📚 Year 11 CIE Economics: Quick Reference Handbook of Formulas and Theorems | CIE 经济公式定理速查手册
This quick reference handbook is designed for Year 11 CIE IGCSE Economics students. It brings together all the key formulas, theorems and definitions you need for your exams, from basic economic principles to macroeconomic indicators. Understanding these tools will help you analyse data, build arguments and excel in both multiple‑choice and structured questions.
本速查手册专为 CIE IGCSE 经济 Year 11 学生编写，汇总了从基本经济原理到宏观经济指标所需的所有关键公式、定理和定义。掌握这些工具将帮助你分析数据、构建论点，并在选择题和结构化问题中脱颖而出。
1. Scarcity and Opportunity Cost | 稀缺性与机会成本
Scarcity is the fundamental economic problem: finite resources cannot satisfy infinite human wants, forcing individuals, firms and governments to make choices. Every choice involves a trade‑off, and the opportunity cost is the value of the next best alternative forgone.
稀缺性是基本的经济问题：有限的资源无法满足无限的欲望，迫使个人、企业和政府做出选择。每一项选择都涉及权衡，而机会成本是所放弃的次优替代品的价值。
The four factors of production — land, labour, capital and enterprise — are scarce, and their ownership and allocation determine what, how and for whom to produce. A good economic decision is one where the expected benefit outweighs the opportunity cost.
四种生产要素——土地、劳动、资本和企业才能——都是稀缺的，它们的归属与配置决定了生产什么、如何生产以及为谁生产。一项好的经济决策，其预期收益应大于机会成本。
2. Demand, Supply and Market Equilibrium | 需求、供给与市场均衡
The law of demand states that, ceteris paribus, as the price of a good rises, the quantity demanded falls (and vice versa). The law of supply states that as price rises, quantity supplied rises. An extension or contraction is a movement along the curve; a shift of the whole curve is caused by a change in a non‑price determinant.
需求定律指出，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）。供给定律指出，价格上升，供给量上升。沿曲线的移动称为需求量的增减；整条曲线平移则由非价格因素引起。
Market equilibrium occurs where the demand and supply curves intersect — the equilibrium price and quantity clear the market, with no excess demand or excess supply. If the market is not in equilibrium, price signals and the invisible hand push it back towards equilibrium.
市场均衡发生在需求曲线与供给曲线相交之处——均衡价格和数量使市场出清，没有超额需求或超额供给。若市场未处于均衡，价格信号和“看不见的手”会将其推回均衡。
3. Price Elasticity of Demand (PED) | 需求价格弹性
Price elasticity of demand (PED) measures the responsiveness of quantity demanded to a change in price. The formula uses percentage changes so that elasticities are unit‑free and can be compared across goods.
需求价格弹性 (PED) 衡量需求量对价格变化的反应程度。公式采用百分比变化，使弹性无单位且可在不同商品间比较。
PED = (% Change in Quantity Demanded) ÷ (% Change in Price)
In practice, PED is always negative but economists usually quote its absolute value. When |PED| > 1, demand is price elastic — a given price change causes a more than proportional change in quantity demanded. When |PED| < 1, demand is price inelastic. If |PED| = 1, demand is unit elastic.
实际上 PED 总是负值，但经济学家通常取其绝对值。当 |PED| > 1 时，需求富有价格弹性——价格变动引起需求量更大比例的变化。当 |PED| < 1 时，需求缺乏价格弹性。若 |PED| = 1，则为单位弹性。
Factors that make demand more price elastic include the availability of close substitutes, the proportion of income spent on the good, whether the good is a luxury or a necessity, and the time period considered.
使需求更富价格弹性的因素包括：存在相近替代品、支出占收入比重较大、商品属于奢侈品而非必需品，以及所考虑的时间长短。
4. Price Elasticity of Supply (PES) | 供给价格弹性
Price elasticity of supply (PES) measures how responsive quantity supplied is to a change in price. It indicates how easily producers can increase output when the market price rises.
供给价格弹性 (PES) 衡量供给量对价格变化的反应程度。它表明当市场价格上升时，生产者增加产量的难易程度。
PES = (% Change in Quantity Supplied) ÷ (% Change in Price)
PES is normally positive. A value greater than 1 indicates elastic supply; less than 1 indicates inelastic supply. The key determinant is the length of time: supply is more elastic in the long run when firms can adjust all factors of production. Spare capacity, ease of storage and the nature of production also affect PES.
PES 通常为正值。大于 1 表示供给富有弹性，小于 1 表示供给缺乏弹性。关键决定因素是时间：长期中企业可调整所有生产要素，供给更富弹性。闲置产能、储存难易程度以及生产特性也会影响 PES。
5. Income Elasticity of Demand (YED) | 需求收入弹性
Income elasticity of demand (YED) measures how quantity demanded responds to a change in consumers' income. It helps classify goods as normal or inferior and assess the impact of economic growth on different sectors.
