📚 AS Cambridge Economics: Formulas & Theorems Quick Reference | AS 剑桥经济：公式定理速查手册
This concise handbook collects the essential formulas, definitions, and theorems required for the Cambridge International AS Level Economics syllabus. It is designed as a rapid revision tool, covering microeconomic and macroeconomic concepts, elasticity calculations, market structures, government intervention, national income accounting, and international trade. Each entry is presented in clear, examination-friendly language, with paired English–Chinese explanations to support bilingual learners.
本速查手册汇集了剑桥国际 AS 阶段经济学所必需的核心公式、定义与定理。它旨在帮助考生快速回顾微观与宏观经济学概念、弹性计算、市场结构、政府干预、国民收入核算与国际贸易等内容。每条要点均以清晰、应试友好的中英双语对照呈现，便于双语学习者掌握。
1. Scarcity, Choice and Opportunity Cost | 稀缺性、选择与机会成本
Scarcity is the fundamental economic problem that arises because resources are finite while human wants are unlimited. It forces individuals, firms, and governments to make choices and incur opportunity costs. The production possibility curve (PPC) illustrates the maximum combinations of two goods an economy can produce with given resources and technology.
稀缺性是根本的经济问题：资源有限而人类欲望无限，这迫使个人、企业和政府做出选择并承担机会成本。生产可能性曲线（PPC）展示了经济体在给定资源与技术条件下所能生产的两种商品的最大组合。
The opportunity cost of a choice is the value of the next best alternative forgone. On a PPC, it is measured as the slope of the tangent or, when moving along the boundary, as the quantity of one good sacrificed to obtain an additional unit of the other.
机会成本是指所放弃的次佳选择的价值。在生产可能性曲线上，它可以用切线的斜率来衡量，或者沿着边界移动时，以牺牲一种商品的数量来表示获得额外一单位另一种商品的成本。
Opportunity cost = Sacrifice / Gain
机会成本 = 牺牲 / 获得
- Points inside the PPC represent inefficient use of resources; points outside are currently unattainable.
- PPC 内部的点表示资源未充分利用；外部的点当前无法达到。
- A concave PPC reflects increasing opportunity cost (the law of diminishing marginal returns).
- 凹向原点的 PPC 反映机会成本递增（边际收益递减规律）。
2. Law of Demand and Law of Supply | 需求定律与供给定律
The law of demand states that, ceteris paribus, as the price of a good rises, the quantity demanded falls (inverse relationship). The law of supply states that, ceteris paribus, as the price rises, the quantity supplied increases (direct relationship). These relationships are driven by the substitution effect, income effect, and the profit motive of producers.
需求定律指在其他条件不变的情况下，价格上升时需求量下降（反向关系）。供给定律指价格上升时供给量增加（正向关系）。这些关系背后的动因包括替代效应、收入效应以及生产者追求利润的动机。
Movements along the demand/supply curves are caused by changes in the good’s own price; shifts of the entire curve are caused by changes in non-price determinants (e.g. income, tastes, input costs, technology).
沿需求/供给曲线的移动由商品自身价格变化引起；整条曲线的平移则由非价格决定因素（如收入、偏好、投入成本、技术）的变化导致。
Qd = f(P) and Qs = f(P)
需求量是价格的函数；供给量是价格的函数
3. Elasticity Formulas | 弹性公式
Elasticity measures the responsiveness of one variable to a change in another. All four main elasticities use the same basic percentage-change method. The table below summarises the formulas, coefficients, and interpretations relevant to the AS examination.
