📚 Year 11 CIE Economics: Formula & Theorem Quick Reference Handbook | CIE 经济：公式定理速查手册
This comprehensive quick reference guide covers all essential formulas and key theorems required for the Cambridge IGCSE Economics (0455) syllabus, designed for Year 11 students. Mastering these calculations and concepts is crucial for success in Paper 1 and Paper 2, where numerical application and definitional precision are tested.
这本全面的速查手册涵盖了剑桥 IGCSE 经济学（0455）大纲所要求的所有基本公式与核心定理，专为 Year 11 学生备战大考设计。熟练掌握这些计算与概念，是在注重数字应用与定义准确性的 Paper 1 和 Paper 2 中斩获高分的关键。
1. Price Elasticity of Demand (PED) | 需求价格弹性
Price elasticity of demand measures the responsiveness of quantity demanded to a change in the own price of a good. It helps firms predict revenue effects of price changes. The basic formula uses percentage changes to obtain a coefficient.
需求价格弹性衡量商品自身价格变动所引起的需求量反应程度。企业可利用它预测价格变动对总收益的影响。基础公式采用变动百分比来计算弹性系数。
PED = %Δ Quantity Demanded ÷ %Δ Price
需求价格弹性 = 需求量变动百分比 ÷ 价格变动百分比
as follows: if PED > 1 demand is price elastic; if PED = 1 demand is unit elastic; if PED < 1 demand is price inelastic. A perfectly inelastic demand has PED = 0, and a perfectly elastic demand has PED = infinity.
弹性系数通常为负值，但经济学家常忽略负号，关注绝对值。系数大于 1 表示需求富有弹性，等于 1 为单位弹性，小于 1 为缺乏弹性。完全无弹性需求 PED = 0，完全有弹性需求则趋近无穷大。
A key theorem is the relationship between PED and total revenue (TR). When demand is price elastic, a price decrease raises total revenue; when demand is price inelastic, a price decrease lowers total revenue. This is a direct numerical application for exam tables.
一条关键定则是 PED 与总收益（TR）的关系。需求富有弹性时，降价可增加总收益；需求缺乏弹性时，降价反而减少总收益。这是考试中常见的结合数据表格进行判断的考点。
2. Price Elasticity of Supply (PES) | 供给价格弹性
Price elasticity of supply measures how responsive quantity supplied is to a change in the market price. It depends mainly on the time period and the availability of resources.
供给价格弹性衡量市场价格变动对供给量的反应程度。它主要取决于时间长短以及资源的可获得性。
PES = %Δ Quantity Supplied ÷ %Δ Price
供给价格弹性 = 供给量变动百分比 ÷ 价格变动百分比
unit elastic, and less than 1 is inelastic supply. An extreme case of perfectly inelastic supply (PES = 0) exists when the quantity supplied cannot change at all in response to price, such as tickets for a sold-out concert in the immediate term.
供给弹性始终为正，因为价格与供给量同向变动。数值大于 1 为富有弹性，等于 1 为单位弹性，小于 1 为缺乏弹性。完全无弹性供给（PES = 0）的极端情况出现在短期内供给量完全无法改变时，比如一场售罄音乐会的当场门票。
3. Income Elasticity of Demand (YED) | 需求收入弹性
Income elasticity of demand shows how the demand for a good changes in response to a change in consumers' real income. It is used to classify normal and inferior goods.
需求收入弹性反映消费者的实际收入变动对某种商品需求的影响。它被用来区分正常商品和低档商品。
YED = %Δ Quantity Demanded ÷ %Δ Real Income
需求收入弹性 = 需求量变动百分比 ÷ 实际收入变动百分比
If YED is positive, the good is a normal good (demand rises as income rises). Within normal goods, YED > 1 indicates a luxury good, while 0 < YED < 1 indicates a necessity. If YED is negative, the good is an inferior good (demand falls as income rises). This categorisation is essential for interpreting data-response questions.
若 YED 为正，则为正常商品（收入增加，需求上升）。正常商品中，YED 大于 1 为奢侈品，介于 0 和 1 之间则为必需品。若 YED 为负，该商品为低档商品（收入上升但需求下降）。这个分类对于解读数据反应题至关重要。
4. Cross Elasticity of Demand (XED) | 需求交叉弹性
Cross elasticity of demand measures how the demand for one good (A) responds to a change in the price of another good (B). It helps identify substitutes and complements.
需求交叉弹性衡量一种商品（A）的需求对另一种商品（B）价格变动的反应程度，用于识别替代品与互补品。
XED = %Δ Quantity Demanded of Good A ÷ %Δ Price of Good B
需求交叉弹性 = 商品 A 需求量变动百分比 ÷ 商品 B 价格变动百分比
A positive XED indicates the two goods are substitutes (an increase in the price of B raises demand for A). A negative XED means the goods are complements (an increase in the price of B reduces demand for A). If XED is close to zero, the goods are unrelated. Numerical interpretation often appears in multiple-choice questions.
