📚 Pre-U OCR Economics: Quick Reference Handbook of Formulas and Theorems | Pre-U OCR 经济：公式定理速查手册
This handbook gathers the essential formulas and theoretical relationships required for the Pre-U OCR Economics syllabus. Use it to revise quantitative methods, elasticity calculations, cost and revenue curves, macroeconomic aggregates, and key economic theorems. Each entry is presented with a concise definition and its application, helping you to tackle data‑response and essay questions confidently.
本手册汇总了 Pre-U OCR 经济学大纲所必需的核心公式和理论关系。可用它来复习定量方法、弹性计算、成本收益曲线、宏观经济总量以及重要的经济定理。每条公式都配以简要定义和应用说明，帮助你从容应对数据分析题和论文题。
1. Price Elasticity of Demand (PED) | 需求的价格弹性
Price elasticity of demand measures the responsiveness of quantity demanded to a change in price. The coefficient is calculated as:
需求的价格弹性衡量需求量对价格变动的反应程度。其计算公式为：
PED = %ΔQd ÷ %ΔP
Using the midpoint (arc) method for discrete changes: PED = (ΔQd / average Qd) ÷ (ΔP / average P).
对于离散变动，采用中点（弧）法：PED = (ΔQd / 平均 Qd) ÷ (ΔP / 平均 P)。
The sign is negative for most goods, but we often discuss the absolute value. |PED| > 1 indicates elastic demand; |PED| < 1 inelastic; |PED| = 1 unit elastic.
大多数商品的 PED 为负值，但我们通常讨论其绝对值。|PED| > 1 表示富有弹性；|PED| < 1 缺乏弹性；|PED| = 1 单位弹性。
Total revenue test: if demand is elastic, a price fall raises total revenue; if inelastic, a price fall lowers total revenue.
总收益检验：若需求富有弹性，降价会增加总收益；若缺乏弹性，降价会减少总收益。
2. Income Elasticity of Demand (YED) | 需求的收入弹性
Income elasticity of demand shows how quantity demanded responds to a change in consumers’ income.
需求的收入弹性表明需求量如何随消费者收入变化而变动。
YED = %ΔQd ÷ %ΔY
A positive YED means the good is normal; a negative YED signifies an inferior good. For normal goods, YED > 1 indicates a luxury, while 0 < YED < 1 indicates a necessity.
YED 为正表示正常品；YED 为负表示低档品。对于正常品，YED > 1 为奢侈品，0 < YED < 1 为必需品。
Knowledge of YED helps firms forecast demand over the business cycle and adjust product portfolios.
了解 YED 有助于企业在经济周期中预测需求并调整产品组合。
3. Cross‑Price Elasticity of Demand (XED) | 需求的交叉价格弹性
Cross‑price elasticity measures the responsiveness of demand for good X to a change in the price of good Y.
交叉价格弹性衡量商品 X 的需求量对商品 Y 价格变化的反应程度。
XED = %ΔQd of X ÷ %ΔP of Y
If XED > 0, the goods are substitutes; if XED < 0, they are complements. A value close to zero suggests independent goods.
若 XED > 0，两商品互为替代品；若 XED < 0，则为互补品。接近于零则表明相互独立。
Firms use XED to anticipate the impact of rivals’ pricing and to plan marketing strategies for related products.
企业利用 XED 预测竞争对手定价的影响，并制定相关产品的营销策略。
4. Price Elasticity of Supply (PES) | 供给的价格弹性
Price elasticity of supply captures the responsiveness of quantity supplied to a change in price.
供给的价格弹性反映供给量对价格变动的反应程度。
PES = %ΔQs ÷ %ΔP
Key determinants include the time period, availability of spare capacity, ease of storage, and mobility of factors of production. PES > 1 indicates elastic supply; PES < 1 inelastic supply; PES = 0 perfectly inelastic; PES = ∞ perfectly elastic.
关键决定因素包括时间周期、闲置产能、储存难易度以及生产要素的流动性。PES > 1 为富有弹性；PES < 1 缺乏弹性；PES = 0 完全无弹性；PES = ∞ 完全弹性。
In the Pre‑U exam, you may be asked to explain why PES differs between primary commodities and manufactured goods.
