📚 IB Economics: Formula Summary Handbook | IB 经济：公式汇总手册
This comprehensive guide collects all essential formulas required for IB Economics examinations at both Standard and Higher Level. Each formula is presented with clear definitions, worked examples, and paired English-Chinese explanations to help you memorise and apply the concepts accurately. Whether you are revising elasticities, costs, national income or international trade, this handbook will serve as your quick reference and revision companion.
本汇总手册收录了 IB 经济学考试（标准水平与高级水平）必备的所有核心公式。每个公式都配有清晰的定义、计算示例以及英中双语解释，帮助你准确记忆和运用概念。不论你正在复习弹性、成本、国民收入还是国际贸易，这份手册都可以作为你快速查阅和考前冲刺的得力助手。
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 price of the good itself. The formula is the percentage change in quantity demanded divided by the percentage change in price. A PED greater than 1 indicates elastic demand, while a PED less than 1 indicates inelastic demand.
需求价格弹性衡量商品自身价格变化所引起的需求量变化的反应程度。公式为需求量变动的百分比除以价格变动的百分比。PED 大于 1 表示需求富有弹性，小于 1 表示需求缺乏弹性。
PED = %ΔQd ÷ %ΔP = (ΔQd / Qd₀) × (P₀ / ΔP)
Example: If the price of cinema tickets rises from $10 to $12 and the quantity demanded falls from 500 to 400 per week, the PED = [(400-500)/500] ÷ [(12-10)/10] = (-20%) ÷ (20%) = -1, so the absolute value is 1, indicating unit elasticity.
示例：如果电影票价格从 10 美元涨至 12 美元，每周需求量从 500 张降至 400 张，则 PED = [(400-500)/500] ÷ [(12-10)/10] = (-20%) ÷ (20%) = -1，取绝对值为 1，表示单位弹性。
IB candidates must remember that PED is always negative due to the law of demand, but the absolute value is used for classification. PED determines how total revenue changes with price: if demand is elastic, a price decrease raises total revenue; if inelastic, a price decrease lowers total revenue.
IB 考生务必注意，由于需求定律，PED 总是为负值，但分类时取其绝对值。PED 决定了总收益如何随价格变化：如果需求富有弹性，降价会增加总收益；如果缺乏弹性，降价会减少总收益。
2. Price Elasticity of Supply (PES) | 供给价格弹性
Price elasticity of supply quantifies how much the quantity supplied of a good responds to a change in its price. The formula takes the percentage change in quantity supplied over the percentage change in price. PES is normally positive because of the positive relationship between price and quantity supplied.
供给价格弹性衡量商品供给量对其价格变化的反应程度。公式为供给量变动的百分比除以价格变动的百分比。由于价格与供给量呈正相关，PES 通常为正值。
PES = %ΔQs ÷ %ΔP = (ΔQs / Qs₀) × (P₀ / ΔP)
Example: A farm increases its supply of wheat from 2000 kg to 2200 kg when the price rises from $5 to $5.50 per kg. PES = [(2200-2000)/2000] ÷ [(5.50-5)/5] = (10%) ÷ (10%) = 1, so supply is unit elastic.
示例：当小麦价格从每公斤 5 美元涨至 5.50 美元时，农场将其供给量从 2000 公斤增至 2200 公斤。PES = [(2200-2000)/2000] ÷ [(5.50-5)/5] = (10%) ÷ (10%) = 1，供给单位弹性。
The key determinants of PES are the time period, the flexibility of factors of production, and the ability to store stocks. IB diagrams often require you to illustrate perfectly inelastic supply (PES = 0) or perfectly elastic supply (PES = ∞).
PES 的主要决定因素包括时间周期、生产要素的灵活性以及储存存货的能力。IB 图表题常要求你画出完全无弹性供给（PES = 0）或完全弹性供给（PES = ∞）的情况。
3. Cross Elasticity of Demand (XED) | 需求交叉弹性
Cross elasticity of demand measures the responsiveness of demand for one good (A) to a change in the price of another good (B). It is calculated as the percentage change in quantity demanded of good A divided by the percentage change in price of good B. The sign of XED tells you whether goods are substitutes or complements.
需求交叉弹性衡量商品 A 的需求量对商品 B 价格变化的反应程度。计算公式为商品 A 需求量变动的百分比除以商品 B 价格变动的百分比。XED 的正负号可判断两种商品是替代品还是互补品。
XED = %ΔQd of A ÷ %ΔP of B
If XED is positive, goods A and B are substitutes (e.g. tea and coffee). If XED is negative, they are complements (e.g. printers and ink cartridges). A value near zero suggests independent goods.
