IB WJEC Economics: Calculation Practice | IB WJEC 经济：计算题专项训练

📚 IB WJEC Economics: Calculation Practice | IB WJEC 经济：计算题专项训练

Calculation questions form a vital part of both IB Economics and WJEC Economics assessments. They require precise application of formulas, accurate data interpretation, and a clear understanding of underlying concepts. This article provides a structured revision of the most common calculation topics, blending IB and WJEC syllabi to help you master quantitative skills for your exams.

计算题是 IB 经济和 WJEC 经济考试的重要组成部分。它们要求准确应用公式、精准解读数据，并清晰理解相关概念。本文系统梳理了最常见的计算题型，融合 IB 与 WJEC 大纲，帮助你在考试中掌握定量分析技能。

1. Price Elasticity of Demand (PED) | 需求价格弹性 (PED)

Price elasticity of demand measures how responsive quantity demanded is to a change in price. The formula is: PED = (% change in quantity demanded) / (% change in price). Always take the absolute value after calculation; PED is treated as a positive number though demand curves slope downwards. A value greater than 1 indicates elastic demand, less than 1 inelastic demand, and equal to 1 unitary elasticity.

需求价格弹性衡量需求量对价格变化的反应程度。公式为：PED = (需求量变动百分比) / (价格变动百分比)。计算后通常取绝对值；虽然需求曲线向下倾斜，但 PED 视为正数。大于 1 表示富有弹性，小于 1 表示缺乏弹性，等于 1 表示单位弹性。

Percentage change formula: ((New – Old) / Old) × 100 | 百分比变化公式：((新值 – 旧值) / 旧值) × 100
Midpoint (arc) elasticity for larger changes: PED = (ΔQ / ((Q₁+Q₂)/2)) ÷ (ΔP / ((P₁+P₂)/2)) | 中点（弧）弹性用于较大变化：PED = (ΔQ / ((Q₁+Q₂)/2)) ÷ (ΔP / ((P₁+P₂)/2))
Total revenue test: if price rises and TR falls → elastic; if TR rises → inelastic | 总收入检验：涨价若总收入下降则为弹性；若总收入上升则为缺乏弹性

2. Price Elasticity of Supply (PES) | 供给价格弹性 (PES)

Price elasticity of supply quantifies the responsiveness of quantity supplied to a price change. The formula: PES = (% change in quantity supplied) / (% change in price). Unlike PED, PES is usually positive. Values above 1 are elastic, below 1 inelastic. Key determinants include production time, spare capacity, and substitutability of inputs.

供给价格弹性衡量供给量对价格变化的反应程度。公式：PES = (供给量变动百分比) / (价格变动百分比)。与 PED 不同，PES 通常为正值。大于 1 表示富有弹性，小于 1 表示缺乏弹性。关键决定因素包括生产时间、闲置产能和投入品的替代性。

Perfectly inelastic supply: PES = 0 (e.g., fixed number of seats in a stadium) | 完全无弹性供给：PES = 0（如体育场固定座位数）
Unit elastic supply: PES = 1; any straight line supply curve from the origin has unitary PES | 单位弹性供给：PES = 1；任何通过原点的直线供给曲线都具有单位弹性
Using the same percentage change approach as PED | 使用与 PED 相同的百分比变化方法

3. Income Elasticity of Demand (YED) | 需求收入弹性 (YED)

Income elasticity of demand shows how demand changes with consumer income. Formula: YED = (% change in quantity demanded) / (% change in income). The sign matters: positive for normal goods, negative for inferior goods. A YED greater than 1 indicates a luxury good; between 0 and 1 a necessity.

