📚 Pre-U CAIE Economics: Essential Formulas & Theorems Quick Reference | Pre-U CAIE 经济：公式定理速查手册
This quick reference handbook covers the core formulas, theorems, and key quantitative relationships required for the Cambridge Pre-U Economics syllabus. It is designed to support revision and retrieval practice, helping you move from memorisation to confident application in both Paper 1 and Paper 2.
本速查手册涵盖剑桥Pre-U经济学大纲的核心公式、定理与关键数量关系。手册旨在辅助复习与检索练习，帮助你从死记硬背过渡到在Paper 1和Paper 2中自信应用。
1. Price Elasticity of Demand (PED) | 需求价格弹性
PED measures the responsiveness of quantity demanded to a change in the good’s own price. It is always negative due to the law of demand, but the absolute value is often used to classify elasticity. The formula uses percentage changes to avoid unit dependency.
PED衡量需求量对商品自身价格变化的反应程度。由于需求定律，它始终为负值，但通常使用绝对值对弹性进行分类。该公式使用百分比变化以避免单位依赖。
PED = (%ΔQd) / (%ΔP)
Where %ΔQd = (ΔQd / Qd) × 100 and %ΔP = (ΔP / P) × 100. Alternatively, the mid-point (arc) elasticity formula can be used to obtain the same result regardless of direction: PED = (ΔQd / average Qd) ÷ (ΔP / average P). PED > 1 elastic; PED < 1 inelastic; PED = 1 unit elastic; PED = 0 perfectly inelastic; PED = ∞ perfectly elastic.
其中%ΔQd = (ΔQd / Qd) × 100, %ΔP = (ΔP / P) × 100。也可以使用中点（弧）弹性公式，使结果不因变动方向而异：PED = (ΔQd / Qd平均值) ÷ (ΔP / P平均值)。PED > 1 富有弹性；PED < 1 缺乏弹性；PED = 1 单位弹性；PED = 0 完全无弹性；PED = ∞ 完全弹性。
2. Income Elasticity of Demand (YED) | 需求收入弹性
YED quantifies how quantity demanded responds to a change in consumers’ income. It shows whether a good is normal, luxury or inferior, and is a key tool for firms making output decisions over the business cycle.
YED量化需求量对消费者收入变化的反应。它表明商品是正常品、奢侈品还是劣等品，也是企业在经济周期中制定产量决策的重要工具。
YED = (%ΔQd) / (%ΔY)
If YED > 0, the good is normal; between 0 and 1 it is a necessity, above 1 it is a luxury. If YED < 0, the good is inferior. An increasing share of income spent on luxury goods as income rises reflects Engel's Law.
若YED > 0，商品为正常品；介于0与1之间为必需品，大于1为奢侈品。若YED < 0，商品为劣等品。收入增长时花在奢侈品上的收入比例上升，这反映了恩格尔定律。
3. Cross Elasticity of Demand (XED) | 需求交叉弹性
XED measures the sensitivity of demand for one good to a change in the price of another. The sign and magnitude reveal whether goods are substitutes, complements or unrelated.
XED衡量一种商品的需求对另一种商品价格变动的敏感程度。正负号与大小可以揭示商品之间是替代品、互补品还是无关品。
XED = (%ΔQd of good A) / (%ΔP of good B)
Positive XED indicates substitutes; the larger the value, the closer the substitutes. Negative XED indicates complements; the more negative, the stronger the complement relationship. An XED near zero suggests independent goods. This information is critical for pricing strategy and competitive analysis.
XED为正表示替代品；数值越大，替代性越强。XED为负表示互补品；负值越大，互补关系越强。XED接近零则表明商品独立。这一信息对于定价策略与竞争分析至关重要。
4. Price Elasticity of Supply (PES) | 供给价格弹性
PES captures the responsiveness of quantity supplied to a change in the good’s price. It reflects the flexibility of producers to adjust output, determined primarily by time period, spare capacity, and the mobility of factors of production.
PES反映供给量对商品价格变动的反应程度。它体现了生产者调整产量的灵活程度，主要由时间周期、闲置产能以及生产要素的流动性决定。
PES = (%ΔQs) / (%ΔP)
Because the supply curve slopes upward, PES is typically positive. PES > 1 indicates elastic supply; PES < 1 inelastic supply; PES = 0 perfectly inelastic (momentary run); PES = ∞ perfectly elastic. The momentary, short run and long run supply curves exhibit increasing elasticity as firms can adjust all inputs.
