📚 Quick Reference Handbook: Key Formulas and Theorems for Year 13 CIE Economics | 公式定理速查手册
Welcome to your essential companion for Year 13 CIE Economics. This handbook brings together every core formula, theorem, and quantitative relationship you are expected to master—from elasticity calculations and cost curves to macroeconomic multipliers and exchange rate mechanics. Keep it close as you work through past papers so you can apply each concept accurately and confidently under timed conditions.
欢迎使用这份针对 Year 13 CIE 经济的必备速查手册。本手册汇集了你在 A-Level 经济阶段需要掌握的所有核心公式、定理和数量关系——从弹性计算、成本曲线到宏观经济乘数、汇率机制。在你做历年真题时，请把它放在手边，这样你就能在限时条件下准确且自信地运用每一个概念。
1. Price Elasticity of Demand (PED) | 需求价格弹性
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.
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。它的计算方法是需求量变动的百分比除以价格变动的百分比。
PED = %ΔQd ÷ %ΔP = (ΔQd / Qd) ÷ (ΔP / P)
y inelastic, and PED = ∞ is perfectly elastic. Total revenue rises when price falls in the elastic range, and rises when price rises in the inelastic range.
当 PED > 1 时，需求富有价格弹性（奢侈品）；当 PED < 1 时，需求缺乏价格弹性（必需品）。PED = 1 为单位弹性，PED = 0 为完全无弹性，PED = ∞ 为完全弹性。在弹性区间，价格下降总收益增加；在缺乏弹性区间，价格上升总收益增加。
2. Income Elasticity of Demand (YED) | 需求收入弹性
Income elasticity of demand captures how quantity demanded responds to changes in consumer income. The formula is the percentage change in quantity demanded divided by the percentage change in income.
需求收入弹性反映需求量如何随消费者收入变化而变化。公式为需求量变动的百分比除以收入变动的百分比。
YED = %ΔQd ÷ %ΔY
Normal goods have positive YED (YED > 0): necessities have YED between 0 and 1, while luxury goods have YED > 1. Inferior goods have negative YED (YED < 0). For CIE exams, you must interpret YED values to predict shifts in demand as economies grow or contract.
正常品具有正的收入弹性（YED > 0）：必需品的收入弹性在 0 到 1 之间，奢侈品大于 1。低档品的收入弹性为负（YED < 0）。在 CIE 考试中，你必须会解读收入弹性值，以预测经济增长或收缩时需求的移动。
3. Cross Elasticity of Demand (XED) | 需求交叉弹性
Cross elasticity of demand shows the responsiveness of demand for one good to a change in the price of another good. It equals the percentage change in quantity demanded of good A divided by the percentage change in price of good B.
需求交叉弹性显示一种商品的需求对另一种商品价格变化的反应程度。它等于商品 A 需求量变动的百分比除以商品 B 价格变动的百分比。
XED = %ΔQd of A ÷ %ΔP of B
Substitutes have positive XED (e.g. tea and coffee). Complements have negative XED (e.g. printers and ink cartridges). Unrelated goods have XED close to zero. The magnitude of XED indicates the closeness of the relationship, which firms use to assess competitive threats and pricing strategies.
替代品具有正的交叉弹性（如茶与咖啡）。互补品具有负的交叉弹性（如打印机与墨盒）。无关商品的交叉弹性接近于零。交叉弹性的绝对值大小表示关系的紧密程度，企业可据此评估竞争威胁和定价策略。
4. Price Elasticity of Supply (PES) | 供给价格弹性
Price elasticity of supply measures the responsiveness of quantity supplied to a change in price. It is the percentage change in quantity supplied divided by the percentage change in price.
供给价格弹性衡量供给量对价格变化的反应程度。它是供给量变动的百分比除以价格变动的百分比。
PES = %ΔQs ÷ %ΔP
(fixed supply like seats in a stadium), and perfectly elastic when PES = ∞ (constant cost industry). Key determinants include time period, spare capacity, and ease of factor substitution.
当 PES > 1 时供给富有弹性（工业制成品）；PES < 1 时供给缺乏弹性（存在时滞的农产品）；PES = 0 为完全无弹性（固定供给，如体育场座位数）；PES = ∞ 为完全弹性（成本不变行业）。主要决定因素包括时间跨度、闲置产能和要素替代的难易程度。
5. Short-Run Cost and Revenue Relationships | 短期成本与收益关系
In the short run, at least one factor is fixed. Total cost (TC) equals total fixed cost (TFC) plus total variable cost (TVC). Average total cost (ATC) is TC divided by output (Q). Marginal cost (MC) is the addition to total cost from producing one more unit.
