Price Elasticity of Demand
Introduced| English |
|---|
| price elasticity of demand/praɪs ɪlæˈstɪsɪti ɒv dɪˈmænd/ |
| absolute value/ˈæbsəluːt ˈvæljuː/ |
| midpoint method/ˈmɪdpɔɪnt ˈmeθəd/ |
| elastic/ɪˈlæstɪk/ |
| inelastic/ɪnɪˈlæstɪk/ |
| unit elastic/ˈjuːnɪt ɪˈlæstɪk/ |
| total revenue/ˈtəʊtl ˈrevənjuː/ |
Should the shop cut its price?
- Cut the price and you sell more — but each sale earns less.
- Sometimes the extra sales win; sometimes the lower price wins.
- Which one happens depends on how sensitive buyers are to price.
- That sensitivity has a name: price elasticity of demand 需求价格弹性 (PED).
Measuring PED
- PED answers: "if price changes by 1%, by what % does quantity demanded change?"
- Formula: $\text{PED} = \dfrac{\%\,\Delta\,\text{quantity demanded}}{\%\,\Delta\,\text{price}}$.
- Because price and quantity move in opposite directions, PED is negative — so we read its absolute value 绝对值.
- To get one clean answer, AP uses the midpoint method 中点法: divide each change by the average of the start and end values.
Price elasticity of demand is calculated as:
PED divides the percentage change in quantity by the percentage change in price.
Put the midpoint-method steps to find PED in order.
The midpoint method divides each change by the average of the two values, then you take |PED|.
Elastic, inelastic, or unit elastic
- Elastic 富有弹性: $|\text{PED}| > 1$ — quantity responds strongly (buyers are sensitive).
- Inelastic 缺乏弹性: $|\text{PED}| < 1$ — quantity barely responds.
- Unit elastic 单位弹性: $|\text{PED}| = 1$ — the two percentages are equal.
Steep vs flat demand
A steep demand curve is inelastic — quantity barely responds to price. A flat one is elastic. Drag to feel the difference and see it in total revenue.
Price rises from 4 to 6; quantity demanded falls from 120 to 80. Using the midpoint method, what is |PED|?
%ΔQ = -40/100 = -0.40 and %ΔP = 2/5 = 0.40, so PED = -1 and |PED| = 1 (unit elastic).
When |PED| equals exactly 1, demand is said to be ______ elastic.
Unit elastic means the two percentage changes are equal; total revenue is at its maximum.
PED and total revenue
- Total revenue 总收入 is $\text{TR} = P \times Q$.
- The total revenue test: if demand is elastic, price and TR move in opposite directions (cut price → TR rises).
- If demand is inelastic, price and TR move in the same direction (raise price → TR rises).
- If demand is unit elastic, total revenue is at its maximum.
Demand for a good is inelastic. To raise total revenue, the firm should:
With inelastic demand, price and total revenue move together — raising price raises TR.
What makes demand elastic
- More substitutes available → more elastic (easy to switch away).
- A larger share of income spent on the good → more elastic.
- More time to adjust → more elastic in the long run.
Select all that make demand more elastic.
Substitutes, a big income share and more time raise elasticity; a necessity with no substitute is inelastic.
PED = %ΔQ ÷ %ΔP (read as an absolute value, via the midpoint method). $|\text{PED}|>1$ is elastic, $<1$ inelastic, $=1$ unit elastic. The total revenue test: cut price when elastic, raise it when inelastic. More substitutes, a bigger income share, and more time all raise elasticity.