若 XED 为正值，则 A 与 B 互为替代品（如茶与咖啡）。若 XED 为负值，则互为互补品（如打印机与墨盒）。XED 接近零则表示两种商品相互独立。
Example: The price of bus tickets falls by 5% and the demand for train journeys decreases by 2%. XED = (-2%) ÷ (-5%) = +0.4, so these modes of transport are weak substitutes.
示例：公共汽车票价下降 5%，火车出行需求减少 2%。XED = (-2%) ÷ (-5%) = +0.4，说明两者是较弱的替代品。
4. Income Elasticity of Demand (YED) | 需求收入弹性
Income elasticity of demand shows how quantity demanded changes in response to a change in consumers’ income. The formula uses the percentage change in quantity demanded over the percentage change in income. YED helps classify normal goods, inferior goods, necessities and luxuries.
需求收入弹性反映消费者收入变化时需求量的变动程度。公式为需求量变动的百分比除以收入变动的百分比。YED 有助于区分正常商品、低档商品、必需品与奢侈品。
YED = %ΔQd ÷ %ΔIncome
A positive YED indicates a normal good; within that, YED between 0 and 1 identifies a necessity, while YED greater than 1 signals a luxury. A negative YED refers to an inferior good, where demand falls as income rises.
YED 为正表示正常商品；其中 YED 介于 0 与 1 之间为必需品，YED 大于 1 为奢侈品。YED 为负则为低档商品，即收入上升时需求反而下降。
Example: If consumer incomes rise by 4% and the demand for organic vegetables grows by 10%, YED = 10% ÷ 4% = 2.5, so organic vegetables are a luxury good.
示例：若消费者收入上升 4%，有机蔬菜需求上升 10%，YED = 10% ÷ 4% = 2.5，有机蔬菜属于奢侈品。
5. Total, Average and Marginal Product in the Short Run | 短期总产量、平均产量与边际产量
In the theory of the firm, these measures explain the relationship between inputs (labour) and output. Total product (TP) is the total output produced by a given number of workers. Average product (AP) is TP divided by the quantity of labour. Marginal product (MP) is the addition to total output from hiring one more worker.
在厂商理论中，这些指标解释投入（劳动力）与产出之间的关系。总产量（TP）是一定数量工人生产的总产出。平均产量（AP）等于总产量除以劳动数量。边际产量（MP）是额外雇佣一个工人所带来的总产出增加量。
AP = TP ÷ L
MP = ΔTP ÷ ΔL
The law of diminishing marginal returns states that as more units of a variable factor are added to fixed factors, MP eventually falls. The relationship between AP and MP is crucial: when MP > AP, AP rises; when MP < AP, AP falls; MP intersects AP at its maximum point.
边际报酬递减规律指出，随着更多可变要素加到固定要素上，边际产量最终会下降。AP 与 MP 的关系至关重要：当 MP > AP 时，AP 上升；当 MP < AP 时，AP 下降；MP 与 AP 相交于 AP 的最高点。
6. Short-Run Costs: Total, Average and Marginal | 短期成本：总成本、平均成本与边际成本
In microeconomics, cost functions are fundamental. Total cost (TC) is the sum of total fixed cost (TFC) and total variable cost (TVC). Average total cost (ATC) is TC divided by output (Q). Average fixed cost (AFC) is TFC ÷ Q, and average variable cost (AVC) is TVC ÷ Q. Marginal cost (MC) is the change in total cost when one more unit is produced.
在微观经济学中，成本函数是基础。总成本（TC）等于总固定成本（TFC）与总可变成本（TVC）之和。平均总成本（ATC）等于 TC 除以产量（Q）。平均固定成本（AFC）= TFC ÷ Q，平均可变成本（AVC）= TVC ÷ Q。边际成本（MC）是额外生产一单位产品所带来的总成本变动。
TC = TFC + TVC
ATC = TC ÷ Q = AFC + AVC
MC = ΔTC ÷ ΔQ
Example: A bakery has fixed costs of $200 per day and variable costs of $3 per loaf. When it produces 100 loaves, TC = 200 + 3×100 = $500, ATC = 500/100 = $5 per loaf.