需求收入弹性显示需求如何随消费者收入变化。公式：YED = (需求量变动百分比) / (收入变动百分比)。符号很重要：正值为正常品，负值为低档品。YED 大于 1 表示奢侈品；介于 0 和 1 之间表示必需品。

Normal necessity: 0 < YED < 1 | 正常必需品：0 < YED < 1
Luxury: YED > 1 | 奢侈品：YED > 1
Inferior good: YED < 0 (demand falls as income rises) | 低档品：YED < 0（收入增加需求下降）
Engel curve implications for firms’ planning | 恩格尔曲线对企业规划的启示

4. Cross Elasticity of Demand (XED) | 需求交叉弹性 (XED)

Cross elasticity of demand measures the responsiveness of demand for one good to a change in the price of another good. Formula: XED = (% change in quantity demanded of good A) / (% change in price of good B). Positive XED indicates substitutes; negative XED indicates complements. The magnitude indicates the strength of the relationship.

需求交叉弹性衡量一种商品的需求量对另一种商品价格变化的反应程度。公式：XED = (商品 A 需求量变动百分比) / (商品 B 价格变动百分比)。正 XED 表示替代品；负 XED 表示互补品。绝对值表明关系的强弱。

Substitutes: XED > 0 (e.g., tea and coffee) | 替代品：XED > 0（例如茶和咖啡）
Complements: XED < 0 (e.g., printers and ink cartridges) | 互补品：XED < 0（例如打印机和墨盒）
Unrelated goods: XED ≈ 0 | 无关商品：XED ≈ 0
Useful for pricing strategies of multiproduct firms | 对多产品企业的定价策略很有用

5. Market Equilibrium and Surplus | 市场均衡与剩余

At equilibrium, quantity demanded equals quantity supplied. Calculations often require solving for equilibrium price and quantity from demand and supply equations (e.g., Q_d = a − bP, Q_s = c + dP). Consumer surplus is the area between the demand curve and the market price; producer surplus is the area between the price and the supply curve. Total surplus measures economic welfare.

均衡时，需求量等于供给量。计算题通常要求从需求和供给方程求解均衡价格和数量（例如 Q_d = a − bP, Q_s = c + dP）。消费者剩余是需求曲线与市场价格之间的面积；生产者剩余是市场价格与供给曲线之间的面积。总剩余衡量经济福利。

Equilibrium: set Q_d = Q_s, solve for P, then substitute back for Q | 均衡：令 Q_d = Q_s，解出 P，再回代求 Q
Consumer surplus = ½ × (maximum willingness to pay − P_e) × Q_e | 消费者剩余 = ½ × (最高支付意愿 − P_e) × Q_e
Producer surplus = ½ × (P_e − minimum supply price) × Q_e | 生产者剩余 = ½ × (P_e − 最低供给价格) × Q_e
Deadweight loss occurs away from equilibrium due to taxes, subsidies, or price controls | 由于税收、补贴或价格管制，偏离均衡会产生无谓损失

6. Tax and Subsidy Analysis | 税收与补贴分析

Indirect taxes shift supply curves vertically upwards by the amount of the tax. The new supply function becomes Q_s = c + d(P − t), where t is the per-unit tax. Buyers pay P_b, sellers receive P_s (where P_b − P_s = t). Tax revenue = t × Q_new. The burden shared between consumers and producers depends on relative elasticities. Subsidies are treated similarly, shifting supply down.

间接税会使供给曲线垂直向上移动税额。新的供给函数变为 Q_s = c + d(P − t)，其中 t 为单位税额。买方支付 P_b，卖方获得 P_s（P_b − P_s = t）。税收收入 = t × Q_新。消费者和生产者分担的税负取决于相对弹性。补贴类似，但使供给曲线下移。

Consumer burden = (elasticity of supply / (elasticity of supply + elasticity of demand)) × tax | 消费者负担 = (供给弹性 / (供给弹性 + 需求弹性)) × 税收
Producer burden = (elasticity of demand / (elasticity of supply + elasticity of demand)) × tax | 生产者负担 = (需求弹性 / (供给弹性 + 需求弹性)) × 税收
Subsidy: Q_s = c + d(P + s), P_s − P_b = s | 补贴：Q_s = c + d(P + s)，P_s − P_b = s
Welfare effects: calculate changes in consumer surplus, producer surplus, government cost, and deadweight loss | 福利效应：计算消费者剩余、生产者剩余、政府成本和无谓损失的变化

7. Costs, Revenue and Profit | 成本、收益与利润

Firms face various cost structures. Key calculations include total fixed cost (TFC), total variable cost (TVC), total cost (TC = TFC + TVC), average costs (AFC, AVC, ATC = TC / Q), and marginal cost (MC = ΔTC / ΔQ). Revenue concepts: total revenue (TR = P × Q), average revenue (AR = TR / Q = P), and marginal revenue (MR = ΔTR / ΔQ). Profit maximisation occurs where MR = MC.