需求收入弹性 (YED) 衡量需求量对消费者收入变化的反应程度。它有助于将商品分为正常品和劣质品，并评估经济增长对不同部门的影响。
YED = (% Change in Quantity Demanded) ÷ (% Change in Income)
For normal goods, YED is positive. Among normal goods, those with YED > 1 are luxury goods (income‑elastic), while those with 0 < YED < 1 are necessities (income‑inelastic). If YED is negative, the good is an inferior good — demand falls as income rises.
对于正常品，YED 为正值。在正常品中，YED > 1 的属于奢侈品（富有收入弹性），而 0 < YED < 1 的属于必需品（缺乏收入弹性）。若 YED 为负值，则该商品是劣质品——收入增加时需求反而下降。
6. Cross Elasticity of Demand (XED) | 需求交叉弹性
Cross elasticity of demand (XED) measures the responsiveness of demand for one good to a change in the price of another good. This reveals whether two goods are substitutes or complements.
需求交叉弹性 (XED) 衡量一种商品的需求对另一种商品价格变化的反应程度。这可以揭示两种商品是替代品还是互补品。
XED = (% Change in Quantity Demanded of Good A) ÷ (% Change in Price of Good B)
A positive XED means the goods are substitutes (e.g. tea and coffee). A negative XED means they are complements (e.g. printers and ink cartridges). The larger the absolute value, the stronger the relationship. An XED of zero indicates independent goods.
XED 为正值表示两种商品是替代品（如茶和咖啡）。XED 为负值表示它们是互补品（如打印机和墨盒）。绝对值越大，关系越强。XED 为零则表示二者为独立商品。
7. Production and Costs | 生产与成本
Understanding cost structures is essential for analysing firm behaviour. The time frame distinguishes between the short run, where at least one factor is fixed, and the long run, where all factors are variable. Total cost (TC) is made up of total fixed cost (TFC) and total variable cost (TVC).
理解成本结构是分析企业行为的基础。时间框架分为短期（至少一种生产要素固定）和长期（所有要素可变）。总成本 (TC) 由总固定成本 (TFC) 和总可变成本 (TVC) 构成。
TC = TFC + TVC
From these, average and marginal costs are derived. Average total cost (ATC or AC) is cost per unit; average fixed cost (AFC) and average variable cost (AVC) show the unit contributions of fixed and variable factors. Marginal cost (MC) is the addition to total cost from producing one more unit.
由此可导出平均成本和边际成本。平均总成本 (ATC 或 AC) 是单位成本；平均固定成本 (AFC) 和平均可变成本 (AVC) 分别反映固定和可变要素的单位贡献。边际成本 (MC) 是多生产一单位产品所带来的总成本增加量。
ATC = TC ÷ Q, AFC = TFC ÷ Q, AVC = TVC ÷ Q
MC = ΔTC ÷ ΔQ
In diagrams, the MC curve cuts the ATC and AVC curves at their minimum points. Productivity gains and the law of diminishing returns influence the shapes of these cost curves.
在图形中，MC 曲线在 ATC 和 AVC 曲线的最低点与之相交。生产率提高和边际报酬递减规律影响着这些成本曲线的形状。
8. Revenue and Profit | 收益与利润
A firm's revenue depends on the price it charges and the quantity it sells. Total revenue (TR) is simply price multiplied by quantity. Average revenue (AR) equals price, and marginal revenue (MR) is the extra revenue from selling one more unit.
企业的收益取决于其索价和销售量。总收益 (TR) 就是价格乘以数量。平均收益 (AR) 等于价格，边际收益 (MR) 是多销售一单位产品所带来的额外收益。
TR = P × Q, AR = TR ÷ Q = P, MR = ΔTR ÷ ΔQ
Profit (π) is the difference between total revenue and total cost. Firms aim to maximise profit by producing where marginal cost equals marginal revenue, provided MC cuts MR from below. This is the profit‑maximising condition in all market structures.
利润 (π) 是总收益与总成本之间的差额。企业通过将产量定在边际成本等于边际收益的水平来实现利润最大化，前提是 MC 在 MR 下方与其相交。这是所有市场结构下的利润最大化条件。
Profit = TR - TC, Profit‑maximisation rule: MC = MR
9. Market Structures | 市场结构
Market structures differ by number of firms, type of product, barriers to entry and the degree of price control. The main models at CIE IGCSE level are perfect competition, monopoly, oligopoly and — where relevant — monopolistic competition. Each structure has different implications for efficiency and consumer welfare.
市场结构因厂商数量、产品类型、进入壁垒以及价格控制程度而不同。CIE IGCSE 阶段的主要模型包括完全竞争、垄断、寡头以及相关的垄断竞争。每种结构对效率和消费者福利都有不同影响。
| Feature (English) | 特征 (中文) | Perfect Competition | Monopoly | Oligopoly |
|---|---|---|---|---|
| Number of firms | 厂商数量 | Very many | One | Few large firms |
| Product type | 产品类型 | Homogeneous (identical) | Unique, no close substitutes | Differentiated or homogeneous |
| Barriers to entry | 进入壁垒 | None | Very high | High (economies of scale, branding) |
| Price control | 价格控制力 | Price‑taker | Price‑maker | Interdependent pricing |
In perfect competition, firms achieve both productive and allocative efficiency in the long run. A monopolist can earn supernormal profits in the long run because of entry barriers, but this may result in higher prices and lower output compared to a competitive market.
