📚 Pre-U Cambridge Economics: Formula & Theorem Quick Reference Handbook | Pre-U 剑桥经济：公式定理速查手册
This quick reference handbook brings together the essential formulas, theorems and quantitative relationships that underpin analysis in the Cambridge Pre-U Economics syllabus. From basic microeconomic elasticities to macroeconomic multipliers and the Phillips curve, each entry is explained with clarity and accompanied by its Chinese equivalent, making it a bilingual revision tool. Use it to consolidate your understanding, practise numerical applications and build confidence for examination questions that demand precise, technically accurate reasoning.
本速查手册汇集了剑桥 Pre-U 经济学课程中支撑分析的核心公式、定理与数量关系。从基础的微观弹性到宏观乘数以及菲利普斯曲线，每个条目均附有清晰解释及中文对照，构成双语复习工具。可利用本手册巩固理解、练习数字应用，并在面对要求精确且技术性严密推理的试题时树立信心。
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 the good’s own price. It is defined as the percentage change in quantity demanded divided by the percentage change in price.
需求价格弹性衡量需求量对商品自身价格变动的反应程度。它定义为需求量变动百分比除以价格变动百分比。
PED = %ΔQd ÷ %ΔP
其中 %ΔQd 表示需求量变动的百分比，%ΔP 表示价格变动的百分比。弹性值通常为负数，反映需求定律，但通常比较其绝对值。
Because PED is usually negative (owing to the law of demand), economists typically refer to its absolute value. When |PED| > 1, demand is elastic; when |PED| < 1, demand is inelastic; and when |PED| = 1, demand is unit elastic. A perfectly inelastic demand curve is vertical (PED = 0), while a perfectly elastic demand curve is horizontal (PED = ∞).
由于 PED 通常为负（需求定律），经济学家通常取其绝对值讨论。当 |PED| > 1 时，需求富有弹性；当 |PED| < 1 时，需求缺乏弹性；当 |PED| = 1 时，需求为单位弹性。完全无弹性的需求曲线是垂直的（PED = 0），而完全有弹性的需求曲线是水平的（PED = ∞）。
Total revenue (TR) responds predictably to price changes depending on PED. If demand is elastic, a price cut raises TR; if demand is inelastic, a price rise raises TR. At unit elasticity, TR is maximised for a linear demand curve.
总收入（TR）对价格变动的反应取决于 PED。若需求富有弹性，降价会提高总收入；若需求缺乏弹性，提价会提高总收入。在单位弹性点，线性需求曲线上的总收入最大化。
Using the midpoint formula improves accuracy when calculating PED over an arc: PED = (ΔQ / Qavg) ÷ (ΔP / Pavg), where Qavg and Pavg are the average quantity and price.
使用中点公式能提高弧弹性计算的精确度：PED = (ΔQ / Qavg) ÷ (ΔP / Pavg)，其中 Qavg 和 Pavg 分别为平均数量与平均价格。
2. Income Elasticity of Demand (YED) | 需求的收入弹性
Income elasticity of demand captures how quantity demanded changes as consumer income changes. It is the ratio of the percentage change in quantity demanded to the percentage change in income.
需求收入弹性捕捉需求量如何随消费者收入变化而变化。它是需求量变动百分比与收入变动百分比之比。
YED = %ΔQd ÷ %ΔY
YED enables classification of goods. A positive YED indicates a normal good; a negative YED identifies an inferior good. Among normal goods, a YED greater than 1 denotes a luxury, while a YED between 0 and 1 signifies a necessity.
YED 可用来对商品进行分类。正的 YED 表明正常品；负的 YED 则为劣等品。在正常品中，YED 大于 1 的是奢侈品，介于 0 和 1 之间的则是必需品。
The Engel curve illustrates the relationship between income and expenditure on a good. For necessities, the curve flattens as income rises; for luxuries, expenditure rises more than proportionally.