由于供给曲线向上倾斜，PES通常为正。PES > 1 表示供给富于弹性；PES < 1 表示供给缺乏弹性；PES = 0 完全无弹性（瞬时供给）；PES = ∞ 完全弹性。瞬时、短期与长期供给曲线弹性递增，因为企业可以调整所有投入。
5. Costs, Revenue and Profit | 成本、收益与利润
Understanding cost and revenue structures is fundamental to the theory of the firm. The formulas below link total, average and marginal quantities, which are then used to determine the profit-maximising output level.
理解成本与收益结构是厂商理论的基础。以下公式将总量、平均量与边际量联系起来，进而用于决定利润最大化产量。
Total Cost (TC) = Total Fixed Cost (TFC) + Total Variable Cost (TVC)
Average Cost (AC) = TC / Q
Marginal Cost (MC) = ΔTC / ΔQ
Total Revenue (TR) = Price (P) × Quantity (Q)
Average Revenue (AR) = TR / Q = P
Marginal Revenue (MR) = ΔTR / ΔQ
Profit (π) = TR – TC
Normal profit occurs when TR = TC (i.e., zero economic profit, AC = AR). Supernormal profit arises when TR > TC. The shutdown condition in the short run is P < AVC; in the long run, the firm exits if P < ATC.
正常利润出现在TR = TC（即经济利润为零，AC = AR）。超额利润出现在TR > TC。短期停业条件为P < AVC；长期若P < ATC，企业将退出市场。
6. Market Structures and Profit Maximisation | 市场结构与利润最大化
All profit-maximising firms follow the golden rule: produce where Marginal Revenue equals Marginal Cost, provided price covers average variable cost in the short run. The shape of AR and MR curves differs across market structures, influencing price, output and efficiency outcomes.
所有追求利润最大化的企业都遵循黄金法则：在边际收益等于边际成本处生产，前提是短期价格高于平均可变成本。AR与MR曲线的形状因市场结构而异，影响了价格、产量与效率结果。
Profit-maximising condition: MR = MC
| Market Structure | AR & MR characteristics | Long-run equilibrium |
|---|---|---|
| Perfect Competition | AR = MR = P (horizontal) | P = MC = AC (normal profit, productive & allocative efficiency) |
| Monopoly | AR downward sloping; MR lies below AR | P > MC; may earn supernormal profit even in long run |
| Monopolistic Competition | Downward sloping AR & MR but relatively elastic | P > MC, AR = AC (normal profit, excess capacity) |
| Oligopoly | Kinked demand curve possible; interdependent pricing | Price rigidity; competition often non-price |
In perfect competition, allocative efficiency is achieved (P = MC). Monopoly tends to produce lower output at higher price, causing a deadweight welfare loss. Price discrimination can partly transfer consumer surplus to producer surplus.
在完全竞争中，配置效率得以实现（P = MC）。垄断倾向于以更高的价格生产更低的产量，造成无谓福利损失。价格歧视能将部分消费者剩余转为生产者剩余。
7. Aggregate Demand and Supply | 总需求与总供给
Macroeconomic equilibrium is established where aggregate demand equals aggregate supply. The components of AD and the shape of the AS curve determine national output, price level and potential inflationary or deflationary gaps.
宏观经济均衡在总需求等于总供给处建立。AD的构成与AS曲线的形状决定了国民产出、价格水平以及可能出现的通胀缺口或通缩缺口。
AD = Consumption (C) + Investment (I) + Government Spending (G) + (Exports (X) – Imports (M))
Aggregate supply can be represented by a Keynesian AS curve with horizontal, upward-sloping and vertical sections, or by a classical long-run AS (LRAS) which is vertical at the full employment level of output. A rise in AD in the vertical zone is purely inflationary.
总供给可以用凯恩斯AS曲线表示，该曲线具有水平区、上升区和垂直区；或者用古典长期AS (LRAS)表示，它在充分就业产出水平处垂直。垂直区内AD的增加只会引发通胀。
Inflationary gap: actual output > potential output; Deflationary gap: actual output < potential output
The multiplier process amplifies any initial change in AD, making the eventual shift in income larger than the initial injection. The simple multiplier assumes no taxes or imports.
乘数过程将初始AD变动放大，使得收入的最终变化大于初始注入。简单乘数假定不存在税收或进口。
8. Multiplier and National Income | 乘数与国民收入
The multiplier is central to Keynesian demand management. It captures the proportional increase in final income arising from an injection of spending. The size of the multiplier depends on the marginal propensities to consume, save, tax and import.