XED 为正说明两者互为替代品（B 涨价导致 A 的需求增加）；XED 为负说明两者为互补品（B 涨价导致 A 的需求下降）。若 XED 接近零，则两者无关。对弹性符号和数值的快速解读常见于选择题中。
5. Costs, Revenue and Profit | 成本、收益与利润
A firm's fundamental objective is to maximise profit. Understanding the structure of costs and revenue is vital for market analysis. The core identity connects all three concepts.
企业的根本目标是利润最大化。理解成本与收益的结构对市场分析至关重要。以下核心恒等式将三者联系在一起。
Total Revenue (TR) = Price × Quantity
总收益 (TR) = 价格 × 数量
Total Cost (TC) = Total Fixed Cost (TFC) + Total Variable Cost (TVC)
总成本 (TC) = 总固定成本 (TFC) + 总可变成本 (TVC)
Profit = Total Revenue − Total Cost
利润 = 总收益 − 总成本
ses, diseconomies of scale occur. Break-even occurs when TR = TC, meaning normal profit is earned but no supernormal profit.
平均成本（AC 或 ATC）等于总成本除以产出。当平均成本随产出增加而下降时，企业享有规模经济；反之则为规模不经济。盈亏平衡点出现在总收益等于总成本时，此时企业获得正常利润但无超额利润。
| Term | Formula |
|---|---|
| Average Total Cost (ATC) | TC ÷ Quantity |
| Average Fixed Cost (AFC) | TFC ÷ Quantity |
| Average Variable Cost (AVC) | TVC ÷ Quantity |
表格中的公式同样是高频考点：平均总成本 = 总成本 ÷ 产量；平均固定成本 = 总固定成本 ÷ 产量；平均可变成本 = 总可变成本 ÷ 产量。配合数据能快速绘制成本曲线。
6. Productivity and Average Cost | 生产率与平均成本
Labour productivity measures the efficiency of workers in the production process. Increases in productivity directly lower unit costs, boosting competitiveness.
劳动生产率衡量工人在生产过程中的效率。生产率的提升直接降低单位成本，增强企业竞争力。
Labour Productivity = Total Output ÷ Number of Workers
劳动生产率 = 总产出 ÷ 工人数量
Higher labour productivity reduces average variable cost and therefore average total cost, shifting the firm's cost curves downwards. An important theorem is that any improvement in productivity, ceteris paribus, will increase the economy's productive capacity and shift the production possibility curve (PPC) outwards.
劳动生产率提高会降低平均可变成本，进而拉低平均总成本，使企业的成本曲线下移。一条重要定理是：在其他条件不变的情况下，生产率的任何提升都会增加经济的生产能力，并使生产可能性曲线（PPC）向外移动。
7. Inflation Rate (CPI) | 通货膨胀率 (CPI)
Inflation is the sustained increase in the general price level. The Consumer Price Index (CPI) is the primary measure. The calculation involves a fixed basket of goods and a base year.
通货膨胀指整体物价水平持续上升。消费者价格指数（CPI）是主要衡量工具，其计算涉及一篮子固定商品和基年。
CPI = (Cost of basket in current year ÷ Cost of basket in base year) × 100
CPI =（当年一篮子费用 ÷ 基年一篮子费用）× 100
Once CPI figures are available for two consecutive periods, the inflation rate is calculated as the percentage change in the index. This is a typical numerical skill tested in IGCSE Economics.
获得连续两期的 CPI 数值后，通货膨胀率可通过指数变动的百分比算出。这是 IGCSE 经济中必考的计算技能。
Inflation Rate = [(CPI this year − CPI last year) ÷ CPI last year] × 100
通胀率 = [（今年 CPI − 去年 CPI）÷ 去年 CPI] × 100
Deflation (negative inflation rate) and disinflation (a fall in the inflation rate) must be distinguished. A key theorem is that cost-push inflation reduces real GDP, while demand-pull inflation can initially accompany rising output until full capacity is reached.
必须区分通货紧缩（负通胀率）与反通胀（通胀率下降）。重要定理是：成本推动型通胀会减少实际 GDP，而需求拉动型通胀在达到充分产能前可能暂时伴随产出增加。
8. Unemployment Rate | 失业率
The unemployment rate is a critical macroeconomic indicator. It expresses the percentage of the labour force that is willing and able to work but cannot find employment.
失业率是关键宏观经济指标，它表示愿意且有能力工作但找不到工作的劳动力占劳动力总量的百分比。
Unemployment Rate = (Number of Unemployed ÷ Labour Force) × 100
失业率 =（失业人数 ÷ 劳动力总数）× 100
The labour force includes all people of working age who are either in employment or actively seeking work. It excludes full-time students, retirees, homemakers not seeking paid work, and those unable to work. The formula may appear alongside definitions of cyclical, structural and frictional unemployment as underlying theorems.
劳动力包括所有处于工作年龄且已就业或正在积极寻找工作的人，不包括全日制学生、退休者、不寻求有酬工作的家庭主妇以及丧失工作能力者。公式常与周期性失业、结构性失业和摩擦性失业等定义性定理一同出现。
9. Gross Domestic Product (GDP) & GDP per Capita | 国内生产总值与人均GDP
Gross Domestic Product measures the total value of all final goods and services produced within a country in a given period. It is the prime indicator of economic size and growth.