在短期，至少有一种生产要素固定。总成本 (TC) 等于总固定成本 (TFC) 加总变动成本 (TVC)。平均总成本 (ATC) 等于 TC 除以产量 (Q)。边际成本 (MC) 是每多生产一单位产品所带来的总成本增加量。
ATC = TC ÷ Q = (TFC + TVC) ÷ Q
MC = ΔTC ÷ ΔQ
ompetition). Marginal revenue (MR) = ΔTR ÷ ΔQ. The profit-maximising condition is MC = MR.
总收益 (TR) = 价格 × 数量。平均收益 (AR) = TR ÷ Q = 价格（在完全竞争下）。边际收益 (MR) = ΔTR ÷ ΔQ。利润最大化条件是 MC = MR。
When MC < MR, the firm should expand output.
当 MC < MR 时，企业应扩大产量。
When MC > MR, the firm should contract output.
当 MC > MR 时，企业应减少产量。
Shutdown point in the short run: P < AVC.
短期停业点：价格低于平均变动成本。
6. Long-Run Average Cost and Returns to Scale | 长期平均成本与规模报酬
In the long run, all factors are variable. The long-run average cost curve (LRAC) traces the minimum cost per unit for each level of output. Economies of scale cause LRAC to fall, diseconomies of scale cause it to rise, and constant returns to scale keep it flat.
长期中，所有要素都可变。长期平均成本曲线 (LRAC) 表示每一产量水平下的最低单位成本。规模经济使 LRAC 下降，规模不经济使其上升，规模报酬不变则保持平坦。
The minimum efficient scale (MES) is the smallest output at which LRAC is minimised. Returns to scale can be measured as the proportional change in output resulting from a proportional increase in all inputs: increasing returns to scale (output rises more than inputs), decreasing returns (output rises less), and constant returns (same proportion).
最低有效规模 (MES) 是使 LRAC 达到最小的最低产量。规模报酬可以通过所有投入同比例增加时产出的变化比例来衡量：规模报酬递增（产出增加比例超过投入）、规模报酬递减（产出增加比例小于投入）和规模报酬不变（相同比例）。
7. National Income Identity and Multipliers | 国民收入恒等式与乘数
The fundamental national income identity for an open economy states that aggregate expenditure equals output and income. In the CIE syllabus, you work with both closed and open economy versions.
开放经济的基本国民收入恒等式指出，总支出等于总产出和总收入。在 CIE 大纲中，你需要掌握封闭经济和开放经济两种版本。
Y = C + I + G + (X - M)
Here C is consumption, I is investment, G is government spending, X is exports, and M is imports. The simple multiplier in a closed economy without government is:
其中 C 为消费，I 为投资，G 为政府支出，X 为出口，M 为进口。无政府部门的封闭经济中，简单乘数为：
k = 1 ÷ (1 - MPC) = 1 ÷ MPS
k = 1 ÷ (1 - MPC×(1 - t) + m). Always reference these formulas to explain how fiscal policy injections ripple through the economy.
MPC 是边际消费倾向，MPS 是边际储蓄倾向（MPC + MPS = 1）。引入税收 (t) 和进口 (m) 后，乘数变为 k = 1 ÷ (1 - MPC×(1 - t) + m)。在解释财政政策注入如何在整个经济中传导时，一定要引用这些公式。
8. Comparative Advantage and the 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. To identify comparative advantage, compute opportunity cost ratios: what is given up per unit of the other good. The pattern of specialisation follows the lowest opportunity cost.
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，就具有比较优势。要识别比较优势，需要计算机会成本比率：每多生产一单位某种商品所必须放弃的另一种商品的数量。专业化分工模式遵循机会成本最低的原则。
The terms of trade index measures the ratio of export prices to import prices. In CIE exams you may calculate it as:
贸易条件指数衡量出口价格与进口价格的比率。在 CIE 考试中，你可以这样计算：
Terms of Trade Index = (Index of Export Prices ÷ Index of Import Prices) × 100
An improvement in the terms of trade means a country can buy more imports for a given volume of exports. A deterioration means the opposite. Factors such as relative inflation rates, productivity, and exchange rates all influence the terms of trade.
贸易条件改善意味着给定出口量能换回更多的进口品；恶化则相反。相对通胀率、生产率和汇率等因素都会影响贸易条件。
9. Exchange Rate and Trade Weighted Index | 汇率与贸易加权指数
Exchange rates express the price of one currency in terms of another. In a floating system, the value is determined by supply and demand. You are often required to calculate percentage changes in exchange rates and interpret their impact on trade balances.
