📚 A-Level CIE Economics: Formula Handbook | A-Level CIE 经济：公式汇总手册
This handbook brings together the essential formulas that every A-Level CIE Economics student must know. From elasticity and cost calculations to national income accounting and international trade, mastering these expressions will sharpen your analysis and boost your exam confidence. Use this revision tool to consolidate your quantitative skills and link each formula to key economic concepts.
这本手册汇总了每位 A-Level CIE 经济学生必须掌握的核心公式。从弹性和成本计算，到国民收入核算与国际贸易，掌握这些表达式将提升你的分析能力并增强考试信心。利用这份复习工具巩固你的量化技能，并将每个公式与关键经济概念联系起来。
1. Elasticity Formulas | 弹性公式
Price elasticity of demand (PED) measures how responsive quantity demanded is to a change in price. It is the percentage change in quantity demanded divided by the percentage change in price. Because price and quantity normally move in opposite directions, PED carries a negative sign, and examiners usually expect you to quote the absolute value when judging elasticity.
需求价格弹性 (PED) 衡量需求量对价格变动的反应程度。它等于需求量变化的百分比除以价格变化的百分比。由于价格与数量通常反向变动，PED 带有负号，考试中通常要求你使用绝对值来判断弹性大小。
PED = (%ΔQd) ÷ (%ΔP)
Income elasticity of demand (YED) captures the responsiveness of demand to changes in income. A positive YED indicates a normal good; a negative YED signals an inferior good. Values above 1 identify luxury goods, while values between 0 and 1 identify necessities.
需求收入弹性 (YED) 衡量需求对收入变动的反应程度。正的 YED 表示正常品；负的 YED 表示低档品。大于 1 的数值对应奢侈品，介于 0 与 1 之间的数值对应必需品。
YED = (%ΔQd) ÷ (%ΔY)
Cross-price elasticity of demand (XED) shows how the demand for one good reacts to a price change in another good. Positive XED implies substitutes, while negative XED suggests complements. A value close to zero means the two goods are unrelated.
需求交叉价格弹性 (XED) 显示一种商品的需求对另一种商品价格变动的反应。正的 XED 意味着替代品，负的 XED 意味着互补品。接近零的数值说明两种商品互不相关。
XED = (%ΔQd of Good A) ÷ (%ΔP of Good B)
Price elasticity of supply (PES) measures the responsiveness of quantity supplied to price changes. A value greater than 1 indicates elastic supply; less than 1 indicates inelastic supply. Time period, spare capacity and stock availability are the main determinants.
供给价格弹性 (PES) 衡量供给量对价格变动的反应程度。大于 1 表示供给富有弹性；小于 1 表示供给缺乏弹性。时间长短、闲置产能和库存可得性是主要决定因素。
PES = (%ΔQs) ÷ (%ΔP)
Use the following table to convert a numerical elasticity straight into a clear written judgement in your answers.
下表帮助你把弹性数值直接转化为答题中的明确判断句。
| Measure | 指标 | Value | 数值 | Meaning | 含义 |
| PED | |PED| > 1 | Elastic demand | 需求富有弹性 |
| PED | |PED| < 1 | Inelastic demand | 需求缺乏弹性 |
| YED | YED < 0 | Inferior good | 低档品 |
| XED | XED > 0 | Substitutes | 替代品 |
| PES | PES = 0 | Perfectly inelastic supply | 供给完全无弹性 |
2. Revenue, Cost and Profit | 收益、成本与利润
Total revenue (TR) is the total income a firm receives from selling its output, calculated as price multiplied by quantity sold. It is the starting point for every profitability calculation in the syllabus.
总收益 (TR) 是企业销售产出所获得的全部收入，等于价格乘以销售量。它是大纲中一切盈利计算的起点。
TR = P × Q
Average revenue (AR) is revenue per unit sold and is identical to the price of the good under all market structures. Marginal revenue (MR) is the addition to total revenue from selling one more unit.
平均收益 (AR) 是每单位售出产品带来的收益，在任何市场结构下都等于商品价格。边际收益 (MR) 是多销售一单位产品所增加的总收益。
AR = TR ÷ Q MR = ΔTR ÷ ΔQ
Total cost (TC) is the sum of total fixed cost and total variable cost. Average cost (AC) is cost per unit, and marginal cost (MC) is the extra cost of producing one additional unit.