国内生产总值衡量一经济体在一定时期内生产的所有最终产品和服务的总价值，是反映经济规模与增长的首要指标。
GDP per Capita = Real GDP ÷ Population
人均 GDP = 实际 GDP ÷ 人口
While IGCSE does not require the full expenditure approach (C + I + G + (X − M)) in complex calculations, students must recognise that GDP or national output can be measured by output, expenditure or income methods, which are theoretically identical. A vital comparison theorem is that an increase in nominal GDP may simply reflect inflation, so real GDP (adjusted for inflation) is used to show true economic growth. GDP per capita is a better living standard indicator than total GDP.
尽管 IGCSE 不要求用支出法（C + I + G + (X − M)）进行复杂计算，但学生必须认识到 GDP 或国民产出可通过产出法、支出法和收入法三种方法衡量，理论上三者相等。关键的对比定理是：名义 GDP 增长可能仅仅反映物价上涨，因此要用剔除通胀的实际 GDP 反映真实经济增长；人均 GDP 较 GDP 总量更能代表生活水平。
10. Terms of Trade | 贸易条件
The terms of trade indicate the relative movement of a country's export and import prices. An improvement in the terms of trade means a country can buy more imports for a given quantity of exports.
贸易条件反映一国进出口价格的相对变动。贸易条件改善意味着用既定出口量可以换回更多的进口品。
Terms of Trade Index = (Index of Export Prices ÷ Index of Import Prices) × 100
贸易条件指数 =（出口价格指数 ÷ 进口价格指数）× 100
An index above 100 relative to a base year signals an improvement; below 100 signals a deterioration. However, an improvement in the terms of trade is not always beneficial if it results from falling export volumes because demand for exports has collapsed. This paradox features in typical theorem-style analysis.
相较于基年，指数高于 100 表示贸易条件改善，低于 100 表示恶化。但若改善是因出口需求锐减导致出口量暴跌，则不一定有益。这个悖论是典型的定理式分析素材。
11. Opportunity Cost & Comparative Advantage | 机会成本与比较优势
Opportunity cost is the next best alternative forgone when an economic choice is made. It is the foundation of the basic economic problem of scarcity.
机会成本是作出经济选择时所放弃的次优选项，是稀缺性这一基本经济问题的理论基石。
A key computation for IGCSE is determining comparative advantage using opportunity cost ratios. A country has a comparative advantage in producing a good if it can produce it at a lower opportunity cost than another country. The formula involves comparing output ratios or input ratios.
IGCSE 的关键计算之一是利用机会成本比率确定比较优势。若一国生产某商品的机会成本低于另一国，它就拥有该商品的比较优势。计算涉及比较产出比率或投入比率。
Opportunity Cost of Good X = Units of Good Y sacrificed ÷ Units of Good X gained
商品 X 的机会成本 = 牺牲的商品 Y 单位数 ÷ 获得的商品 X 单位数
The theorem of comparative advantage states that even if one country has an absolute advantage in all goods, mutual gains from trade are still possible if countries specialise according to their comparative advantage and trade with each other.
比较优势定理指出，即便一国在所有商品上都具有绝对优势，只要各国根据各自的比较优势进行专业化生产并开展贸易，双方仍能从贸易中获益。
12. Market Equilibrium & Disequilibrium (Shortage/Surplus) | 市场均衡与非均衡（短缺与过剩）
Market equilibrium occurs where quantity demanded equals quantity supplied at a given price. It is the state of balance with no tendency for price change, ceteris paribus.
市场均衡出现在给定价格下需求量等于供给量之时。这是一种平衡状态，在其他条件不变下价格没有变动的趋势。
A surplus (excess supply) exists when the market price is above the equilibrium price: the quantity supplied exceeds the quantity demanded, putting downward pressure on price. A shortage (excess demand) exists when the market price is below the equilibrium price: the quantity demanded exceeds the quantity supplied, putting upward pressure on price.
当市场价格高于均衡价格时出现过剩（超额供给）：供给量大于需求量，价格承受下行压力。当市场价格低于均衡价格时出现短缺（超额需求）：需求量大于供给量，价格承受上行压力。
Surplus = Quantity Supplied − Quantity Demanded (at a given price)
过剩 = 供给量 − 需求量（在某一价格下）
Shortage = Quantity Demanded − Quantity Supplied (at a given price)
短缺 = 需求量 − 供给量（在某一价格下）
The fundamental theorem of the price mechanism is that prices act as a signal, incentive and rationing device, automatically moving markets towards equilibrium without central planning. Shortages and surpluses are temporary disequilibrium states that trigger price adjustments.
价格机制的基本定理是：价格充当信号、激励和配给功能，能自动引导市场趋向均衡而无需中央计划。短缺与过剩属于暂时性的非均衡状态，会触发价格调整过程。
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