在 Pre‑U 考试中，你可能需要解释初级产品和制成品的供给弹性为何不同。
5. Elasticity and Tax Incidence | 弹性与税收归宿
The burden of an indirect tax is shared between consumers and producers depending on relative elasticities.
间接税的负担在消费者和生产者之间分摊，具体取决于相对弹性。
The consumer share of a specific tax t is given approximately by: proportion borne by consumers = PES / (PES + |PED|), and by producers = |PED| / (PES + |PED|). (Note: use absolute PED.)
每单位从量税 t 中消费者承担的份额近似为：消费者负担比例 = PES / (PES + |PED|)，生产者负担比例 = |PED| / (PES + |PED|)。（注意：PED 取绝对值。）
When demand is more inelastic than supply, consumers bear a larger share. This concept explains why governments often impose heavy taxes on goods like tobacco and petrol.
当需求比供给更缺乏弹性时，消费者承担更大份额。这一概念解释了政府为何常对烟草和汽油等商品征收高额税收。
6. Costs, 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 or ATC) = TC ÷ Q. Marginal cost (MC) = ΔTC ÷ ΔQ.
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。
Total revenue (TR) = P × Q. Average revenue (AR) = TR ÷ Q = P. Marginal revenue (MR) = ΔTR ÷ ΔQ.
总收益 (TR) = P × Q。平均收益 (AR) = TR ÷ Q = P。边际收益 (MR) = ΔTR ÷ ΔQ。
The profit‑maximising condition for any firm is MR = MC. In perfect competition, P = MR = AR = MC in the long run. A monopolist restricts output where MR = MC and charges a price on the demand curve above MC.
所有企业的利润最大化条件均为 MR = MC。在完全竞争中，长期均衡时 P = MR = AR = MC。垄断者则在 MR = MC 处限制产量，并依据需求曲线收取高于 MC 的价格。
Normal profit occurs when AC = AR; supernormal profit when AR > AC.
正常利润出现在 AC = AR 时；超额利润出现在 AR > AC 时。
7. Macroeconomic Aggregates and the Multiplier | 宏观经济总量与乘数
GDP can be measured via expenditure: GDP = C + I + G + (X − M), where C is consumption, I investment, G government spending, X exports, M imports.
GDP 可通过支出法衡量：GDP = C + I + G + (X − M)，其中 C 为消费，I 为投资，G 为政府支出，X 为出口，M 为进口。
The marginal propensity to consume (MPC) = ΔC / ΔY, and the marginal propensity to save (MPS) = 1 − MPC. The simple Keynesian multiplier k = 1 / (1 − MPC) = 1 / MPS. With taxes and imports, the multiplier becomes k = 1 / (1 − MPC(1 − t) + MPM), where t is the marginal tax rate and MPM the marginal propensity to import.
边际消费倾向 (MPC) = ΔC / ΔY，边际储蓄倾向 (MPS) = 1 − MPC。简单凯恩斯乘数 k = 1 / (1 − MPC) = 1 / MPS。若包含税收和进口，乘数变为 k = 1 / (1 − MPC(1 − t) + MPM)，其中 t 为边际税率，MPM 为边际进口倾向。
A change in autonomous spending (ΔA) leads to a multiplied change in national income: ΔY = k × ΔA. This is central to fiscal policy analysis.
自发支出的变动 (ΔA) 会导致国民收入若干倍的变动：ΔY = k × ΔA。这是财政政策分析的核心。
8. Money, Banking and the Credit Multiplier | 货币、银行与信贷乘数
The money multiplier shows how an initial increase in bank reserves can lead to a larger increase in the money supply. Under the simple model: Money multiplier = 1 / reserve requirement ratio (RRR). So Δ Money supply = initial excess reserves × (1 / RRR).
货币乘数表明银行体系初始准备金的增加如何带来货币供给更大幅度的增加。在简单模型中：货币乘数 = 1 / 法定准备金率 (RRR)。因此 Δ 货币供给 = 初始超额准备金 × (1 / RRR)。
Modern monetary policy focuses more on interest rate channels than on strict reserve requirements, but the concept is still tested in the Pre‑U.
现代货币政策更侧重利率渠道而非严格的准备金要求，但该概念在 Pre‑U 考试中仍有涉及。
9. Exchange Rates and the Terms of Trade | 汇率与贸易条件
The terms of trade index = (index of export prices ÷ index of import prices) × 100. An improvement means a country can buy more imports for a given volume of exports.