企业面临各种成本结构。关键计算包括总固定成本 (TFC)、总可变成本 (TVC)、总成本 (TC = TFC + TVC)、平均成本 (AFC、AVC、ATC = TC / Q) 和边际成本 (MC = ΔTC / ΔQ)。收益概念：总收益 (TR = P × Q)、平均收益 (AR = TR / Q = P) 和边际收益 (MR = ΔTR / ΔQ)。利润最大化在 MR = MC 处实现。

Break-even price = minimum ATC; shutdown price = minimum AVC | 盈亏平衡价格 = 最低 ATC；停业价格 = 最低 AVC
Normal profit: AR = ATC; supernormal profit: AR > ATC | 正常利润：AR = ATC；超额利润：AR > ATC
Loss but continue production: AVC < AR < ATC | 亏损但继续生产：AVC < AR < ATC
Profit = (AR − ATC) × Q, or TR − TC | 利润 = (AR − ATC) × Q，或 TR − TC

8. National Income and the Multiplier | 国民收入与乘数

National income can be measured through expenditure, income, and output approaches. Key aggregates: GDP = C + I + G + (X − M). The marginal propensity to consume (MPC) = ΔC / ΔY; the marginal propensity to save (MPS) = 1 − MPC. The simple multiplier k = 1 / (1 − MPC) or 1 / MPS. The full multiplier may also include taxes and imports: k = 1 / (MPS + MPT + MPM), where MPT is marginal propensity to tax and MPM is marginal propensity to import.

国民收入可通过支出法、收入法和产出法衡量。关键总量：GDP = C + I + G + (X − M)。边际消费倾向 (MPC) = ΔC / ΔY；边际储蓄倾向 (MPS) = 1 − MPC。简单乘数 k = 1 / (1 − MPC) 或 1 / MPS。完整乘数可能包含税收和进口：k = 1 / (MPS + MPT + MPM)，其中 MPT 为边际税率，MPM 为边际进口倾向。

Change in equilibrium GDP = multiplier × change in autonomous spending (ΔA) | 均衡 GDP 变动 = 乘数 × 自主支出变动 (ΔA)
With tax rate t: k = 1 / (1 − MPC(1 − t)) for a simple tax model | 含税率 t：k = 1 / (1 − MPC(1 − t))（简单税收模型）
Note: IB syllabus often uses k = 1/(1 − MPC) for a closed economy without taxes | 注意：IB 大纲常使用封闭无税经济下的 k = 1/(1 − MPC)
WJEC may include the expenditure multiplier with government sector | WJEC 可能包含政府部门的支出乘数

9. Unemployment and Inflation Rates | 失业率与通货膨胀率

Unemployment rate = (number of unemployed / labour force) × 100. The labour force includes those employed plus those actively seeking work. Inflation is measured by a price index, such as the Consumer Price Index (CPI). Inflation rate = ((CPI_current − CPI_previous) / CPI_previous) × 100. Weighted price indices assign importance to different spending categories.

失业率 = (失业人数 / 劳动力) × 100。劳动力包括就业者和积极寻找工作的人。通货膨胀通过价格指数衡量，如消费者价格指数 (CPI)。通货膨胀率 = ((CPI_当前 − CPI_前一期) / CPI_前一期) × 100。加权价格指数对不同支出类别赋予不同重要性。

Labour force participation rate = (labour force / working-age population) × 100 | 劳动参与率 = (劳动力 / 劳动年龄人口) × 100
Real GDP = (Nominal GDP / Price index) × 100 | 实际 GDP = (名义 GDP / 价格指数) × 100
GDP deflator = (Nominal GDP / Real GDP) × 100 | GDP 平减指数 = (名义 GDP / 实际 GDP) × 100
Inflation may be calculated using basket weights: Σ (weight × price relative) | 通胀可通过一篮子权重计算：Σ (权重 × 价格比率)

10. Comparative Advantage and 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. Calculations involve constructing output-per-unit-of-input tables and determining the opportunity cost ratios. For instance, if Country A can produce 10 units of cloth or 20 units of wine per hour, the opportunity cost of 1 unit of cloth is 2 wine. Terms of trade must lie between the two opportunity cost ratios for trade to be mutually beneficial.

