📚 Year 12 CIE Economics: Formula & Theorem Quick Reference Handbook | 公式定理速查手册
This quick reference handbook gathers essential formulas and theorems for the Year 12 CIE AS-Level Economics syllabus. It is designed as a concise revision tool to help you master quantitative and conceptual elements of the course. Each section presents key relationships, definitions, and calculation methods with immediate dual-language explanations to support both English and Chinese learners.
本速查手册汇集了 Year 12 CIE AS 阶段经济学的核心公式与定理，旨在作为高效复习工具，帮助你掌握课程中的数量分析和概念要点。每个小节都先提供英文关键公式或定理并解释，随后紧接中文对应内容，便于双语学习与记忆。
1. Price Elasticity of Demand (PED) | 需求的价格弹性（PED）
quantity demanded of a good is to a change in its own price. The basic formula is: PED = (% ΔQd) ÷ (% ΔP), where % ΔQd is the percentage change in quantity demanded and % ΔP is the percentage change in price. The value of PED is normally negative due to the inverse relationship, but the absolute value is often used for interpretation.
需求的价格弹性衡量一种商品的需求量对其自身价格变化的反应程度。基本公式为：PED = (需求量变动的百分比) ÷ (价格变动的百分比)，其中 Δ 表示变动量。PED 数值通常为负，因为价格与需求量呈反向关系，但在解释时一般取其绝对值。
calculation uses average quantity and average price to give a symmetric result: PED = [(Q2 – Q1) / ((Q1+Q2)/2)] ÷ [(P2 – P1) / ((P1+P2)/2)].
当使用中点（弧弹性）公式测量两点之间的弹性时，利用平均数量和平均价格给出对称的结果：PED = [(Q₂ – Q₁) / ((Q₁+Q₂)/2)] ÷ [(P₂ – P₁) / ((P₁+P₂)/2)]。
Interpretation: |PED| > 1 indicates elastic demand (responsive); |PED| < 1 indicates inelastic demand (unresponsive); |PED| = 1 is unit elastic; |PED| = 0 is perfectly inelastic; and |PED| → ∞ is perfectly elastic.
解释：|PED| > 1 表示需求富有弹性；|PED| < 1 表示缺乏弹性；|PED| = 1 为单位弹性；|PED| = 0 为完全无弹性；|PED| → ∞ 为完全弹性。
2. Income Elasticity of Demand (YED) | 需求的收入弹性（YED）
YED measures the responsiveness of quantity demanded to a change in consumers' income. Formula: YED = (% ΔQd) ÷ (% ΔY), where Y denotes income. A positive YED indicates a normal good; a negative YED indicates an inferior good. For normal goods, a YED > 1 signals a luxury good (income elastic), while 0 < YED < 1 signals a necessity (income inelastic).
需求的收入弹性衡量需求量对消费者收入变化的反应程度。公式：YED = (需求量变动%) ÷ (收入变动%)。正 YED 表示正常品；负 YED 表示低档品。对于正常品，YED > 1 为奢侈品（富有收入弹性），0 < YED < 1 为必需品（缺乏收入弹性）。
3. Cross Elasticity of Demand (XED) | 需求的交叉弹性（XED）
siveness of demand for one good to a change in the price of another good. Formula: XED = (% ΔQd of good A) ÷ (% ΔP of good B). A positive XED indicates substitutes; a negative XED indicates complements; a value near zero suggests independent goods. The magnitude of XED shows the strength of the relationship.
交叉弹性衡量一种商品的需求量对另一种商品价格变化的反应程度。公式：XED = (A商品需求量变动%) ÷ (B商品价格变动%)。正 XED 表示替代品；负 XED 表示互补品；接近零则表明两种商品不相关。XED 的绝对值大小反映了关系的紧密程度。
4. Price Elasticity of Supply (PES) | 供给的价格弹性（PES）
ES measures the responsiveness of quantity supplied to a change in price. Formula: PES = (% ΔQs) ÷ (% l limited by fixed factors; in the long run supply tends to become more elastic. PES > 1 is elastic supply; PES < 1 is inelastic; PES = 0 is perfectly inelastic; PES → ∞ is perfectly elastic.
