3.3.1 Revenue

Edexcel A-Level Economics (9EC0) | Theme 3.3.1

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, explain the relationship between marginal revenue and price elasticity of demand, and apply the total revenue rule to price changes.

Key Definitions

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

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

Marginal Revenue (MR): \( \Delta TR / \Delta Q \). 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 perfect competition
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, 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 for imperfect competition
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 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

When demand is unit elastic, \( MR = 0 \) and TR is maximised.

Summary of Key Relationships

  • AR is always the demand curve.
  • MR is linked to PED: when MR is positive, demand is elastic; when MR is negative, demand is inelastic.
  • TR is maximised where \( MR = 0 \), which also corresponds to \( PED = 1 \).
  • In imperfect competition, the TR curve rises at a decreasing rate until MR equals zero, and then it falls.

Exam Preparation

  • Define TR, AR, and MR accurately.
  • Draw and explain the difference between the horizontal AR/MR curve of a price taker and the downward-sloping AR and MR curves of a price maker.
  • Explain why the MR curve lies below the AR curve in imperfect competition.
  • Apply the total revenue rule to explain how a price change will affect TR given the PED of the product.
  • Link the point where \( MR = 0 \) to maximum TR and unitary elasticity.