当一国以低于另一国的机会成本生产某种商品时，就存在比较优势。计算包括构造单位投入产出表并确定机会成本比率。例如，若 A 国每小时可生产 10 单位布匹或 20 单位酒，则 1 单位布匹的机会成本为 2 单位酒。贸易条件必须介于两国机会成本比率之间才能使贸易互利。

Opportunity cost of X = (loss in Y) / (gain in X) | X 的机会成本 = (Y 的损失) / (X 的收益)
Absolute advantage: producing more with the same resources; basis for specialisation | 绝对优势：用相同资源生产更多；专业化的基础
Terms of trade index = (index of export prices / index of import prices) × 100 | 贸易条件指数 = (出口价格指数 / 进口价格指数) × 100
Gains from trade arise if each country specialises in its comparative advantage good | 若各国专业化生产其比较优势商品，则会产生贸易收益

11. Exchange Rate Calculations | 汇率计算

Exchange rates can be expressed as currency per unit of foreign currency or foreign currency per unit of domestic currency. To convert between currencies: amount in foreign currency = amount in domestic currency × exchange rate (given as foreign/domestic). Appreciation means a rise in value; depreciation a fall. Calculating percentage change: ((New rate − Old rate) / Old rate) × 100. Trade-weighted exchange rate indices aggregate bilateral rates.

汇率可表示为每单位外币的本币数或每单位本币的外币数。货币换算：外币金额 = 本币金额 × 汇率（以外币/本币计）。升值意味着价值上升；贬值则下降。计算百分比变化：((新汇率 − 旧汇率) / 旧汇率) × 100。贸易加权汇率指数综合了双边汇率。

If £1 = $1.25, then $100 = £100 / 1.25 = £80 | 若 £1 = $1.25，则 $100 = £100 / 1.25 = £80
Exchange rate impact on prices: a stronger domestic currency makes imports cheaper and exports more expensive | 汇率对价格的影响：本币升值使进口变便宜、出口变贵
Real exchange rate = nominal exchange rate × (domestic price / foreign price) | 实际汇率 = 名义汇率 × (国内价格 / 国外价格)
Effective exchange rate: weighted average against a basket of currencies | 有效汇率：对一篮子货币的加权平均

12. Balance of Payments and Trade Balances | 国际收支与贸易差额

The balance of payments records transactions between a country and the rest of the world. The current account includes trade in goods (visible), trade in services (invisible), primary income (investment income, compensation of employees), and secondary income (transfers). The trade balance = value of exports − value of imports. A current account deficit must be matched by a financial account surplus (or vice versa), ensuring the overall balance sums to zero.

国际收支记录一国与世界其他地区之间的交易。经常账户包括货物贸易（有形）、服务贸易（无形）、初次收入（投资收益、雇员报酬）和二次收入（转移）。贸易差额 = 出口价值 − 进口价值。经常账户逆差必须由金融账户顺差弥补（反之亦然），确保总收支为零。

Current account balance = (X − M) + net income + net transfers | 经常账户余额 = (X − M) + 净收入 + 净转移
Net errors and omissions is a balancing item | 净误差与遗漏是平衡项目
Terms of trade improvement: (export price index / import price index) > 1 | 贸易条件改善：(出口价格指数 / 进口价格指数) > 1
J-curve effect: trade balance worsens after depreciation before improving | J 曲线效应：贬值后贸易差额先恶化再改善

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IB WJEC Economics: Calculation Practice | IB WJEC 经济：计算题专项训练