在完全竞争市场中，企业长期可实现生产效率和配置效率。垄断者因进入壁垒可在长期获得超额利润，但与竞争市场相比，可能导致更高的价格和更低的产出。
10. Macroeconomic Indicators | 宏观经济指标
Macroeconomic performance is tracked using key indicators: economic growth (GDP), unemployment, and inflation. Governments use these to steer fiscal and monetary policy.
宏观经济表现通过关键指标进行跟踪：经济增长 (GDP)、失业和通货膨胀。政府利用这些指标指导财政和货币政策。
Gross Domestic Product (GDP) measures the total value of goods and services produced in a country over a period. Real GDP strips out the effect of inflation. The economic growth rate is the percentage change in real GDP from one period to the next.
国内生产总值 (GDP) 衡量一经济体在特定时期内生产的商品和服务的总价值。实际 GDP 剔除了通货膨胀的影响。经济增长率即实际 GDP 从一个时期到下一时期的百分比变化。
Growth Rate = [(Real GDP current - Real GDP previous) ÷ Real GDP previous] × 100
Unemployment rate is the share of the labour force that is actively seeking work but unable to find it. The labour force includes those employed plus unemployed.
失业率 是劳动力中积极寻找工作但未能就业的人数占比。劳动力包括就业者和失业者。
Unemployment Rate = (Number of Unemployed ÷ Labour Force) × 100
Inflation is a sustained increase in the general price level. The Consumer Price Index (CPI) tracks the prices of a typical basket of goods. The inflation rate is the annual percentage change in the CPI.
通货膨胀 是价格总水平的持续上升。消费者价格指数 (CPI) 跟踪一篮子代表性商品的价格。通货膨胀率即 CPI 的年度百分比变化。
Inflation Rate = [(CPI Year 2 - CPI Year 1) ÷ CPI Year 1] × 100
11. Money and Banking | 货币与银行
Money serves four key functions: a medium of exchange, a unit of account, a store of value, and a standard of deferred payment. These functions require that money be durable, portable, divisible, scarce and generally acceptable.
货币具有四项关键职能：交换媒介、计价单位、价值储藏和延期支付标准。这些职能要求货币具备耐久性、便携性、可分性、稀缺性和普遍可接受性。
Central banks, such as the Bank of England or the Federal Reserve, are responsible for issuing currency, managing monetary policy, setting interest rates, acting as a lender of last resort and ensuring financial stability. Commercial banks accept deposits, make loans and create credit through fractional‑reserve banking.
中央银行（如英格兰银行或美联储）负责发行货币、管理货币政策、设定利率、充当最后贷款人并确保金融稳定。商业银行接受存款、发放贷款并通过部分准备金制度创造信用。
is a classical theorem linking the money supply to the price level, but its full treatment appears at Advanced level. At IGCSE, the key take‑away is that excessive growth in the money supply tends to be inflationary.
货币数量论 (MV = PY) 是将货币供应与价格水平联系起来的古典定理，但其完整论述出现在高级课程。在 IGCSE 阶段，关键启示是货币供应量的过度增长往往导致通货膨胀。
12. International Trade and Exchange Rates | 国际贸易与汇率
The principle of comparative advantage states that countries should specialise in producing goods in which they have a lower opportunity cost and then trade, even if one country has an absolute advantage in all goods. Specialisation and trade increase total global output.
比较优势原理指出，各国应专业化生产机会成本较低的商品并进行贸易，即使一国在所有商品上都具有绝对优势。专业化和贸易能增加全球总产出。
To find comparative advantage, calculate the opportunity cost of producing one unit of a good in each country. For example, if Country A can produce 1 unit of cloth or 2 units of wine, the opportunity cost of 1 cloth is 2 wine. Compare with Country B's ratio: the country with the lower opportunity cost should specialise in cloth.
要找出比较优势，需计算每个国家生产一单位某种商品的机会成本。例如，若 A 国能生产 1 单位布或 2 单位酒，则 1 单位布的机会成本是 2 单位酒。与 B 国的比率比较：机会成本较低的国家应专业化生产布。
Exchange rates express the price of one currency in terms of another. An appreciation (rise in value) makes exports dearer and imports cheaper; a depreciation (fall in value) does the opposite. The impact on the trade balance depends on price elasticities of demand for exports and imports — summarised by the Marshall‑Lerner condition at a higher level.
汇率表示一种货币以另一种货币计价的价格。升值（价值上升）使出口更贵、进口更便宜；贬值（价值下跌）则相反。对贸易差额的影响取决于出口和进口的需求价格弹性——这由更高阶的马歇尔‑勒纳条件总结。
Governments may intervene in foreign exchange markets by buying or selling reserves to influence the exchange rate, or adopt fixed, floating or managed exchange rate systems.
政府可通过买卖外汇储备来干预外汇市场，影响汇率，或采用固定汇率制、浮动汇率制或有管理的浮动汇率制。
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