📚 Year 13 CIE Economics: Formula & Theorem Quick Reference | A2经济公式定理速查手册
This quick reference handbook compiles essential formulas, theorems, and key relationships required for the CIE A2 Economics syllabus. It covers microeconomic and macroeconomic concepts from elasticities to multiplier effects, international trade, and development indicators. Use this as a revision checklist to ensure you have mastered all quantitative and theoretical elements.
本速查手册汇编了CIE A2经济课程所需的核心公式、定理和关键关系，涵盖从弹性到乘数效应、国际贸易与发展指标的微观与宏观经济概念。请以此为复习清单，确保掌握所有定量与理论要点。
1. Price, Income, Cross & Supply Elasticities | 需求、收入、交叉与供给弹性
Price Elasticity of Demand (PED) = %ΔQd / %ΔP. It measures responsiveness of quantity demanded to price changes. If |PED| > 1, demand is elastic; |PED| < 1, inelastic; |PED| = 1, unit elastic.
需求价格弹性 (PED) = 需求量变化百分比 / 价格变化百分比。它衡量需求量对价格变化的反应程度。若 |PED| > 1，需求富有弹性；|PED| < 1，缺乏弹性；|PED| = 1，单位弹性。
Total revenue rule: when demand is elastic, a price cut raises total revenue; when demand is inelastic, a price rise raises total revenue. The relationship follows from TR = P × Q.
总收益规则：当需求富有弹性时，降价可增加总收益；当需求缺乏弹性时，提价可增加总收益。这一关系源于 TR = P × Q。
Income Elasticity of Demand (YED) = %ΔQd / %ΔY. Normal goods have YED > 0; inferior goods have YED < 0. Luxury goods typically show YED > 1.
需求收入弹性 (YED) = 需求量变化百分比 / 收入变化百分比。正常品的 YED > 0；劣等品 YED < 0；奢侈品的 YED 通常大于 1。
Cross Elasticity of Demand (XED) = %ΔQd of good A / %ΔP of good B. Substitutes give positive XED; complements give negative XED.
需求交叉弹性 (XED) = A 商品需求量变化百分比 / B 商品价格变化百分比。替代品的 XED 为正；互补品的 XED 为负。
Price Elasticity of Supply (PES) = %ΔQs / %ΔP. PES tends to be higher in the long run than in the short run as firms can adjust all inputs.
供给价格弹性 (PES) = 供给量变化百分比 / 价格变化百分比。由于厂商能调整所有投入，长期 PES 通常高于短期。
2. Consumer and Producer Surplus | 消费者与生产者剩余
Consumer surplus (CS) = willingness to pay − market price. On a linear demand curve, CS = ½ × (maximum price − market price) × quantity. Producer surplus (PS) = market price − minimum supply price; area above supply curve and below price.
消费者剩余 (CS) = 支付意愿 − 市场价格。在线性需求曲线下，CS = ½ × (最高支付价格 − 市场价格) × 数量。生产者剩余 (PS) = 市场价格 − 最低供应价格；即供给曲线上方、价格下方的面积。
Total welfare = CS + PS. A deadweight loss occurs when output is not at the socially optimal level (where MSB = MSC).
社会总福利 = CS + PS。当产量未达到社会最优水平 (MSB = MSC) 时，会产生无谓损失。
3. Cost, Revenue and Profit Maximisation | 成本、收益与利润最大化
Total Cost (TC) = Total Fixed Cost (TFC) + Total Variable Cost (TVC). Average Cost (AC) = TC / Q. Marginal Cost (MC) = ΔTC / ΔQ. When MC < AC, AC falls; when MC > AC, AC rises.
总成本 (TC) = 总固定成本 (TFC) + 总可变成本 (TVC)。平均成本 (AC) = TC / Q。边际成本 (MC) = ΔTC / ΔQ。当 MC < AC 时，AC 下降；当 MC > AC 时，AC 上升。
Total Revenue (TR) = P × Q. Average Revenue (AR) = TR / Q = P. Marginal Revenue (MR) = ΔTR / ΔQ. For a linear demand curve P = a − bQ, MR = a − 2bQ.
