Cross Elasticity of Demand | 需求的交叉弹性

📚 Cross Elasticity of Demand | 需求的交叉弹性

Cross elasticity of demand (XED) measures the responsiveness of the quantity demanded for one good to a change in the price of another good. It is a vital concept in A-Level Economics, helping students and analysts understand the relationship between products in a market.

需求的交叉弹性（XED）衡量的是，当另一种商品的价格发生变化时，某一种商品需求量的反应程度。这是A-Level经济学中的一个核心概念，帮助学生和分析师理解市场中产品之间的关系。

1. Definition and Formula | 定义与公式

The cross elasticity of demand is defined as the percentage change in quantity demanded of good A divided by the percentage change in price of good B. It shows whether two goods are substitutes, complements, or unrelated.

需求的交叉弹性定义为：商品A需求量的百分比变化除以商品B价格的百分比变化。它显示两种商品是替代品、互补品还是无关品。

XED = %ΔQd of Good A / %ΔP of Good B

For example, if the price of coffee rises by 10% and the quantity demanded for tea increases by 5%, the XED would be +0.5. This positive value indicates that coffee and tea are substitutes.

例如，如果咖啡价格上升10%，而茶的需求量增加5%，那么交叉弹性为+0.5。这个正值表明咖啡和茶是替代品。

2. Calculating XED | 计算交叉弹性

To calculate XED, you must first determine the percentage change in quantity demanded of good A and the percentage change in price of good B. The midpoint method is often used to ensure accuracy, especially when dealing with large changes.

要计算交叉弹性，首先需要确定商品A需求量的百分比变化和商品B价格的百分比变化。通常使用中点法来确保准确性，尤其是在处理较大变化时。

Suppose the price of petrol increases from $1.50 to $1.80 per litre, and the quantity demanded for cars falls from 100,000 to 90,000 units per month. The percentage change in price is (0.30 / 1.50) × 100 = 20%. The percentage change in quantity demanded for cars is (-10,000 / 100,000) × 100 = -10%. Thus, XED = -10% / 20% = -0.5.

假设汽油价格从每升1.50美元上升到1.80美元，而汽车的需求量从每月100,000辆下降到90,000辆。价格的百分比变化是（0.30 / 1.50）× 100 = 20%。汽车需求量的百分比变化是（-10,000 / 100,000）× 100 = -10%。因此，XED = -10% / 20% = -0.5。

3. Positive XED: Substitutes | 正交叉弹性：替代品

When XED is positive, the two goods are substitutes. A rise in the price of one good leads to an increase in demand for the other, as consumers switch to the cheaper alternative.

当交叉弹性为正值时，两种商品是替代品。一种商品价格的上升会导致另一种商品需求的增加，因为消费者会转向更便宜的选择。

Common examples include tea and coffee, butter and margarine, or different brands of smartphones. The higher the positive value, the closer the substitutes are in the eyes of consumers.

常见的例子包括茶和咖啡、黄油和人造黄油，或者不同品牌的智能手机。正值越高，说明消费者认为这两种商品的可替代性越强。

For instance, if the XED between two brands of cereal is +2.0, a 10% increase in the price of one brand would lead to a 20% increase in demand for the other. This indicates strong substitutability.

例如，如果两个品牌麦片之间的交叉弹性是+2.0，那么一个品牌价格上涨10%会导致另一个品牌的需求量增加20%。这表明它们具有很强的可替代性。

4. Negative XED: Complements | 负交叉弹性：互补品

When XED is negative, the two goods are complements. A rise in the price of one good leads to a fall in demand for the other, because they are often consumed together.

当交叉弹性为负值时，两种商品是互补品。一种商品价格的上升会导致另一种商品需求的下降，因为它们通常一起消费。

Examples include printers and ink cartridges, smartphones and apps, or cars and fuel. The more negative the value, the stronger the complementary relationship.

例子包括打印机和墨盒、智能手机和应用程序，或者汽车和燃料。负值越大，互补关系越强。

For example, if the XED between cars and petrol is -0.8, a 10% rise in petrol prices would cause a fall in car demand by 8%. This is because higher fuel costs make owning and running a car more expensive.

