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A LevelEconomicsEdexcelEconomics ARevision Notes1. Introduction to Markets and Market Failure1.2 How Markets WorkPrice, Income & Cross Elasticities of Demand

Price, Income & Cross Elasticities of Demand (Edexcel A Level Economics A)

Revision Note

Steve Vorster

Written by: Steve Vorster

Reviewed by: Jenna Quinn

Price Elasticity of Demand (PED)

  • The law of demand states that when there is an increase in price, there will be a fall in quantity demanded

    • Economists are interested by how much the quantity demanded will fall

  • Price elasticity of demand reveals how responsive the change in quantity demanded is to a change in price

    • The responsiveness is different for different types of products

Calculation of PED

  • PED can be calculated using the following formula:

text PED =  end text fraction numerator percent sign space change space in space quantity space demanded over denominator percent sign space change space in space price end fraction space equals space fraction numerator percent sign triangle space in thin space QD over denominator percent sign triangle in space straight P end fraction

  • To calculate a % change, use the following formula:

percent sign space Change space equals space fraction numerator new space value space minus space old space value over denominator old space value end fraction space cross times space 100 

Worked Example

A firm raises the price of its products from £10 to £15. Its sales fall from 100 to 40 units per day. Calculate the PED of its products

Step 1:  Calculate the % change in QD

  percent sign triangle QD space equals space fraction numerator 40 minus 100 over denominator 100 end fraction space cross times 100 percent sign triangle QD space equals space minus 60 percent sign 


Step 2: Calculate the % change in P

percent sign triangle straight P space equals space fraction numerator 15 space minus space 10 over denominator 10 end fraction space straight x space 100 percent sign triangle straight P space equals space 50 percent sign

Step 3: Insert the above values in the PED formula

PED space equals space fraction numerator percent sign triangle space in thin space QD over denominator percent sign triangle in space straight P end fraction PED space equals space fraction numerator negative space 60 over denominator space space space space 50 end fraction PED space equals space minus 1.2

The PED value will always be negative, so the answer must clearly state this. However, to explain the degree of elasticity, ignore the minus sign to apply the values below

Interpreting PED values

The Size of PED Varies From 0 to Infinity (∞) and Is Classified As Follows

Value

Name

Explanation

0

 Perfectly Inelastic

 The QD is completely unresponsive to a
change in P (very theoretical value e.g. heart transplant is extremely inelastic but possibly not perfectly)

0→1

Relatively Inelastic

The %∆ in QD is less than proportional
to the %∆ in P (e.g. addictive products)

1

Unitary Elasticity

The %∆ in QD is exactly equal to the %∆ in P

1→ ∞

Relatively Elastic

The %∆ in QD is more than proportional
to the %∆ in P (e.g. luxury products)

∞

Perfectly Elastic

The %∆ in QD will fall to zero with any
%∆ in P (highly theoretical elasticity)

Factors that influence the PED

  • Some products are more responsive to changes in prices than other products

  • The factors that determine the responsiveness are called the determinants of PED and include:

  1. Availability of substitutes: high availability of substitutes results in a higher value of PED (relatively price elastic)

  2. Addictiveness of the product: addictiveness turns products into necessities and habitual consumption, resulting in a low value of PED (relatively price inelastic)

  3. Price of product as a proportion of income: the lower the proportion of income the price represents, the lower the PED value will be. Consumers are less responsive to price changes on cheaper products (relatively price inelastic)

  4. Time period: In the short term, consumers are less responsive to price increases, resulting in a low value of PED (relatively price inelastic). Over a longer time period, consumers may feel the price increase more and so look for substitutes, resulting in a higher value of PED (relatively price elastic)

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

Calculation of YED

  • YED can be calculated using the following formula:

text YED =  end text fraction numerator percent sign space c h a n g e space i n space q u a n t i t y space d e m a n d e d over denominator percent sign space c h a n g e space i n space i n c o m e end fraction space equals space fraction numerator percent sign triangle space i n thin space Q D over denominator percent sign triangle i n space 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 plus 25 percent sign 


Step 2: Calculate the % change in Y

percent sign triangle Y space equals space fraction numerator 125 space minus space 100 over denominator 100 end fraction space straight x space 100 percent sign triangle Y space equals plus 25 percent sign


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 plus space 1

Even when the YED value is positive, the answer must clearly state this.

