📚 Formula Handbook for A-Level CCEA Economics | A-Level CCEA 经济公式汇总手册
This handbook compiles the essential formulas for the CCEA A-Level Economics specification. Mastering these equations is crucial for analysing elasticities, production costs, macroeconomic equilibrium, and international trade. Each formula is presented with its definition and a brief example to reinforce understanding.
本手册汇集了 CCEA A-Level 经济学课程中的核心公式。掌握这些公式对于分析弹性、生产成本、宏观经济均衡和国际贸易至关重要。每个公式都附有定义和简要说明，以加深理解。
1. Price Elasticity of Demand (PED) | 需求价格弹性 (PED)
Price Elasticity of Demand (PED) measures the responsiveness of quantity demanded to a change in the price of the good itself.
需求价格弹性（PED）衡量需求量对商品自身价格变化的反应程度。
The basic formula for PED is:
PED的基本公式为：
PED = (% change in quantity demanded) / (% change in price)
Using symbols, PED = (ΔQd / Qd) ÷ (ΔP / P).
用符号表示：PED = (ΔQd / Qd) ÷ (ΔP / P)。
For arc elasticity, the midpoint formula removes bias from the choice of starting values:
对于弧弹性，中点公式可消除起始值选择带来的偏差：
PED = (ΔQd / [(Qd1 + Qd2)/2]) ÷ (ΔP / [(P1 + P2)/2])
Interpretation: |PED| > 1 elastic (revenue falls after a price rise), |PED| < 1 inelastic (revenue rises after a price rise), |PED| = 1 unit elastic. Extreme values: perfectly inelastic (|PED| = 0) and perfectly elastic (|PED| = ∞).
解释：|PED| > 1 富有弹性（涨价后总收益减少），|PED| < 1 缺乏弹性（涨价后总收益增加），|PED| = 1 单位弹性。极端值：完全无弹性（|PED| = 0）和完全弹性（|PED| = ∞）。
The PED coefficient is always negative, but the absolute value is used for classification.
PED 系数始终为负，但分类时使用绝对值。
2. Income Elasticity of Demand (YED) | 需求收入弹性 (YED)
Income Elasticity of Demand (YED) measures how quantity demanded responds to a change in consumers’ income.
需求收入弹性（YED）衡量需求量如何随消费者收入变化而变化。
YED = (% change in quantity demanded) / (% change in income)
YED = (ΔQd / Qd) ÷ (ΔY / Y), where Y represents income.
YED = (ΔQd / Qd) ÷ (ΔY / Y)，其中 Y 代表收入。
If YED > 0, the good is normal; YED > 1 indicates a luxury good, while 0 < YED < 1 indicates a necessity. If YED < 0, the good is inferior.
若 YED > 0，该商品为正常品；YED > 1 表示奢侈品，0 < YED < 1 表示必需品。若 YED < 0，该商品为劣质品。
3. Cross Elasticity of Demand (XED) | 需求交叉弹性 (XED)
Cross Elasticity of Demand (XED) measures the responsiveness of demand for one good (A) to a change in the price of another good (B).
需求交叉弹性（XED）衡量一种商品（A）的需求对另一种商品（B）价格变化的反应程度。
XED = (% change in Qd of good A) / (% change in price of good B)
XED = (ΔQdA / QdA) ÷ (ΔPB / PB).
XED = (ΔQdA / QdA) ÷ (ΔPB / PB)。
A positive XED indicates substitutes (e.g. tea and coffee), while a negative XED indicates complements (e.g. printers and ink cartridges). Values close to zero suggest unrelated goods.
正的 XED 表示替代品（如茶和咖啡），负的 XED 表示互补品（如打印机和墨盒）。接近零的值表示不相关商品。
4. Price Elasticity of Supply (PES) | 供给价格弹性 (PES)
Price Elasticity of Supply (PES) measures the responsiveness of quantity supplied to a change in price.
