📚 Formula Handbook for IB & CIE Economics | IB CIE 经济公式汇总手册
This comprehensive handbook brings together the essential formulas for IB and CIE Economics examinations, spanning microeconomics, macroeconomics, and international trade. Mastery of these quantitative tools will enable you to calculate elasticities with precision, evaluate market outcomes, and interpret key economic indicators with confidence. Each formula is presented with a concise explanation and is immediately followed by its Chinese translation to support bilingual learners.
本手册全面汇总了 IB 和 CIE 经济学考试所需的核心公式，涵盖微观经济学、宏观经济学和国际贸易。熟练掌握这些定量工具，你将能精确计算弹性、评估市场结果，并自信地解读关键经济指标。每个公式都附有简要说明，并立即提供中文翻译，以帮助双语学习者巩固知识。
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 always negative due to the law of demand, but the absolute value is normally used to indicate the degree of elasticity.
需求价格弹性衡量需求量对商品自身价格变化的反应程度。由于需求定律，它总是负值，但通常用绝对值来表示弹性程度。
PED = %ΔQd / %ΔP = (ΔQd/Qd) / (ΔP/P) = (ΔQd/ΔP) × (P/Qd)
Using the arc (midpoint) method for greater accuracy when working with discrete data: PED = [ (Q2 − Q1) / ((Q1+Q2)/2) ] / [ (P2 − P1) / ((P1+P2)/2) ].
使用弧（中点）法处理离散数据时更精确：PED = [ (Q2 − Q1) / ((Q1+Q2)/2) ] / [ (P2 − P1) / ((P1+P2)/2) ]。
Interpretation: |PED| > 1 means elastic (luxuries), |PED| < 1 means inelastic (necessities), and |PED| = 1 means unit elastic. The total revenue test states that if demand is elastic, a price cut raises total revenue; if inelastic, a price cut lowers total revenue.
解读：|PED| > 1 为富有弹性（奢侈品），|PED| < 1 为缺乏弹性（必需品），|PED| = 1 为单位弹性。总收益检验表明：若需求富有弹性，降价会增加总收益；若缺乏弹性，降价会减少总收益。
2. Cross-Price Elasticity of Demand (XED) | 需求交叉价格弹性
Cross-price elasticity of demand measures how the quantity demanded of one good (X) responds to a change in the price of another good (Y).
需求交叉价格弹性衡量一种商品（X）的需求量如何随另一种商品（Y）的价格变化而变动。
XED = %ΔQd of good X / %ΔP of good Y
A positive XED indicates substitute goods (e.g., tea and coffee); a negative XED indicates complementary goods (e.g., printers and ink). The larger the absolute value, the stronger the relationship.
XED 为正表示替代品（如茶与咖啡）；为负表示互补品（如打印机与墨水）。绝对值越大，关系越强。
3. Income Elasticity of Demand (YED) | 需求收入弹性
Income elasticity of demand quantifies how quantity demanded changes as consumer income changes. It helps classify goods as normal or inferior.
需求收入弹性量化需求量如何随消费者收入变化而变化，用于区分正常品和劣等品。
YED = %ΔQd / %ΔIncome
A positive YED denotes a normal good; if YED > 1, it is a luxury (income elastic), while 0 < YED < 1 is a necessity. A negative YED denotes an inferior good (demand falls as income rises).
YED 为正代表正常品；若 YED > 1，则为奢侈品（富有收入弹性）；0 < YED < 1 为必需品。YED 为负代表劣等品（收入增加时需求减少）。
4. Price Elasticity of Supply (PES) | 供给价格弹性
Price elasticity of supply captures the sensitivity of quantity supplied to price changes. Its value depends mainly on the time period and the mobility of factors of production.
供给价格弹性反映供给量对价格变化的敏感程度，其数值主要取决于时间周期和生产要素的流动性。
PES = %ΔQs / %ΔP = (ΔQs/Qs) / (ΔP/P)
PES > 1 indicates elastic supply (producers can quickly adjust output); PES < 1 indicates inelastic supply; PES = 0 is perfectly inelastic; and PES = ∞ is perfectly elastic.
PES > 1 表示供给富有弹性（生产者可快速调整产量）；PES < 1 表示缺乏弹性；PES = 0 为完全无弹性；PES = ∞ 为完全弹性。
5. Revenue, Cost and Profit | 收益、成本与利润
Understanding revenue and cost structures is vital for analysing firm behaviour and market outcomes. Profit maximisation occurs where marginal revenue equals marginal cost.
理解收益与成本结构对分析企业行为和市场结果至关重要。利润最大化发生在边际收益等于边际成本时。
Total Revenue (TR) = P × Q
Average Revenue (AR) is TR / Q, which equals the price in perfect competition, but may diverge under imperfect competition.
平均收益（AR）为 TR / Q，在完全竞争中等于价格，但在不完全竞争下可能不同。
AR = TR / Q = P
Marginal Revenue (MR) = ΔTR / ΔQ
Total Cost (TC) is the sum of total fixed costs (TFC) and total variable costs (TVC).
总成本（TC）为总固定成本（TFC）与总可变成本（TVC）之和。
TC = TFC + TVC
Average Total Cost (ATC) = TC / Q
Average Variable Cost (AVC) = TVC / Q
Average Fixed Cost (AFC) = TFC / Q
Marginal Cost (MC) = ΔTC / ΔQ
The profit-maximising condition: MR = MC. In the short run, a firm should shut down if price falls below AVC (P < AVC); in the long run, it should exit the market if price falls below ATC.
