📚 Cross Elasticity of Demand | 需求交叉弹性
Cross elasticity of demand is a key concept in A-Level Economics because it links the markets for different goods. It explains how the demand for one product responds when the price of another product changes, helping firms and policymakers understand competitive relationships and complementary links in the economy.
需求交叉弹性是 A-Level 经济学中的一个关键概念，因为它将不同商品的市场联系起来。它解释了一种产品的需求如何响应另一种产品价格的变化，帮助企业和政策制定者理解经济中的竞争关系和互补联系。
1. Definition of Cross Elasticity of Demand | 需求交叉弹性的定义
Cross elasticity of demand (XED) measures the responsiveness of the quantity demanded of one good to a change in the price of another good. It shows how demand for product A reacts when the price of product B changes, holding other factors constant.
需求交叉弹性（XED）衡量一种商品的需求量对另一种商品价格变化的反应程度。它表明当商品 B 的价格发生变化时，商品 A 的需求量如何变动，并假定其他因素保持不变。
XED is particularly important because many goods are related in consumption. A change in the price of one product can shift the demand curve for a related product, rather than causing a movement along its own demand curve.
交叉弹性尤为重要，因为许多商品在消费中相互关联。一种商品价格的变化会使相关商品的需求曲线发生移动，而不是沿着该商品自身需求曲线的移动。
2. Formula and Calculation | 公式与计算
The formula for cross elasticity of demand is:
需求交叉弹性的公式为：
XED = %ΔQd (good A) ÷ %ΔP (good B)
For example, if a 10% rise in the price of coffee increases the quantity demanded of tea by 5%, the XED is +0.5. The percentage changes are calculated using the midpoint formula where data permits.
例如，如果咖啡价格上升 10% 使茶的需求量增加 5%，则 XED 为 +0.5。在数据允许的情况下，百分比变化通常使用中点公式计算。
Because price and quantity changes can be positive or negative, the sign of XED is meaningful. Economists always report XED with its sign, unlike price elasticity of demand where the sign is often ignored.
由于价格和数量的变化可以是正数或负数，XED 的符号具有经济含义。经济学家在报告 XED 时总是保留其符号，而不像需求价格弹性那样通常忽略负号。
3. Interpreting the Sign: Substitutes | 解读符号：替代品
A positive cross elasticity of demand indicates that the two goods are substitutes. When the price of good B rises, consumers switch away from B and buy more of good A, so the quantity demanded of A increases.
正的交叉弹性表明两种商品是替代品。当商品 B 的价格上升时，消费者会减少购买 B，转而购买更多商品 A，因此 A 的需求量增加。
For close substitutes, the positive XED value tends to be large. Examples include Coca-Cola and Pepsi, butter and margarine, or bus travel and train travel on the same route.
对于密切的替代品，正的 XED 数值往往较大。例如可口可乐与百事可乐、黄油与人造黄油，或同一线路上的公共汽车与火车出行。
The stronger the substitutability, the greater the shift in demand for good A when the price of good B changes, and hence the higher the positive XED.
替代性越强，当商品 B 的价格变化时，商品 A 的需求移动就越大，因此正交叉弹性值越高。
4. Interpreting the Sign: Complements | 解读符号：互补品
A negative cross elasticity of demand indicates that the two goods are complements. When the price of good B rises, consumers buy less of B, and therefore they also buy less of good A, which is used together with B.
负的交叉弹性表明两种商品是互补品。当商品 B 的价格上升时，消费者减少购买 B，因此也减少购买与 B 一起使用的商品 A。
For strong complements, the negative XED value tends to be large in absolute terms. Examples include printers and ink cartridges, cars and petrol, or smartphones and mobile apps.
对于强互补品，负的 XED 绝对值往往较大。例如打印机与墨盒、汽车与汽油、智能手机与移动应用程序。
If the price of petrol rises sharply, the demand for cars that are fuel-intensive may fall, giving a negative XED between petrol and such vehicles.
如果汽油价格大幅上涨，高油耗汽车的需求可能下降，从而使汽油与这类汽车之间出现负的交叉弹性。
5. Zero Cross Elasticity: Unrelated Goods | 零交叉弹性：无关商品
When the cross elasticity of demand is zero or very close to zero, the two goods are said to be unrelated or independent. A change in the price of one good has no significant effect on the quantity demanded of the other.
当交叉弹性为零或非常接近零时，这两种商品被称为无关商品或独立商品。一种商品的价格变化对另一种商品的需求量没有显著影响。
For example, a change in the price of toothpaste is unlikely to affect the demand for bananas. The demand curves for unrelated goods do not shift in response to each other’s price changes.
例如，牙膏价格的变化不太可能影响香蕉的需求。无关商品的需求曲线不会因彼此价格变化而移动。
In reality, many goods have small positive or negative XED values even if they appear unrelated, because income effects and consumer budget constraints can create weak links.
