A LevelEconomicsCambridge (CIE)Revision NotesThe Price System & the MicroeconomyElasticities of DemandCross Elasticity of Demand (XED)

Cross Elasticity of Demand (XED) (Cambridge (CIE) A Level Economics): Revision Note

Exam code: 9708

Steve Vorster

Written by: Steve Vorster

Reviewed by: Lisa Eades

Updated on

Defining and calculating XED

  • Changes in the prices of complementary goods and substitutes affect the demand for related products

  • Cross price elasticity of demand (XED) reveals how responsive the change in quantity demanded for good A is to a change in price of good B

    • The responsiveness is different for different types of products

  • XED can be calculated using the following formula:

begin mathsize 16px style text XED =  end text fraction numerator percent sign space change space in space quantity space demanded space of space good space straight A over denominator percent sign space change space in space price space of space good space straight B end fraction space equals space fraction numerator percent sign triangle space in thin space QD subscript straight A over denominator percent sign triangle in space straight P subscript straight B end fraction end style

Worked Example

Leading into the release of FIFA 22 Ultimate, EA Sports discounted the price of FIFA 21 from £90 to £60. A game store in Winchester saw an increase in sales of their PlayStation 5 consoles. Prior to the discount, they were selling 50 units a week, and after the discount this increased to 80 units.

Calculate the XED and explain the relationship between the two products

Step 1:  Calculate the % change in QDA

  percent sign triangle QD subscript A space equals space fraction numerator 80 minus 50 over denominator 50 end fraction space cross times 100 percent sign triangle Q D subscript A space equals space 60 percent sign 


Step 2: Calculate the % change in PB

percent sign triangle P subscript B space equals space fraction numerator 60 space minus space 90 over denominator 90 end fraction space straight x space 100 percent sign triangle P subscript B space equals space minus 33.3 percent sign


Step 3: Insert the above values in the XED formula

X ED space equals space fraction numerator percent sign triangle space in thin space QD subscript A over denominator percent sign triangle in space P subscript B end fraction X ED space equals space fraction numerator 60 percent sign over denominator negative 33.3 percent sign end fraction X ED space equals space minus 1.8

Step 4: Explain the relationship between the two products

The negative sign indicates that these two products are complements and the high value suggests they are strong complements

Worked Example

The price of good Y, a substitute for X, rises from £50 to £60. As a result, the quantity demanded of good X rises from 2 units to 3 units per month. 

What is the value of the cross elasticity of demand for good X with respect to Y?

A: +0.4

B: -0.4

C: +2.5

D:-2.5

Step 1: Calculate % change in QDA using formula

   percent sign triangle QD subscript A space equals space fraction numerator 3 minus 2 over denominator 2 end fraction space cross times 100 percent sign triangle QD subscript straight A space equals space 50 percent sign

Step 2: Calculate % change in PB using formula

   begin mathsize 16px style percent sign triangle straight P subscript straight B space equals space fraction numerator 60 space minus space 50 over denominator 50 end fraction space straight x space 100 percent sign triangle straight P subscript straight B space equals space 20 percent sign end style


Step 3: Insert the above values in the XED formula

   XED space equals space fraction numerator percent sign triangle space in thin space QD subscript straight A over denominator percent sign triangle in space straight P subscript straight B end fraction XED space equals space fraction numerator plus 50 percent sign over denominator plus 20 percent sign end fraction XED space equals space plus 2.5

The positive sign indicates that these two products are substitutes and the high value suggests they are strong substitutes

Interpreting the XED coefficient

  • Economists use the concept of Cross Elasticity of Demand (XED) to measure how the demand for one product responds when the price of another changes.

  • The sign and size of XED reveal whether goods are substitutes, complements, or unrelated

Identifying complements, substitutes, and unrelated goods


Value


Explanation

XED < 0

Complementary goods

  • The negative value indicates the two goods are complements

  • The higher the value the stronger the relationship

XED > 0

Substitutes

  • The positive value indicates the two goods are substitutes

  • The higher the value, the stronger the relationship

XED = 0

Unrelated goods

  • A value of zero indicates that there is no relationship between the two goods.

