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3.3.1 Revenue

Revenue Concepts

Total, Average and Marginal Revenue

Definition

Total revenue (TR): the total income a firm receives from selling its output, found by multiplying price by quantity.

Average revenue (AR): revenue per unit sold, which equals the price and so traces the firm's demand curve.

Marginal revenue (MR): the change in total revenue from selling one more unit.

TR=P×Q TR = P \times Q TR=P×Q AR=TRQ AR = \dfrac{TR}{Q} AR=QTR​ MR=ΔTRΔQ MR = \dfrac{\Delta TR}{\Delta Q} MR=ΔQΔTR​
Example
  • A firm sells 10 units at a price of £5, and the 11th unit lifts total revenue to £53.
TR=5×10=50 TR = 5 \times 10 = 50 TR=5×10=50 AR=5010=5 AR = \dfrac{50}{10} = 5 AR=1050​=5 MR=53−5011−10=3 MR = \dfrac{53 - 50}{11 - 10} = 3 MR=11−1053−50​=3
  • Total revenue is £50, average revenue (the price) is £5, and the 11th unit brings marginal revenue of £3.

Definition and calculation of revenue: total, average and marginal revenue (TR, AR, MR)

The Revenue Relationships

  1. Total revenue rises while marginal revenue is positive, because each extra unit still adds to revenue.
  2. Total revenue peaks when marginal revenue is zero, then falls once marginal revenue turns negative.
  3. The average revenue curve is the firm's demand curve, since average revenue is the price at each quantity.
  4. For a price-taker average revenue equals marginal revenue equals price, while for a price-maker marginal revenue lies below average revenue.

Elasticity and Revenue

Definition

Price elasticity of demand: the responsiveness of quantity demanded to a change in price.

  1. When demand is elastic, a price cut raises total revenue and a price rise lowers it.
  2. When demand is inelastic, a price rise raises total revenue and a price cut lowers it.
  3. Total revenue is maximised where price elasticity of demand equals one, the same output at which marginal revenue is zero.
  4. On a straight-line demand curve the upper half is elastic with positive marginal revenue, and the lower half is inelastic with negative marginal revenue.
  5. A budget airline such as easyJet cutting a £10 fare to £8 that lifts seats sold from 100 to 150 raises total revenue from £1,000 to £1,200, confirming elastic demand.
  6. A streaming platform such as Netflix raising its subscription when demand is inelastic increases total revenue, because the proportionate loss of subscribers is smaller than the proportionate price rise.
Example
  • Take the easyJet fare above: price falls from £10 to £8 and seats sold rise from 100 to 150.
%ΔQd=150−100100×100=+50 \%\Delta Q_d = \dfrac{150 - 100}{100} \times 100 = +50 %ΔQd​=100150−100​×100=+50 %ΔP=8−1010×100=−20 \%\Delta P = \dfrac{8 - 10}{10} \times 100 = -20 %ΔP=108−10​×100=−20 PED=+50−20=−2.5 PED = \dfrac{+50}{-20} = -2.5 PED=−20+50​=−2.5 TR1=10×100=1000 TR_1 = 10 \times 100 = 1000 TR1​=10×100=1000 TR2=8×150=1200 TR_2 = 8 \times 150 = 1200 TR2​=8×150=1200
  • PED is 2.5 in magnitude, so demand is elastic (greater than one); because demand is elastic the price cut raises total revenue, here from £1,000 to £1,200.
Exam technique
  • Use total revenue as price times quantity, and marginal revenue as the change in total revenue, to work through the numbers.
  • Establish whether demand is elastic or inelastic before predicting revenue.
Common Mistake
  • Do not assume marginal revenue always equals price, as that holds only for a price-taker.
  • Do not assume raising price always raises revenue, since it lowers revenue when demand is elastic.
Self review
  • State the formulae for total, average and marginal revenue.
  • Why is the average revenue curve the firm's demand curve?
  • What is marginal revenue when total revenue is at its peak?
  • When does a price cut raise total revenue?
  • Where on a straight-line demand curve is revenue maximised?

Relationship between price elasticity of demand and a firm’s revenue

Recap questions

1 of 5

A firm sells 80 units at £6 each, charging the same price for every unit. What are its total revenue and average revenue?

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Revenue is the income a firm receives from selling output before costs are deducted. It depends on price, written as PPP, and quantity sold, written as QQQ.

Total revenue is sales income in total, defined by the formula:

TR=P×Q TR = P \times Q TR=P×Q

If a firm sells 100 units at £12 each, its total revenue is £1,200.

Average revenue is revenue per unit sold, calculated as

AR=TRQ AR = \frac{TR}{Q} AR=QTR​

Marginal revenue is the extra revenue from selling one more unit, or

MR=ΔTRΔQ MR = \frac{\Delta TR}{\Delta Q} MR=ΔQΔTR​

Total revenue is measured in £, while AR and MR are measured in £ per unit.

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How does revenue differ from profit?

3.3.1 Revenue Revision Guide

  1. A Level
  2. /Economics
  3. /3.3.1 Revenue