弹性衡量一个变量对另一个变量变化的反应程度。AS 考试涉及的四种主要弹性均采用相同的百分比变动基本方法。下表总结了公式、系数及解释。
| Price elasticity of demand (PED) 需求价格弹性 |
PED = %ΔQd / %ΔP | |PED| > 1: elastic; <1: inelastic; =1: unit elastic; =0: perfectly inelastic; ∞: perfectly elastic |
| Price elasticity of supply (PES) 供给价格弹性 |
PES = %ΔQs / %ΔP | PES > 1: elastic; <1: inelastic; =1: unit elastic; determinants include time period and spare capacity |
| Income elasticity of demand (YED) 需求收入弹性 |
YED = %ΔQd / %ΔIncome | YED > 0: normal good (>1 luxury); YED < 0: inferior good |
| Cross elasticity of demand (XED) 需求交叉弹性 |
XED = %ΔQd of A / %ΔP of B | XED > 0: substitutes; XED < 0: complements; XED = 0: unrelated goods |
For accurate measurement of elasticity between two points on a demand or supply curve, the midpoint (arc) formula is often preferred because it gives the same result regardless of the direction of change. It is provided below for reference, though the simple percentage-change method is sufficient for most AS questions.
为了在需求或供给曲线上两点间精确地测算弹性，常使用中点（弧）公式，因为它无论从哪个方向计算都能得到相同结果。尽管大多数 AS 题目用简单的百分比变动法即可，但中点公式也列在下方供参考。
PED (midpoint) = [(Q2 − Q1) ÷ ((Q1+Q2)/2)] ÷ [(P2 − P1) ÷ ((P1+P2)/2)]
PED（中点法）= [(Q2 − Q1) ÷ ((Q1+Q2)/2)] ÷ [(P2 − P1) ÷ ((P1+P2)/2)]
4. Market Equilibrium and Welfare | 市场均衡与福利
Market equilibrium occurs where quantity demanded equals quantity supplied (Qd = Qs). There is no tendency for price to change at this point. Any price above equilibrium creates a surplus; any price below creates a shortage. The price mechanism automatically adjusts to restore equilibrium in a free market.
市场均衡发生在需求量等于供给量（Qd = Qs）时。此时价格没有变动的趋势。高于均衡价格会产生过剩，低于均衡价格会产生短缺。在自由市场中，价格机制会自动调整以恢复均衡。
Consumer surplus is the difference between the maximum price consumers are willing to pay and the market price they actually pay. Producer surplus is the difference between the market price and the minimum price producers are willing to accept. Total welfare is the sum of consumer and producer surplus, maximised at equilibrium.
消费者剩余是消费者愿意支付的最高价格与实际支付的市场价格之间的差额。生产者剩余是市场价格与生产者愿意接受的最低价格之间的差额。总福利是消费者剩余与生产者剩余之和，在均衡时达到最大。
Consumer Surplus = Willingness to pay − Market price
Producer Surplus = Market price − Willingness to accept
消费者剩余 = 支付意愿 − 市场价格
生产者剩余 = 市场价格 − 接受意愿
Deadweight loss (welfare loss) occurs when the market is not in competitive equilibrium, e.g. due to taxes, subsidies, price ceilings or floors. It is the net reduction in total surplus.
当市场未处于竞争均衡时（例如由于税收、补贴、最高或最低限价），会出现无谓损失（福利损失），即总剩余的净减少。
5. Taxes, Subsidies and Price Controls | 税收、补贴与价格控制
Indirect taxes (specific and ad valorem) shift the supply curve vertically upwards by the amount of the tax. The burden of the tax is shared between consumers and producers depending on relative elasticities. Subsidies shift the supply curve downwards by the amount of the subsidy.
间接税（从量税和从价税）使供给曲线垂直上移，幅度等于税额。税负在消费者与生产者之间的分摊取决于相对弹性。补贴使供给曲线垂直下移，幅度等于补贴额。
The division of a tax between buyers and sellers can be determined using the elasticity rule: the more inelastic side of the market bears a greater share. The same principle applies to the benefit of a subsidy.
税收在买方与卖方之间的划分可由弹性法则确定：市场越缺乏弹性的一方承担的份额越大。补贴利益的分配也同样适用这一原则。
Consumer tax burden per unit = (PES / (PED + PES)) × Tax per unit
消费者单位税负 = (PES / (PED + PES)) × 单位税额
Price ceilings (maximum price) set below equilibrium cause persistent shortages; price floors (minimum price) set above equilibrium cause persistent surpluses. Both create deadweight loss and may generate black markets or government storage costs.
