firm in perfect competition, AR = P.
Marginal Revenue (MR)
Marginal revenue is the additional revenue generated by selling one more unit of output. It is calculated as the change in total revenue resulting from a one-unit increase in quantity sold.
DEFINITION
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Marginal Revenue (MR): The additional revenue that a firm gains from selling one more unit of output, calculated as the change in total revenue divided by the change in quantity sold.
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Formula:
MR = ΔTR ÷ ΔQ
Where:
ΔTR = Change in total revenue
ΔQ = Change in quantity sold (in units)
As a firm increases its output, marginal revenue often decreases in imperfectly competitive markets, due to the need to lower prices to sell more units. This is a key feature of firms with market power.
Relationship Between Revenue Measures
Average Revenue and Demand Curve
For a firm, average revenue is synonymous with the demand curve in competitive markets. In perfect competition, the firm is a price taker, meaning it cannot influence the price. The price is determined by the market, and each unit of output is sold at the same price.
In this context, the average revenue curve is horizontal, reflecting the constant price.
The demand curve faced by the firm is identical to the average revenue curve, as the firm can sell any quantity at the given price.
For a monopolist or firm with some market power, the demand curve is downward sloping, and the firm must lower its price to sell additional units. In such cases, AR will be higher than MR for any quantity produced, reflecting the reduction in price needed to increase sales.
Marginal Revenue and Total Revenue
The relationship between marginal revenue and total revenue is key to understanding how firms determine their optimal level of output. As a firm increases its output, marginal revenue initially increases, reaches a peak, and then begins to decrease.
In the case of total revenue, it will increase as long as marginal revenue is positive.
Total revenue reaches its maximum point when marginal revenue equals zero. After this point, any further increase in output leads to a decrease in total revenue, as marginal revenue becomes negative.
This negative relationship occurs because the firm must lower the price of all units sold to sell an additional unit, which reduces overall revenue. Hence, firms seek to operate at a point where MR = 0, as this maximises their total revenue.
Key Relationships
AR = P in perfect competition, but AR > MR in imperfect competition.
MR < AR in monopolistic and oligopolistic markets because the firm faces a downward-sloping demand curve and must lower prices to sell more units.
As output increases, MR declines due to the price reduction needed to sell additional units, while TR increases initially, then decreases once MR turns negative.
By understanding the relationships between these three revenue measures, firms can make informed decisions about output levels and pricing strategies that maximise profit.
FAQ
In perfect competition, firms are price takers, meaning they sell their output at the market-determined price.
Since every unit is sold at the same price, total revenue divided by output equals that price.
Therefore, AR = P always holds in perfect competition.
When a firm lowers its price to sell more units, the price drop affects all units sold, not just the additional one.
This reduces the extra revenue gained from each extra unit.
As a result, MR declines more steeply than AR.
Total revenue reaches its peak when marginal revenue equals zero.
Before this point, MR is positive, so TR is still rising.
After this point, MR turns negative, and TR begins to fall.
When demand is elastic (PED > 1), lowering price increases total revenue, so MR is positive.
When demand is inelastic (PED < 1), lowering price reduces total revenue, so MR is negative.
At unit elasticity (PED = 1), MR = 0, and TR is maximised.
The AR curve shows the revenue per unit, which equals the price the firm can charge at each output level.
Since price and quantity demanded are linked by the demand curve, AR directly represents the firm’s demand curve.
In perfect competition, it is horizontal; in imperfect competition, it slopes downward.
Practice Questions
Define marginal revenue and explain how it is calculated. (2 marks)
1 mark for correctly stating that marginal revenue is the additional revenue from selling one more unit of output.
1 mark for explaining that it is calculated as the change in total revenue divided by the change in quantity sold.
(Max: 2 marks)
Using a diagram, explain the relationship between average revenue (AR) and marginal revenue (MR) for a firm with market power. Why does MR always lie below AR in this case? (6 marks)
1 mark for including a correctly labelled diagram showing AR and MR curves (downward-sloping AR, MR below AR).
1 mark for stating that AR represents the price per unit or the firm’s demand curve.
1 mark for stating that MR is the additional revenue from selling one more unit.
1 mark for recognising that to sell an extra unit, the firm must lower the price on all units.
1 mark for linking this price reduction to MR being less than AR.
1 mark for explaining the implication: MR curve lies below the AR curve in imperfect competition.
(Max: 6 marks)