供给的价格弹性衡量供给量对价格变化的反应程度。公式：PES = (供给量变动%) ÷ (价格变动%)。时间周期是关键决定因素：瞬时情况下 PES 常为零或很低；短期中 PES > 0 但受固定要素限制；长期供给通常更具弹性。PES > 1 富有弹性；PES < 1 缺乏弹性；PES = 0 完全无弹性；PES → ∞ 完全弹性。
5. Utility Theory | 效用理论
ginal utility (MU) is the additional satisfaction from consuming one more unit: MU = ΔTU ÷ ΔQ. The law of diminishing marginal utility states that as more of a good is consumed, the MU of each extra unit eventually falls.
效用是消费者从商品和服务中获得的满足感。总效用（TU）是消费获得的总满足程度，边际效用（MU）是多消费一单位带来的额外满足：MU = 总效用变动量 ÷ 数量变动量。边际效用递减规律指出，随着对同一商品消费增多，每增加一单位的边际效用最终会下降。
The consumer equilibrium condition under utility theory is the equi-marginal principle: MUA/PA = MUB/PB = … good yields the same marginal utility, maximising total utility given a budget constraint.
效用理论下的消费者均衡条件是等边际原则：MUₐ/Pₐ = MU_B/PB = … = 每单位货币支出的边际效用。这保证了花费在每种商品上的最后一英镑带来相同的边际效用，从而在预算约束下实现总效用最大化。
6. Costs, Revenues and Profit | 成本、收益与利润
st (AFC) = TFC ÷ Q, average variable cost (AVC) = TVC ÷ Q. Marginal cost (MC) = ΔTC ÷ ΔQ = ΔTVC ÷ ΔQ. These cost relationships underpin the shape of the firm's cost curves.
总成本（TC）= 总固定成本（TFC）+ 总可变成本（TVC）。平均成本（AC）= TC ÷ Q，也称平均总成本。平均固定成本（AFC）= TFC ÷ Q，平均可变成本（AVC）= TVC ÷ Q。边际成本（MC）= ΔTC ÷ ΔQ = ΔTVC ÷ ΔQ。这些成本关系决定了企业成本曲线的形状。
rfect competition AR = MR, while under imperfect competition MR lies below AR. Profit = TR – TC. Normal profit is included in economic cost; supernormal profit arises when TR > TC.
总收益（TR）= 价格 × 销售量。平均收益（AR）= TR ÷ Q = 价格。边际收益（MR）= ΔTR ÷ ΔQ。完全竞争下 AR = MR，不完全竞争下 MR 低于 AR。利润 = TR – TC。经济成本中包含正常利润；当 TR > TC 时存在超额利润。
7. Profit Maximisation and Market Equilibrium | 利润最大化与市场均衡
= MC. In imperfect markets, the firm will still set output at MR = MC, but price is determined from the demand curve above that output.
利润最大化的基本法则是使 MR = MC，且边际成本处于上升阶段。对完全竞争厂商而言，即 P = MC。在不完全市场中，企业仍然将产量定在 MR = MC 处，但价格由该产量对应的需求曲线决定。
Market equilibrium occurs where quantity demanded equals quantity supplied (Qd = Qs). At the equilibrium price, there is no excess demand or excess supply. Consumer surplus is the area below the demand curve and above price; producer surplus is the area above the supply curve and below price. Total welfare is maximised at equilibrium in the absence of market failures.
市场均衡出现在需求量等于供给量（Qd = Qs）时。在均衡价格下，不存在超额需求或超额供给。消费者剩余是需求曲线以下、价格线以上的面积；生产者剩余是供给曲线以上、价格线以下的面积。在没有市场失灵时，均衡状态使总福利最大化。
8. Multiplier Effect | 乘数效应
on national income. The simple closed-economy multiplier with no government is k = 1 ÷ (1 – MPC) = 1 ÷ MPS, where MPC is the marginal propensity to consume and MPS = 1 – MPC. A higher MPC leads to a larger multiplier.