恩格尔曲线刻画了收入与商品支出之间的关系。必需品的曲线随收入增加而趋于平坦，奢侈品则支出上升比例超过收入上升比例。
3. Cross Elasticity of Demand (XED) | 需求的交叉弹性
Cross elasticity of demand measures the sensitivity of demand for one good to a change in the price of another good. It is computed as the percentage change in quantity demanded of good A divided by the percentage change in the price of good B.
需求的交叉弹性衡量一种商品的需求对另一种商品价格变动的敏感程度。其计算方式为 A 商品需求量变动的百分比除以 B 商品价格变动的百分比。
XED = %ΔQdA ÷ %ΔPB
A positive XED reveals that the two goods are substitutes; a negative XED indicates complements. A value close to zero suggests the goods are independent. Strong substitutability or complementarity corresponds to a larger absolute value of XED.
正的 XED 表明两种商品为替代品，负的 XED 则表明两者为互补品。接近零的数值意味着商品相互独立。替代性或互补性越强，XED 的绝对值就越大。
Firms use XED to anticipate the impact of rivals’ pricing strategies on their own sales and to design product portfolios. Governments may examine XED when assessing the likely consequences of indirect taxes on related markets.
企业利用 XED 预判竞争对手定价策略对自身销售的影响，并设计产品组合。政府在评估间接税对相关市场可能造成的后果时，也会考察 XED。
4. Price Elasticity of Supply (PES) | 供给的价格弹性
Price elasticity of supply gauges the responsiveness of quantity supplied to a variation in the good’s own price. Its definition mirrors that of PED but uses quantity supplied.
供给的价格弹性衡量供给量对商品自身价格变动的反应程度。其定义与 PED 类似，但使用的是供给量。
PES = %ΔQs ÷ %ΔP
PES is typically positive because a higher price provides an incentive to expand output. When PES > 1, supply is elastic; when PES < 1, supply is inelastic; and when PES = 1, it is unit elastic. Perfectly inelastic supply (PES = 0) is vertical, and perfectly elastic supply (PES = ∞) is horizontal.
PES 通常为正值，因为更高的价格激励厂商扩大产出。PES > 1 时供给富有弹性，PES < 1 时供给缺乏弹性，PES = 1 时为单位弹性。完全无弹性供给（PES = 0）为垂直线，完全有弹性供给（PES = ∞）为水平线。
Determinants include time period, availability of spare capacity, flexibility of the production process, ability to store stocks and the ease with which factors of production can be reallocated. Supply tends to be more elastic in the long run than in the short run.
决定因素包括时间长短、闲置产能可用性、生产过程的灵活性、储存能力以及生产要素重新配置的难易程度。长期供给弹性通常大于短期。
5. Costs, Revenue and Profit Maximisation | 成本、收益与利润最大化
Cost analysis begins with total cost (TC), which comprises total fixed cost (TFC) and total variable cost (TVC): TC = TFC + TVC. Average cost (AC) is total cost divided by output, and it can be split into average fixed cost (AFC) and average variable cost (AVC): AC = AFC + AVC.
成本分析始于总成本（TC），它包含总固定成本（TFC）与总可变成本（TVC）：TC = TFC + TVC。平均成本（AC）等于总成本除以产量，并可拆分为平均固定成本（AFC）与平均可变成本（AVC）：AC = AFC + AVC。
MC = ΔTC ÷ ΔQ
Marginal cost (MC) is the extra cost of producing one additional unit of output. It is calculated as the change in total cost (or total variable cost) divided by the change in quantity.
边际成本（MC）是多生产一单位产出所带来的额外成本，其计算为总成本（或总可变成本）的变动量除以数量的变动量。
On the revenue side, total revenue is price multiplied by quantity: TR = P × Q. Average revenue (AR) equals TR ÷ Q, which is simply the price. Marginal revenue (MR) is the additional revenue from selling one more unit: MR = ΔTR ÷ ΔQ.
在收益方面，总收入等于价格乘以数量：TR = P × Q。平均收益（AR）等于 TR ÷ Q，即为价格。边际收益（MR）是多销售一单位所带来的额外收益：MR = ΔTR ÷ ΔQ。
A firm aiming to maximise profit produces the output at which marginal cost equals marginal revenue.
