📚 Year 10 Cambridge Economics Formula & Theorem Quick Reference Handbook | 剑桥Year 10经济公式定理速查手册
This handbook compiles the essential formulas, definitions, and theorems you need to master for the Year 10 Cambridge IGCSE Economics course. Each section presents a core concept with its formula, followed by a brief English explanation and a matching Chinese explanation. Use this guide to revise quickly and reinforce your understanding of how economists measure and analyse the world.
本手册汇集了剑桥Year 10 IGCSE经济课程中必须掌握的核心公式、定义和定理。每个小节呈现一个核心概念及其公式，先给出英文解释，再配上对应的中文解释。借助这份指南，你可以快速复习并强化对经济学家如何衡量和分析世界的理解。
1. Scarcity and Opportunity Cost | 稀缺性与机会成本
Scarcity means that wants are unlimited but resources are finite, forcing choices to be made. Opportunity cost is the next best alternative forgone when a choice is made.
稀缺性意味着欲望无限但资源有限，迫使人们做出选择。机会成本是做出某项选择时所放弃的次优选项。
The formula for opportunity cost is not numeric but a statement: when you allocate a resource to one use, the opportunity cost is the value of the best alternative use you give up.
机会成本的公式并非数字表达，而是陈述：当你将资源投入一种用途时，机会成本便是你放弃的最佳替代用途的价值。
2. Law of Demand and Supply | 需求与供给定理
The law of demand states that, ceteris paribus, when the price of a good rises, the quantity demanded falls, and vice versa. The law of supply states that, ceteris paribus, when the price rises, the quantity supplied rises, and vice versa.
需求定理指出，在其他条件不变的情况下，商品价格上升，需求量下降，反之亦然。供给定理指出，在其他条件不变的情况下，价格上升，供给量增加，反之亦然。
These relationships are expressed in equilibrium analysis, not as a single formula, but they underpin the market mechanism.
这些关系在均衡分析中体现，并非单一公式，但它们构成了市场机制的基础。
3. Price Elasticity of Demand (PED) | 需求价格弹性
PED measures the responsiveness of quantity demanded to a change in price. Formula: PED = (% change in quantity demanded) / (% change in price).
PED衡量需求量对价格变化的反应程度。公式：PED = (需求量变动百分比) / (价格变动百分比)。
If PED > 1, demand is elastic (quantity changes proportionally more than price). If PED = 1, it is unit elastic. If PED < 1, demand is inelastic.
如果 PED > 1，需求富有弹性（需求量变动比例大于价格变动比例）。如果 PED = 1，为单位弹性。如果 PED < 1，需求缺乏弹性。
PED = (ΔQd / Qd) × 100 ÷ (ΔP / P) × 100
4. Price Elasticity of Supply (PES) | 供给价格弹性
PES measures the responsiveness of quantity supplied to a change in price. Formula: PES = (% change in quantity supplied) / (% change in price).
PES衡量供给量对价格变化的反应程度。公式：PES = (供给量变动百分比) / (价格变动百分比)。
Elastic supply means producers can quickly adjust output; inelastic supply means they cannot. The division point is 1, just as with PED.
供给富有弹性意味着生产者能够快速调整产量；缺乏弹性则意味着难以调整。区分点同样是1，与PED一样。
PES = (ΔQs / Qs) × 100 ÷ (ΔP / P) × 100
5. Income Elasticity of Demand (YED) | 需求收入弹性
YED measures how quantity demanded responds to a change in income. Formula: YED = (% change in quantity demanded) / (% change in income).
YED衡量需求量对收入变化的反应程度。公式：YED = (需求量变动百分比) / (收入变动百分比)。
If YED is positive, the good is a normal good; if YED is negative, it is an inferior good. For normal goods, YED > 1 indicates a luxury, YED between 0 and 1 a necessity.
如果 YED 为正，该商品为正常品；如果 YED 为负，则为低档品。对于正常品，YED > 1 表示为奢侈品，YED 在 0 到 1 之间表示为必需品。
YED = (ΔQd / Qd) × 100 ÷ (ΔY / Y) × 100
6. Cross Elasticity of Demand (XED) | 需求交叉弹性
XED measures the responsiveness of demand for one good (A) to a change in the price of another good (B). Formula: XED = (% change in quantity demanded of good A) / (% change in price of good B).
XED衡量一种商品（A）的需求量对另一种商品（B）价格变化的反应程度。公式：XED = (商品A需求量变动百分比) / (商品B价格变动百分比)。
If XED is positive, the goods are substitutes; if XED is negative, they are complements; if XED is zero, they are unrelated.
