# 弹性

> 爱德思国际普通中等教育证书（IGCSE）经济学 · 4EC1
> 来源: https://www.owlsprep.com/zh/study/edexcel-igcse-economics-s1-elasticity/

本指南覆盖爱德思IGCSE经济学（4EC1）1.1.4节全部弹性相关内容，包括PED、PES、YED的计算、图示、数值解读、影响因素与实际应用。

**先修:** [市场体系：需求、供给与均衡](https://www.owlsprep.com/zh/study/edexcel-igcse-economics-s1-demand-supply-equilibrium/)

## 学习目标

- 使用给定的百分比变动定义、计算并解读PED、PES与YED
- 绘制并标注富有弹性/缺乏弹性的需求曲线与供给曲线图示
- 解释影响PED与PES数值的核心因素
- 将PED与企业总收益的变动相关联
- 评估弹性对企业定价策略与政府税收/补贴政策的重要意义

## 1. 需求价格弹性（PED）

**需求价格弹性（PED）** — 衡量商品需求量对其自身价格变动的反应程度的指标

*记法:* $PED = \frac{\% \Delta Q_d}{\% \Delta P}$

*例:* If a 10% price rise leads to a 5% fall in quantity demanded, PED = -0.5

由于价格与需求量之间存在反向关系（需求定律），PED的数值始终为负，你可以按照以下区间解读数值：

- Perfectly inelastic: $PED = 0$ (quantity demanded does not change when price changes)
- Inelastic: $|PED| < 1$ (quantity changes less than proportionally to price)
- Unitary elastic: $|PED| = 1$ (quantity changes proportionally to price)
- Elastic: $|PED| > 1$ (quantity changes more than proportionally to price)
- Perfectly elastic: $PED = \infty$ (quantity demanded falls to zero if price rises even slightly)

> **tip**
>
> 需求曲线越陡峭，弹性越缺乏；曲线越平缓，弹性越充足。完全无弹性的需求曲线是一条竖直线，完全弹性的需求曲线是一条水平线。

**例题:** 牛奶价格上涨15%，需求量下降3%，计算PED并解读该数值。

1. 步骤1：回忆PED计算公式

   $$PED = \frac{\% \Delta Q_d}{\% \Delta P}$$
2. 步骤2：代入给定数值

   $$PED = \frac{-3\%}{+15\%} = -0.2$$
3. 步骤3：解读：$|-0.2| < 1$，因此牛奶的需求是缺乏价格弹性的。

影响PED的四大核心因素包括：相近替代品的可获得性、商品的必需程度、该商品支出占消费者收入的比例，以及消费者适应价格变动的调整时间长度。

> **考试提示:** 绘制PED图示时，务必标注坐标轴（纵轴为价格，横轴为数量），并明确标注曲线属于富有弹性还是缺乏弹性，以拿到全部分数。

*计算器:* allowed

## 2. PED与总收益

**总收益（TR）** — 企业销售商品获得的全部收入，未扣除成本

*记法:* $TR = P \times Q$

价格变动对总收益的影响完全取决于PED：

- If demand is elastic: Price rise → TR falls; Price cut → TR rises
- If demand is inelastic: Price rise → TR rises; Price cut → TR falls
- If demand is unitary elastic: Price change has no impact on TR

**例题:** 某面包店将可颂的价格从2英镑下调至1.8英镑，日销量从50份上升至75份，计算总收益的变动，并说明需求属于富有弹性还是缺乏弹性。

1. 步骤1：计算初始总收益

   $$TR_{original} = 2 \times 50 = £100$$
2. 步骤2：计算新的总收益

   $$TR_{new} = 1.80 \times 75 = £135$$
3. 步骤3：总收益变动 = 135英镑 - 100英镑 = +35英镑。价格下降而总收益上升，因此需求是富有价格弹性的。

> **考试提示:** 作答价格变动与总收益关联的题目时，务必先展示初始总收益与新总收益的计算过程，再说明PED的类型，才能拿到全部分数。

*计算器:* allowed

## 3. 供给价格弹性（PES）

**供给价格弹性（PES）** — 衡量商品供给量对其自身价格变动的反应程度的指标

*记法:* $PES = \frac{\% \Delta Q_s}{\% \Delta P}$

供给价格弹性（PES）始终为正，这是由价格与供给量之间的正相关关系（供给定律）决定的。其数值的解读标准与需求价格弹性（PED）完全一致。供给曲线越陡峭，代表供给越缺乏弹性；曲线越平缓，代表供给越富有弹性。

影响供给价格弹性（PES）的核心因素包括：生产要素的流动性、成品库存的可获得性、闲置生产能力的规模，以及生产者调整产出所允许的时间周期。

**例题:** 短期内玉米价格上涨20%，供给量增加4%。计算供给价格弹性（PES）并解释该数值偏低的原因。

1. 步骤1：套用供给价格弹性（PES）公式

   $$PES = \frac{+4\%}{+20\%} = 0.2$$
2. 步骤2：0.2 < 1，因此玉米的供给缺乏价格弹性。
3. 步骤3：PES数值偏低的原因是玉米属于初级农产品，生长周期长达数月，因此生产者无法在短期内快速提升产出。