以利润最大化为目标的厂商会在边际成本等于边际收益的产量水平上进行生产。
Profit maximisation: MC = MR
Normal profit, the minimum return required to keep resources in their current use, is included in AC. Supernormal (or abnormal) profit arises when TR exceeds TC, i.e. when AR > AC.
正常利润是维持资源当前用途所需的最低回报，已包含在平均成本中。当总收入超过总成本，即 AR > AC 时，产生超额（或经济）利润。
6. Market Power and the Lerner Index | 市场势力与勒纳指数
The Lerner Index quantifies a firm’s market power by measuring the markup of price over marginal cost as a proportion of price.
勒纳指数通过衡量价格高于边际成本的幅度占价格的比例来量化厂商的市场势力。
L = (P – MC) ÷ P
The index ranges from 0 (perfect competition, where P = MC) to nearly 1 (extreme monopoly power). A higher Lerner Index indicates greater ability to set prices above competitive levels.
该指数介于 0（完全竞争，P = MC）到接近 1（极强垄断势力）之间。勒纳指数越高，表明定价高于竞争水平的能力越强。
Under profit‑maximisation, the Lerner Index is inversely related to the absolute value of the price elasticity of demand facing the firm.
在利润最大化条件下，勒纳指数与厂商面临的需求价格弹性的绝对值存在反向关系。
L = 1 ÷ |PED|
Hence, the more inelastic the demand, the greater the market power. This relationship helps competition authorities assess the welfare costs of monopoly and evaluate regulatory interventions.
因此，需求愈缺乏弹性，市场势力愈大。这一关系有助于竞争监管机构评估垄断的福利成本并审视监管干预措施。
7. The Multiplier Effect | 乘数效应
The multiplier measures the magnification of an initial change in autonomous spending into a larger change in national income. In a simple closed economy without a government, the size of the multiplier depends on the marginal propensity to consume (MPC).
乘数衡量自主支出的初始变动被放大为更大的国民收入变动的倍数。在一个无政府的简单封闭经济中，乘数的大小取决于边际消费倾向（MPC）。
k = 1 ÷ (1 – MPC) = 1 ÷ MPS
MPC + MPS = 1, where MPS is the marginal propensity to save. A high MPC (low MPS) produces a large multiplier, because a greater fraction of additional income is respent.
MPC + MPS = 1，其中 MPS 为边际储蓄倾向。高 MPC（低 MPS）会产生较大的乘数，因为额外收入中被再支出的比例更大。
In an open economy with government, leakages include saving, taxation and imports. The multiplier shrinks when marginal propensity to tax (MPT) and marginal propensity to import (MPM) are introduced.
在包含政府的开放经济中，漏出项包括储蓄、税收和进口。当引入边际税收倾向（MPT）和边际进口倾向（MPM）时，乘数会缩小。
k = 1 ÷ (MPS + MPT + MPM)
Understanding the multiplier is critical for evaluating the likely impact of fiscal policy. A tax multiplier, such as –MPC/MPS, indicates that an increase in taxation reduces national income by a multiple of the initial tax rise.
理解乘数对于评估财政政策的可能影响至关重要。税收乘数，例如 –MPC/MPS，表明增税会使国民收入以初始增税额的倍数减少。
8. Quantity Theory of Money | 货币数量论
The quantity theory of money is encapsulated in the equation of exchange, which links the money supply to the price level and real output.
货币数量论集中体现在交易方程式中，该方程式将货币供给与价格水平和实际产出联系起来。
M × V = P × Y
Here M is the money supply, V is the velocity of circulation, P is the general price level and Y is real GDP (or real output). An alternative formulation uses T for the volume of transactions: MV = PT.
其中 M 为货币供给，V 为货币流通速度，P 为总体物价水平，Y 为实际 GDP（或实际产出）。另一个表达式用 T 代表交易量：MV = PT。
Classical economists assume that V is stable in the short run and that real output Y is determined by supply‑side factors (the classical dichotomy). In this framework, changes in the money supply lead to proportionate changes in the
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