📚 Year 8 CAIE Economics: Formulae & Theorems Quick Reference Handbook | Year 8 CAIE 经济：公式定理速查手册
This handbook is your fast-track revision guide for Year 8 CAIE Economics. It brings together all the essential formulae, laws and core theorems you need to master – from scarcity and opportunity cost to market equilibrium, elasticity and profit maximisation. Each concept is presented as a concise point, first in English then in Chinese, so you can switch between languages with ease.
本手册是 Year 8 CAIE 经济学的快速复习指南，汇集了所有必须掌握的公式、定律与核心定理，从稀缺性、机会成本到市场均衡、弹性与利润最大化。每个概念都采用“先英文后中文”的简洁配对形式，方便你在双语之间轻松切换。
1. The Basic Economic Problem: Scarcity and Choice | 基本经济问题：稀缺与选择
Resources (land, labour, capital, enterprise) are limited, while human wants are unlimited. This situation is called scarcity. Because of scarcity, individuals, firms and governments must make choices about how to use resources.
资源（土地、劳动、资本、企业）是有限的，而人类的欲望是无限的。这种状况被称为稀缺性。由于稀缺性的存在，个人、企业和政府必须就如何使用资源做出选择。
The three fundamental economic questions arising from scarcity are: What to produce? How to produce? For whom to produce?
由稀缺性引发的三个基本经济问题是：生产什么？如何生产？为谁生产？
2. Opportunity Cost Formula | 机会成本公式
Opportunity cost is the value of the next best alternative that is forgone when a choice is made. Every economic decision involves an opportunity cost.
机会成本是指做出一种选择时所放弃的次优替代方案的价值。每一个经济决策都包含着机会成本。
Opportunity Cost = Value of next best alternative forgone
机会成本 = 所放弃的次优替代方案的价值
For example, if a student spends two hours studying economics instead of working part-time and earning £15, the opportunity cost of studying is £15.
例如，如果一名学生花费两小时学习经济学，而不是去做兼职赚取 15 英镑，那么学习的机会成本就是这 15 英镑。
3. Factors of Production | 生产要素
There are four factors of production that turn inputs into goods and services:
生产要素共有四种，它们将投入转化为商品和服务：
Land – all natural resources (e.g. soil, water, minerals). The reward is rent.
土地 – 所有自然资源（如土壤、水、矿产）。其报酬是地租。
Labour – human effort, both physical and mental. The reward is wages.
劳动 – 人类体力和脑力的付出。其报酬是工资。
Capital – man-made goods used to produce other goods (e.g. machinery, tools). The reward is interest.
资本 – 用于生产其他商品的人造物品（如机器、工具）。其报酬是利息。
Enterprise – the ability to combine the other three factors, taking risks. The reward is profit.
企业 – 组合其他三种要素并承担风险的能力。其报酬是利润。
4. Demand and the Law of Demand | 需求与需求定律
Demand is the quantity of a good or service that consumers are willing and able to buy at various prices over a given period, ceteris paribus (all else being equal).
需求是指在给定时期内、其他条件不变（ceteris paribus）的情况下，消费者愿意并能够购买的商品或服务的数量。
The Law of Demand: As price rises, quantity demanded falls; as price falls, quantity demanded rises.
需求定律：价格上升，需求量下降；价格下降，需求量上升。
A movement along the demand curve is caused by a change in price (change in quantity demanded). A shift of the entire demand curve is caused by changes in other factors such as income, tastes, prices of related goods, and population.
价格变化引起沿需求曲线的移动（需求量变动）。而收入、偏好、相关商品价格和人口等其他因素的变化，则会引起整条需求曲线的平移。
5. Supply and the Law of Supply | 供给与供给定律
Supply is the quantity of a good or service that producers are willing and able to offer for sale at various prices over a given period, ceteris paribus.
供给是指在给定时期内、其他条件不变（ceteris paribus）的情况下，生产者愿意并能够提供出售的商品或服务的数量。
The Law of Supply: As price rises, quantity supplied rises; as price falls, quantity supplied falls.
供给定律：价格上升，供给量上升；价格下降，供给量下降。
A movement along the supply curve occurs when price changes. A shift of the supply curve is caused by changes in costs of production, technology, taxes, subsidies, and the number of sellers.
价格变化引起沿供给曲线的移动。生产成本、技术、税收、补贴和卖家数量的变化会引起供给曲线的平移。
6. Market Equilibrium | 市场均衡
Market equilibrium occurs where the quantity demanded equals the quantity supplied at a given price. The equilibrium price is also called the market-clearing price.
市场均衡发生在给定价格下需求量等于供给量时。均衡价格也称为市场出清价格。
Equilibrium condition: Qd = Qs
均衡条件：需求量 = 供给量
When the market price is above equilibrium, there is excess supply (surplus), pushing the price down. When the price is below equilibrium, there is excess demand (shortage), pushing the price up. The market tends to move towards equilibrium automatically.
当市场价格高于均衡价格时，会出现超额供给（过剩），推动价格下降。当价格低于均衡价格时，会出现超额需求（短缺），推动价格上升。市场会自发趋向于均衡。
7. 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 price.