如果 XED 为正，则两种商品互为替代品；如果 XED 为负，则为互补品；如果 XED 为零，则互不相关。
XED = (ΔQdA / QdA) × 100 ÷ (ΔPB / PB) × 100
7. Total, Average, and Marginal Cost/Revenue | 总成本/收益、平均成本/收益与边际成本/收益
Total cost (TC) = Total fixed cost (TFC) + Total variable cost (TVC). Average cost (AC) = TC / Quantity. Marginal cost (MC) = ΔTC / ΔQ. For revenue, total revenue (TR) = Price × Quantity. Average revenue (AR) = TR / Q = Price. Marginal revenue (MR) = ΔTR / ΔQ.
总成本 (TC) = 总固定成本 (TFC) + 总可变成本 (TVC)。平均成本 (AC) = TC / 产量。边际成本 (MC) = ΔTC / ΔQ。对于收益，总收益 (TR) = 价格 × 销售量。平均收益 (AR) = TR / Q = 价格。边际收益 (MR) = ΔTR / ΔQ。
Profit maximisation occurs where MC = MR, a fundamental theorem in production.
利润最大化出现在 MC = MR 时，这是生产理论中的基本原理。
Profit = TR – TC
8. Market Equilibrium and Surplus/Shortage | 市场均衡与过剩/短缺
Market equilibrium occurs where quantity demanded equals quantity supplied: Qd = Qs. At any price above equilibrium, a surplus exists (Qs > Qd); at any price below equilibrium, a shortage exists (Qd > Qs).
市场均衡出现在需求量等于供给量时，即 Qd = Qs。任何高于均衡价格的价格都会产生过剩（Qs > Qd）；任何低于均衡价格的价格都会产生短缺（Qd > Qs）。
The free market adjusts through price mechanism until equilibrium is restored.
自由市场通过价格机制进行调整，直至恢复均衡。
9. Multiplier Effect | 乘数效应
The multiplier measures how much national income changes as a result of an initial change in one of the injections (investment, government spending, exports). The simple multiplier formula is: Multiplier = 1 / (1 – MPC) = 1 / MPS, where MPC is the marginal propensity to consume and MPS is the marginal propensity to save.
乘数衡量国民收入因注入项（投资、政府支出、出口）的初始变化而发生的变化程度。简单乘数公式为：乘数 = 1 / (1 – MPC) = 1 / MPS，其中 MPC 是边际消费倾向，MPS 是边际储蓄倾向。
Thus, the change in national income = Initial injection × Multiplier.
因此，国民收入变动 = 初始注入 × 乘数。
Multiplier = 1 / (1 – MPC)
10. Gross Domestic Product (GDP) and Growth | 国内生产总值与增长
GDP can be measured by the expenditure approach: GDP = C + I + G + (X – M), where C = consumption, I = investment, G = government spending, X = exports, M = imports. Alternatively, the output and income methods also give the same total.
GDP 可通过支出法计算：GDP = C + I + G + (X – M)，其中 C 为消费，I 为投资，G 为政府支出，X 为出口，M 为进口。另外，产出法和收入法也会得出相同的结果。
Economic growth is typically the percentage change in real GDP from one year to the next: Growth rate = [(GDP year 2 – GDP year 1) / GDP year 1] × 100.
经济增长通常指实际 GDP 从一年到下一年变动的百分比：增长率 = [(GDP₂ – GDP₁) / GDP₁] × 100。
GDP Growth = (ΔReal GDP / Real GDP₀) × 100
11. Unemployment and Inflation Rates | 失业率与通胀率
Unemployment rate = (Number of unemployed / Labour force) × 100. Labour force includes those employed plus those actively seeking work.
失业率 = (失业人数 / 劳动力人数) × 100。劳动力人数包括就业者与积极寻找工作者。
Inflation rate is measured by the percentage change in a price index, commonly the Consumer Price Index (CPI): Inflation rate = [(CPI current – CPI previous) / CPI previous] × 100.
通胀率通过价格指数的百分比变动来衡量，通常使用消费者价格指数 (CPI)：通胀率 = [(CPI 当期 – CPI 前期) / CPI 前期] × 100。
Inflation = (ΔCPI / CPI₀) × 100
12. Exchange Rate and Terms of Trade | 汇率与贸易条件
Exchange rate is the price of one currency in terms of another. If £1 = $1.30, then to convert pounds to dollars multiply by 1.30; to convert dollars to pounds divide by 1.30.
汇率是一种货币以另一种货币表示的价格。如果 £1 = $1.30，那么将英镑换算成美元乘以 1.30；将美元换算成英镑则除以 1.30。
Terms of trade index measures the relative price of exports compared to imports: Terms of Trade = (Index of export prices / Index of import prices) × 100. An improvement occurs when export prices rise relative to import prices.
贸易条件指数衡量出口价格相对于进口价格的变动：贸易条件 = (出口价格指数 / 进口价格指数) × 100。当出口价格相对于进口价格上涨时，贸易条件改善。
TOT = (Export Price Index / Import Price Index) × 100
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