> **考试提示:** 比较初级产品与制成品的PES时，务必至少引用一个影响因素（例如农产品的生产时滞）来支撑你的结论。

*计算器:* allowed

## 4. 需求收入弹性（YED）

**需求收入弹性（YED）** — 衡量一种商品的需求量对消费者收入变动的反应程度的指标

*记法:* $YED = \frac{\% \Delta Q_d}{\% \Delta Y}$

- Negative YED: Inferior good (demand falls as income rises, e.g. value supermarket goods)
- Positive YED < 1: Normal necessity good (demand rises slower than income, e.g. toothpaste)
- Positive YED > 1: Luxury good (demand rises faster than income, e.g. international holidays)

**例题:** 家庭平均收入上涨10%，平价外卖餐食的需求下降5%。计算需求收入弹性（YED）并对该商品进行分类。

1. 步骤1：套用需求收入弹性（YED）公式

   $$YED = \frac{-5\%}{+10\%} = -0.5$$
2. 步骤2：YED为负值说明平价外卖属于劣等品（低档商品）。

*计算器:* allowed

## 5. 弹性对企业与政府的现实意义

弹性数据是企业和政府制定核心战略决策的重要依据：

- Businesses: Use PED to set pricing strategies (raise prices for inelastic goods to boost revenue, cut prices for elastic goods to increase sales volume). Use YED to plan production during economic booms and recessions.
- Governments: Use PED when imposing indirect taxes: taxes on inelastic goods (cigarettes, petrol) raise more revenue and cause smaller falls in quantity demanded. Use YED to forecast demand for public services during periods of income change.

**例题:** 解释政府为了筹集收入，会选择对汽油而非名牌服饰征税的原因。

1. 步骤1：汽油的需求缺乏价格弹性（替代品极少，是大多数家庭出行的必需品）。
2. 步骤2：对汽油征税只会带来需求量的小幅下降，因此政府可以筹集大量税收收入，同时还能小幅激励碳排放的削减。
3. 步骤3：名牌服饰的需求富有弹性，对其征税会导致销量大幅下滑，不仅筹集到的税收极少，还会损害服饰零售商的利益。

> **考试提示:** 对于评价类题目，务必加入对立观点：例如，对缺乏弹性的商品征税虽然能带来高额税收收入，但可能会对低收入家庭造成不成比例的负担。

*计算器:* allowed

## 常见错误

- **错误做法:** Forgetting the negative sign for PED and YED in calculations
  - 原因: The negative sign signals the inverse relationship between price and demand for PED, and inferior good status for YED. Omitting it leads to incorrect interpretation of values.
  - 正确做法: Always include the sign unless the question explicitly asks for the absolute value.
- **错误做法:** Mixing up PED and PES formulas or influencing factors
  - 原因: Both use % change in quantity over % change in price, but PED refers to quantity demanded while PES refers to quantity supplied, and their influencing factors are distinct.
  - 正确做法: Label $Q_d$ and $Q_s$ explicitly in formulas, and memorize factor lists separately for PED and PES.
- **错误做法:** Drawing inelastic curves as flat and elastic curves as steep
  - 原因: Steeper curves mean quantity changes very little for a given price change, which is the definition of inelastic, not elastic.
  - 正确做法: Use the mnemonic: Flat = Flexible = Elastic; Steep = Stuck = Inelastic.
- **错误做法:** Stating that price increases always raise total revenue
  - 原因: This is only true if demand is inelastic. If demand is elastic, a price increase will lead to a large fall in quantity sold, reducing total revenue.
  - 正确做法: Always link price changes to total revenue via the PED value before drawing a conclusion.
- **错误做法:** Confusing YED value interpretations for normal/inferior goods
  - 原因: Mixing up positive and negative YED values leads to incorrect classification of good types, losing marks on interpretation questions.
  - 正确做法: Use the mnemonic: N-I-P (Normal = Positive, Inferior = Negative), and YED > 1 = Luxury good.

## 速查表

| Elasticity Type | Core Formula | Value Interpretations | Key Influencing Factors |
| --- | --- | --- | --- |
| PED | $\frac{\%\Delta Q_d}{\%\Delta P}$ | <1 Inelastic, =1 Unitary, >1 Elastic, 0 Perfectly Inelastic, ∞ Perfectly Elastic | Substitutes, Necessity, % of income spent, Time |
| PES | $\frac{\%\Delta Q_s}{\%\Delta P}$ | <1 Inelastic, =1 Unitary, >1 Elastic, 0 Perfectly Inelastic, ∞ Perfectly Elastic | Factor mobility, Stocks, Spare capacity, Time |
| YED | $\frac{\%\Delta Q_d}{\%\Delta Y}$ | <0 Inferior, 0<YED<1 Normal Necessity, >1 Luxury | N/A |

## 下一步

Now that you have mastered elasticity concepts, you can apply this knowledge to analyse how demand and supply shifts affect market outcomes, including the impact of government interventions like indirect taxes and subsidies. Elasticity is a foundational concept for later topics in market failure and business strategy, so solidifying your understanding now will help you score high marks on extended response questions in Paper 1. Be sure to practice past paper calculation and diagram questions to build speed and accuracy for your exam.

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