需求价格弹性衡量需求量对价格变化的反应程度。
PED = (% Change in Quantity Demanded) / (% Change in Price)
PED = (需求量变动的百分比) / (价格变动的百分比)
t is usually negative, but we often ignore the minus sign and focus on the absolute value. |PED| > 1 means elastic demand (consumers are very responsive). |PED| < 1 means inelastic demand (consumers are less responsive). |PED| = 1 is unitary elastic demand.
计算结果通常为负值，但我们通常忽略负号而关注绝对值。|PED| > 1 表示富有弹性（消费者反应敏感）。|PED| < 1 表示缺乏弹性（消费者反应不敏感）。|PED| = 1 为单位弹性。
8. Total Revenue, Total Cost and Profit | 总收入、总成本与利润
Firms are interested in their revenues, costs and the resulting profit. These relationships are central to understanding business decisions.
企业关注其收入、成本以及由此产生的利润。这些关系是理解商业决策的核心。
Total Revenue (TR) = Price (P) × Quantity Sold (Q)
总收入 (TR) = 价格 (P) × 销量 (Q)
Total Cost (TC) = Fixed Cost (FC) + Variable Cost (VC)
总成本 (TC) = 固定成本 (FC) + 可变成本 (VC)
Profit = Total Revenue – Total Cost
利润 = 总收入 – 总成本
per unit: AC = TC / Q. When price exceeds average cost, the firm makes a profit per unit.
平均成本 (AC) 表示单位成本：AC = 总成本 / 产量。当价格高于平均成本时，企业获得单位利润。
9. Marginal Analysis and Profit Maximisation | 边际分析与利润最大化
Marginal means “additional” or “one more”. Marginal cost (MC) is the extra cost of producing one more unit. Marginal revenue (MR) is the extra revenue from selling one more unit.
边际意为“额外的”或“多一个”。边际成本 (MC) 是多生产一单位产品所带来的额外成本。边际收益 (MR) 是多销售一单位产品所带来的额外收益。
isation Theorem: A firm maximises profit where Marginal Revenue = Marginal Cost (MR = MC).
利润最大化定理：企业在边际收益等于边际成本 (MR = MC) 时实现利润最大化。
e firm should reduce output. The rule MR = MC gives the profit-maximising level of output.
如果 MR > MC，多生产一单位带来的收益多于成本，利润增加。如果 MR < MC，额外一单位的成本高于收益，企业应减少产出。MR = MC 法则给出了利润最大化时的产出水平。
10. Production Possibility Frontier (PPF) | 生产可能性边界
A production possibility frontier (PPF) shows the maximum combinations of two goods an economy can produce using all its resources efficiently. It illustrates scarcity, choice and opportunity cost.
生产可能性边界 (PPF) 展示了一个经济体在充分利用其资源时所能生产的两种商品的最大组合。它说明了稀缺性、选择和机会成本。
Points on the curve are efficient (full employment of resources). Points inside the curve show underemployment or inefficiency. Points outside the curve are unattainable with current resources. Moving along the PPF involves an opportunity cost – to produce more of one good, you must give up some of the other.
曲线上的是有效率（资源充分利用）的点。曲线内的点表示资源未充分利用或低效率。曲线外的点是当前资源下无法达到的。沿 PPF 移动意味着机会成本——要多生产一种商品，就必须放弃部分另一种商品。
ost on a PPF = Δ Quantity of the good given up / Δ Quantity of the good gained
PPF 上的机会成本 = 放弃的商品数量变化量 ÷ 获得的商品数量变化量
11. Economic Systems | 经济体系
An economic system answers the three basic questions: What, How and For whom to produce. Three main types exist:
经济体系回答三个基本问题：生产什么、如何生产和为谁生产。主要有三种类型：
Market economy – decisions are made by the forces of demand and supply with little government intervention. The price mechanism allocates resources.
市场经济 – 决策由供需力量决定，政府干预极少。价格机制配置资源。
Command (planned) economy – the government owns most resources and makes all key economic decisions.
指令（计划）经济 – 政府拥有大部分资源，并做出所有关键经济决策。
Mixed economy – a combination of market forces and government intervention. Most real-world economies are mixed.
混合经济 – 市场力量与政府干预的结合。现实世界中大多数经济体都是混合经济。
12. Specialisation and Trade | 专业化与贸易
Specialisation occurs when individuals, firms or countries concentrate on producing a limited range of goods or tasks. It increases productivity because workers become more skilled and can use machinery more efficiently.
专业化是指个人、企业或国家集中生产有限范围的商品或任务。由于工人变得更加熟练并能更有效地使用机器，专业化提高了生产率。
The division of labour is a form of specialisation where the production process is broken into small, repeating tasks.
劳动分工是专业化的一种形式，将生产过程分解为许多重复的小任务。
Trade allows countries to specialise according to comparative advantage and then exchange goods. Both trading partners can consume beyond their own PPF, making them better off.
贸易使各国能够根据比较优势进行专业化生产，然后交换商品。贸易双方都可以消费超过本国 PPF 的商品组合，使自身状况变得更好。
Gains from trade: Consumption outside the PPF becomes possible.
贸易利得：消费超越本国 PPF 成为可能。
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