📚 Cambridge Year 12 Economics: Key Formulas & Theorems Quick Reference | 剑桥 Year 12 经济：公式定理速查手册
This quick-reference handbook compiles the essential formulas, definitions, and theorems you need for the Cambridge International AS-Level Economics (Year 12) syllabus. Use it to master elasticity calculations, cost and revenue relationships, national income multipliers, and more. Each entry is presented with a concise explanation followed by its Chinese equivalent so that you can revise bilingually and build a solid foundation for exam success.
这本速查手册汇集了剑桥国际 AS-Level 经济学（十二年级）大纲中的核心公式、定义和定理。你可以用它来掌握弹性计算、成本与收益关系、国民收入乘数等等。每一条内容都配有简洁的英文说明和对应的中文解释，便于双语复习，为考试成功打下坚实基础。
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 calculated as the percentage change in quantity demanded divided by the percentage change in price. The sign is always negative for ordinary goods, but economists often quote the absolute value.
需求的价格弹性衡量需求量对商品自身价格变化的反应程度。它等于需求量变化的百分比除以价格变化的百分比。对于普通商品，该值恒为负数，但经济学家通常引用其绝对值。
PED = %ΔQd / %ΔP
Using the midpoint method to avoid asymmetry, the formula becomes:
为避免不对称性，采用中点法时公式为：
PED = [(Q₂ - Q₁) / ((Q₁ + Q₂)/2)] / [(P₂ - P₁) / ((P₁ + P₂)/2)]
If |PED| > 1 demand is elastic; if |PED| < 1 it is inelastic; if |PED| tal demand curve has PED → ∞ (perfectly elastic). The PED value directly influences a firm's total revenue when price changes.
若 |PED| > 1，需求富有弹性；若 |PED| < 1，需求缺乏弹性；若 |PED| = 1，则为单位弹性。完全垂直的需求曲线 PED = 0（完全无弹性），完全水平的需求曲线 PED → ∞（完全弹性）。PED 的值直接影响价格变动时厂商的总收入变化。
2. Income Elasticity of Demand (YED) | 需求的收入弹性
Income elasticity of demand captures how quantity demanded responds to a change in consumers' real income. It is the percentage change in demand divided by the percentage change in income. The sign is crucial for classifying goods.
需求的收入弹性反映需求量如何对消费者实际收入的变化作出反应。它等于需求量变动的百分比除以收入变动的百分比。其符号对商品分类至关重要。
YED = %ΔQd / %ΔY
Normal goods have a positive YED: necessities have 0 < YED < 1, while luxuries have YED > 1. Inferior goods exhibit a negative YED, because demand falls as income rises. YED helps firms forecast demand shifts during economic booms and recessions.
正常商品具有正的收入弹性：必需品满足 0 < YED < 1，奢侈品则 YED > 1。低档商品的收入弹性为负，因为收入增加时需求反而下降。YED 有助于企业在经济繁荣和衰退期预测需求的变化。
3. Cross Elasticity of Demand (XED) | 需求的交叉弹性
Cross elasticity of demand measures how the quantity demanded of one good (A) changes in response to a price change of another good (B). The formula uses percentage changes and its sign reveals the relationship between the two goods.
需求的交叉弹性衡量一种商品（A）的需求量对另一种商品（B）价格变化的反应程度。公式使用百分比变化，其符号揭示了两种商品之间的关系。
XED = %ΔQd of good A / %ΔP of good B
A positive XED indicates substitute goods (e.g. tea and coffee). A negative XED indicates complement goods (e.g. printers and ink cartridges). XED close to zero suggests the goods are independent. The magnitude of XED indicates the strength of the relationship, which is vital for pricing strategies and merger analyses.
正的 XED 表示替代品（如茶与咖啡）。负的 XED 表示互补品（如打印机与墨盒）。XED 接近零则表明两种商品独立。XED 的大小反映关系的强弱，这对定价策略和并购分析至关重要。
4. Price Elasticity of Supply (PES) | 供给的价格弹性
Price elasticity of supply quantifies how responsive quantity supplied is to a change in the market price. It is always positive, reflecting the law of supply. The calculation closely mirrors that of PED.
供给的价格弹性量化了供给量对市场价格变化的反应程度。它恒为正值，符合供给规律。其计算与 PED 非常相似。
PES = %ΔQs / %ΔP
With the midpoint formula, this is:
使用中点法时则为：
PES = [(Q₂ - Q₁) / ((Q₁ + Q₂)/2)] / [(P₂ - P₁) / ((P₁ + P₂)/2)]
PES > 1 indicates elastic supply; PES < 1 indicates inelastic supply. The elasticity depends mainly on production time, spare capacity, and the ease of accumulating stocks. In the very short run, supply tends to be highly inelastic; over longer periods, it becomes more elastic.
