A-Level经济学 需求价格弹性 PED计算与应用

A-Level经济学 需求价格弹性 PED计算与应用

1. 需求价格弹性的定义 Definition of Price Elasticity of Demand

Price Elasticity of Demand (PED) measures the responsiveness of quantity demanded to a change in price. It is one of the most important concepts in A-Level microeconomics, forming the foundation for understanding how markets react to price changes and how firms make pricing decisions. 需求价格弹性（PED）衡量需求量对价格变化的反应程度。这是A-Level微观经济学中最重要的概念之一，为理解市场如何应对价格变动以及企业如何制定定价策略奠定了基础。

The concept of elasticity was developed by Alfred Marshall in his 1890 work “Principles of Economics”. Unlike slope, which depends on the units of measurement, elasticity is a unit-free measure that allows us to compare responsiveness across different goods and markets. 弹性概念由阿尔弗雷德·马歇尔在其1890年的著作《经济学原理》中提出。与取决于测量单位的斜率不同，弹性是一种无量纲的度量，使我们能够比较不同商品和市场之间的反应程度。

2. PED的计算公式 Formula and Calculation

The basic formula for PED is: PED = (% change in quantity demanded) / (% change in price). The percentage change in quantity demanded is calculated as (Q2 – Q1) / Q1 × 100, and the percentage change in price is calculated as (P2 – P1) / P1 × 100. PED的基本公式为：PED =（需求量变动百分比）/（价格变动百分比）。需求量变动百分比计算为(Q2 – Q1) / Q1 × 100，价格变动百分比计算为(P2 – P1) / P1 × 100。

Because of the law of demand, PED is almost always negative： when price rises, quantity demanded falls, and vice versa. In A-Level exams, you should state the sign in your working but typically compare the absolute values. PED is often reported as a positive number for convenience, but the negative sign is important for understanding the direction of the relationship. 由于需求定律，PED几乎总是负值：价格上涨时需求量下降，反之亦然。在A-Level考试中，你应该在计算过程中标明符号，但通常比较绝对值。PED为方便起见常报告为正数，但负号对于理解关系的方向很重要。

Worked Example: A cinema raises ticket prices from £10 to £12, and daily attendance falls from 500 to 400. Calculate the PED. % change in Qd = (400 – 500) / 500 × 100 = -20%. % change in P = (12 – 10) / 10 × 100 = 20%. PED = -20% / 20% = -1.0. The absolute value is 1, so demand is unit elastic. 计算示例：一家电影院将票价从10英镑提高到12英镑，每日观影人数从500下降到400。计算PED。需求量变动% = (400 – 500) / 500 × 100 = -20%。价格变动% = (12 – 10) / 10 × 100 = 20%。PED = -20% / 20% = -1.0。绝对值为1，因此需求是单位弹性的。

3. PED数值的解读 Interpreting PED Values

When |PED| > 1, demand is price elastic. A given percentage change in price leads to a larger percentage change in quantity demanded. Luxury goods, goods with many close substitutes, and goods that take up a large proportion of income typically have elastic demand. 当|PED| > 1时，需求是价格弹性的。给定的价格变动百分比导致需求量更大的百分比变动。奢侈品、有许多近似替代品的商品以及占收入较大比例的商品通常具有弹性需求。

When |PED| < 1, demand is price inelastic. A given percentage change in price leads to a smaller percentage change in quantity demanded. Necessities, addictive goods, goods with few substitutes, and goods that take up a small proportion of income typically have inelastic demand. 当|PED| < 1时，需求是价格非弹性的。给定的价格变动百分比导致需求量更小的百分比变动。必需品、成瘾性商品、替代品少的商品以及占收入比例小的商品通常具有非弹性需求。

When |PED| = 1, demand is unit elastic. The percentage change in quantity demanded exactly equals the percentage change in price. When |PED| = 0, demand is perfectly inelastic (vertical demand curve), meaning quantity demanded does not change regardless of price. When |PED| approaches infinity, demand is perfectly elastic (horizontal demand curve), meaning any price increase causes quantity demanded to drop to zero. 当|PED| = 1时，需求是单位弹性的。需求量变动的百分比恰好等于价格变动的百分比。当|PED| = 0时，需求是完全非弹性的（垂直需求曲线），意味着无论价格如何变化，需求量都不变。当|PED|趋近于无穷大时，需求是完全弹性的（水平需求曲线），意味着任何价格上涨都会导致需求量降至零。

