| English | 意味 |
|---|---|
| price elasticity of demand/praɪs ɪlæˈstɪsɪti ɒv dɪˈmænd/ | 需要価格弾性 |
| absolute value/ˈæbsəluːt ˈvæljuː/ | 絶対値 |
| midpoint method/ˈmɪdpɔɪnt ˈmeθəd/ | 中点法 |
| elastic/ɪˈlæstɪk/ | 弾力がある |
| inelastic/ɪnɪˈlæstɪk/ | 非弾力的 |
| unit elastic/ˈjuːnɪt ɪˈlæstɪk/ | 単一弾力 |
| total revenue/ˈtəʊtl ˈrevənjuː/ | 総収入 |
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:
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
PED divides the percentage change in quantity by the percentage change in price.
Put the midpoint-method steps to find PED in order.
難易度 3/5 · 200 コイン + 今日初回完了時に小ボーナス付与
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|?
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
%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.
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
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:
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
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.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
Substitutes, a big income share and more time raise elasticity; a necessity with no substitute is inelastic.
Worked examples
1. The price rises from 4 to 6 and quantity demanded falls from 100 to 80. Midpoint method: $\%\Delta Q = \dfrac{80-100}{90} = -22.2\%$ and $\%\Delta P = \dfrac{6-4}{5} = 40\%$, so $|\text{PED}| = \dfrac{22.2}{40} = 0.56$: inelastic.
2. Check with the total revenue test: TR rises from $4 \times 100 = 400$ to $6 \times 80 = 480$. With inelastic demand, price and TR move together.
Price rises from 10 to 14 and quantity demanded falls from 90 to 60. Using the midpoint method, what is the absolute price elasticity of demand, and what happens to total revenue if price rises?
0.40 divided by one third is 1.2, which is above 1.
What is the absolute elasticity, and the revenue effect of a higher price?
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
0.40 divided by one third is 1.2, so the price rise cuts revenue.
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.
Write from a midpoint elasticity of 1.2
- Price rises from 10 to 14. Quantity demanded falls from 90 to 60.
- Find the absolute price elasticity with the midpoint method.