乘数是凯恩斯需求管理的核心。它反映由支出注入所引致的最终收入成比例增加。乘数大小取决于边际消费倾向、边际储蓄倾向、边际税率和边际进口倾向。
Multiplier (k) = 1 / (1 – MPC) = 1 / MPS
Where MPC + MPS = 1. In an open economy with a government, the formula extends to k = 1 / (MPS + MPT + MPM), where MPT is the marginal propensity to tax and MPM is the marginal propensity to import. Effectively, a higher withdrawal rate reduces the multiplier.
其中MPC + MPS = 1。在存在政府的开放经济中，公式扩展为k = 1 / (MPS + MPT + MPM)，其中MPT为边际税收倾向，MPM为边际进口倾向。实际上，漏出率越高，乘数越小。
ΔNational Income = k × ΔInjection (e.g., ΔI or ΔG)
The circular flow model reveals three injections (I, G, X) and three withdrawals (S, T, M). Equilibrium occurs when total injections equal total withdrawals. Any disequilibrium will be corrected by a change in national income via the multiplier.
收入循环流动模型表明三组注入（I, G, X）和三组漏出（S, T, M）。当总注入等于总漏出时实现均衡。任何非均衡将通过乘数效应引起的国民收入变化得以校正。
9. Balance of Payments and Exchange Rates | 国际收支与汇率
The balance of payments records all transactions between a country and the rest of the world. Exchange rates adjust to bring the overall balance into equilibrium, though managed floats and fixed regimes are common. Several indices help analyse external competitiveness.
国际收支记录一国与世界其他地区之间的所有交易。汇率调整以促使总体收支平衡，不过管理浮动汇率与固定制度也很常见。若干指数有助于分析外部竞争力。
Current Account = Trade in Goods + Trade in Services + Primary Income + Secondary Income
A current account deficit must be matched by a capital and financial account surplus (and vice versa) under a floating exchange rate, where the supply and demand for the currency determine its external value. Changes in relative inflation, interest rates, productivity and speculative sentiment drive exchange rate movements.
在浮动汇率下，经常账户赤字必须由资本与金融账户盈余加以匹配（反之亦然），而货币供求决定其对外价值。相对通胀、利率、生产率和投机情绪的变化驱动汇率波动。
Real Exchange Rate = (Nominal Exchange Rate × Foreign Price Level) / Domestic Price Level
A rise in the real exchange rate implies a real appreciation, making exports less competitive. The Marshall-Lerner condition states that a depreciation will improve the current account if the sum of the absolute values of PED for exports and PED for imports is greater than 1.
实际汇率上升意味着实际升值，使出口竞争力下降。马歇尔-勒纳条件指出，若出口PED与进口PED的绝对值之和大于1，货币贬值将改善经常账户。
10. Terms of Trade and Trade | 贸易条件与贸易
The terms of trade measure the rate at which one country’s exports exchange for imports. Improvements in the terms of trade do not automatically improve the current account, as volume effects depend on elasticities.
贸易条件衡量一国出口商品交换进口商品的比率。贸易条件的改善并不会自动改善经常账户，因为数量效应取决于弹性。
Terms of Trade Index = (Index of Export Prices / Index of Import Prices) × 100
A rise in the index indicates a favourable movement: fewer exports are needed to buy a given quantity of imports. Yet this can reduce export volume, potentially worsening the trade balance if demand is elastic. Prebisch-Singer hypothesis suggests long-run deterioration for primary commodity exporters.
该指数上升表示有利变动：购买一定量进口品所需的出口品减少。但这可能减少出口量，若需求富有弹性则可能恶化贸易平衡。普雷维什-辛格假说认为初级产品出口国面临长期贸易条件恶化。
Gains from trade: world price ratio lies between domestic opportunity cost ratios
Comparative advantage remains the foundation of trade, with the theory extended by factor endowments (Heckscher-Ohlin). The tariff diagram demonstrates deadweight loss through higher domestic prices and reduced consumption, while a quota yields similar welfare effects with an additional quota rent.
比较优势仍然是贸易的基础，要素禀赋理论（赫克歇尔-俄林）将其扩展。关税图示表明，国内价格上升和消费减少导致无谓损失，而配额产生类似的福利效应，并额外带来配额租金。
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