Cross Price and Income Elasticity of Demand
Unit 2 · Demand, supply, elasticity and market equilibrium
How demand responds to changes in the price of another good and to changes in income; classifying substitutes, complements, and normal, essential, luxury and inferior goods.
Cross price elasticity of demand (XED)
The demand for one good often depends on the price of another good. Cross price elasticity of demand measures this:
XED = % change in quantity demanded of good A / % change in price of good B
Example. The price of tea rises by 10% and the quantity demanded of coffee rises by 4%. XED = +4 / +10 = +0.4
| XED | Relationship | Example |
|---|---|---|
| Positive | Substitutes (the higher the value, the closer the substitutes) | Tea and coffee; bus and train |
| Negative | Complements (the larger the absolute value, the stronger the link) | Petrol and cars; bread and butter |
| Zero | Unrelated goods | Salt and bicycles |
Example (complements). The price of petrol rises by 20% and the demand for cars falls by 6%. XED = -6 / +20 = -0.3: the goods are complements, though not strongly.
Importance of XED
- A firm can predict how a rival's price change will move its own sales (a high positive XED means rivals' prices matter a lot).
- A firm selling complements (printers and ink cartridges) can set pricing strategies for both.
- Governments, for example, may expect a tax on petrol to reduce demand for cars too.
Income elasticity of demand (YED)
YED = % change in quantity demanded / % change in consumers' income
Example. Monthly income rises from Rs. 20,000 to Rs. 24,000 (+20%) and a household's restaurant meals rise from 10 to 14 a month (+40%). YED = +40 / +20 = +2
| YED | Type of good | Meaning | Example |
|---|---|---|---|
| Negative | Inferior good | Demand falls when income rises | Cheap dried fish, low-quality rice, second-hand clothes |
| 0 to 1 | Normal good: essential (necessity) | Demand rises less than income | Rice, salt, vegetables |
| More than 1 | Normal good: luxury | Demand rises more than income | Restaurant meals, foreign travel, cars |
All goods with positive YED are normal goods; essential (necessity) goods have 0 < YED < 1.
Example (inferior good). Income rises 20% and a household's bus rides fall from 100 to 90 a month (-10%). YED = -10 / +20 = -0.5: bus travel is an inferior good for this household.
Importance of YED
- Firms planning for growth should expand the production of goods with a high YED and phase out inferior goods.
- Governments can forecast how demand patterns and the structure of the economy shift as incomes grow: agriculture's share tends to fall and services' share to rise.
- Retailers decide what to stock in rich and poor areas.
- In a recession, demand for luxury goods falls more than demand for essentials.
Mind map
Remember:
- XED > 0: substitutes; XED < 0: complements; XED = 0: unrelated
- XED = %ΔQd of A ÷ %ΔP of B
- YED < 0: inferior good; 0 < YED < 1: essential; YED > 1: luxury
- YED = %ΔQd ÷ %Δincome
- Sign = type of good; size = how strong the link is
- Tea + sugar = complements (negative XED); tea + coffee = substitutes (positive XED)