汇率是用一种货币表示的另一种货币的价格。在浮动汇率制下，其价值由供求决定。考试常要求你计算汇率的百分比变化，并解释其对贸易收支的影响。
%Δ Exchange Rate = (New Rate - Old Rate) ÷ Old Rate × 100
The trade-weighted exchange rate index weights bilateral exchange rates by the share of trade with each partner. A rise in the index indicates an appreciation of the domestic currency against a basket of trading partners' currencies, making exports less competitive and imports cheaper. The Marshall-Lerner condition states that a depreciation improves the trade balance only if the sum of PED for exports and PED for imports is greater than 1.
贸易加权汇率指数以与各贸易伙伴的贸易份额为权重，对双边汇率进行加权。指数上升表明本币相对于一篮子贸易伙伴货币升值，这会削弱出口竞争力并使进口更便宜。马歇尔-勒纳条件指出，只有当出口需求价格弹性和进口需求价格弹性之和大于 1 时，货币贬值才会改善贸易收支。
10. The J-Curve, Phillips Curve and Inflation | J 曲线、菲利普斯曲线与通货膨胀
The J-curve effect illustrates that a depreciation initially worsens the current account before improving it, because demand takes time to adjust to new prices. In the short run, export and import volumes are inelastic, so the trade deficit widens; over time, volumes become more elastic, and the trade balance improves.
J 曲线效应说明，货币贬值在改善经常账户之前会在短期内先使其恶化，因为需求需要时间适应新的价格。短期出口和进口量缺乏弹性，贸易逆差扩大；随着时间推移，数量弹性增强，贸易收支才会改善。
The short-run Phillips curve suggests an inverse relationship between unemployment and inflation. CIE requires you to understand the trade-off and the role of expectations. You may also need to calculate inflation rates using a consumer price index (CPI) or GDP deflator:
短期菲利普斯曲线表明失业与通胀之间存在反向关系。CIE 要求你理解这种权衡取舍以及预期的作用。你可能还需要用消费者价格指数 (CPI) 或 GDP 平减指数计算通货膨胀率：
Inflation Rate = (CPIₜ - CPIₜ₋₁) ÷ CPIₜ₋₁ × 100
where CPIₜ is the current period index and CPIₜ₋₁ is the previous period index. Long-run Phillips curve is vertical at the natural rate of unemployment, indicating no permanent trade-off.
其中 CPIₜ 为本期指数，CPIₜ₋₁ 为上期指数。长期菲利普斯曲线在自然失业率处垂直，表明不存在永久的权衡取舍。
11. Balance of Payments Components | 国际收支各组成部分
The balance of payments is divided into the current account, the capital account, and the financial account. For CIE analysis, the current account is central: it records trade in goods, trade in services, primary income (investment income and compensation of employees), and secondary income (current transfers).
国际收支分为经常账户、资本账户和金融账户。对 CIE 分析而言，经常账户是核心：它记录货物贸易、服务贸易、初次收入（投资收入和雇员报酬）以及二次收入（经常转移）。
The current account balance (CAB) can be expressed as:
经常账户余额 (CAB) 可表达为：
CAB = X - M + Net Primary Income + Net Secondary Income
A surplus means receipts exceed payments; a deficit means payments exceed receipts. You must link persistent current account deficits to exchange rate pressures, foreign debt accumulation, and structural competitiveness issues.
盈余意味着收入大于支出；逆差意味着支出大于收入。你必须将持续的经常账户逆差与汇率压力、外债累积和结构性的竞争力问题联系起来。
12. Summary of Decision-Making Rules | 决策规则小结
Exam success often rests on linking formulas to firms' and governments' ther a price change raises TR depends on PED. For resource allocation in free trade: specialise according to comparative advantage. For macroeconomic stabilisation: use fiscal multipliers to estimate the needed injection size.
考试成功的关键往往在于将公式与企业、政府的决策规则联系起来。对任何市场结构中追求利润最大化的企业而言：在 MC = MR 处进行生产。对收益而言：价格变动是否提高总收益取决于 PED。对自由贸易中的资源配置而言：按照比较优势进行专业化分工。对宏观经济稳定而言：使用财政乘数来估算需要追加的注入规模。
Keep this handbook as your anchor: each formula encodes a piece of economic logic, and CIE examiners prize the ability to translate these quantitative relationships into clear, real-world economic reasoning.
将此手册作为你的基础参照：每个公式都编码了一段经济逻辑，而 CIE 考官看重的是将这些数量关系转化为清晰、现实的经济推理的能力。
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