PES > 1 表明供给富有弹性，PES < 1 表明供给缺乏弹性。弹性主要取决于生产时间、闲置产能以及库存积累的难易程度。在极短期，供给往往高度缺乏弹性；随着时间延长，供给会变得更有弹性。
5. Consumer Surplus and Producer Surplus | 消费者剩余与生产者剩余
Consumer surplus is the difference between the total amount consumers are willing to pay for a good and the total amount they actually pay. Producer surplus is the difference between the price producers receive and the minimum price they are willing to accept. These concepts underpin welfare economics.
消费者剩余是消费者愿意为商品支付的最高总金额与实际支付金额的差额。生产者剩余是生产者实际收到的价格与其愿意接受的最低价格之间的差额。这些概念是福利经济学的基础。
Graphically, consumer surplus is the area below the demand curve and above the market price. Producer surplus is the area above the supply curve and below the market price. In a competitive market, the sum of consumer and producer surplus is maximised at the equilibrium point.
在图形中，消费者剩余是需求曲线下方、市场价格上方的面积。生产者剩余是供给曲线上方、市场价格下方的面积。在竞争性市场中，消费者剩余与生产者剩余之和在均衡点达到最大。
Total Welfare = Consumer Surplus + Producer Surplus
Any deadweight loss from a tax or price control represents a reduction in total surplus.
税收或价格管制造成的无谓损失代表着总剩余的减少。
6. Utility Maximization and the Equi-Marginal Principle | 效用最大化与边际均等原则
Consumers are assumed to maximise utility given a budget constraint. The equi-marginal principle states that utility is maximised when the marginal utility per dollar spent is equal across all goods. This is the consumer's equilibrium condition.
假设消费者在预算约束下追求效用最大化。边际均等原则指出，当花在每一种商品上的最后一元所带来的边际效用都相等时，效用达到最大。这就是消费者的均衡条件。
MUₓ / Pₓ = MUᵧ / Pᵧ
nding toward the good with the higher marginal utility per dollar. Indifference curve analysis illustrates the same optimum where the budget line is tangent to the highest attainable indifference curve (MRS = price ratio).
其中 MUₓ 是商品 X 的边际效用，Pₓ 是其价格。如果比率不等，消费者可以通过将支出转向每元边际效用更高的商品来增加总效用。无差异曲线分析展示了同样的最优解，即预算线与可达到的最高无差异曲线相切（MRS = 价格比）。
7. Costs and Revenue in the Short Run | 短期成本与收益
In short-run production theory, firms face both fixed costs (FC) and variable costs (VC). Total cost (TC) is the sum of the two. Marginal cost (MC) is the additional cost of producing one more unit, while average costs are per-unit measures.
在短期生产理论中，企业面临着固定成本（FC）与可变成本（VC）。总成本（TC）为两者之和。边际成本（MC）是多生产一单位产品所增加的成本，而平均成本是衡量单位成本的各种指标。
TC = TFC + TVC
AFC = TFC / Q AVC = TVC / Q ATC = TC / Q
MC = ΔTC / ΔQ
ge in TR from selling one more unit. Under perfect competition, AR = MR = P. For a monopoly or imperfectly competitive firm, MR lies below AR and can become negative.
总收益（TR）等于价格乘以数量：TR = P × Q。平均收益（AR）等于 TR/Q，即价格。边际收益（MR）是多销售一单位产品所带来的总收益变动。在完全竞争条件下，AR = MR = P。对于垄断或不完全竞争企业，MR 位于 AR 之下且可能为负。
8. Profit Maximization Condition | 利润最大化条件
MR). This is the first-order condition. At this output level, the firm cannot add to its profit by producing either more or less.
无论市场结构如何，所有企业都在边际成本等于边际收益（MC = MR）处实现利润最大化。这是一阶条件。在该产量水平上，企业无论增产还是减产都无法增加利润。
Profit Maximization: MC = MR
ut-down condition in the short run is P < AVC, meaning the firm is better off shutting down to minimise losses. In the long run, exit occurs if P < ATC.