Interpreting YED Values

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

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

Value

Type of Good

Explanation

0→1

Normal necessity

Demand increases proportionately less when income increases. Income inelastic, which means that demand is relatively less responsive to a change in income 

YED > 1

Normal luxury

Demand increases proportionately more when income increases. Income elastic, which means demand is relatively more responsive to a change in income 

YED < 0

Inferior Good

Demand decreases when income increases or vice versa so YED is negative

Factors that influence YED

  • YED is influenced by any factors in an economy which change the wages or salaries of workers

    • During a recession, incomes usually fall so the demand for inferior goods rises and the demand for normal goods fall

    • During a period of economic growth and rising incomes, demand for normal goods rises and the demand for inferior goods fall

    • Other influences on income include minimum wage legislation, taxation, and increased international trade

  • The sign + or - shows the relationship: Normal good or inferior good

  • The number shows the strength of the relationship. For example, YED = +2.5 means there is a strong relationship between a change in income and demand

Cross Price 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

Calculation of XED

  • XED can be calculated using the following formula:

begin mathsize 14px style text XED =  end text fraction numerator percent sign space c h a n g e space i n space q u a n t i t y space d e m a n d e d space o f space g o o d space A over denominator percent sign space c h a n g e space i n space p r i c e space o f space g o o d space B end fraction space equals space fraction numerator percent sign triangle space i n thin space Q D subscript A over denominator percent sign triangle i n space P subscript 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 plus 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 33.33 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 plus 60 percent sign over denominator negative 33.33 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, which is greater than 1 (ignoring the minus sign), suggests that they are strong complements

Interpreting XED Values

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

Significance of Elasticities to Firms & Governments

  • Knowledge of PED is important to firms seeking to maximise their revenue

    • If their product is price inelastic in demand, they should raise their prices

    • If price elastic in demand, then they should lower their prices

  • Knowledge of PED is important to Governments with regard to taxation and subsidies

    • If they tax price inelastic in demand products, they can raise tax revenue without harming firms too much

    • Consumers are less responsive to price changes so firms will pass on the tax to the consumer

    • If they subsidies price elastic in demand products, there can be a greater than proportional increase in demand

  • 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

  • Knowledge of YED is important to firms as they seek to maintain sales and maximise profits through periods of recession or economic growth

    • Firms should consider providing more inferior goods in a recessionary environment

    • Firms should consider providing more income elastic normal goods/ luxury products during periods of economic growth

The Revenue Rule of PED

  • The total revenue rule states that in order to maximise revenue, firms should increase the price of products that are price inelastic in demand and decrease prices on products that are price elastic in demand

Worked Example

A firm raises the price of its products from £10 to £15. Its sales have fallen from 100 to 40 units per day. Explain if it made the correct decision

Step 1: Calculate the initial sales revenue

Sales space Revenue space equals space Price space of space product space straight X space Quantity space sold space space space space space space space space space space space space space space space space space space space space space space space space space equals £ 10 space straight x space 100 space space space space space space space space space space space space space space space space space space space space space space space space space equals space £ 1 comma 000

Step 2: Calculate the sales revenue after the price change

Sales space Revenue space equals space Price space of space product space straight X space Quantity space sold space space space space space space space space space space space space space space space space space space space space space space space space space equals £ 15 space straight x space 40 space space space space space space space space space space space space space space space space space space space space space space space space space equals space £ 600

Step 3: Explain the decision

By raising the price, the total revenue has fallen by £400. This indicates that the product is price elastic in demand and the firm should have lowered their price in order to increase revenue

Examiner Tips and Tricks

A common error students make is to say that when prices increase and the product is price inelastic in demand, the quantity demanded does not fall. It does! But it is a less than proportionate fall than the increase in price 

Remember that the demand curve is downward sloping and the PED is measuring the extent to which the quantity demanded moves along the demand curve when price changes. Even though water is essential, households would find ways to contract their consumption if the supply of water to their homes became more expensive

When governments tax demerit goods such as cigarettes, the increase in price is greater than the decrease in QD, but QD still falls

The values of YED and XED determine the size of the shift in the demand curve. For example, if XED = -0.2, the demand for product A will fall by a relatively smaller percentage than the rise in price of product B. The shift in the demand curve to the left will be small

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    Author
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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.

    Jenna Quinn

    Author: Jenna Quinn

    Expertise: Head of New Subjects

    Jenna studied at Cardiff University before training to become a science teacher at the University of Bath specialising in Biology (although she loves teaching all three sciences at GCSE level!). Teaching is her passion, and with 10 years experience teaching across a wide range of specifications – from GCSE and A Level Biology in the UK to IGCSE and IB Biology internationally – she knows what is required to pass those Biology exams.