利润最大化条件：MR = MC。短期内，若价格低于平均可变成本（P < AVC），企业应停产；长期中，若价格低于平均总成本，企业应退出市场。
6. Market Efficiency and Government Intervention | 市场效率与政府干预
Consumer surplus, producer surplus, and deadweight loss measure welfare. Indirect taxes and subsidies alter market prices and quantities, creating efficiency losses.
消费者剩余、生产者剩余和无谓损失衡量福利。间接税和补贴改变市场价格与数量，造成效率损失。
Consumer Surplus (CS) = Area above price and below demand curve
Producer Surplus (PS) = Area below price and above supply curve
Deadweight Loss (DWL) = ½ × (tax per unit) × (Q* − Qtax)
Tax incidence shows how the burden of a tax is shared. Using elasticities: the share borne by consumers ≈ |PES| / (|PED| + PES), and the share borne by producers ≈ |PED| / (|PED| + PES). Alternatively, consumers’ tax burden per unit = Pc − P*, and producers’ tax burden = P* − Pp.
税收归宿表明税负如何分摊。利用弹性：消费者承担份额 ≈ |PES| / (|PED| + PES)，生产者承担份额 ≈ |PED| / (|PED| + PES)。也可用每单位税额：消费者负担 = Pc − P*，生产者负担 = P* − Pp。
For a per-unit subsidy, the consumer benefit is P* − Pc, the producer benefit is Pp − P*, and the total government cost is subsidy per unit × Qsub.
对于单位补贴，消费者获益为 P* − Pc，生产者获益为 Pp − P*，政府总支出为单位补贴额 × Qsub。
7. National Income Accounting | 国民收入核算
Macroeconomic performance is tracked through national income accounts, price indices, and growth rates.
宏观经济表现通过国民收入账户、价格指数和增长率来追踪。
GDP (Expenditure) = C + I + G + (X − M)
C is consumption, I is investment, G is government spending, X is exports, and M is imports. GDP deflator and CPI are alternative price level measures.
C 为消费，I 为投资，G 为政府支出，X 为出口，M 为进口。GDP 平减指数和 CPI 是衡量价格水平的替代指标。
GDP Deflator = (Nominal GDP / Real GDP) × 100
CPI = (Cost of basket in current year / Cost of basket in base year) × 100
Inflation Rate = [(CPIt − CPIt-1) / CPIt-1] × 100
Real GDP growth rate is calculated analogously: [(Real GDPt − Real GDPt-1) / Real GDPt-1] × 100.
实际GDP增长率类似计算：[(实际GDPt − 实际GDPt-1) / 实际GDPt-1] × 100。
8. Macroeconomic Multipliers | 宏观经济乘数
Multipliers capture the magnified impact of an initial change in autonomous spending on national income. The size depends on the marginal propensities to consume, save, tax, and import.
乘数反映自发支出初始变动对国民收入的放大效应，其大小取决于边际消费倾向、边际储蓄倾向、边际税收倾向和边际进口倾向。
Simple Multiplier (k) = 1 / (1 − MPC) = 1 / MPS
With taxes and imports, the multiplier becomes k = 1 / (MPS + MPT + MPM), where MPT is the marginal propensity to tax and MPM is the marginal propensity to import.
考虑税收和进口后，乘数变为 k = 1 / (MPS + MPT + MPM)，其中 MPT 为边际税收倾向，MPM 为边际进口倾向。
Tax multiplier = −MPC / MPS
The balanced budget multiplier is 1, meaning an equal increase in government spending and lump-sum taxes raises income by the same amount.
平衡预算乘数为 1，即等额增加政府支出和一次性税收会使收入增加同等数额。
9. Unemployment Rate | 失业率
Labour market indicators are computed from the labour force survey data. The unemployment rate is a key measure of spare capacity.
劳动力市场指标根据劳动力调查数据计算，失业率是衡量闲置产能的关键指标。
Unemployment Rate = (Number of unemployed / Labour force) × 100
The labour force includes those employed and those actively seeking work. The participation rate shows the proportion of the working-age population that is in the labour force.
劳动力包括就业者和积极求职者。劳动参与率反映适龄工作人口中进入劳动力市场的比例。
Labour Force Participation Rate = (Labour force / Working-age population) × 100
10. International Trade and Finance | 国际贸易与金融
Formulas for trade and exchange rates help evaluate a country’s international competitiveness and the gains from specialisation.
贸易与汇率公式有助于评估一国的国际竞争力和专业化带来的收益。
Terms of Trade Index = (Index of export prices / Index of import prices) × 100
An improvement (increase) in the terms of trade means a country can buy more imports for a given volume of exports.
贸易条件改善（指数上升）意味着一国用一定量的出口能换回更多进口。
Comparative advantage is identified by comparing opportunity costs: the country with the lower opportunity cost in producing a good should specialise in it. Opportunity cost of good X = Amount of Y given up / Amount of X gained.
比较优势通过比较机会成本确定：生产一种商品机会成本较低的国家应专产该商品。商品X的机会成本 = 放弃的Y数量 / 获得的X数量。
Exchange rate changes are expressed as a percentage: Appreciation/Depreciation (%) = [(New rate − Old rate) / Old rate] × 100. A negative value indicates depreciation of the domestic currency.
汇率变动以百分比表示：升值/贬值（%）= [(新汇率 − 旧汇率) / 旧汇率] × 100。负值表示本币贬值。
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