例如，如果汽车和汽油之间的交叉弹性是-0.8，汽油价格上涨10%将导致汽车需求下降8%。这是因为更高的燃料成本使得拥有和运行汽车更加昂贵。

5. Zero XED: Independent Goods | 零交叉弹性：无关商品

When XED is zero or close to zero, the two goods are unrelated. A change in the price of one good has no significant effect on the demand for the other.

当交叉弹性为零或接近零时，两种商品不相关。一种商品价格的变化对另一种商品的需求没有显著影响。

For instance, the price of umbrellas has little or no effect on the demand for bread. Such independence is common for goods in completely different markets.

例如，雨伞的价格对面包的需求几乎没有影响。这种独立性在完全不同的市场中的商品之间很常见。

In real-world analysis, zero XED is rare because all goods compete for limited consumer income. However, for practical purposes, many goods are treated as independent.

在实际分析中，零交叉弹性很少见，因为所有商品都在竞争有限的消费者收入。然而，为了实用目的，许多商品被视为相互独立。

6. Magnitude of XED | 交叉弹性的大小

The absolute value of XED indicates the strength of the relationship between two goods. A high positive value (e.g., +3.0) suggests very close substitutes, while a low positive value (e.g., +0.2) indicates weak substitutability.

交叉弹性的绝对值表示两种商品之间关系的强度。高正值（如+3.0）表明非常接近的替代品，而低正值（如+0.2）则表明可替代性较弱。

Similarly, a high negative value (e.g., -2.5) indicates strong complements, while a low negative value (e.g., -0.1) suggests weak complementary usage. Understanding this helps firms price their products strategically.

同样，高负值（如-2.5）表示强互补品，而低负值（如-0.1）则表明互补性较弱。理解这一点有助于企业制定定价策略。

Economists often use the following thresholds: if XED > +0.5, the goods are considered close substitutes; if XED < -0.5, they are considered close complements. Values between -0.5 and +0.5 indicate weak or no relationship.

经济学家通常使用以下阈值：如果XED > +0.5，则视为接近替代品；如果XED < -0.5，则视为接近互补品。介于-0.5和+0.5之间的值表明关系较弱或无关。

7. Determinants of XED | 交叉弹性的决定因素

Several factors influence the cross elasticity of demand between two goods. The most important factor is the degree of substitutability or complementarity, which depends on consumer preferences and product characteristics.

有几个因素影响两种商品之间需求的交叉弹性。最重要的因素是替代性或互补性的程度，这取决于消费者偏好和产品特征。

First, the availability of close substitutes: if many similar products exist, XED will be high. For example, different brands of washing powder are close substitutes, so XED is likely to be significantly positive.

首先，接近替代品的可用性：如果存在许多类似的产品，交叉弹性将很高。例如，不同品牌的洗衣粉是接近的替代品，因此交叉弹性可能显著为正。

Second, the time period considered: in the short run, consumers may not easily adjust their behaviour, so XED is lower. Over time, they can find alternatives or change consumption patterns, increasing XED.

其次，考虑的时间周期：短期内，消费者可能不易调整其行为，因此交叉弹性较低。随着时间的推移，他们能够找到替代品或改变消费模式，从而增加交叉弹性。

Third, the definition of the market: narrowly defined markets (e.g., a specific brand) show higher XED than broadly defined markets (e.g., all beverages).

第三，市场的定义：狭义定义的市场（如特定品牌）比广义定义的市场（如所有饮料）显示出更高的交叉弹性。

8. XED vs. Price Elasticity of Demand | 交叉弹性与需求价格弹性

Price elasticity of demand (PED) measures how quantity demanded responds to a change in the good’s own price. XED, in contrast, measures responsiveness to the price of another good.

需求价格弹性（PED）衡量的是需求量如何对商品自身价格的变化作出反应。相比之下，交叉弹性衡量的是对另一种商品价格变化的反应程度。

PED always focuses on a single product, while XED always involves two products. PED can be negative (for normal goods) or positive (for Giffen goods), but XED’s sign determines the relationship between goods.

需求价格弹性始终关注单一产品，而交叉弹性始终涉及两种产品。需求价格弹性可以是负的（对于正常商品）或正的（对于吉芬商品），但交叉弹性的符号决定了商品之间的关系。

For business decisions, both elasticities are useful. PED helps set the price of a firm’s own product, while XED helps anticipate the impact of competitors’ pricing strategies.

