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A LevelEconomicsAQARevision NotesIndividuals, Firms, Markets & Market Failure3. Price Determination in Competitive MarketsIncome & Cross Elasticities of Demand

Income & Cross Elasticities of Demand (AQA A Level Economics)

Revision Note

Lorraine

Written by: Lorraine

Reviewed by: Steve Vorster

Defining & Calculating Income Elasticity of Demand (YED)

  • Changes in income result in changes to the demand for goods/services

    • Economists are interested in how much the quantity demanded will change for different products

  • Income elasticity of demand (YED) reveals how responsive the change in quantity demanded is to a change in income

  • YED can be calculated using the following formula

text YED =  end text fraction numerator percent sign space change space in space quantity space demanded over denominator percent sign space change space in space income end fraction space equals space fraction numerator percent sign triangle space in thin space QD over denominator percent sign triangle in space straight Y end fraction

Worked Example

A consumer's income rises from £100 to £125 a week. They originally consumed 12 bagels at the local bakery, but this increased to 15 bagels a week.

Calculate the YED of the bagels

Step 1:  Calculate the % change in QD

  percent sign triangle QD space equals space fraction numerator 15 minus 12 over denominator 12 end fraction space cross times 100 percent sign triangle QD space equals space 25 percent sign 


Step 2: Calculate the % change in Y

begin mathsize 16px style percent sign triangle straight Y space equals space fraction numerator 125 space minus space 100 over denominator 100 end fraction space straight x space 100 percent sign triangle straight Y space equals space 25 percent sign end style


Step 3: Insert the above values in the YED formula

PED space equals space fraction numerator percent sign triangle space in thin space QD over denominator percent sign triangle in space straight Y end fraction Y ED space equals space 25 over 25 Y ED space equals space space 1

Interpreting YED Values

  • The YED value can be positive or negative and the value is important in determining the type of good

    • A good with a positive YED value is considered to be a normal good

      • Normal goods can be classified as necessities or luxuries 

    • A good with a negative YED value is considered to be an label goes here

The Value Of YED Determines the Type of Good & Response to Changes in Income


Value


Type of Good


Explanation

0→1

Normal necessity

  • Demand increases when income increases

  • Income inelastic, which means that it is relatively unresponsive to a change in income 

YED > 1

Normal luxury

  • Demand increases when income increases

  • Income elastic, which means that it is relatively responsive to a change in income 

YED < 0

Inferior Good

  • Demand decreases when income increases

Defining & Calculating Cross Elasticity of Demand (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 4 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 4 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 XED Values

  • The XED value can be negative or positive, and the value is important in determining the type of good. The size of the number determines how closely related goods are

    • A good with a negative XED value is considered to be a complementary good

    • A good with a positive XED value is considered to be a substitute good

Using XED Values to Identify if Goods are Complements, Substitutes, or Unrelated


Value


Name


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

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    Previous:Price Elasticity of Demand (PED)Next:Price Elasticity of Supply (PES)
    Author
    Reviewer
    Lorraine

    Author: Lorraine

    Expertise: Economics Content Creator

    Lorraine brings over 12 years of dedicated teaching experience to the realm of Leaving Cert and IBDP Economics. Having served as the Head of Department in both Dublin and Milan, Lorraine has demonstrated exceptional leadership skills and a commitment to academic excellence. Lorraine has extended her expertise to private tuition, positively impacting students across Ireland. Lorraine stands out for her innovative teaching methods, often incorporating graphic organisers and technology to create dynamic and engaging classroom environments.

    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.