4. 影响PED的因素 Determinants of PED

Number and closeness of substitutes is the most important determinant. The more close substitutes a good has, the more elastic its demand will be, because consumers can easily switch to alternatives when the price rises. For example, demand for a specific brand of bottled water is very elastic, while demand for insulin is highly inelastic. 替代品的数量和近似程度是最重要的决定因素。一种商品的近似替代品越多，其需求就越具弹性，因为消费者在价格上涨时可以轻易转向替代品。例如，特定品牌瓶装水的需求非常有弹性，而胰岛素的需求则高度非弹性。

The proportion of income spent on the good matters. Goods that take up a large share of a consumer’s budget, such as cars and houses, tend to have more elastic demand because price changes have a significant impact on purchasing power. Goods that take up a small share, such as salt or matches, tend to have inelastic demand. 商品占收入的比例很重要。占消费者预算较大份额的商品，如汽车和房屋，往往具有更具弹性的需求，因为价格变动对购买力有显著影响。占较小份额的商品，如盐或火柴，往往具有非弹性需求。

Time period is another key factor. Demand tends to be more elastic in the long run because consumers have more time to find substitutes and adjust their behaviour. In the short run, consumers may be locked into habits or contracts, making demand more inelastic. For example, when petrol prices rise, demand falls only slightly in the short run but much more significantly over several years as people switch to more fuel-efficient cars or alternative transport. 时间周期是另一个关键因素。长期来看需求往往更具弹性，因为消费者有更多时间寻找替代品并调整行为。短期内消费者可能受习惯或合同的约束，使需求更非弹性。例如，当汽油价格上涨时，短期内需求仅略微下降，但经过几年后，随着人们转向更节能的汽车或替代交通方式，需求下降更为显著。

Whether the good is a necessity or luxury also affects elasticity. Necessities like basic food, water, and electricity have inelastic demand because consumers must buy them regardless of price. Luxuries like designer clothing and overseas holidays have elastic demand because consumers can easily postpone or cancel these purchases. 商品是必需品还是奢侈品也会影响弹性。基本食品、水和电力等必需品的需求是非弹性的，因为消费者无论价格如何都必须购买。设计师服装和海外度假等奢侈品的需求是弹性的，因为消费者可以轻易推迟或取消这些购买。

5. PED与总收益的关系 PED and Total Revenue

Total revenue (TR) is calculated as price multiplied by quantity sold: TR = P × Q. Understanding the relationship between PED and total revenue is crucial for A-Level exams, especially for evaluation questions that ask you to assess the impact of a price change on a firm’s revenue. 总收益（TR）计算为价格乘以销售量：TR = P × Q。理解PED与总收益之间的关系对A-Level考试至关重要，特别是那些要求你评估价格变动对企业收入影响的评价题。

When demand is elastic (|PED| > 1), a price decrease increases total revenue because the percentage increase in quantity demanded outweighs the percentage decrease in price. Conversely, a price increase reduces total revenue. For instance, if a cinema with elastic demand lowers ticket prices, the increase in attendance more than compensates for the lower price per ticket. 当需求具有弹性时（|PED| > 1），降价会增加总收益，因为需求量增加的百分比超过了价格下降的百分比。相反，涨价会减少总收益。例如，如果一家需求弹性的电影院降低票价，观影人数的增加足以弥补单张票价的下降。

When demand is inelastic (|PED| < 1), a price increase increases total revenue because the percentage decrease in quantity demanded is smaller than the percentage increase in price. A price decrease would reduce total revenue. This explains why governments often impose high taxes on inelastic goods like cigarettes and alcohol: demand barely falls, so tax revenue is high. 当需求非弹性时（|PED| < 1），涨价会增加总收益，因为需求量减少的百分比小于价格上涨的百分比。降价则会减少总收益。这解释了为什么政府通常对香烟和酒精等非弹性商品征收高税：需求几乎不降，因此税收收入很高。

When demand is unit elastic (|PED| = 1), total revenue stays constant regardless of price changes; the percentage changes in price and quantity exactly offset each other. 当需求是单位弹性时（|PED| = 1），无论价格如何变化，总收益保持不变；价格和数量变动的百分比恰好相互抵消。

6. 弧弹性计算方法 Arc Elasticity (Midpoint Method)

In A-Level exams, you may be asked to use the arc elasticity (midpoint) formula, which gives a more accurate measure when price changes are large. The formula uses average values: Arc PED = [(Q2 – Q1) / ((Q1 + Q2)/2)] / [(P2 – P1) / ((P1 + P2)/2)]. This method gives the same elasticity value regardless of whether price rises or falls, unlike the simple percentage method. 在A-Level考试中，你可能需要用到弧弹性（中点）公式，当价格变化较大时，该公式能提供更准确的度量。公式使用平均值：弧PED = [(Q2 – Q1) / ((Q1 + Q2)/2)] / [(P2 – P1) / ((P1 + P2)/2)]。无论价格是上涨还是下跌，这种方法都能给出相同的弹性值，这与简单百分比法不同。