贸易条件指数 = (出口价格指数 ÷ 进口价格指数) × 100。贸易条件改善意味着一国在出口量不变的情况下能购买更多的进口品。
Exchange rates can be quoted directly (domestic currency per unit of foreign) or indirectly. For the Pre‑U, you should be able to calculate effective exchange rates using trade‑weighted indices.
汇率可用直接标价法（一单位外币的本币价格）或间接标价法表示。在 Pre‑U 中，你应能运用贸易加权指数计算有效汇率。
Purchasing power parity (PPP) states that in the long run exchange rates should adjust so that identical goods cost the same across countries: Exchange rate = Price level abroad ÷ Price level domestic (using the correct quotation).
购买力平价 (PPP) 指出，长期内汇率应调整到使相同商品在不同国家的价格一致：汇率 = 国外物价水平 ÷ 国内物价水平（使用正确的标价法）。
10. Diagrammatic and Game‑Theory Theorems | 图形与博弈论定理
Pre‑U candidates are expected to apply not only formulas but key theorems in market structures and strategic behaviour. In a Cournot duopoly, each firm’s reaction function determines the Nash equilibrium output. The market price lies between the competitive and monopoly levels.
Pre‑U 考生不仅需要运用公式，还需掌握市场结构与策略行为中的关键定理。在古诺双寡头模型中，每家企业的反应函数决定了纳什均衡产量。市场价格介于竞争价格和垄断价格之间。
In a Nash equilibrium, no player can improve their payoff by unilaterally changing strategy. The prisoner’s dilemma illustrates why collusion may break down even when it is mutually beneficial.
在纳什均衡中，任何参与者都无法通过单方面改变策略来改善收益。囚徒困境表明，即使共谋对双方有利，也可能破裂。
The shut‑down point for a firm in the short run is where price falls below average variable cost (AVC). The break‑even point is where price equals average total cost (ATC). These thresholds are essential for evaluating contestability and monopoly diagrams.
企业短期停业点出现在价格低于平均可变成本 (AVC) 时。盈亏平衡点出现在价格等于平均总成本 (ATC) 时。这些临界点对于评估可竞争市场和垄断图表至关重要。
11. Lorenz Curve and Gini Coefficient | 洛伦兹曲线与基尼系数
The Lorenz curve plots the cumulative percentage of income (or wealth) against the cumulative percentage of population. The Gini coefficient is a summary measure of inequality derived from this curve.
洛伦兹曲线描绘了收入（或财富）的累计百分比与人口的累计百分比。基尼系数是从该曲线推导出的衡量不平等程度的汇总指标。
Gini coefficient = A / (A + B)
where A is the area between the line of perfect equality and the Lorenz curve, and B is the area under the Lorenz curve. The coefficient ranges from 0 (perfect equality) to 1 (perfect inequality).
其中 A 是完全平等线与洛伦兹曲线之间的面积，B 是洛伦兹曲线下方的面积。该系数的取值范围为 0（完全平等）至 1（完全不平等）。
12. Phillips Curve and Policy Trade‑offs | 菲利普斯曲线与政策权衡
The short‑run Phillips curve illustrates an inverse relationship between the rate of unemployment and the rate of wage (or price) inflation: π = π^e − β(u − u_n) + supply shocks, where π is inflation, π^e expected inflation, u unemployment, u_n the natural rate, and β a positive parameter.
短期菲利普斯曲线表明失业率与工资（或价格）通胀率之间存在反向关系：π = π^e − β(u − u_n) + 供给冲击，其中 π 为通胀，π^e 为预期通胀，u 为失业率，u_n 为自然失业率，β 为正值参数。
In the long run, the expectations‑augmented Phillips curve is vertical at the natural rate of unemployment, implying no permanent trade‑off between inflation and unemployment.
长期中，附加预期的菲利普斯曲线在自然失业率处垂直，意味着通胀与失业之间不存在持久的权衡取舍。
Pre‑U candidates should be able to use these relationships to analyse stagflation, demand‑side and supply‑side policies, and the role of credibility in central banking.
Pre‑U 考生应能运用这些关系分析滞胀、需求侧与供给侧政策，以及央行可信度的作用。
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