总成本 (TC) 是总固定成本与总可变成本之和。平均成本 (AC) 是单位成本，边际成本 (MC) 是多生产一单位产品所增加的成本。
TC = TFC + TVC AC = TC ÷ Q MC = ΔTC ÷ ΔQ
Profit is the difference between total revenue and total cost. Economists also distinguish normal profit, which is the minimum return needed to keep a firm in the industry, from supernormal (abnormal) profit, which attracts new entrants.
利润等于总收益与总成本之差。经济学家还区分正常利润与超额（异常）利润：正常利润是使企业留在行业中所必需的最低回报，超额利润则会吸引新企业进入。
Profit = TR − TC Supernormal profit: TR > TC
Profit is maximised where marginal revenue equals marginal cost and MC is rising. This rule applies to every market structure from perfect competition to monopoly, and it is the single most examinable condition in microeconomics.
当边际收益等于边际成本且 MC 处于上升阶段时，利润达到最大。该法则适用于从完全竞争到垄断的所有市场结构，是微观经济学中最常考的单一条件。
Profit maximisation: MR = MC (with MC rising)
3. Cost Curves and Returns to a Factor | 成本曲线与要素报酬
Average fixed cost (AFC) falls continuously as output rises because a fixed sum is spread over more units. Average variable cost (AVC) and average total cost (ATC) both follow a U-shape as diminishing returns set in.
平均固定成本 (AFC) 随着产量增加而持续下降，因为固定费用被分摊到更多单位上。随着边际报酬递减出现，平均可变成本 (AVC) 与平均总成本 (ATC) 都呈 U 形。
AFC = TFC ÷ Q AVC = TVC ÷ Q ATC = AFC + AVC
Marginal product (MP) is the extra output from employing one more unit of labour; average product (AP) is output per worker. Both are calculated from physical output, not from money values.
边际产量 (MP) 是增加一单位劳动所带来的额外产出；平均产量 (AP) 是每名工人的产出。二者都以实物产出计算，而非货币价值。
MP = ΔTP ÷ ΔL AP = TP ÷ L
The two famous intersection rules follow directly from these definitions. MC cuts AC at the minimum point of AC, and MP cuts AP at the maximum point of AP, because a marginal value above the average pulls the average up while a marginal value below it pulls the average down.
两个著名的相交法则直接来自这些定义。MC 在 AC 的最低点穿过 AC，MP 在 AP 的最高点穿过 AP，因为边际值高于平均值会拉高平均值，低于平均值则拉低平均值。
MC = AC at minimum AC MP = AP at maximum AP
In the long run all factors are variable, so long-run average cost (LRAC) is the envelope of short-run cost curves and reflects economies and diseconomies of scale. Falling LRAC indicates economies of scale, while rising LRAC indicates diseconomies of scale.
在长期中所有要素都可变，因此长期平均成本 (LRAC) 是各条短期成本曲线的包络线，反映规模经济与规模不经济。LRAC 下降表示规模经济，LRAC 上升表示规模不经济。
4. Market Equilibrium, Surplus and Tax Incidence | 市场均衡、剩余与税收归宿
Market equilibrium occurs where quantity demanded equals quantity supplied. Substituting the equilibrium quantity back into either the demand or the supply equation gives the equilibrium price.
市场均衡出现在需求量等于供给量之时。将均衡数量代回需求或供给方程，即可求出均衡价格。
Equilibrium: Qd = Qs
Consumer surplus is the difference between what consumers are willing to pay and what they actually pay; producer surplus is the difference between the price received and the minimum price producers would accept. Together they measure the welfare generated by a market.
消费者剩余是消费者愿意支付的价格与实际支付价格之差；生产者剩余是实际获得的价格与生产者愿意接受的最低价格之差。二者之和衡量市场创造的福利。
Consumer surplus = area below demand, above price
Producer surplus = area above supply, below price
When a tax is imposed, the burden is split between buyers and sellers according to the relative elasticities. The more inelastic side of the market bears the larger share of the tax.
征税时，税负根据相对弹性在买方与卖方之间分摊。市场中弹性较小的一方承担较大份额的税负。
Consumer share = PES ÷ (PES + |PED|)
Producer share = |PED| ÷ (PES + |PED|)
Taxation and other market interventions also create deadweight loss, the loss of total welfare caused by trades that would have benefited both parties but no longer take place. The more elastic demand and supply are, the larger the deadweight loss at any given tax.