示例：一家面包店每天固定成本 200 美元，每个面包的可变成本为 3 美元。若生产 100 个面包，TC = 200 + 3×100 = 500 美元，ATC = 500/100 = 每个面包 5 美元。
The MC curve intersects both AVC and ATC at their minimum points. These relationships form the basis of short-run cost curves that every IB student must be able to draw and interpret.
MC 曲线分别在 AVC 和 ATC 的最低点与之相交。这些关系构成短期成本曲线的基础，每位 IB 学生都必须能够画出并解读这些曲线。
7. Revenue and Profit Maximisation | 收益与利润最大化
Total revenue (TR) equals price multiplied by quantity sold. Average revenue (AR) is TR ÷ Q, which equals the price of the good if all units are sold at the same price. Marginal revenue (MR) is the change in total revenue from selling one more unit. Profit is maximised where marginal revenue equals marginal cost (MR = MC).
总收益（TR）等于价格乘以销售量。平均收益（AR）= TR ÷ Q，若所有单位以相同价格出售，则 AR 等于商品价格。边际收益（MR）是额外销售一单位产品所带来的总收益变动。当边际收益等于边际成本（MR = MC）时，利润实现最大化。
TR = P × Q
AR = TR ÷ Q = P
MR = ΔTR ÷ ΔQ
Profit maximising condition: MR = MC
利润最大化条件：MR = MC
Economic profit (abnormal profit) is TR minus total cost including opportunity cost. Normal profit is the minimum reward required to keep the entrepreneur in production, where TR equals total economic cost. In perfect competition, firms earn normal profit in the long run (AR = ATC).
经济利润（超额利润）等于总收益减去包含机会成本的总成本。正常利润是使企业家继续留在行业中的最低报酬，此时总收益等于总经济成本。在完全竞争市场中，厂商在长期只获得正常利润（AR = ATC）。
8. Macroeconomic Aggregates and GDP Calculation | 宏观经济总量与 GDP 计算
Gross domestic product measures the value of all final goods and services produced within a country in a given period. IB Economics requires understanding three approaches to calculate GDP: the expenditure approach, the income approach, and the output approach. The expenditure method is the most commonly tested formula.
国内生产总值衡量一国在一定时期内生产的全部最终产品和服务的价值。IB 经济学要求理解三种计算 GDP 的方法：支出法、收入法和产出法。其中支出法是最常考查的公式。
GDP = C + I + G + (X – M)
Where: C = household consumption, I = investment, G = government spending, X = exports, M = imports. (X – M) represents net exports.
其中：C = 家庭消费，I = 投资，G = 政府支出，X = 出口，M = 进口。(X – M) 为净出口。
Nominal GDP values output at current prices, while real GDP adjusts for inflation using a base year’s prices. The GDP deflator is used to convert nominal GDP into real GDP.
名义 GDP 以当期价格计算产出，而实际 GDP 则用基年价格调整了通货膨胀。GDP 平减指数用于将名义 GDP 转换为实际 GDP。
Real GDP = Nominal GDP ÷ GDP Deflator × 100
GDP Deflator = (Nominal GDP ÷ Real GDP) × 100
Example: If nominal GDP is $1 200 billion and the deflator is 120, real GDP = 1200 ÷ 1.20 = $1 000 billion (note: deflator 120 means prices are 20% higher than base year).
示例：若名义 GDP 为 12 000 亿美元，平减指数为 120，则实际 GDP = 1200 ÷ 1.20 = 10 000 亿美元（注意平减指数 120 表示价格比基年高 20%）。
9. Unemployment Rate and the Consumer Price Index (CPI) | 失业率与消费者价格指数
The unemployment rate is the percentage of the labour force that is actively seeking work but unable to find employment. It is one of the key macroeconomic indicators used to assess an economy’s health.
失业率是劳动力中积极寻找工作但未能就业的人口所占的百分比。它是评估经济健康状况的关键宏观经济指标之一。
Unemployment Rate = (Number of Unemployed ÷ Labour Force) × 100
The labour force includes both employed and unemployed people who are of working age and actively participating in the labour market. Discouraged workers who have stopped looking for work are not counted in the labour force.
劳动力包括处于工作年龄并积极投身劳动力市场的就业者与失业者。放弃寻找工作的沮丧劳动者不计入劳动力。
The consumer price index measures changes in the average price of a basket of goods and services. The inflation rate is calculated as the percentage change in CPI from one period to the next.
