📚 Price Elasticity of Demand | 需求价格弹性
Price elasticity of demand is a central concept in Cambridge A-Level Economics. It helps firms, governments and analysts predict how consumers respond to price changes.
需求价格弹性是剑桥A-Level经济学的核心概念。它帮助企业、政府和分析师预测消费者对价格变化的反应。
1. Definition of PED | 需求价格弹性的定义
Price elasticity of demand (PED) is defined as the responsiveness of quantity demanded to a change in the price of the good itself, ceteris paribus. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.
需求价格弹性（PED）定义为需求量对商品自身价格变化的反应程度，在其他条件不变的情况下。它通过需求量变化百分比除以价格变化百分比来计算。
Because price and quantity demanded move in opposite directions along a downward-sloping demand curve, the PED value is usually negative. Economists often ignore the minus sign and quote PED as a positive number.
由于在向下倾斜的需求曲线上，价格与需求量反向变动，PED数值通常为负。经济学家通常忽略负号，将PED引用为正数。
2. Calculating PED: The Formula | 计算PED：公式
The basic PED formula uses percentage changes rather than absolute changes to avoid measurement problems caused by different units.
基础PED公式使用百分比变化而非绝对变化，以避免不同单位带来的测量问题。
PED = %ΔQd ÷ %ΔP
In the formula, %ΔQd is the percentage change in quantity demanded and %ΔP is the percentage change in price. For example, %ΔQd = (Q₂ – Q₁) ÷ Q₁ × 100 and %ΔP = (P₂ – P₁) ÷ P₁ × 100.
在公式中，%ΔQd 是需求量变化百分比，%ΔP 是价格变化百分比。例如，%ΔQd =（Q₂ – Q₁）÷ Q₁ × 100，%ΔP =（P₂ – P₁）÷ P₁ × 100。
3. Worked Example | 计算示例
Suppose a cinema raises its ticket price from £10 to £12, and the number of tickets sold per week falls from 1,000 to 800. The percentage change in quantity demanded is (800 − 1000) ÷ 1000 × 100 = −20%, while the percentage change in price is (12 − 10) ÷ 10 × 100 = +20%.
假设一家电影院将票价从10英镑提高到12英镑，每周售出的票数从1000张下降到800张。需求量变化百分比为（800 − 1000）÷ 1000 × 100 = −20%，而价格变化百分比为（12 − 10）÷ 10 × 100 = +20%。
Using the formula, PED = −20% ÷ +20% = −1.0, so the coefficient is 1.0 in absolute terms. This means demand is unit elastic at this price range.
使用公式，PED = −20% ÷ +20% = −1.0，因此绝对值系数为1.0。这意味着在此价格区间内需求是单位弹性的。
When PED is calculated between two points, the result is called arc elasticity. Using the midpoint formula can give a more consistent result for large price changes, but at A-Level the simple percentage method is usually sufficient.
当在两点之间计算PED时，结果称为弧弹性。对于较大价格变动，使用中点公式可以给出更一致的结果，但在A-Level中，简单百分比方法通常已足够。
4. Interpreting the PED Coefficient | 解读PED系数
The PED coefficient can be classified into five main categories based on its absolute value.
PED系数可以根据绝对值分为五个主要类别。
- Elastic demand (PED > 1): a given percentage change in price causes a larger percentage change in quantity demanded. 弹性需求（PED > 1）：一定比例的价格变化引起更大比例的需求量变化。
- Inelastic demand (PED < 1): a given percentage change in price causes a smaller percentage change in quantity demanded. 缺乏弹性需求（PED < 1）：一定比例的价格变化引起更小比例的需求量变化。
- Unit elastic demand (PED = 1): price and quantity demanded change by the same percentage. 单位弹性需求（PED = 1）：价格与需求量变化百分比相同。
- Perfectly inelastic demand (PED = 0): quantity demanded does not change when price changes. 完全无弹性需求（PED = 0）：价格变化时需求量不变。
- Perfectly elastic demand (PED = ∞): at a certain price, any quantity is demanded; a tiny price rise reduces quantity demanded to zero. 完全弹性需求（PED = ∞）：在某一价格水平，任何数量均可被需求；价格极小幅上升使需求量降为零。
These categories help firms predict the likely impact of price changes on sales volume and revenue.
这些类别帮助企业预测价格变化对销售量和收入的潜在影响。
5. PED Values and Demand Curve Shapes | PED数值与需求曲线形状
Although elasticity and slope are not the same, PED is related to the shape of the demand curve. A relatively flat demand curve suggests more elastic demand, while a relatively steep demand curve suggests more inelastic demand.
尽管弹性与斜率并不相同，PED与需求曲线的形状相关。相对平坦的需求曲线表示需求更具弹性，而相对陡峭的需求曲线表示需求更缺乏弹性。
A perfectly inelastic demand curve is vertical, showing that quantity demanded is fixed regardless of price. A perfectly elastic demand curve is horizontal, showing that consumers are willing to buy any quantity at one price only.
完全无弹性的需求曲线是垂直的，表明无论价格如何，需求量都是固定的。完全弹性的需求曲线是水平的，表明消费者只愿意在一个价格下购买任意数量。
Unit elastic demand can be represented by a rectangular hyperbola, where total revenue remains constant at all points on the curve.
单位弹性需求可以用矩形双曲线表示，曲线上所有点的总收益保持不变。
6. PED and Total Revenue | PED与总收益
Total revenue (TR) is the amount a firm receives from selling its product, calculated as price × quantity. The effect of a price change on total revenue depends on PED.
总收益（TR）是企业销售产品所获得的金额，计算方式为价格 × 数量。价格变化对总收益的影响取决于PED。
If demand is elastic (PED > 1), a price increase reduces total revenue because the percentage fall in quantity demanded is larger than the percentage rise in price. Conversely, a price cut increases total revenue.
如果需求富有弹性（PED > 1），价格上涨会减少总收益，因为需求量下降的百分比大于价格上升的百分比。相反，降价会增加总收益。
If demand is inelastic (PED < 1), a price increase raises total revenue because the percentage fall in quantity demanded is smaller than the percentage rise in price. A price cut lowers total revenue.
如果需求缺乏弹性（PED < 1），价格上涨会增加总收益，因为需求量下降的百分比小于价格上升的百分比。降价会降低总收益。
If demand is unit elastic (PED = 1), total revenue stays the same when price changes.
如果需求是单位弹性（PED = 1），价格变化时总收益保持不变。
| Demand elasticity | 需求弹性 | Price rise | 涨价 | Price fall | 降价 |
|---|---|---|
| Elastic (PED > 1) | 弹性 | TR decreases | 总收益下降 | TR increases | 总收益上升 |
| Inelastic (PED < 1) | 缺乏弹性 | TR increases | 总收益上升 | TR decreases | 总收益下降 |
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