税收及其他市场干预还会造成无谓损失，即本可令双方受益、却因干预而不再发生的交易所带来的总福利损失。需求与供给弹性越大，给定税额下的无谓损失越大。
5. National Income Accounting | 国民收入核算
Gross domestic product (GDP) can be measured through the expenditure approach, which adds up all spending on domestically produced final goods and services. Consumption, investment, government spending and net exports are the four components.
国内生产总值 (GDP) 可用支出法衡量，即加总对本国生产的最终商品与服务的全部支出。消费、投资、政府支出与净出口是四大组成部分。
GDP = C + I + G + (X − M)
The income approach adds all factor incomes generated in production, while the output (value added) approach sums the value added at each stage of production to avoid double counting. All three approaches should produce the same total.
收入法加总生产中产生的全部要素收入，产出（增加值）法则加总各生产阶段的增加值以避免重复计算。三种方法应得出相同总量。
GDP (income) = wages + rent + interest + profit
GDP (output) = Σ value added
Gross national product (GNP) adjusts GDP for net factor income from abroad, and net national product (NNP) then deducts depreciation of capital. These distinctions matter when comparing countries with large inflows or outflows of remittances and profits.
国民生产总值 (GNP) 在 GDP 基础上调整国外净要素收入，国民生产净值 (NNP) 再扣除资本折旧。在比较拥有大量侨汇或利润流入流出的国家时，这些区分十分重要。
GNP = GDP + net factor income from abroad
NNP = GNP − depreciation
Real GDP strips out the effect of price changes so that comparisons over time show genuine changes in output. Per capita GDP divides national output by population and is a better, though still imperfect, indicator of living standards.
实际 GDP 剔除了价格变动的影响，使跨期比较能反映真实产出变化。人均 GDP 把国民产出除以人口，是衡量生活水平的更好但依然不完美的指标。
Real GDP = (Nominal GDP ÷ GDP deflator) × 100
Per capita GDP = GDP ÷ population
6. Growth, Inflation and Unemployment Rates | 增长率、通胀率与失业率
The economic growth rate measures the percentage change in real GDP between two periods. Using real rather than nominal GDP prevents inflation from exaggerating the growth figure.
经济增长率衡量两个时期之间实际 GDP 的百分比变化。使用实际 GDP 而非名义 GDP，可避免通胀夸大增长率。
Growth rate = ((Real GDPₜ − Real GDPₜ₋₁) ÷ Real GDPₜ₋₁) × 100
The consumer price index (CPI) tracks the cost of a representative basket of goods relative to a base year. The inflation rate is then the percentage change in the index between two periods.
消费者价格指数 (CPI) 追踪一篮子代表性商品相对于基年的成本。通胀率则是两个时期之间该指数的百分比变化。
CPI = (Cost of basket in current year ÷ Cost of basket in base year) × 100
Inflation rate = ((CPIₜ − CPIₜ₋₁) ÷ CPIₜ₋₁) × 100
The unemployment rate expresses the number of unemployed people as a percentage of the labour force, where the labour force excludes those who are economically inactive. The participation rate shows what proportion of the working-age population is in the labour force.
失业率表示失业人数占劳动力人数的百分比，其中劳动力不包括非经济活动人口。劳动参与率则显示劳动年龄人口中属于劳动力的比例。
Unemployment rate = (Unemployed ÷ Labour force) × 100
Participation rate = (Labour force ÷ Working-age population) × 100
Real incomes matter more than nominal incomes to households. Converting a nominal wage into real terms shows whether purchasing power has actually risen after inflation is taken into account.
对家庭而言，实际收入比名义收入更重要。把名义工资换算为实际值，可以显示在考虑通胀之后购买力是否真正提高。
Real income = (Nominal income ÷ CPI) × 100
7. The Multiplier, the Accelerator and Circular Flow | 乘数、加速数与循环流量
The multiplier shows how an initial change in spending produces a larger final change in national income. Its size depends on the marginal propensities to save, tax and import, since these are the leakages from the circular flow.
乘数显示初始支出变动如何引起国民收入更大的最终变动。其大小取决于边际储蓄倾向、边际税收倾向与边际进口倾向，因为它们是循环流量中的漏出。
k = 1 ÷ (1 − MPC) or k = 1 ÷ (MPS + MPT + MPM)
Once the multiplier is known, the total effect of an injection such as an increase in investment or government spending can be calculated directly. This is the standard route for evaluating fiscal stimulus in macro papers.
