📚 Year 7 Cambridge Economics Formula & Theorem Quick Reference Handbook | Year 7 剑桥经济：公式定理速查手册
Welcome to your Year 7 Cambridge Economics quick reference. This handbook distills the essential formulas and theorems you will encounter as you begin exploring how people make choices, how markets work, and how we measure economic activity. Use it for fast revision and to build a strong foundation before moving on to IGCSE Economics.
欢迎使用你的 Year 7 剑桥经济速查手册。本手册浓缩了你在开始探索人们如何做出选择、市场如何运作以及我们如何衡量经济活动时会碰到的基本公式和定理。用它来快速复习，并在进入 IGCSE 经济学之前打下扎实基础。
1. Scarcity and Choice | 稀缺与选择
The fundamental economic problem is scarcity: our wants are unlimited, but the resources available to satisfy them are limited. This forces individuals, firms, and governments to make choices.
基本的经济问题是稀缺性：我们的欲望是无限的，但满足这些欲望的资源是有限的。这迫使个人、企业和政府做出选择。
Economics is the study of how society allocates its scarce resources among competing uses.
经济学研究社会如何将其稀缺资源配置到相互竞争的用途上。
The three basic economic questions are: What to produce? How to produce? For whom to produce?
三个基本经济问题是：生产什么？如何生产？为谁生产？
2. Opportunity Cost | 机会成本
Whenever a choice is made, something is given up. The opportunity cost of a decision is the value of the next best alternative foregone. It is not the sum of all rejected options, only the most attractive one you sacrificed.
每当做出一个选择时，总有一些东西被放弃。决策的机会成本是所放弃的次优选择的价值。它不是所有被拒绝选项的总和，而仅仅是你牺牲掉的最具吸引力的那一个。
For example, if a student has £20 and must choose between a cinema ticket (valued at £20) and a book (valued at £15), the opportunity cost of choosing the cinema is the book. If they value the book at £15, the real cost of the film is the foregone enjoyment of reading.
例如，如果一个学生有 20 英镑，必须在电影票（价值 20 英镑）和一本书（价值 15 英镑）之间做出选择，那么选择电影的机会成本就是那本书。如果那本书对他价值 15 英镑，那么看电影的真实成本就是放弃的阅读乐趣。
Opportunity cost = Value of next best alternative given up
机会成本 = 放弃的次优选项的价值
3. Production Possibility Frontier (PPF) | 生产可能性边界
A production possibility frontier shows the maximum combinations of two goods an economy can produce when all resources are fully and efficiently employed. It illustrates scarcity, choice, and opportunity cost.
生产可能性边界展示了一个经济体在资源被充分且有效利用时所能生产的两种商品的最大组合。它揭示了稀缺性、选择和机会成本。
Points on the curve are efficient. Points inside the curve represent unemployed resources or inefficiency. Points outside are unattainable with current resources.
曲线上的点是有效率的。曲线内的点代表资源未充分利用或低效率。曲线外的点在现有资源下无法达到。
The theorem of increasing opportunity cost states that as more of one good is produced, the opportunity cost of producing additional units rises. This is why the PPF is typically bowed outward.
机会成本递增定理指出，随着一种商品生产得更多，生产额外单位的机会成本会上升。这就是 PPF 通常向外弯曲的原因。
4. Law of Demand | 需求定律
The Law of Demand states that, ceteris paribus (all other things being equal), there is an inverse relationship between the price of a good and the quantity demanded. As price rises, quantity demanded falls; as price falls, quantity demanded rises.
需求定律指出，在其他条件不变的情况下，商品的价格与需求量之间存在反向关系。价格上升，需求量下降；价格下降，需求量上升。
A demand curve slopes downwards from left to right. This is due to the income effect (a lower price increases purchasing power) and the substitution effect (consumers switch away from relatively more expensive goods).
需求曲线从左向右向下倾斜。这是由于收入效应（价格降低提高购买力）和替代效应（消费者会远离相对更贵的商品）。
A change in price causes a movement along the demand curve (change in quantity demanded). A change in non-price factors (income, tastes, etc.) shifts the entire demand curve.
价格变动引起沿着需求曲线的移动（需求量变动）。非价格因素（收入、偏好等）的变动会使整条需求曲线移动。
Demand function: QD = f(P) where ∂QD/∂P < 0
需求函数：QD = f(P)，且 ∂QD/∂P < 0
5. Law of Supply | 供给定律
The Law of Supply states that, ceteris paribus, there is a direct relationship between price and quantity supplied. Higher prices incentivise producers to supply more because profit opportunities increase.
供给定律指出，在其他条件不变的情况下，价格与供给量之间存在正向关系。较高的价格激励生产者提供更多产量，因为盈利机会增加了。
A supply curve slopes upwards from left to right. Rising marginal costs of production mean firms need a higher price to cover the cost of extra units.
供给曲线从左向右向上倾斜。不断上升的生产边际成本意味着企业需要更高的价格来覆盖额外单位的成本。
A change in the good's own price causes a movement along the supply curve. Changes in production costs, technology, or the number of sellers shift the supply curve.
商品自身价格的变化引起沿着供给曲线的移动。生产成本、技术或卖家数量的变化会使供给曲线移动。
Supply function: QS = f(P) where ∂QS/∂P > 0
供给函数：QS = f(P)，且 ∂QS/∂P > 0
6. Market Equilibrium | 市场均衡
Equilibrium occurs where the quantity demanded equals the quantity supplied. At this point, there is no tendency for price to change. Graphically, it is where the demand and supply curves intersect.