供给价格弹性（PES）衡量供给量对价格变化的反应程度。
PES = (% change in quantity supplied) / (% change in price)
PES = (ΔQs / Qs) ÷ (ΔP / P).
PES = (ΔQs / Qs) ÷ (ΔP / P)。
Values greater than 1 indicate elastic supply, less than 1 inelastic supply, and zero perfectly inelastic supply. The formula can also use the midpoint method for arc elasticity.
大于 1 的值表示供给富有弹性，小于 1 表示缺乏弹性，零表示完全无弹性。该公式也可使用中点法计算弧弹性。
5. Costs, Revenue and Profit | 成本、收益与利润
Total Cost (TC) is the sum of all fixed and variable costs.
总成本（TC）是所有固定成本和可变成本的总和。
TC = Total Fixed Cost (TFC) + Total Variable Cost (TVC)
Average Cost (AC) is the cost per unit of output: AC = TC / Q.
平均成本（AC）是每单位产出的成本：AC = TC / Q。
Average Fixed Cost (AFC) = TFC / Q, and Average Variable Cost (AVC) = TVC / Q.
平均固定成本（AFC）= TFC / Q，平均可变成本（AVC）= TVC / Q。
Marginal Cost (MC) is the extra cost of producing one more unit: MC = ΔTC / ΔQ.
边际成本（MC）是多生产一单位产品所增加的额外成本：MC = ΔTC / ΔQ。
Total Revenue (TR) = Price (P) × Quantity (Q).
总收益（TR）= 价格（P）× 数量（Q）。
Average Revenue (AR) = TR / Q, which equals the price per unit in perfect competition: AR = P.
平均收益（AR）= TR / Q，在完全竞争中等于单位价格：AR = P。
Marginal Revenue (MR) = ΔTR / ΔQ.
边际收益（MR）= ΔTR / ΔQ。
Profit = Total Revenue − Total Cost (Π = TR − TC).
利润 = 总收益 − 总成本（Π = TR − TC）。
6. Productivity and Cost Concepts | 生产率与成本概念
Total Product (TP) is the total output produced by a given number of workers (L).
总产量（TP）是给定工人数量（L）所生产的总产出。
Average Product (AP) = TP / L
Marginal Product (MP) = ΔTP / ΔL.
边际产量（MP）= ΔTP / ΔL。
Diminishing marginal returns set in when MP begins to fall. The relationship between MP and MC is inverse: when MP rises, MC falls, and vice versa.
当边际产量开始下降时，边际回报递减开始。MP 与 MC 呈反向关系：MP 上升时 MC 下降，反之亦然。
7. The Simple Multiplier and Macroeconomic Injections | 简单乘数与宏观经济注入
The multiplier (k) shows how an initial change in spending leads to a larger final change in national income.
乘数（k）表示初始支出的变动如何导致国民收入最终更大的变动。
k = 1 / (1 − MPC) = 1 / MPS
Where MPC is the marginal propensity to consume and MPS is the marginal propensity to save (MPC + MPS = 1).
其中 MPC 是边际消费倾向，MPS 是边际储蓄倾向（MPC + MPS = 1）。
When taxes and imports are considered, the marginal propensity to withdraw (MPW) is MPS + MPT + MPM, so the multiplier becomes:
当考虑税收和进口时，边际漏出倾向（MPW）为 MPS + MPT + MPM，因此乘数变为：
k = 1 / MPW = 1 / (MPS + MPT + MPM)
The change in national income: ΔY = k × ΔJ, where ΔJ is the initial injection (e.g. ΔG or ΔI).
国民收入变动：ΔY = k × ΔJ，其中 ΔJ 是初始注入（如 ΔG 或 ΔI）。
8. Index Numbers and Real Values | 指数与实际值
An index number expresses a data series relative to a base year (set to 100).