总收益 (TR) = P × Q。平均收益 (AR) = TR / Q = P。边际收益 (MR) = ΔTR / ΔQ。对于线性需求曲线 P = a − bQ，MR = a − 2bQ。
The profit-maximising rule is MR = MC. In perfect competition, P = AR = MR, so the rule becomes P = MC. A firm should shut down in the short run if P < AVC.
利润最大化条件为 MR = MC。在完全竞争市场中，P = AR = MR，因此条件简化为 P = MC。若短期内价格低于平均可变成本 (P < AVC)，厂商应停业。
4. Market Structures and Efficiency | 市场结构与效率
In perfect competition, long‑run equilibrium occurs where P = MC = minimum AC, achieving both allocative efficiency (P = MC) and productive efficiency (AC minimized).
在完全竞争市场中，长期均衡发生在 P = MC = 最低 AC 处，同时实现配置效率 (P = MC) 和生产效率 (AC 最小化)。
A monopoly maximises profit at MR = MC, leading to price > MC and output below the socially optimal level, creating a deadweight loss. Price discrimination can transfer consumer surplus to the producer and may increase output.
垄断厂商按 MR = MC 最大化利润，导致价格高于边际成本、产量低于社会最优水平，产生无谓损失。价格歧视可将消费者剩余转移给生产者，并可能增加总产量。
For monopolistic competition and oligopoly, profit max. condition remains MR = MC. Oligopoly models (e.g. kinked demand curve, game theory) explain price rigidity and interdependence.
垄断竞争和寡头垄断的利润最大化条件仍是 MR = MC。寡头模型（如弯折需求曲线、博弈论）解释了价格刚性和相互依赖性。
5. Macroeconomic Indicators: GDP, CPI and Unemployment | 宏观经济指标：GDP、CPI 与失业
Gross Domestic Product (GDP) by expenditure: GDP = C + I + G + (X − M). By income: GDP = wages + rent + interest + profit. Real GDP = (Nominal GDP / GDP Deflator) × 100.
国内生产总值 (GDP) 的支出法：GDP = C + I + G + (X − M)。收入法：GDP = 工资 + 租金 + 利息 + 利润。实际 GDP = (名义 GDP / GDP 平减指数) × 100。
GDP Deflator = (Nominal GDP / Real GDP) × 100. Consumer Price Index (CPI) = (Cost of basket in current year / Cost of basket in base year) × 100. Inflation rate = (CPIt − CPIt−1) / CPIt−1 × 100%.
GDP平减指数 = (名义 GDP / 实际 GDP) × 100。消费者物价指数 (CPI) = (当年一篮子成本 / 基年一篮子成本) × 100。通货膨胀率 = (CPIt − CPIt−1) / CPIt−1 × 100%。
Unemployment rate = (Number of unemployed / Labour force) × 100. Okun’s law states a negative relationship between GDP growth and changes in unemployment.
失业率 = (失业人数 / 劳动力) × 100。奥肯定律描述了 GDP 增长与失业率变化之间的负相关关系。
6. Aggregate Demand and the Multiplier | 总需求与乘数
Aggregate Demand: AD = C + I + G + (X − M). Consumption function: C = a + bYd, where a is autonomous consumption, b is MPC.
总需求：AD = C + I + G + (X − M)。消费函数：C = a + bYd，其中 a 为自主消费，b 为边际消费倾向。
Marginal Propensity to Consume (MPC) = ΔC / ΔYd. MPS = ΔS / ΔYd, MPT = ΔT / ΔY, MPM = ΔM / ΔY. MPC + MPS = 1; including taxes and imports, the leakage rate is MPS + MPT + MPM.
边际消费倾向 (MPC) = ΔC / ΔYd。MPS = ΔS / ΔYd，MPT = ΔT / ΔY，MPM = ΔM / ΔY。MPC + MPS = 1；考虑税收与进口后，漏出率为 MPS + MPT + MPM。
Simple multiplier (k) = 1 / (1 − MPC) = 1 / (MPS + MPT + MPM). Tax multiplier = −MPC / (1 − MPC). The balanced‑budget multiplier equals 1.
