📚 IB Economics: Comparing Price, Income and Cross Elasticities of Demand | IB经济：需求价格弹性、收入弹性与交叉弹性对比
Elasticities of demand are fundamental concepts in IB Economics that measure the responsiveness of quantity demanded to changes in various determinants. Among them, price elasticity of demand (PED), income elasticity of demand (YED), and cross elasticity of demand (XED) often cause confusion due to their similar calculations but distinct interpretations. This article provides a comprehensive comparison, clarifying definitions, formulas, determinants and real-world applications to help IB students master these concepts.
需求弹性是IB经济学中衡量需求量对各种决定因素变化的响应程度的基本概念。其中，需求价格弹性（PED）、需求收入弹性（YED）和需求交叉弹性（XED）因计算相似但解释不同而常常引起混淆。本文进行全面比较，澄清定义、公式、决定因素及实际应用，帮助IB学生掌握这些概念。
1. Defining the Three Elasticities | 定义三种弹性
Price elasticity of demand (PED) measures how much the quantity demanded of a good responds to a change in its own price. Income elasticity of demand (YED) measures how much the quantity demanded responds to a change in consumers’ income. Cross elasticity of demand (XED) measures how much the quantity demanded of one good responds to a change in the price of another good.
需求价格弹性（PED）衡量一种商品的需求量对其自身价格变化的反应程度。需求收入弹性（YED）衡量需求量对消费者收入变化的反应程度。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。
PED is typically negative due to the law of demand, except for Giffen goods. YED can be positive (normal goods) or negative (inferior goods). XED can be positive (substitutes), negative (complements) or zero (unrelated goods).
PED通常为负值（符合需求定律），吉芬商品除外。YED可为正值（正常品）或负值（低档品）。XED可为正值（替代品）、负值（互补品）或零（无关商品）。
2. Formulas and Calculations | 公式与计算
The standard formula for each elasticity uses percentage changes to allow comparison across different units and scales.
每种弹性的标准公式均采用百分比变动，以便在不同单位和尺度间进行比较。
PED = (%ΔQd) ÷ (%ΔP)
PED = （需求量变动百分比）÷（价格变动百分比）
YED = (%ΔQd) ÷ (%ΔY)
YED = （需求量变动百分比）÷（收入变动百分比）
XED = (%ΔQdA) ÷ (%ΔPB)
XED = （商品A需求量变动百分比）÷（商品B价格变动百分比）
IB often uses the midpoint formula for arc elasticity to avoid asymmetric results: PED = (ΔQd / average Qd) ÷ (ΔP / average P). However, the simple percentage change formula is also acceptable in many exam questions.
IB经常使用中点公式来计算弧弹性，以避免不对称结果：PED = (ΔQd / 平均Qd) ÷ (ΔP / 平均P)。然而许多考题也可接受简单的百分比变动公式。
3. Interpreting the Coefficients | 系数解读
Interpreting the calculated values correctly is essential for analysis and evaluation in IB exams.
正确解读计算出的数值对于IB考试中的分析和评估至关重要。
For PED: if |PED| > 1, demand is price elastic; if |PED| < 1, demand is price inelastic; if |PED| = 1, demand is unit elastic; if PED = 0, perfectly inelastic; if PED → ∞, perfectly elastic.
对于PED：如果 |PED| > 1，需求富有价格弹性；|PED| < 1，缺乏价格弹性；|PED| = 1，单位弹性；PED = 0，完全无弹性；PED → ∞，完全弹性。
For YED: YED > 0 indicates a normal good; YED > 1 indicates a luxury good; 0 < YED < 1 indicates a necessity; YED < 0 indicates an inferior good.
对于YED：YED > 0 表示正常品；YED > 1 表示奢侈品；0 < YED < 1 表示必需品；YED < 0 表示低档品。
For XED: XED > 0 means the two goods are substitutes; XED < 0 means they are complements; XED ≈ 0 means the goods are unrelated.
对于XED：XED > 0 表示两种商品互为替代品；XED < 0 表示互为互补品；XED ≈ 0 表示无关商品。
4. Determinants of Elasticity | 弹性的决定因素
PED determinants include the availability of close substitutes, the proportion of income spent on the good, the degree of necessity, the time horizon, and whether the good is habit-forming or addictive.
PED的决定因素包括：相近替代品的可获得性、商品支出占收入的比例、必需品程度、时间跨度以及商品是否具有成瘾性。
YED is largely determined by the nature of the good (necessity versus luxury) and the income level of consumers. For example, basic food items typically have low YED, while premium travel has high YED.
YED主要取决于商品的性质（必需品 vs 奢侈品）和消费者的收入水平。例如基本食品通常YED较低，而高端旅游的YED较高。
XED depends on how closely related two goods are as substitutes or complements. Strong brand loyalty or unique features can weaken the substitutability and thus reduce XED values.
XED取决于两种商品作为替代品或互补品的关联程度。强烈的品牌忠诚度或独特功能会削弱替代关系，从而降低XED值。
5. PED and Total Revenue | PED与总收益
A unique feature of PED is its direct link to total revenue (TR = P × Q). If demand is elastic, a price increase lowers TR, and a price decrease raises TR. If demand is inelastic, a price increase raises TR, and a price decrease lowers TR. When demand is unit elastic, TR is maximised and remains unchanged with small price changes.
PED的一个独特之处在于它与总收益（TR = P × Q）的直接联系。如果需求富有弹性，提价会降低总收益，降价会提高总收益。如果需求缺乏弹性，提价会提高总收益，降价会降低总收益。当需求为单位弹性时，总收益最大，且在小幅价格变化下保持不变。
YED and XED do not have a direct total revenue relationship in the same way, but they inform pricing and output decisions indirectly. For instance, a high positive XED with a rival’s product may force a firm to lower prices to maintain market share.
YED和XED与总收益没有同样直接的对应关系，但可间接影响定价和产量决策。例如，与竞争对手产品的高度替代关系（高正XED）可能迫使企业降价以维持市场份额。
6. YED and Types of Goods | 收入弹性与商品类型
YED classifies goods into normal and inferior. A normal good has positive YED; within this category, necessities have YED between 0 and 1, while luxuries have YED greater than 1. An inferior good has negative YED, meaning demand falls as income rises (e.g., budget-brand groceries).
YED将商品分为正常品和低档品。正常品的YED为正；其中必需品的YED在0到1之间，奢侈品的YED大于1。低档品的YED为负，意味着随着收入增加，需求反而下降（如平价食品）。
Firms use YED to forecast demand during economic cycles. Luxury goods producers benefit disproportionately in booms and suffer in recessions, whereas producers of necessities experience more stable demand.
企业利用YED预测经济周期中的需求。奢侈品生产商在繁荣期格外受益，在衰退期受挫严重，而必需品生产商的需求则更为稳定。
7. XED and Relationships Between Goods | 交叉弹性与商品间关系
XED reveals the degree of substitutability or complementarity between two goods. A high positive XED indicates close substitutes (e.g., two brands of bottled water). A high negative XED (in absolute terms) indicates strong complements (e
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