AQA Specification focus:
‘Be able to calculate income and cross elasticities of demand; the relationship between income elasticity of demand and normal and inferior goods; the relationship between cross elasticity of demand and substitute and complementary goods; factors that influence these elasticities of demand; interpretation of numerical values.’
Understanding income elasticity of demand and cross elasticity of demand helps economists and businesses analyse how consumer income levels and related goods affect market behaviour and business decisions.
Income Elasticity of Demand (YED)
Definition and Meaning
Income Elasticity of Demand (YED): A measure of the responsiveness of demand for a good to changes in consumer income, ceteris paribus.
Income elasticity identifies whether a product is considered normal or inferior and how strongly demand shifts with income changes.
This graph depicts the Engel curve for inferior goods, showing a downward slope as income increases, indicating a decrease in demand. The curve's negative gradient reflects the inverse relationship between income and demand for inferior goods. Source
Equation for YED
EQUATION
Income Elasticity of Demand (YED) = % Change in Quantity Demanded ÷ % Change in Income
% Change in Quantity Demanded = (New QD – Old QD) ÷ Old QD × 100
% Change in Income = (New Income – Old Income) ÷ Old Income × 100
The value of YED provides important market classifications.
Categories of Goods by YED
Normal goods: YED > 0. Demand rises as income increases.
Luxury goods: YED > 1. Demand rises more than proportionally with income.
Necessities: 0 < YED < 1. Demand rises less than proportionally with income.
Inferior goods: YED < 0. Demand falls as income increases, as consumers switch to higher-quality alternatives.
Market Implications of YED
Businesses with products showing high positive YED (luxuries) benefit during periods of rising incomes but suffer during recessions.
Firms producing inferior goods may thrive in downturns as consumers trade down from premium options.
Policymakers can forecast tax revenues or welfare needs by monitoring shifts in demand linked to income trends.
Cross Elasticity of Demand (XED)
Definition and Meaning
Cross Elasticity of Demand (XED): A measure of the responsiveness of demand for one good to changes in the price of another good.
This measure explains intermarket links, showing how goods are substitutes or complements.
The diagram illustrates the cross elasticity of demand for substitute goods, where an increase in the price of one good leads to an increase in the quantity demanded of its substitute. The positive slope indicates a positive XED, characteristic of substitute goods. Source
Equation for XED
EQUATION
Cross Elasticity of Demand (XED) = % Change in Quantity Demanded of Good A ÷ % Change in Price of Good B
% Change in Quantity Demanded = (New QD – Old QD) ÷ Old QD × 100
% Change in Price = (New Price – Old Price) ÷ Old Price × 100
Types of Market Relationships
Substitutes (XED > 0): An increase in the price of one good leads to higher demand for its substitute. Example: tea and coffee.
Complements (XED < 0): An increase in the price of one good leads to a fall in demand for its complement. Example: printers and ink cartridges.
Unrelated goods (XED ≈ 0): No significant relationship between products. Example: bananas and mobile phones.
The diagram depicts the cross elasticity of demand for complementary goods, where an increase in the price of one good leads to a decrease in the quantity demanded of its complement. The negative slope indicates a negative XED, characteristic of complementary goods. Source
Market Implications of XED
Firms can anticipate competitive responses. A company facing a close substitute must be cautious about pricing strategies.
Retailers often bundle complementary products (e.g., gaming consoles and video games) to maximise revenue.
Policy-makers use XED when evaluating mergers or market competition, ensuring no anti-competitive dominance arises.
Factors Influencing YED and XED
Factors Affecting Income Elasticity
Type of product: Necessities typically have low YED; luxuries high YED.
Consumer preferences: Changing tastes can shift the classification of goods.
Income distribution: Different social groups may respond differently to income changes.
Factors Affecting Cross Elasticity
Closeness of substitutes or complements: The more direct the relationship, the higher the XED magnitude.
Time period considered: Substitutability may rise over time as consumers adapt.
Brand loyalty: Strong brand preference reduces responsiveness to price changes of substitutes.
Interpretation of Numerical Values
YED Interpretation
YED = 1.5 → A 10% rise in income increases demand by 15% (luxury).
YED = 0.4 → A 10% rise in income increases demand by 4% (necessity).
YED = –0.6 → A 10% rise in income decreases demand by 6% (inferior).
XED Interpretation
XED = +0.8 → Goods are substitutes; moderately close.
XED = +2.0 → Goods are strong substitutes; very responsive.
XED = –0.5 → Goods are weak complements.
XED = –1.5 → Goods are strong complements; demand strongly linked.
Market Links and Interrelationships
Understanding income and cross elasticities is crucial to analysing how markets interact:
Joint demand: Complementary goods are demanded together. High negative XED values illustrate the strength of this link.
Competitive demand: Substitutes compete for market share; positive XED reveals their relationship.
Composite demand: One good serves multiple purposes (e.g., oil used in fuel and plastics), affected by income and price shifts elsewhere.
Derived demand: Demand for inputs depends on demand for final products; elasticity patterns determine how strongly changes transmit.
Firms, governments, and economists rely on these elasticity measures to predict shifts, plan production, and assess intermarket connections within the broader economy.
FAQ
A YED close to zero indicates the good is a necessity with demand largely unaffected by income changes.
Typical examples include basic food staples such as bread or rice.
Even when incomes rise or fall, the quantity demanded remains almost constant because consumers cannot significantly increase or decrease their consumption.
Yes, YED values can shift as societies and consumer preferences evolve.
For example, smartphones were once considered luxury goods (high positive YED) but are now often seen as necessities in many economies.
Technological diffusion, changes in income distribution, and lifestyle changes all contribute to altering elasticity values over time.
Governments use XED to assess the degree of competition between firms.
High positive XED suggests goods are close substitutes, indicating markets may be highly competitive.
This is useful when regulators assess mergers: if two firms produce close substitutes, combining them could reduce competition.
Negative XED values (strong complements) can also be analysed to see if firms dominate linked markets, raising concerns about consumer choice.
Weak complements (low negative XED) mean consumers do not strongly adjust their purchases when the price of one product changes. Strong complements (high negative XED) show significant responsiveness.
Firms benefit by:
Designing pricing strategies, such as selling the main product cheaply but charging more for essential complements.
Developing bundles and promotions where complements are strongly linked to encourage higher total sales.
XED can guide firms in identifying substitution risks and opportunities across global markets.
If a firm exports a product with many close substitutes abroad, high positive XED indicates demand will be highly sensitive to competitors’ pricing.
Conversely, identifying strong complements internationally helps firms align with foreign partners to create packages (e.g., electronics and compatible accessories) and strengthen market presence.
Practice Questions
Define income elasticity of demand (YED) and state how the value of YED differs between normal and inferior goods. (2 marks)
1 mark for correctly defining income elasticity of demand: a measure of the responsiveness of demand to a change in consumer income.
1 mark for stating that normal goods have a positive YED, while inferior goods have a negative YED.
Using appropriate examples, explain how cross elasticity of demand (XED) can be used by firms to understand the relationship between substitutes and complements. (6 marks)
1 mark for defining cross elasticity of demand: responsiveness of demand for one good to a change in the price of another.
1 mark for identifying substitutes (positive XED).
1 mark for identifying complements (negative XED).
1 mark for providing a relevant example of substitutes (e.g., tea and coffee).
1 mark for providing a relevant example of complements (e.g., printers and ink cartridges).
1 mark for explanation of how firms use XED to make decisions (e.g., pricing strategies, bundling, assessing competitive threats).