乘数衡量自发支出初始变化对国民收入的放大效应。没有政府部门的简单封闭经济乘数为：k = 1 ÷ (1 – MPC) = 1 ÷ MPS，其中 MPC 是边际消费倾向，MPS = 1 – MPC 是边际储蓄倾向。MPC 越高，乘数越大。
iplier is modified by taxation and imports. The government spending multiplier: k = 1 ÷ (1 – MPC(1 – M is the marginal propensity to import. The tax multiplier is smaller in absolute value: ktax = –MPC ÷ (1 – ernment spending and net taxes raises national income by the same amount (multiplier = 1).
加入政府部门后，乘数受到税收和进口的影响。政府支出乘数：k = 1 ÷ [1 – MPC(1 – t) + MPM]，其中 t 为税率，MPM 为边际进口倾向。税收乘数绝对值较小：ktax = –MPC ÷ (1 – MPC)。平衡预算乘数表明，政府支出与净税收等额增加会使国民收入同额增长（乘数为 1）。
9. Inflation and Price Indices | 通货膨胀与价格指数
is the Consumer Price Index (CPI). The inflation rate using CPI is: Inflation rate = [(CPIcurrent – CPIprevious) ÷ CPIprevious dices assign different importance to goods according to their share in household spending.
通货膨胀是整体物价水平的持续上涨。最常用的衡量指标是消费者价格指数（CPI）。使用 CPI 计算通货膨胀率：通胀率 = [(当期 CPI – 前期 CPI) ÷ 前期 CPI] × 100。加权价格指数根据商品在家庭支出中的比重赋予不同权重。
ds and services. Real GDP = (Nominal GDP ÷ GDP deflator) × 100, providing a measure of output adjusted for inflation.
另一个更广泛的指数是 GDP 平减指数：GDP 平减指数 = (名义 GDP ÷ 实际 GDP) × 100。它反映国内生产的所有商品和服务的价格变化。实际 GDP = (名义 GDP ÷ GDP 平减指数) × 100，提供了剔除通胀后的产出衡量。
10. Unemployment Rate and Labour Market | 失业率与劳动力市场
mber of unemployed ÷ Labour force) × 100, where the labour force is the sum of employed and unemployed. The labour force participation rate = (Labour force ÷ Working-age population) × 100.
失业率是劳动力中无工作但积极寻找工作的人所占的百分比。公式：失业率 = (失业人数 ÷ 劳动力人数) × 100，其中劳动力是就业者与失业者之和。劳动力参与率 = (劳动力 ÷ 劳动年龄人口) × 100。
11. Balance of Payments and Exchange Rates | 国际收支与汇率
provement in TOT means a country can buy more imports for a given amount of exports; a deterioration means the opposite.
贸易条件衡量出口价格相对于进口价格的水平。公式：TOT = (出口价格指数 ÷ 进口价格指数) × 100。贸易条件改善意味着一国能以给定出口量换取更多进口；恶化则相反。
rise in this rate indicates appreciation of the US dollar, while a fall indicates depreciation. Trade-weighted exchange rates aggregate bilateral rates weighted by trade shares.
汇率可以直标或间标。例如 USD/EUR = 0.85 表示 1 美元兑换 0.85 欧元。该比率上升表示美元升值，下降表示贬值。贸易加权汇率是按贸易份额加权的双边汇率综合指标。
12. Government Budget and Fiscal Policy | 政府预算与财政政策
government budget balance is the difference between government revenue (mainly taxation) and government spending. Budget balance = Tax revenue – nce is a budget deficit. The structural deficit removes the effects of the economic cycle.
政府预算平衡是政府收入（主要是税收）与政府支出之差。预算余额 = 税收收入 – 政府支出。正余额为预算盈余，负余额为预算赤字。结构性赤字剔除了经济周期的影响。
100, a key indicator of fiscal sustainability. Automatic stabilisers, such as progressive taxation and unemployment benefits, help smooth the economic cycle without discretionary policy changes.
国债是过往预算赤字的累计总额。债务—GDP 比率 = (国债 ÷ 名义 GDP) × 100，是衡量财政可持续性的关键指标。自动稳定器（如累进税和失业救济金）无需政策主动调整即可平缓经济周期。
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