  • The closer to zero, the weaker the relationship is

Substitutes (XED is positive)

  • Substitute goods are alternatives that serve similar purposes. When the price of one rises, consumers tend to switch to the other, increasing its demand

  • A positive XED indicates this relationship

Examples:

  • If the price of Coca-Cola increases, demand for Pepsi may rise as a comparable alternative

  • A rise in the price of Spotify Premium could lead some consumers to choose Apple Music or YouTube Music instead

  • In a school cafeteria, if burgers become more expensive, students might opt for pizza

Examiner Tips and Tricks

Consumer behaviour assumes rational decision-making. Your personal preferences may override price sensitivity. For instance, a student who only enjoys burgers may not switch to pizza even if prices change

Complements (XED is negative)

  • Complementary goods are typically consumed together

  • When the price of one increases, demand for the other tends to fall. A negative XED reflects this joint relationship

  • These goods rely on each other to deliver full value, so pricing decisions in one area can directly affect demand in another

Examples:

  • An increase in the price of cinema tickets might reduce demand for popcorn, as fewer people attend

  • If mobile data plans become more expensive, usage of streaming apps may decline

  • A price hike on gaming consoles could lead to lower sales of video games and controllers

Unrelated goods (XED = zero)

  • Unrelated goods have no meaningful connection. A change in the price of one does not influence demand for the other

Examples:

  • A rise in the price of beef has no impact on a vegan’s demand for tofu

  • If football boots become more expensive, it won’t affect how many paintbrushes art students buy

  • An increase in the price of concert tickets will not influence demand for mathematics revision guides

Using XED in decision-making

  • Knowledge of XED is important to firms as they seek to maximise their revenue

    • It can help them adjust pricing strategies for substitute and complementary products

    • It can help them understand the likely impact of competitors' pricing strategies on their sales

  • Businesses often monitor how changes in competitors’ prices affect demand for their own products

1. Substitutes: Positive XED

  • When two products are substitutes, a price increase in one tends to boost demand for the other

    • For example, if the price of Netflix rises, more consumers might switch to Disney+ or Amazon Prime Video. In such cases, firms are highly interdependent, and a competitor’s price cut could significantly reduce their own sales

  • If a company discovers that its product has an XED of +1.5 with a rival’s offering, it means that a 10% drop in the competitor’s price could lead to a 15% fall in demand for its own product

    • The higher the XED, the stronger the substitution effect

2. Complements: Negative XED

  • Complementary goods are jointly demanded, so a price increase in one can reduce demand for the other

    • For instance, if the price of mobile phones goes up, fewer people may buy phone cases or screen protectors. Similarly, if gym memberships become more expensive, demand for fitness clothing might decline

  • Companies often aim to sell bundles of complementary products—like gaming consoles with exclusive games - and use XED to design pricing strategies that maximize overall revenue

Strategic pricing and consumer Behaviour

  • Families might spend more at theme parks when entry tickets are discounted, even if the price elasticity of the tickets themselves is low

  • Lower ticket prices encourage spending on snacks, souvenirs, or rides, which are products with strong complementary relationships

  • In such cases, firms may need to rethink pricing across their entire product range rather than focusing on one item alone

Examiner Tips and Tricks

You can evaluate XED by explaining why calculating accurate elasticity values is complex

If a drop in demand for electric scooters follows a price increase, was this due to cost or changing consumer preferences, weather conditions, or new regulations?

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Steve Vorster

Author: Steve Vorster

Expertise: Economics & Business Subject Lead

Steve has taught A Level, GCSE, IGCSE Business and Economics - as well as IBDP Economics and Business Management. He is an IBDP Examiner and IGCSE textbook author. His students regularly achieve 90-100% in their final exams. Steve has been the Assistant Head of Sixth Form for a school in Devon, and Head of Economics at the world's largest International school in Singapore. He loves to create resources which speed up student learning and are easily accessible by all.

Lisa Eades

Reviewer: Lisa Eades

Expertise: Business Content Creator

Lisa has taught A Level, GCSE, BTEC and IBDP Business for over 20 years and is a senior Examiner for Edexcel. Lisa has been a successful Head of Department in Kent and has offered private Business tuition to students across the UK. Lisa loves to create imaginative and accessible resources which engage learners and build their passion for the subject.