指数以基年（设为 100）为基准，表示数据序列的相对变化。
Index = (Value in current period / Value in base period) × 100
Real GDP removes the effect of inflation: Real GDP = (Nominal GDP / GDP Deflator) × 100.
实际 GDP 剔除了通胀影响：实际 GDP =（名义 GDP / GDP 平减指数）× 100。
The GDP deflator itself is a price index: GDP deflator = (Nominal GDP / Real GDP) × 100.
GDP 平减指数本身就是一个价格指数：GDP 平减指数 =（名义 GDP / 实际 GDP）× 100。
Real wage or real income can be found by dividing nominal income by a relevant price index and multiplying by 100.
实际工资或实际收入可以通过名义收入除以相关的价格指数再乘以 100 得到。
9. Unemployment and Inflation Rates | 失业率与通货膨胀率
The unemployment rate is the percentage of the labour force that is unemployed and actively seeking work.
失业率是劳动力中失业且正在积极寻找工作的人所占的百分比。
Unemployment rate = (Number of unemployed / Labour force) × 100
The labour force is the sum of employed and unemployed individuals.
劳动力是就业者和失业者的总和。
Inflation is measured as the percentage change in a price index, typically the Consumer Price Index (CPI).
通货膨胀以价格指数（通常是消费者价格指数 CPI）的百分比变化来衡量。
Inflation rate = [(CPI_current − CPI_previous) / CPI_previous] × 100
The same formula applies to any price index, such as the Retail Price Index (RPI) or GDP deflator.
同样的公式适用于任何价格指数，如零售价格指数（RPI）或 GDP 平减指数。
10. Exchange Rates and the Balance of Payments | 汇率与国际收支
A bilateral nominal exchange rate shows the value of one currency against another, e.g. £1 = $1.30.
双边名义汇率表示一种货币对另一种货币的价值，例如 £1 = $1.30。
The percentage change in an exchange rate is: %ΔE = [(E_new − E_old) / E_old] × 100.
汇率变动的百分比为：%ΔE = [（E新 − E旧）/ E旧] × 100。
An effective exchange rate (EER) index is a weighted average of bilateral rates against trading partners.
有效汇率（EER）指数是对贸易伙伴双边汇率的加权平均值。
EER index = Σ (weight_i × exchange rate index_i)
The balance of payments always balances by construction, where Current account + Capital account + Financial account + Net errors and omissions = 0.
国际收支在编制上总是平衡的，即经常账户 + 资本账户 + 金融账户 + 净误差与遗漏 = 0。
11. Comparative Advantage | 比较优势
Comparative advantage exists when a country can produce a good at a lower opportunity cost than another country.
当一个国家生产某种商品的机会成本低于另一个国家时，就存在比较优势。
Opportunity cost of producing one unit of good X is the amount of good Y sacrificed: OC_X = ΔY / ΔX.
生产一单位商品 X 的机会成本是所放弃的商品 Y 的数量：OC_X = ΔY / ΔX。
A country should specialise in the good where its opportunity cost is lowest, and trade arises if the terms of trade (international price) lie between the two opportunity cost ratios.
一国应专业化生产其机会成本最低的商品，当贸易条件（国际价格）处于两国机会成本比率之间时，贸易就会发生。
12. Terms of Trade | 贸易条件
The terms of trade (TOT) measure the relative price of exports to imports, indicating a country’s trading gain.
贸易条件（TOT）衡量出口相对于进口的价格，反映一国的贸易收益。
TOT index = (Index of export prices / Index of import prices) × 100
An improvement in the terms of trade means export prices rise relative to import prices (the index rises), which may improve living standards but worsen the trade balance if volumes adjust.
贸易条件改善意味着出口价格相对于进口价格上升（指数上升），这可能提高生活水平，但如果数量调整，可能导致贸易余额恶化。
A deterioration in the terms of trade implies export prices fall or import prices rise, making imports more expensive.
贸易条件恶化意味着出口价格下降或进口价格上升，使得进口更加昂贵。
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