📚 Year 7 CAIE Economics: Formula & Theorem Quick Reference Handbook | 七年级CAIE经济学：公式定理速查手册
This quick reference handbook is written for Year 7 learners following the CAIE Economics curriculum. It pulls together the essential formulas, theorems and core definitions that appear most often in classwork, homework and topic tests. Each entry is kept short and clear so that you can find what you need in seconds.
本速查手册为学习CAIE经济学课程的七年级学生编写，集中整理了课堂、作业和单元测验中最常出现的基本公式、定理与核心定义。每个条目都简短清晰，让你能在数秒内找到所需内容。
Throughout the handbook, an English explanation is immediately followed by its Chinese translation. This parallel structure helps you build subject knowledge in both languages and makes revision faster and more effective.
整本手册中，英文解释之后紧接中文翻译，这种对照结构有助于你在两种语言中巩固学科知识，并使复习更快速、更高效。
1. Scarcity and Choice | 稀缺性与选择
Scarcity is the basic economic problem. It exists because our wants are unlimited but the resources available to satisfy them are limited. Land, labour, capital and enterprise are all finite.
稀缺性是基本的经济问题。它的存在是因为我们的欲望是无限的，但用来满足这些欲望的资源却是有限的。土地、劳动、资本和企业家才能都是有限的。
Because of scarcity, individuals, firms and governments must make choices. Every time a choice is made, something else is given up. This is summarised by the scarcity → choice → opportunity cost chain.
由于稀缺性，个人、企业和政府都必须做出选择。每次做出选择，就有其他东西被放弃。这可以用稀缺 → 选择 → 机会成本的链条来概括。
Theorem: Scarcity forces choice, and every choice involves a trade‑off.
定理：稀缺性迫使人们做出选择，而每个选择都涉及权衡取舍。
2. Opportunity Cost Formula | 机会成本公式
Opportunity cost is the value of the next best alternative that is given up when a decision is made. It is not the sum of all other options, only the best forgone alternative.
机会成本是做出决定时放弃的次优选择的价值。它不是所有其他选项的总和，仅指放弃的最佳替代选项。
Opportunity Cost = Value of the next best alternative given up
For example, if you have £10 and you choose to buy a book instead of a cinema ticket, and the cinema ticket was your next favourite option, the opportunity cost of the book is the enjoyment you would have gained from the cinema ticket.
例如，如果你有10英镑并选择买一本书而不是买一张电影票，且电影票是你次优的选择，那么这本书的机会成本就是你从电影票中本可获得的享受。
Opportunity cost can be expressed in money, time, or satisfaction. It is a central idea in economics because it reveals the true cost of any action.
机会成本可以用金钱、时间或满足感来表示。它是经济学的核心思想，因为它揭示了任何行动的真实成本。
3. Factors of Production | 生产要素
Resources used to produce goods and services are called factors of production. There are four factors, each with its own reward or payment.
用于生产商品和服务的资源被称为生产要素。共有四类要素，每一种都有其对应的回报或报酬。
| Factor | Definition | Reward |
|---|---|---|
| Land | Natural resources (soil, water, minerals, forests) | Rent |
| Labour | Human effort, both physical and mental | Wages / Salaries |
| Capital | Man‑made goods used to produce other goods (machinery, tools, factories) | Interest |
| Enterprise | The willingness to take risks and combine the other three factors | Profit |
Theorem: The four factors of production are land, labour, capital and enterprise; their respective rewards are rent, wages, interest and profit.
定理：四种生产要素为土地、劳动、资本和企业家才能；它们的回报分别为地租、工资、利息和利润。
4. Production Possibility Frontier (PPF) | 生产可能性边界
A PPF diagram shows the maximum combination of two goods that an economy can produce when all resources are fully and efficiently used. Points on the curve are efficient; points inside the curve show unemployed resources.
生产可能性边界图显示了一个经济体在全部资源得到充分有效利用时所能生产的两种商品的最大组合。曲线上的点表示有效率的生产；曲线内的点表示资源未能充分利用。
The typical concave (bowed‑out) shape of a PPF illustrates the law of increasing opportunity cost. As more of one good is produced, the opportunity cost of producing extra units tends to rise because resources are not equally suited to all tasks.
生产可能性边界通常内凹的形状反映了机会成本递增定律。随着一种商品产量增加，多生产额外一单位这种商品的机会成本往往会上升，因为资源并非同样适合所有任务。
Theorem: A PPF demonstrates scarcity (points beyond are unattainable), choice (where to produce along the curve) and opportunity cost (the slope).
定理：生产可能性边界展示了稀缺性（边界外的点无法达到）、选择（沿曲线在何处生产）和机会成本（曲线的斜率）。
5. Law of Demand | 需求定律
The law of demand states that, ceteris paribus (all other things being equal), as the price of a good rises, the quantity demanded of that good falls, and vice versa. There is an inverse relationship between price and quantity demanded.
需求定律指出，在其他条件不变的前提下，当一种商品的价格上升时，该商品的需求量下降；反之亦然。价格与需求量之间存在反向关系。
Individual demand can be written as a linear function:
Qd = a − bP
where Qd is quantity demanded, P is price, ‘a’ is the quantity demanded when price is zero, and ‘b’ shows how much Qd changes when price changes by £1.
其中 Qd 为需求量，P 为价格，a 是价格为零时的需求量，b 表示价格每变动1英镑时需求量的变化量。
A demand curve slopes downwards from left to right. A movement along the curve is caused by a change in price, whereas a shift of the whole curve is caused by changes in non‑price factors such as income, tastes or the price of related goods.