最高限价（价格上限）若设在均衡价格以下会导致持续短缺；最低限价（价格下限）若设在均衡价格以上会导致持续过剩。两者都会造成无谓损失，并可能催生黑市或增加政府储存成本。
6. Market Failure and Externalities | 市场失灵与外部性
Market failure occurs when the free market fails to allocate resources efficiently, leading to a net welfare loss. Key causes include externalities, public goods, information asymmetry, and monopoly power. Externalities are third-party spillover effects not reflected in the market price.
市场失灵指自由市场未能有效配置资源而导致的净福利损失。主要成因包括外部性、公共物品、信息不对称和垄断力量。外部性是指未反映在市场价格中的第三方溢出效应。
Marginal social cost (MSC) = marginal private cost (MPC) + marginal external cost (MEC). Marginal social benefit (MSB) = marginal private benefit (MPB) + marginal external benefit (MEB). A negative production externality leads to overproduction because MSC > MPC; a positive consumption externality leads to underconsumption because MSB > MPB.
边际社会成本（MSC）= 边际私人成本（MPC）+ 边际外部成本（MEC）。边际社会收益（MSB）= 边际私人收益（MPB）+ 边际外部收益（MEB）。负生产外部性会导致过度生产，因 MSC > MPC；正消费外部性会导致消费不足，因 MSB > MPB。
- Public goods are non-excludable and non-rivalrous, causing the free-rider problem.
- 公共物品具有非排他性和非竞争性，导致搭便车问题。
- Information asymmetry (adverse selection, moral hazard) prevents markets from reaching efficient outcomes.
- 信息不对称（逆向选择、道德风险）使市场无法达到有效结果。
Government interventions include Pigouvian taxes (tax equal to MEC), subsidies (equal to MEB), regulations, tradable permits, and state provision of public goods.
政府干预手段包括庇古税（税额等于边际外部成本）、补贴（等于边际外部收益）、管制、可交易许可证及公共物品的国家提供。
7. Costs, Revenue and Profit | 成本、收益与利润
In the short run, a firm faces at least one fixed factor of production. Total cost (TC) = total fixed cost (TFC) + total variable cost (TVC). Average cost (ATC) = AFC + AVC. Marginal cost (MC) is the additional cost of producing one more unit.
短期内，企业至少有一种固定生产要素。总成本（TC）= 总固定成本（TFC）+ 总可变成本（TVC）。平均成本（ATC）= 平均固定成本（AFC）+ 平均可变成本（AVC）。边际成本（MC）为多生产一单位产品所增加的成本。
TC = TFC + TVC
ATC = TC / Q
AFC = TFC / Q
AVC = TVC / Q
MC = ΔTC / ΔQ
TC = TFC + TVC · ATC = TC ÷ Q
AFC = TFC ÷ Q · AVC = TVC ÷ Q · MC = ΔTC ÷ ΔQ
Total revenue (TR) = Price × Quantity. Average revenue (AR) = TR / Q = Price. Marginal revenue (MR) = ΔTR / ΔQ. A firm maximises profit when marginal cost equals marginal revenue (MC = MR), provided that price covers average variable cost in the short run.
总收益（TR）= 价格 × 数量。平均收益（AR）= TR ÷ Q = 价格。边际收益（MR）= ΔTR ÷ ΔQ。当边际成本等于边际收益（MC = MR）时企业实现利润最大化，且短期内价格须能覆盖平均可变成本。
Profit = TR − TC
Profit per unit = AR − ATC
利润 = 总收益 − 总成本
单位利润 = 平均收益 − 平均总成本
8. Market Structures | 市场结构
The AS syllabus requires an understanding of the characteristics of perfect competition, monopoly, and (briefly) imperfect competition. The profit-maximising condition MC = MR applies to all market structures, but the relationship between price, AR and MR differs.