对于商业决策，这两种弹性都很有用。需求价格弹性有助于制定企业自身产品的价格，而交叉弹性则有助于预测竞争对手定价策略的影响。

Moreover, XED can be used to identify the competitive structure of a market. High positive XED indicates a competitive market with many substitutes, while low or zero XED suggests a monopoly or niche market.

此外，交叉弹性可用于识别市场的竞争结构。高正交叉弹性表明一个具有许多替代品的竞争市场，而低或零交叉弹性则表明垄断或利基市场。

9. Applications of XED | 交叉弹性的应用

Firms use XED to make pricing and marketing decisions. If a firm knows that its product is a close substitute for a rival’s product, it may respond aggressively to price cuts or use non-price competition.

企业利用交叉弹性来制定定价和营销决策。如果企业知道其产品是竞争对手产品的接近替代品，它可能会对降价作出积极反应，或使用非价格竞争手段。

For example, a company producing coffee might monitor the XED between coffee and tea. If XED is high, a fall in tea prices could significantly reduce coffee sales, prompting the firm to adjust its marketing strategy.

例如，一家生产咖啡的公司可能会监测咖啡和茶之间的交叉弹性。如果交叉弹性很高，茶价下跌可能显著减少咖啡销量，促使公司调整其营销策略。

Governments also use XED when designing indirect taxes or subsidies. For instance, if two goods are complements, taxing one good (e.g., fuel) can reduce the demand for the other (e.g., cars), achieving a policy goal such as reducing pollution.

政府在设计间接税或补贴时也使用交叉弹性。例如，如果两种商品是互补品，对一种商品征税（如燃料）会减少另一种商品（如汽车）的需求，从而实现减少污染等政策目标。

In merger and acquisition analysis, regulators examine XED. A high positive XED between two merging firms indicates that they are competitors, which might lead to a monopoly concern.

在并购分析中，监管机构会审查交叉弹性。如果两个合并企业之间的交叉弹性为正且很高，则表明它们是竞争对手，这可能会引起垄断方面的担忧。

10. Limitations of XED | 交叉弹性的局限性

Despite its usefulness, XED has several limitations. First, it assumes other factors remain constant (ceteris paribus), which is rare in real-world markets.

尽管交叉弹性很有用，但它有几个局限性。首先，它假设其他因素保持不变（ceteris paribus），而在现实市场中这很少见。

Second, XED values may change over time due to shifts in consumer tastes, income levels, or technology. A coefficient calculated for one period may not remain valid for another.

其次，由于消费者品味、收入水平或技术的变化，交叉弹性值可能会随时间变化。在某一时期计算出的系数可能不适用于另一个时期。

Third, measuring XED requires accurate data on two goods, which may not always be available. Small errors in data can lead to large errors in the XED estimate, making it unreliable for precise predictions.

第三，测量交叉弹性需要两种商品的准确数据，而这些数据并不总是可获得的。数据中的小误差可能导致交叉弹性估算中的大误差，使其在精确预测方面不可靠。

Finally, XED is a static measure and does not capture dynamic interactions. For example, a price change might have a lagged effect, which is not accounted for in the simple formula.

最后，交叉弹性是一种静态测量，无法捕捉动态相互作用。例如，价格变化可能产生滞后效应，而简单的公式并未考虑这一点。

11. Summary and Exam Tips | 总结与考试提示

In summary, cross elasticity of demand is a key concept that shows how the quantity demanded of one good responds to a change in the price of another. A positive XED indicates substitutes, a negative XED indicates complements, and zero indicates unrelated goods.

总之，需求的交叉弹性是一个关键概念，显示了一种商品的需求量如何对另一种商品价格的变动作出反应。正的交叉弹性表明替代品，负的交叉弹性表明互补品，零则表明无关商品。

For exams, remember the formula: XED = %ΔQd of Good A / %ΔP of Good B. Always interpret the sign and magnitude, and give real-world examples to illustrate your points.

在考试中，记住公式：XED = %ΔQd of商品A / %ΔP of商品B。始终解释符号和大小，并给出实际例子来说明你的观点。

Practice calculating XED with different price and quantity changes, and understand the factors that affect its value. This will help you answer both calculation and essay questions effectively.

练习用不同的价格和数量变化来计算交叉弹性，并理解影响其价值的因素。这将帮助你有效回答计算题和论文题。

Published by TutorHao | Economics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

Cross Elasticity of Demand | 需求的交叉弹性