Worked Example (Midpoint Method): A coffee shop raises the price of a latte from £3.00 to £3.60, and daily sales fall from 200 to 150 cups. Using the midpoint formula: Average Q = (200 + 150)/2 = 175. Average P = (3.00 + 3.60)/2 = 3.30. % change Q = (150 – 200)/175 × 100 = -28.6%. % change P = (3.60 – 3.00)/3.30 × 100 = 18.2%. Arc PED = -28.6%/18.2% = -1.57. Demand is elastic. 计算示例（中点法）：一家咖啡店将拿铁价格从3.00英镑提高到3.60英镑，每日销量从200杯下降到150杯。使用中点公式：平均Q = (200 + 150)/2 = 175。平均P = (3.00 + 3.60)/2 = 3.30。Q变动% = (150 – 200)/175 × 100 = -28.6%。P变动% = (3.60 – 3.00)/3.30 × 100 = 18.2%。弧PED = -28.6%/18.2% = -1.57。需求是弹性的。

7. PED与市场结构 PED and Market Structure

PED varies significantly across different market structures. In perfectly competitive markets where many firms sell identical products, individual firms face perfectly elastic demand because consumers can instantly switch to a competitor’s identical product if one firm raises its price. PED在不同市场结构中差异显著。在完全竞争市场中，许多企业销售相同的产品，个别企业面临完全弹性的需求，因为如果一家企业提价，消费者可以立即转向竞争对手的相同产品。

In monopoly markets, the firm faces the entire market demand curve, which is downward-sloping and typically inelastic in the range where the monopolist operates. This gives the monopolist significant pricing power. In oligopoly markets, the kinked demand curve theory suggests that demand is elastic above the prevailing price (rivals do not follow price increases) but inelastic below it (rivals match price cuts), creating price rigidity. 在垄断市场中，企业面临整个市场的需求曲线，该曲线向下倾斜，在垄断者运营的范围内通常是非弹性的。这赋予垄断者显著的定价能力。在寡头市场中，弯折的需求曲线理论表明，在现行价格之上需求是弹性的（竞争对手不跟随涨价），但在现行价格之下是非弹性的（竞争对手匹配降价），从而形成价格刚性。

8. 考试技巧与常见错误 Exam Tips and Common Mistakes

Always show your working step by step in PED calculations. Examiners award method marks even if the final answer is wrong. Write down the formula first, substitute the numbers, and then calculate. Remember to state whether demand is elastic or inelastic based on your result. 在PED计算中始终逐步展示你的计算过程。即使最终答案错误，考官也会给予方法分。先写下公式，代入数字，然后计算。记得根据结果说明需求是弹性的还是非弹性的。

A common mistake is confusing the sign convention. PED is nearly always negative because of the inverse relationship between price and quantity demanded; dropping the negative sign without explanation can lose marks. Another frequent error is using the wrong base for percentage changes: always divide by the original value (Q1, P1), not the new value, unless explicitly asked to use the midpoint method. 一个常见错误是混淆符号规则。由于价格与需求量之间的反向关系，PED几乎总是负值；不解释就省略负号可能会丢分。另一个常见错误是百分比变化使用了错误的基数：始终除以原始值（Q1, P1），而非新值，除非题目明确要求使用中点法。

For evaluation questions (typically 9-15 marks), go beyond the basic PED calculation. Discuss the limitations of PED: it only measures responsiveness along a demand curve at a specific point; PED can vary at different price levels along the same demand curve; and real-world data may be unreliable or outdated. Link your analysis to real examples and consider both short-run and long-run effects. 对于评价题（通常9-15分），超越基本的PED计算。讨论PED的局限性：它只衡量需求曲线上某一点的响应程度；PED在同一需求曲线上不同价格水平可能不同；现实数据可能不可靠或过时。将你的分析与真实案例联系起来，并考虑短期和长期效应。

Remember the key diagram: a demand curve with elastic and inelastic regions labelled. For a straight-line demand curve, PED is elastic above the midpoint, unit elastic at the midpoint, and inelastic below the midpoint. Drawing and explaining this diagram correctly can earn you significant marks in A-Level Economics exams. 记住关键图表：标注了弹性和非弹性区域的需求曲线。对于直线型需求曲线，中点以上PED是弹性的，中点处是单位弹性的，中点以下是非弹性的。正确绘制和解释这个图表可以在A-Level经济学考试中为你赢得可观的分数。