消费者价格指数衡量一篮子商品和服务平均价格的变化。通货膨胀率按 CPI 从一期到下一期的百分比变化计算。
CPI = (Cost of basket in current year ÷ Cost of basket in base year) × 100
Inflation Rate = [(CPIₜ – CPIₜ₋₁) ÷ CPIₜ₋₁] × 100
10. The Multiplier and the Keynesian Model | 乘数与凯恩斯模型
The multiplier effect explains how an initial injection into the circular flow of income leads to a larger final increase in national income. The formula is derived from the marginal propensity to consume (MPC) or the marginal propensity to save (MPS). For IB Economics, the multiplier is a cornerstone of demand-side policies.
乘数效应解释了对收入循环流的初始注入如何导致国民收入最终更大幅度的增长。公式由边际消费倾向（MPC）或边际储蓄倾向（MPS）导出。在 IB 经济学中，乘数是需求侧政策的核心概念。
Multiplier (k) = 1 ÷ (1 – MPC) = 1 ÷ MPS
Where MPC is the fraction of extra income that households spend on domestic goods and services, and MPS is the fraction saved. MPC + MPS = 1. In an open economy with taxation and imports, the multiplier is smaller.
其中 MPC 是家庭将额外收入用于购买国内商品和服务的比例，MPS 是储蓄的比例。MPC + MPS = 1。在存在税收和进口的开放经济中，乘数会变小。
Example: If MPC = 0.75, then k = 1 ÷ (1 – 0.75) = 4. An initial increase in government spending of $100 million would ultimately raise real GDP by $400 million, ceteris paribus.
示例：若 MPC = 0.75，则 k = 1 ÷ (1 – 0.75) = 4。政府支出若初始增加 1 亿美元，在其他条件不变下，最终将使实际 GDP 增加 4 亿美元。
11. Exchange Rates and Trade Weighted Index | 汇率与贸易加权指数
The exchange rate expresses the value of one currency in terms of another. In a floating system, the rate is determined by supply and demand. A formula often tested is the calculation of an appreciation or depreciation percentage.
汇率表示一种货币以另一种货币计量的价值。在浮动汇率制度中，汇率由供求决定。常考的公式是计算货币升值或贬值的百分比。
%Δ Exchange Rate = [(New Rate – Old Rate) ÷ Old Rate] × 100
When converting an amount from one currency to another, use: Amount in foreign currency = Amount in domestic currency × Exchange rate. When the exchange rate is expressed as the domestic price of foreign currency, a rise indicates depreciation of the domestic currency.
将一种货币金额换算为另一种时，使用：外币金额 = 本币金额 × 汇率。若汇率以外币的本币价格表示，上升意味着本币贬值。
A trade-weighted exchange rate index measures the value of a currency against a basket of trading partners’ currencies, weighted by their shares in trade. It is calculated as:
贸易加权汇率指数衡量货币相对一篮子贸易伙伴货币的价值，并按贸易份额加权。计算公式为：
Trade Weighted Index = Σ (Exchange rate index for each partner × Weight) ÷ 100
12. Comparative Advantage, Terms of Trade and Financial Ratios | 比较优势、贸易条件与财务比率
Comparative advantage is based on the concept of opportunity cost: the country with the lower opportunity cost of producing a good should specialise in it. The formula for terms of trade (TOT) measures the relationship between export and import prices.
比较优势的基础是机会成本概念：生产某种商品机会成本较低的国家应专门生产该商品。贸易条件（TOT）公式衡量出口价格与进口价格之间的关系。
Terms of Trade Index = (Index of Export Prices ÷ Index of Import Prices) × 100
An improvement in TOT means a country can buy more imports for a given quantity of exports. A deterioration implies the opposite. Students are also expected to know simple financial ratios such as the productivity gap, although these are not heavily examined.
贸易条件改善意味着一国用一定量的出口可以买到更多进口商品。恶化则相反。学生还应了解简单的财务比率，如生产率差距，尽管这些考查不多。
A useful development economics formula is the rate of economic growth:
Growth Rate = [(Real GDPₜ – Real GDPₜ₋₁) ÷ Real GDPₜ₋₁] × 100
Example: If real GDP rises from $800 billion to $824 billion, growth rate = (24 ÷ 800) × 100 = 3.0%.
示例：若实际 GDP 从 8 000 亿美元增至 8 240 亿美元，增长率 = (24 ÷ 800) × 100 = 3.0%。
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