Income, Cross and Supply Elasticity

Work in progress. This note is still being written and incomplete.

Income elasticity of demand measures the responsiveness of quantity demanded to a change in consumer income.

Ei=% change in quantity demanded% change in incomeE_i = \frac{\%\text{ change in quantity demanded}} {\%\text{ change in income}}

Types of Goods

Income ElasticityType of GoodEffect of Income Increase
Ei > 1Normal luxuryQuantity demanded increases by a larger percentage
0 < Ei < 1Normal necessityQuantity demanded increases by a smaller percentage
Ei < 0Inferior goodQuantity demanded decreases

Normal Goods

Income elasticity is positive.

Normal goods can be divided into:

Necessities: 0 < Ei < 1

Luxuries: Ei > 1

Inferior Goods

Income elasticity is negative.

When consumer income increases, quantity demanded decreases.

Cross Elasticity of Demand

Cross elasticity of demand measures the responsiveness of quantity demanded of one good to a change in the price of another good.

Exy=% change in quantity demanded of X% change in price of YE_{xy} = \frac{\%\text{ change in quantity demanded of X}} {\%\text{ change in price of Y}}
Cross ElasticityRelationship
Exy > 0Substitute goods
Exy < 0Complementary goods
Exy approximately 0Independent goods

Substitute Goods

Substitute goods can be used instead of each other.

Cross elasticity is positive.

Example: Coca-Cola and Pepsi.

If the price of Coca-Cola increases, demand for Pepsi may increase.

Complementary Goods

Complementary goods are normally consumed together.

Cross elasticity is negative.

Example: Mobile phones and mobile phone services.

If the price of mobile phones decreases, demand for mobile phone services may increase.

Independent Goods

Independent goods have little or no relationship in consumption.

Their cross elasticity is approximately zero.

Price Elasticity of Supply

Price elasticity of supply measures the responsiveness of quantity supplied to a change in price.

Es=% change in quantity supplied% change in priceE_s = \frac{\%\text{ change in quantity supplied}} {\%\text{ change in price}}

Categories of Price Elasticity of Supply

TypeElasticityMeaning
Elastic SupplyEs > 1Quantity supplied changes by a larger percentage than price
Inelastic SupplyEs < 1Quantity supplied changes by a smaller percentage than price
Unit Elastic SupplyEs = 1Quantity supplied changes by the same percentage as price

Worked Examples

Income Elasticity Calculation

Income rises from 1,000 to 2,000 and quantity demanded rises from 10 to 20. Find the income elasticity of demand.

Solution Reveal Hide
%ΔY=+100%,%ΔQ=+100%\%\Delta Y = +100\%, \quad \%\Delta Q = +100\%Ei=100%100%=1E_i = \frac{100\%}{100\%} = 1

The good is a normal good with unitary income elasticity.

Identifying Complements

The price of good A falls and the demand for good B rises. Identify the relationship between A and B.

Solution Reveal Hide

The cross elasticity is negative, so A and B are complements.

For example: printers and ink.

Zero Cross Elasticity

What is the relationship between 2 goods with a cross elasticity of zero?

Solution Reveal Hide

A price change in one good does not affect the demand for the other, so the goods are independent and have no relationship.

Substitutes have positive cross elasticity and complements have negative cross elasticity.

Elasticities and a Price Rise

For a good, Ed=−2E_d = -2 and Es=1E_s = 1. The price rises by 10%. Find the changes in quantity demanded and quantity supplied.

Solution Reveal Hide
%ΔQd=−2×10%=−20%\%\Delta Q_d = -2 \times 10\% = -20\%%ΔQs=1×10%=+10%\%\Delta Q_s = 1 \times 10\% = +10\%

Quantity supplied exceeds quantity demanded, so there is a surplus that puts downward pressure on price.

Written by October 16, 2026 3 min read
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