求出乘数后，即可直接计算投资或政府支出增加等注入的总效应。这是宏观题中评估财政刺激的标准路径。
ΔNational income = k × ΔInjection
The accelerator theory argues that investment depends on the change in national income rather than its level, so firms invest when demand is growing. The capital-output ratio links the size of that investment response to the change in output.
加速数理论认为投资取决于国民收入的变化量而非其水平，因此企业会在需求增长时投资。资本产出比率把投资反应的大小与产出变化联系起来。
I = α × ΔY（α = capital-output ratio | 资本产出比率）
Equilibrium in the circular flow occurs when total injections equal total leakages. Any imbalance causes national income to expand or contract until the two sides balance again.
当总注入等于总漏出时，循环流量达到均衡。任何失衡都会使国民收入扩张或收缩，直至两侧重新平衡。
I + G + X = S + T + M
8. Money, Interest Rates and the Quantity Theory | 货币、利率与货币数量论
The quantity theory of money links the money supply and the velocity of circulation to the price level and real output. If velocity and real output are constant, an increase in the money supply translates directly into a rise in the price level.
货币数量论把货币供应量与货币流通速度同价格水平和实际产出联系起来。若流通速度与实际产出不变，货币供应量增加会直接转化为价格水平上升。
M × V = P × Y
The credit multiplier shows how an initial deposit in the banking system can generate a much larger expansion of bank deposits, given the reserve ratio that banks must hold. A lower reserve ratio produces a larger multiplier.
信用乘数显示，在给定银行必须持有的准备金率下，银行体系中的初始存款如何派生出规模大得多的存款扩张。准备金率越低，乘数越大。
Credit multiplier = 1 ÷ Reserve ratio
The Fisher equation distinguishes the nominal interest rate, which is the rate quoted by banks, from the real interest rate, which is what borrowers and savers actually experience after inflation. Real interest rates drive investment and saving decisions.
费雪方程区分名义利率与实际利率：名义利率是银行报价的利率，实际利率是借贷双方在通胀之后真正承受的利率。实际利率决定投资与储蓄决策。
Real interest rate ≈ Nominal interest rate − Inflation rate
Rising real interest rates raise the cost of borrowing and tend to reduce investment and consumption of durables, while also attracting capital inflows that appreciate the exchange rate. This chain of reasoning is frequently required in evaluation questions.
实际利率上升会提高借贷成本，往往减少投资与耐用消费品支出，同时吸引资本流入并推动汇率升值。这一推理链条常在评价题中被要求展开。
9. International Trade and Exchange Rates | 国际贸易与汇率
The terms of trade measure the rate at which a country's exports exchange for its imports. An improvement means a country can buy more imports with a given quantity of exports, though the effect on the trade balance depends on price elasticities.
贸易条件衡量一国出口与进口的交换比率。贸易条件改善意味着用给定数量的出口可以换回更多进口，但其对贸易收支的影响取决于价格弹性。
Terms of trade = (Index of export prices ÷ Index of import prices) × 100
The real exchange rate adjusts the nominal exchange rate for relative price levels and so measures genuine competitiveness. A fall in the real exchange rate makes exports cheaper and imports dearer, improving competitiveness.
实际汇率用相对价格水平调整名义汇率，因而衡量真实竞争力。实际汇率下降使出口更便宜、进口更昂贵，从而提升竞争力。
Real exchange rate = Nominal exchange rate × (Domestic price level ÷ Foreign price level)
The balance of payments must always balance in the accounting sense, because a current account deficit is matched by a financial account surplus. Understanding this identity prevents the common error of treating the accounts as independent.
从会计意义上说，国际收支必然平衡，因为经常账户逆差会被金融账户顺差所抵消。理解这一恒等式可以避免把各账户视为彼此独立的常见错误。
Current account + Capital and financial account = 0
The Marshall-Lerner condition states that a depreciation will improve the trade balance only if the sum of the price elasticities of export and import demand exceeds one. In the short run, inelastic demand may worsen the balance first, producing the J-curve effect.
马歇尔-勒纳条件指出，只有当出口需求与进口需求的价格弹性之和大于 1 时，货币贬值才会改善贸易收支。在短期内，需求缺乏弹性可能先使贸易收支恶化，形成 J 曲线效应。
Marshall-Lerner condition: |PEDx| + |PEDm| >
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图