AS 考纲要求理解完全竞争、垄断及（简要的）不完全竞争的特征。利润最大化条件 MC = MR 适用于所有市场结构，但价格、AR 与 MR 之间的关系各有不同。
- Perfect competition: large number of buyers and sellers, homogeneous products, no barriers to entry. Firms are price-takers; AR = MR = Price. Long-run equilibrium occurs where P = MC = ATC (normal profit).
- 完全竞争：买卖双方众多，产品同质，无进入壁垒。企业为价格接受者；AR = MR = 价格。长期均衡在 P = MC = ATC 处实现（正常利润）。
- Monopoly: single seller, high barriers to entry, price maker. The firm faces the market demand curve; MR lies below AR. Equilibrium output is where MC = MR, and price is set on the demand curve above MC, generating abnormal profit in the long run.
- 垄断：单一卖方，高进入壁垒，价格制定者。企业面临市场需求曲线；MR 位于 AR 之下。均衡产量由 MC = MR 确定，价格在需求曲线上高于 MC，长期可获得超额利润。
Concentration ratios (e.g. the N-firm concentration ratio) measure the combined market share of the largest firms and give an indication of market power.
集中度比率（如 N 企业集中度）衡量最大几家企业合计的市场份额，用以反映市场垄断程度。
9. Macroeconomic Indicators | 宏观经济指标
Macroeconomic performance is assessed using indicators such as the rate of inflation, unemployment rate, economic growth, and the current account balance. These are based on nationally defined statistics and standard formulas.
宏观经济表现通过通货膨胀率、失业率、经济增长率以及经常账户余额等指标加以评估，这些指标基于各国统计数据与标准公式计算。
Inflation rate = (CPI current − CPI previous) / CPI previous × 100
通货膨胀率 = (本期CPI − 上期CPI) ÷ 上期CPI × 100
CPI = (Cost of basket in current year / Cost of basket in base year) × 100
居民消费价格指数 = (当期篮子成本 ÷ 基期篮子成本) × 100
Unemployment rate = (Number of unemployed / Labour force) × 100
失业率 = (失业人数 ÷ 劳动力人数) × 100
Real GDP growth = (Real GDP this year − Real GDP last year) / Real GDP last year × 100
实际GDP增长率 = (本年实际GDP − 上年实际GDP) ÷ 上年实际GDP × 100
Real GDP is nominal GDP adjusted for inflation using the GDP deflator: Real GDP = (Nominal GDP / GDP deflator) × 100. The GDP deflator covers all domestically produced goods and services, unlike CPI which relates to a consumer basket.
实际GDP是用GDP平减指数剔除通胀影响后的名义GDP：实际GDP = (名义GDP ÷ GDP平减指数) × 100。GDP平减指数涵盖国内生产的所有商品和服务，区别于仅涉及消费品篮子的CPI。
10. Aggregate Demand, Aggregate Supply and the Multiplier | 总需求、总供给与乘数
Aggregate demand (AD) is the total spending on domestic goods and services at a given price level. Its components are consumption (C), investment (I), government spending (G), and net exports (X − M). AD = C + I + G + (X − M). A change in any component shifts the AD curve.
总需求是指在给定价格水平下对国内商品与服务的总支出。其构成包括消费（C）、投资（I）、政府支出（G）和净出口（X − M）。AD = C + I + G + (X − M)。任何组成部分的变动都会导致 AD 曲线平移。
The multiplier effect describes how an initial injection into the circular flow of income can lead to a larger final increase in national income. The size of the multiplier (k) depends on the marginal propensity to withdraw from the circular flow.
乘数效应描述了最初注入经济循环流的一笔支出如何导致国民收入更大幅度的最终增加。乘数的大小（k）取决于从循环流中漏出的边际倾向。
Simple multiplier (closed economy, no government): k = 1 / MPS = 1 / (1 − MPC)
简单乘数（封闭经济，无政府）：k = 1 ÷ MPS = 1 ÷ (1 − MPC)
Full multiplier (with government and foreign trade): k = 1 / (MPS + MPT + MPM)
完整乘数（含政府和对外贸易）：k = 1 ÷ (M
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