Income and cross-price elasticity
Income elasticity shows how demand reacts to higher income, cross-price elasticity how it reacts to the price of another good. The sign classifies the good.
Formulas and rules
- Income elasticity η = % change in quantity / % change in income
- η < 0 inferior · 0 < η < 1 necessity · η > 1 luxury good
- Cross-price elasticity = % change in quantity of B / % change in price of A
- Positive: substitutes · negative: complements · close to zero: unrelated
Your turn
Three problems on this topic. Type numbers like 12.5 or 1,250 and elasticities with their sign.
Task
A household's average monthly income rises from €1,900.00 to €2,090.00. Its demand for concert tickets changes from 200 to 216 units a year. Work out the income elasticity and classify the good.
Percentage change in income in %
Percentage change in quantity in % (fall with a minus)
Income elasticity
For this household the good is …
Numbers like 12.5 or 1,250; elasticities with their sign (−0.75); percentages as a number (12.5). Round to 2 decimal places.
Worked example
A household's average monthly income rises from €2,800.00 to €3,080.00. Its demand for train journeys changes from 800 to 960 units a year. Work out the income elasticity and classify the good.
Worked solution
- 1.Income: (3,080 − 2,800) / 2,800 = 10.00%
- 2.Quantity: (960 − 800) / 800 = 20.00%
- 3.η = 20.00% / 10.00% = 2
- 4.η < 0: inferior · 0 < η < 1: normal good, necessity · η > 1: luxury good
Typical mistake: Calling a good with an income elasticity between 0 and 1 inferior. Inferior means quantity falls as income rises (η < 0).
The price of tennis rackets rises by 10%. As a result, the quantity of tennis balls demanded changes by −8%. Work out the cross-price elasticity and classify the relationship between the goods.
Worked solution
- 1.ε_AB = %Δ quantity of tennis balls / %Δ price of tennis rackets = −8.00% / 10.00% = −0.8
- 2.Negative: when one good gets dearer, demand for the other falls too → complements (used together).
Typical mistake: Mixing up the sign: cross-price elasticity is negative for complements and positive for substitutes.
Common questions
Is an inferior good a bad good?
Not necessarily. Inferior only means people buy less of it as their income rises because they switch to something else (e.g. the coach instead of the train).