对于完全竞争企业，由于 P = MR，该条件变为 MC = P。每单位利润为 AR - ATC；总经济利润为 (AR - ATC) × Q 或 TR - TC。短期内的停业条件是 P < AVC，即企业停业以最小化损失。长期中，若 P < ATC 则企业退出市场。
9. The Multiplier Effect | 乘数效应
ends on the marginal propensity to consume (MPC) and the marginal propensity to save (MPS), where MPC + MPS = 1.
乘数描述了注入经济循环流转的一笔初始支出将如何导致国民收入最终以更大倍数增加。其大小取决于边际消费倾向（MPC）与边际储蓄倾向（MPS），且 MPC + MPS = 1。
Multiplier (k) = 1 / (1 - MPC) = 1 / MPS
+ MPM). The final change in national income equals the initial injection multiplied by k.
如果引入边际税收倾向（MPT）和边际进口倾向（MPM），乘数会变小：k = 1 / (MPS + MPT + MPM)。国民收入的最终变动等于初始注入量乘以 k。
ΔY = k × ΔJ
A high MPC generates a larger multiplier, making fiscal policy more potent but also amplifying the effects of economic shocks.
高 MPC 会产生较大的乘数，使财政政策更有效力，但也会放大经济冲击的影响。
10. The Quantity Theory of Money | 货币数量论
The quantity theory of money, expressed through Fisher's equation of exchange, states that the money supply multiplied by the velocity of circulation equals the price level multiplied by real output. It provides a link between the money stock and nominal GDP.
货币数量论通过费雪交易方程式表达：货币供应量乘以货币流通速度等于价格水平乘以实际产出。该理论建立了货币存量与名义 GDP 之间的联系。
MV = PY
M is the stock of money, V is the income velocity of circulation, P is the average price level, and Y is real national output. Monetarists assume V is stable and Y is determined by real factors, so changes in M lead to proportional changes in P, i.e. inflation is 'always and everywhere a monetary phenomenon'.
M 是货币存量，V 是收入的流通速度，P 是平均价格水平，Y 是实际国民产出。货币主义者假设 V 稳定，Y 由实际因素决定，因此 M 的变化会导致 P 同比例变化，即通胀“无论何时何地都是一种货币现象”。
11. Real vs. Nominal GDP and the GDP Deflator | 实际与名义 GDP 及 GDP 平减指数
Nominal GDP measures the value of output at current prices, while real GDP adjusts for inflation to reflect actual changes in physical output. To compare living standards over time, real GDP must be used.
名义 GDP 以当期价格衡量产出的价值，而实际 GDP 剔除了通货膨胀的影响以反映实际产出的变动。进行跨时期生活水平比较时必须使用实际 GDP。
Real GDP = (Nominal GDP / GDP Deflator) × 100
The GDP deflator is a broad price index calculated as:
GDP 平减指数是一个广义价格指数，计算公式为：
GDP Deflator = (Nominal GDP / Real GDP) × 100
An increase in the deflator indicates a rise in the general price level. Unlike the CPI, the GDP deflator tracks the prices of all domestically produced goods and services and its basket adjusts automatically each year.
GDP 平减指数上升表示总体价格水平上涨。与消费者物价指数（CPI）不同，GDP 平减指数追踪国内生产的所有商品和服务的价格，且其商品篮子每年自动调整。
12. Comparative Advantage and Terms of Trade | 比较优势与贸易条件
Comparative advantage exists when a country can produce a good at a lower opportunity cost than another country. This is the foundation of gains from trade, even when one country has an absolute advantage in all goods. Specialization according to comparative advantage allows trading partners to consume beyond their production possibility frontiers.
当一个国家能够以比另一国更低的机会成本生产某种商品时，它就具有比较优势。这是贸易收益的基础，即使一国在所有商品上都具有绝对优势依然成立。按照比较优势进行专业化分工可使贸易双方消费超出各自的生产可能性边界。
The terms of trade index measures the ratio of a country's export prices to its import prices. An improvement in the terms of trade means a country can buy more imports for a given quantity of exports.
贸易条件指数衡量一国出口价格与进口价格之比。贸易条件的改善意味着一国用一定量的出口可以换回更多的进口。
Terms of Trade Index = (Index of Export Prices / Index of Import Prices) × 100
Negotiating favourable trade balances requires understanding both opportunity cost ratios and the terms of trade. A rise in the index above 100 signals an improvement, but it must be interpreted alongside changes in export and import volumes.
获得有利的贸易平衡需要同时理解机会成本比率和贸易条件。指数上升至 100 以上表明贸易条件改善，但必须结合出口量与进口量的变动加以解读。
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