需求曲线从左向右向下倾斜。沿需求曲线的移动是由价格变化引起的，而整条曲线平移则是由收入、偏好或相关商品价格等非价格因素的变化引起的。
6. Law of Supply | 供给定律
The law of supply says that, ceteris paribus, as the price of a good increases, the quantity supplied also increases. Producers are willing to offer more for sale when they can earn higher revenue per unit.
供给定律指出，在其他条件不变的情况下，当一种商品的价格上升时，供给量也会增加。当生产者每单位能获得更高收入时，他们愿意提供更多产品用于出售。
A simple supply function can be written as:
Qs = c + dP
where Qs is quantity supplied, P is price, ‘c’ represents the minimum quantity supplied (often zero or negative), and ‘d’ is the slope coefficient.
其中 Qs 表示供给量，P 表示价格，c 表示最低供给量（常为零或负值），d 是斜率系数。
A supply curve typically slopes upwards. Changes in production costs, technology, taxes or subsidies shift the entire supply curve, while a change in price causes a movement along the supply curve.
供给曲线通常向右上方倾斜。生产成本、技术、税收或补贴的变化会使整条供给曲线平移，而价格变化则引起沿供给曲线的移动。
7. Market Equilibrium | 市场均衡
Market equilibrium occurs at the price where quantity demanded equals quantity supplied. At this point there is no excess demand (shortage) and no excess supply (surplus).
市场均衡出现在需求量等于供给量的价格水平上。在均衡点上既没有超额需求（短缺），也没有超额供给（过剩）。
Equilibrium condition: Qd = Qs
If the market price is above equilibrium, a surplus pushes the price down. If the market price is below equilibrium, a shortage pushes the price up. This automatic adjustment is sometimes called the invisible hand mechanism.
若市场价格高于均衡水平，过剩会促使价格下跌。若市场价格低于均衡水平，短缺会推动价格上涨。这种自动调节有时被称为“看不见的手”机制。
To find the exact equilibrium price and quantity from linear functions, equate Qd and Qs and solve for P, then substitute P back into either function.
要从线性函数求出确切的均衡价格和数量，可令 Qd 与 Qs 相等，解出 P，再将 P 代入任一函数求得数量。
8. Revenue, Cost and Profit Formulas | 收入、成本与利润公式
Total revenue (TR) is the income a firm receives from selling its output. It is calculated by multiplying the price per unit by the number of units sold.
总收入（TR）是企业销售产品所得到的收入。它等于每单位价格乘以销售数量。
Total Revenue = Price × Quantity sold or TR = P × Q
Total cost (TC) is the sum of all costs of production. It can be split into fixed costs (FC), which do not vary with output in the short run, and variable costs (VC), which do vary with output.
总成本（TC）是所有生产成本的总和。它可以分为固定成本（FC）和可变成本（VC）。在短期内固定成本不随产量变化，可变成本则随产量变化。
Total Cost = Fixed Cost + Variable Cost or TC = FC + VC
Profit is the difference between total revenue and total cost. A positive profit means the firm is earning more than it spends; a negative profit is a loss.
利润是总收入与总成本之间的差额。正数利润表示企业收入大于支出；负数利润为亏损。
Profit = Total Revenue − Total Cost or π = TR − TC
Example: A baker sells 200 loaves at £2.50 each. TR = £500. If total cost is £430, profit = £70.
示例：面包师以每个2.50英镑售出200条面包。总收入为500英镑。若总成本为430英镑，利润为70英镑。
9. Budget Constraint | 预算约束
A budget constraint shows all combinations of two goods that a consumer can afford with a given income and given prices. It is a useful tool for illustrating scarcity and choice at the individual level.
预算约束表示在既定收入和既定价格下消费者能够负担的两种商品的所有组合。它是说明个人层面稀缺与选择的有用工具。
The budget constraint equation is:
Y = P₁ × Q₁ + P₂ × Q₂
where Y is money income, P₁ and P₂ are the prices of good 1 and good 2, and Q₁ and Q₂ are the quantities purchased.
式中 Y 为货币收入，P₁ 和 P₂ 分别为商品1和商品2的价格，Q₁ 和 Q₂ 为购买量。
The slope of the budget line is:
Slope = −P₁ / P₂
This tells us how many units of good 2 must be given up to obtain one extra unit of good 1. An increase in income shifts the budget line outward; a change in one price rotates it.
它告诉我们，为了多获得一单位商品1必须放弃多少单位商品2。收入增加使预算线向外平移；某一种商品价格变动会引起预算线旋转。
10. Price Elasticity of Demand (Basic) | 需求价格弹性（基础）
Price elasticity of demand (PED) measures how responsive quantity demanded is to a change in price. It is calculated using the percentage‑change method.
需求价格弹性（PED）衡量需求量对价格变化的反应程度。它使用百分比变化法计算。
PED = (% change in quantity demanded) / (% change in price)
When the result is greater than 1 (ignoring the minus sign), demand is elastic — quantity changes by a greater percentage than price. When it is less than 1, demand is inelastic. A PED of exactly 1 is called unit elastic.
当结果的绝对值大于1时，需求富有弹性——数量变化的百分比大于价格变化的百分比。小于1时，需求缺乏弹性。等于1时称为单位弹性。
PED helps businesses decide if a price rise will increase or decrease total revenue. If demand is elastic, raising price lowers TR. If demand is inelastic, raising price raises TR.
需求价格弹性帮助企业判断提价会增加还是减少总收入。若需求富有弹性，提价会降低总收入；若缺乏弹性，提价则会增加总收入。
Example: If a 10% price rise causes a 5% fall in quantity demanded, PED = 5% / 10% = 0.5 (inelastic).
示例：若价格上涨10%导致需求量下降5%，PED = 5% / 10% = 0.5（缺乏弹性）。
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