在现实中，许多商品即使看似无关，也可能有较小的正或负 XED 值，因为收入效应和消费者预算约束会产生微弱的联系。
6. Magnitude and Strength of Relationship | 弹性大小与关系强度
The absolute size of XED indicates the strength of the relationship between two goods. A larger positive value means closer substitutes, while a larger negative absolute value means closer complements.
XED 的绝对值大小表明两种商品之间关系的强度。正数越大表示替代品越接近，负数绝对值越大表示互补品越接近。
There is no fixed threshold, but many exam examples treat XED values above +1 or below -1 as strong relationships, and values between 0 and ±1 as weaker relationships. However, this is only a guide.
虽然没有固定门槛，但许多考试例子将 XED 大于 +1 或小于 -1 视为强关系，而将 0 到 ±1 之间视为较弱关系。但这只是一个参考。
The magnitude also matters for firms because a high positive XED means a price rise by a rival will significantly boost the firm’s own sales, while a high negative XED means a fall in the price of a complement could greatly increase demand.
弹性大小对企业也很重要，因为较高的正 XED 意味着竞争对手提价会显著增加本企业销量，而较高的负 XED 意味着互补品降价可能大幅增加需求。
7. Determinants of XED | 影响交叉弹性的因素
The main determinant of XED is how closely related the two goods are in consumption. Goods that satisfy similar wants or are used together tend to have stronger positive or negative XED values.
影响 XED 的主要因素是两种商品在消费中的关联程度。满足相似需求或需要一起使用的商品往往具有更强的正或负 XED 值。
Consumer perception also matters: even if two products are technically different, if consumers view them as close substitutes, the XED will be high. Brand loyalty can reduce substitutability and hence lower XED.
消费者认知也很重要：即使两种产品在技术上不同，如果消费者认为它们是接近的替代品，XED 就会较高。品牌忠诚度会降低替代性，从而降低 XED。
The time period can influence XED, as consumers need time to adjust their consumption habits. Over longer periods, more substitutes may become available, raising positive XED values.
时间周期也会影响 XED，因为消费者需要时间调整消费习惯。在较长时间内，可能会出现更多替代品，从而提高正的 XED 值。
8. Business Applications of XED | 交叉弹性的商业应用
Firms use XED to assess the impact of competitors’ pricing strategies. If a rival cuts prices, a firm with a high positive XED between its product and the rival’s product may lose significant sales, so it may need to respond.
企业利用 XED 来评估竞争对手定价策略的影响。如果竞争对手降价，本企业产品与竞争对手产品之间的正 XED 较高，企业可能会失去大量销售，因此需要作出反应。
XED also helps in product line pricing. Firms that sell complements, such as razors and blades, may lower the price of one product to increase demand for the other, based on negative XED.
XED 也有助于产品线定价。销售互补品的企业（如剃须刀和刀片）可以根据负 XED 降低一种产品的价格，以增加另一种产品的需求。
Marketing managers use XED to identify close competitors and potential market boundaries. A high positive XED suggests that two brands are in the same market and competing directly.
营销经理利用 XED 识别密切的竞争对手和潜在的市场边界。较高的正 XED 表明两个品牌处于同一市场并直接竞争。
9. XED and Market Structure | 交叉弹性与市场结构
Cross elasticity of demand can help define an industry or market. If two products have a high positive XED, they are close substitutes and should be considered part of the same market.
需求交叉弹性有助于界定一个行业或市场。如果两种产品具有较高的正 XED，它们是接近的替代品，应被视为同一市场的一部分。
This is significant in competition policy. Regulators may use XED to decide whether a proposed merger would reduce competition by combining two close substitutes with high positive XED.
这在竞争政策中具有重要意义。监管机构可以利用 XED 来判断一项拟议合并是否会因为将两个具有高正 XED 的密切替代品合并而减少竞争。
Conversely, if XED is low between two firms’ products, they may operate in separate markets, so a merger is less likely to harm consumers through reduced competition.
相反，如果两家公司的产品之间 XED 较低，它们可能在不同的市场中经营，因此合并通过减少竞争而损害消费者的可能性较小。
10. Limitations and Common Confusions | 局限性与常见混淆
One common confusion is between cross elasticity of demand and price elasticity of demand. Price elasticity measures the response of quantity demanded to a change in the good’s own price; XED measures the response to another good’s price.
一个常见的混淆是需求交叉弹性与需求价格弹性之间的区别。价格弹性衡量需求量对商品自身价格变化的反应；XED 衡量的是对另一种商品价格变化的反应。
Another limitation is that XED estimates can vary over time and across different consumer groups. A positive XED at one price level may become negative at another if goods switch from substitutes to complements in consumers’ usage.
另一个局限是 XED 的估计值可能随时间和不同消费者群体而变化。在某个价格水平上为正的 XED，可能在另一个价格水平上变为负值，因为商品在消费者使用中可能从替代品变为互补品。
Students should also avoid simply reporting the sign without interpretation. The sign tells you substitutes or complements; the size tells you the strength of the relationship.
学生还应避免只报告符号而不作解释。符号说明是替代品还是互补品；数值大小说明关系的强弱。
Published by TutorHao | Economics Revision Series | aleveler.com
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