均衡发生在需求量等于供给量的时候。在这一点上，价格没有变动的趋势。从图形上看，它是需求曲线和供给曲线的交点。
Equilibrium condition: QD = QS → Market-clearing price P* and quantity Q*
均衡条件：QD = QS → 市场出清价格 P* 和数量 Q*
Excess demand (shortage) arises when price is below equilibrium. Competition among buyers pushes the price up.
当价格低于均衡价格时会出现超额需求（短缺）。买家之间的竞争推高价格。
Excess supply (surplus) arises when price is above equilibrium. Competition among sellers pushes the price down.
当价格高于均衡价格时会出现超额供给（过剩）。卖家之间的竞争压低价格。
7. Total Revenue | 总收入
Total revenue (TR) is the income a firm receives from selling its output. It is a simple but vital calculation used to analyse business performance and the effects of price changes.
总收入（TR）是企业通过出售其产出所获得的收入。这是一个简单但至关重要的计算，用于分析企业业绩和价格变动的影响。
Total Revenue = Price × Quantity sold
总收益 = 价格 × 销售数量
Or simply: TR = P × Q
或者简写为：TR = P × Q
If a bakery sells 200 loaves at £1.50 each, TR = 200 × £1.50 = £300.
如果一家面包店以每块 1.50 英镑的价格售出 200 块面包，总收入 = 200 × 1.50 = 300 英镑。
The effect of a price change on total revenue depends on the price elasticity of demand (see Section 9).
价格变动对总收入的影响取决于需求价格弹性（见第 9 节）。
8. Costs and Profit | 成本与利润
Firms need to understand their costs to make production decisions. Profit is the reward for risk-taking and efficient operation.
企业需要了解自己的成本以做出生产决策。利润是对承担风险和高效经营的回报。
| Concept 概念 | Formula 公式 |
|---|---|
| Total Cost (TC) 总成本 | TC = Fixed Cost (FC) + Variable Cost (VC) |
| Average Cost (AC) 平均成本 | AC = TC ÷ Q |
| Profit (π) 利润 | Profit = Total Revenue − Total Cost |
reaks even when TR = TC. If TR > TC, the firm makes a profit; if TR < TC, it makes a loss.
当 TR = TC 时企业盈亏平衡。如果 TR > TC，企业盈利；如果 TR < TC，企业亏损。
For example, if a stall sells lemonade with FC = £10 (rent) and VC = £0.50 per cup, selling 50 cups at £1 each gives TR = £50, TC = £10 + £25 = £35, so profit = £15.
例如，如果一个摊位出售柠檬水，固定成本为 10 英镑（租金），每杯可变成本 0.50 英镑，以每杯 1 英镑售出 50 杯，则 TR = 50 英镑，TC = 10 + 25 = 35 英镑，利润 = 15 英镑。
9. Price Elasticity of Demand (PED) | 需求价格弹性
Price elasticity of demand measures how responsive quantity demanded is to a change in price. It helps firms and governments predict the effects of tax changes or pricing strategies.
需求价格弹性衡量需求量对价格变动的反应程度。它帮助企业及政府预测税收变化或定价策略的效果。
PED = (% change in quantity demanded) ÷ (% change in price)
需求价格弹性 = （需求量变化的百分比）÷（价格变化的百分比）
The formula can be written as:
该公式可以写作：
PED = (ΔQ / Q) ÷ (ΔP / P) = (ΔQ / ΔP) × (P / Q)
If PED > 1 (ignoring the negative sign), demand is elastic: consumers are very responsive to price changes.
如果 |PED| > 1，需求富有弹性：消费者对价格变化非常敏感。
If PED < 1, demand is inelastic: quantity demanded changes proportionally less than price.
如果 |PED| < 1，需求缺乏弹性：需求量变化的比例小于价格变化的比例。
If PED = 1, demand is unit elastic: total revenue stays constant when price changes.
如果 |PED| = 1，需求是单位弹性：价格变动时总收入保持不变。
Worked example: A cinema raises ticket price from £8 to £10 (a 25% increase) and ticket sales fall from 100 to 75 (a 25% decrease). PED = 25% ÷ 25% = 1. Demand is unit elastic here.
计算示例：一家影院将票价从 8 英镑提高到 10 英镑（上涨 25%），售票量从 100 张降至 75 张（下降 25%）。PED = 25% ÷ 25% = 1。此处需求为单位弹性。
10. Inflation Rate | 通货膨胀率
Inflation is the sustained rise in the general level of prices over time. It reduces the purchasing power of money. Central banks monitor and target a low, stable inflation rate.
通货膨胀是指价格总水平在一段时间内持续上升的现象。它降低了货币的购买力。中央银行会监测通胀率并追求一个低而稳定的通胀目标。
The most common measure uses the Consumer Price Index (CPI):
最常用的衡量指标是消费者价格指数（CPI）：
Inflation Rate = [(CPI this year − CPI last year) ÷ CPI last year] × 100%
通货膨胀率 = [（今年 CPI − 去年 CPI）÷ 去年 CPI] × 100%
CPI tracks the cost of a fixed basket of consumer goods and services over time.
CPI 追踪一篮子固定消费品和服务随时间变化的成本。
If CPI rose from 105 to 110.25, inflation rate = (110.25 − 105) ÷ 105 × 100% = 5%.
如果 CPI 从 105 升至 110.25，通货膨胀率 = (110.25 − 105) ÷ 105 × 100% = 5%。
Mild inflation is normal in a growing economy; deflation (falling prices) can be harmful.
在增长中的经济里，轻微的通货膨胀是正常的；通货紧缩（物价下跌）可能有害。
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