Revenue

Specification Coverage: Edexcel unit 3.3.1 - Revenue. Students should be able to define and calculate total revenue, average revenue, and marginal revenue, distinguish between revenue conditions in perfect and imperfect competition, and apply the total revenue rule to price changes.

Key Definitions

Total Revenue (TR): \( P \times Q \)

Average Revenue (AR): \( \frac{TR}{Q} \). This is the price per unit and also the firm's demand curve.

Marginal Revenue (MR): \( \frac{\Delta TR}{\Delta Q} \). This is the additional revenue from selling one more unit.

Revenue in Perfect Competition

Firms in perfect competition are price takers, so they sell at the market price.

This means \( AR = MR = Price \), and the demand curve facing the firm is perfectly elastic, so it is horizontal.

Revenue diagram for a price taker with horizontal average revenue equal to marginal revenue at the market price — Figure 1: Revenue in Perfect Competition - AR and MR are horizontal at the market price. TR increases at a constant rate as quantity increases.

Revenue in Imperfect Competition

Firms in imperfect competition have market power and are therefore price makers, so to sell more output they must lower the price.

As a result, AR, which is the demand curve, is downward sloping, and MR is also downward sloping but lies below AR.

Revenue diagram with a downward-sloping average revenue curve and marginal revenue falling twice as steeply below it — Figure 2: Revenue in Imperfect Competition - AR is downward sloping, and MR lies below AR. TR increases at a decreasing rate until MR equals zero, then it decreases.

A key point is that in a linear diagram the MR curve is twice as steep as the AR curve. The right hand diagram shows that total revenue is maximised when \( MR = 0 \).

Worked Example: Total, Average and Marginal Revenue

A firm with market power must lower its price to sell more. This schedule is read off its demand curve:

Price (AR)	Quantity	TR = P × Q	MR
£10	1	£10	—
£8	2	£16	£6
£6	3	£18	£2
£4	4	£16	−£2

Price and AR are the same figure in every row. MR falls twice as fast and stays below AR, because to sell one more unit the firm must cut the price on every unit, not just the last one. Total revenue peaks at £18, at the output where MR turns from positive to negative.

The Total Revenue Rule and PED

The relationship between PED and total revenue is crucial when firms make pricing decisions.

If Demand Is...	And the Firm...	Then Total Revenue Will...
Price elastic (\( PED > 1 \))	Lowers price	Increase
Price elastic (\( PED > 1 \))	Raises price	Decrease
Price inelastic (\( PED < 1 \))	Raises price	Increase
Price inelastic (\( PED < 1 \))	Lowers price	Decrease
Unitary elastic (\( PED = 1 \))	Changes price	Remain unchanged

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Nine original multiple-choice questions on total, average and marginal revenue, revenue under perfect and imperfect competition, and the total revenue rule.

Practice Questions: 3.3.1 Revenue

Past paper questions on this topic

Six questions on Revenue from the Edexcel A-Level papers, 2018–2023, 12 to 15 marks. Each one links straight to the page of the official mark scheme where its answer begins.

Past Paper Questions: 3.3.1 Revenue