Other Elasticities
Introduced| English | Meaning |
|---|---|
| cross-price elasticity of demand/krɒs praɪs ɪlæˈstɪsɪti ɒv dɪˈmænd/ | The percentage change in quantity demanded of one good divided by the percentage change in the price of another good. |
| substitutes/ˈsʌbstɪtjuːts/ | Goods or services that can be used in place of each other. |
| complements/ˈkɒmplɪmənts/ | Goods or services typically used together, so demand for one is linked to the use of the other. |
| income elasticity of demand/ˈɪŋkʌm ɪlæˈstɪsɪti ɒv dɪˈmænd/ | The percentage change in quantity demanded divided by the percentage change in consumer income. |
| normal good/ˈnɔːml ɡʊd/ | A good for which demand increases as consumer income rises, with other factors held constant. |
| inferior good/ɪnˈfɪərɪə ɡʊd/ | A good for which demand falls as consumer income rises, with other factors held constant. |
What tea tells you about coffee
- When the price of tea jumps, something happens to coffee — its demand rises.
- When incomes rise, people buy more of some goods and less of others.
- Demand does not only react to a good's own price.
- Two more elasticities capture these other reactions.
Cross-price elasticity (XED)
- Cross-price elasticity of demand 交叉价格弹性 measures how demand for good X reacts to the price of good Y.
- Formula: $\text{XED} = \dfrac{\%\,\Delta\,Q_X}{\%\,\Delta\,P_Y}$.
- Positive XED → the goods are substitutes 替代品 (tea dearer → more coffee bought).
- Negative XED → the goods are complements 互补品 (printers dearer → less ink bought).
Two goods have a positive cross-price elasticity. They are:
Difficulty 1/5 · 100 coins + a small bonus on first completion today
Positive XED: a dearer Y sends buyers to X — the goods substitute for each other.
Printers and ink are complements, so their cross-price elasticity is negative.
Difficulty 1/5 · 100 coins + a small bonus on first completion today
A dearer printer lowers ink demand — a negative XED marks complements.
Income elasticity (YED)
- Income elasticity of demand 收入弹性 measures how demand reacts to a change in income.
- Formula: $\text{YED} = \dfrac{\%\,\Delta\,Q}{\%\,\Delta\,\text{income}}$.
- Positive YED → a normal good 正常商品 (buy more as income rises).
- Negative YED → an inferior good 低档商品 (buy less as income rises).
Read the sign
The sign of cross-price elasticity tells you substitutes (+) from complements (−); the sign of income elasticity tells you normal (+) from inferior (−) goods.
A good with a positive income elasticity of demand is a:
Difficulty 1/5 · 100 coins + a small bonus on first completion today
Positive YED: buyers want more as income rises — a normal good.
A good you buy less of as your income rises is called an ______ good.
Difficulty 1/5 · 100 coins + a small bonus on first completion today
An inferior good has a negative income elasticity of demand.
Read the sign, not just the size
- Worked idea. Income rises 10% and quantity of bus tickets demanded falls 5%.
- Then $\text{YED} = \dfrac{-5\%}{10\%} = -0.5$.
- The sign is negative, so bus travel is an inferior good here — richer people switch to taxis or cars.
- With these elasticities, the sign classifies the relationship; the size shows how strong it is.
Income rises 10% and quantity of bus tickets demanded falls 5%. What is the income elasticity of demand (keep the sign)?
Difficulty 2/5 · 140 coins + a small bonus on first completion today
$\text{YED} = -5\% \div 10\% = -0.5$; the negative sign means bus travel is an inferior good here.
Match each elasticity sign to what it tells you.
Difficulty 2/5 · 140 coins + a small bonus on first completion today
The sign does the classifying: substitutes/complements for XED, normal/inferior for YED.
XED = %ΔQ of X ÷ %ΔP of Y: positive → substitutes, negative → complements. YED = %ΔQ ÷ %Δincome: positive → normal good, negative → inferior good. Always read the sign first.
Write from a cross-price elasticity of 0.4
- The price of tea rises 20 percent.
- Coffee quantity demanded rises 8 percent.
The price of tea rises by 20 percent and the quantity of coffee demanded rises by 8 percent. What is the cross-price elasticity, and are tea and coffee substitutes or complements?
8 divided by 20 is 0.4, and a positive cross-price elasticity means substitutes.
What is the cross-price elasticity of coffee with respect to tea?
Difficulty 1/5 · 100 coins + a small bonus on first completion today
8 divided by 20 is 0.4, and the positive sign means substitutes.