简单乘数 (k) = 1 / (1 − MPC) = 1 / (MPS + MPT + MPM)。税收乘数 = −MPC / (1 − MPC)。平衡预算乘数为 1。
7. Money, Inflation and the Quantity Theory | 货币、通货膨胀与货币数量论
The Quantity Theory of Money: MV = PT (or MV = PY). M is money supply, V is velocity, P is price level, T (or Y) is real output. Assuming V and Y constant in the long run, changes in M lead directly to changes in P.
货币数量论：MV = PT (或 MV = PY)。M 为货币供给，V 为流通速度，P 为物价水平，T (或 Y) 为实际产出。假设长期内 V 和 Y 不变，M 的变化直接引起 P 的同向变化。
The Fisher equation: nominal interest rate ≈ real interest rate + expected inflation. This helps explain the relationship between money, inflation and borrowing costs.
费雪方程式：名义利率 ≈ 实际利率 + 预期通货膨胀率。这有助于解释货币、通胀与借贷成本之间的关系。
Deflationary and inflationary gaps can be analysed using the AD‑AS model; an inflationary gap exists when actual GDP > potential GDP, putting upward pressure on the price level.
通货紧缩缺口与通货膨胀缺口可通过 AD‑AS 模型分析；当实际 GDP 大于潜在 GDP 时，存在通胀缺口，物价水平面临上涨压力。
8. International Trade and Exchange Rates | 国际贸易与汇率
Comparative advantage: a country has a comparative advantage in producing a good if its opportunity cost is lower. The terms of trade must lie between the two opportunity cost ratios for mutually beneficial trade.
比较优势：若一国生产某商品的机会成本较低，则其在该商品上具有比较优势。互利的贸易条件必须介于两国的机会成本比率之间。
Terms of trade = (Index of export prices / Index of import prices) × 100. An improvement means a given volume of exports can buy more imports.
贸易条件 = (出口价格指数 / 进口价格指数) × 100。贸易条件改善意味着同等数量的出口能换回更多的进口。
Real exchange rate = nominal exchange rate × (Domestic price level / Foreign price level). The Marshall‑Lerner condition states that a depreciation improves the trade balance if |PEDexports| + |PEDimports| > 1. The J‑curve effect describes a temporary worsening before improvement.
实际汇率 = 名义汇率 × (国内价格水平 / 国外价格水平)。马歇尔‑勒纳条件表明，若进出口需求弹性之和大于 1，本币贬值将改善贸易收支。J 曲线效应描述了先恶化后改善的短暂过程。
9. Economic Development Measures | 经济发展衡量
Human Development Index (HDI) = (Ihealth × Ieducation × Iincome)1/3. Health index uses life expectancy, education index uses mean and expected years of schooling, income index uses log of GNI per capita (PPP$).
人类发展指数 (HDI) = (健康指数 × 教育指数 × 收入指数)1/3。健康指数采用预期寿命，教育指数采用平均与预期受教育年限，收入指数采用人均 GNI (购买力平价) 的对数。
The Gini coefficient = A / (A + B), where A is the area between the Lorenz curve and the line of perfect equality, B the area under the Lorenz curve. It measures income inequality (0 = perfect equality, 1 = perfect inequality).
基尼系数 = A / (A + B)，其中 A 为洛伦兹曲线与绝对平等线之间的面积，B 为洛伦兹曲线下方的面积。它衡量收入不平等程度（0 表示绝对平等，1 表示绝对不平等）。
The Multidimensional Poverty Index (MPI) captures overlapping deprivations in health, education and living standards. The Purchasing Power Parity (PPP) exchange rate adjusts GDP comparisons by equalising the cost of a common basket of goods.
多维贫困指数 (MPI) 反映了健康、教育及生活标准方面的重叠剥夺。购买力平价 (PPP
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