📚 IB & CIE Economics: Calculation Practice Drills | IB CIE 经济：计算题专项训练
Economics is not just a theoretical subject; quantitative analysis and calculation questions appear frequently in IB and CIE exam papers, especially in Paper 2, Paper 3 (IB), and Data Response (CIE). Mastering these calculations can significantly boost your final grade. This drill article covers the most common calculation topics — from elasticity to multipliers, from costs to exchange rates — with step‑by‑step examples and explanations, designed to build your confidence and speed in exam numerical tasks.
经济学并非纯理论学科；在 IB 和 CIE 考试的 Paper 2、Paper 3（IB）与数据分析题（CIE）中，定量分析与计算题频繁出现。熟练掌握这些计算能大幅提升你的最终成绩。本文涵盖最常见的计算专题——从弹性到乘数，从成本到汇率——配以逐步示例和讲解，旨在帮助你在考场上建立信心、提高解题速度。
1. Price Elasticity of Demand (PED) | 需求价格弹性
Price elasticity of demand (PED) measures the responsiveness of quantity demanded to a change in price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.
需求价格弹性 (PED) 衡量需求量对价格变动的反应程度，计算公式为需求量变动百分比除以价格变动百分比。
The basic formula using the midpoint method is:
PED = %ΔQd ÷ %ΔP, where
%ΔQd = (Q₂ - Q₁) ÷ [(Q₂ + Q₁) ÷ 2] × 100,
%ΔP = (P₂ - P₁) ÷ [(P₂ + P₁) ÷ 2] × 100.
使用中点法的基本公式为：
PED = %ΔQd ÷ %ΔP，其中
%ΔQd = (Q₂ - Q₁) ÷ [(Q₂ + Q₁) ÷ 2] × 100，
%ΔP = (P₂ - P₁) ÷ [(P₂ + P₁) ÷ 2] × 100。
Example: The price of a chocolate bar falls from $4 to $3, and the quantity demanded rises from 60 to 90 units per week. Calculate PED using the midpoint method.
例题：巧克力棒价格从 $4 降至 $3，每周需求量从 60 单位升至 90 单位。请用中点法计算 PED。
Solution: %ΔQd = (90 - 60) ÷ [(90 + 60) ÷ 2] × 100 = 30 ÷ 75 × 100 = 40%.
%ΔP = (3 - 4) ÷ [(3 + 4) ÷ 2] × 100 = -1 ÷ 3.5 × 100 ≈ -28.57%.
PED = 40% ÷ (-28.57%) ≈ -1.4. Ignoring the sign, |PED| = 1.4, so demand is elastic. When demand is elastic, a price fall increases total revenue.
解答：%ΔQd = (90 − 60) ÷ [(90 + 60) ÷ 2] × 100 = 40%；%ΔP ≈ −28.57%。PED = 40% ÷ (−28.57%) ≈ −1.4。忽略符号，|PED| = 1.4，需求富有弹性。在弹性需求下，降价会增加总收益。
The following table summarises PED values and their implications:
| |PED| Value | Term | Effect on Total Revenue when Price Falls |
|---|---|---|
| > 1 | Elastic | Revenue increases |
| < 1 | Inelastic | Revenue decreases |
| = 1 | Unit elastic | Revenue unchanged |
下表概述了 PED 值及其含义：
| |PED| 值 | 术语 | 降价对总收益的影响 |
|---|---|---|
| > 1 | 富有弹性 | 总收益增加 |
| < 1 | 缺乏弹性 | 总收益减少 |
| = 1 | 单位弹性 | 总收益不变 |
2. Income Elasticity of Demand (YED) | 需求收入弹性
YED measures the responsiveness of demand to a change in income. It is calculated as the percentage change in quantity demanded divided by the percentage change in income.
需求收入弹性 (YED) 衡量需求对收入变动的反应程度，计算公式为需求量变动百分比除以收入变动百分比。
YED = %ΔQd ÷ %ΔY
If YED > 0, the good is a normal good; if YED < 0, it is an inferior good. Among normal goods, YED > 1 indicates a luxury.
若 YED > 0，该商品为正常品；若 YED < 0，则为劣等品。在正常品中，YED > 1 说明是奢侈品。
Example: Jessica's income rises from $2,500 to $3,000 per month, and her demand for movie tickets increases from 4 to 5 per month. Calculate YED.
例题：杰西卡月收入从 $2,500 升至 $3,000，每月电影票需求量从 4 张增至 5 张。请计算 YED。
Solution: %ΔQd = (5 - 4) ÷ [(5 + 4) ÷ 2] × 100 = 1 ÷ 4.5 × 100 ≈ 22.22%.
%ΔY = (3,000 - 2,500) ÷ [(3,000 + 2,500) ÷ 2] × 100 = 500 ÷ 2,750 × 100 ≈ 18.18%.
YED = 22.22% ÷ 18.18% ≈ 1.22. Since YED > 1, movie tickets are a luxury good for Jessica.
解答：%ΔQd ≈ 22.22%，%ΔY ≈ 18.18%。YED ≈ 1.22。由于 YED > 1，电影票对杰西卡而言属于奢侈品。
3. Cross-price Elasticity of Demand (XED) | 需求交叉价格弹性
XED measures the responsiveness of demand for good A to a change in the price of good B. The formula is:
需求交叉价格弹性 (XED) 衡量 A 商品需求量对 B 商品价格变动的反应程度。公式为：
XED = %ΔQd of good A ÷ %ΔP of good B
A positive XED means the goods are substitutes; a negative XED means they are complements. A value close to zero indicates the goods are independent.
XED 为正值说明二者互为替代品；负值则为互补品；接近零则说明商品相互独立。
Example: The price of coffee rises by 10%, and the quantity demanded of tea increases by 8%. Calculate XED for tea with respect to coffee.
例题：咖啡价格上涨 10%，茶叶需求量增加 8%。计算茶叶对咖啡的交叉价格弹性。
Solution: XED = +8% ÷ +10% = +0.8. The positive sign indicates tea and coffee are substitutes.
解答：XED = +8% ÷ +10% = +0.8。正值表明茶叶与咖啡互为替代品。
4. Price Elasticity of Supply (PES) | 供给价格弹性
PES captures the responsiveness of quantity supplied to a change in price. The formula is the same as PED but uses quantity supplied.
供给价格弹性 (PES) 衡量供给量对价格变动的反应程度。其公式与 PED 相同，但采用供给量数据。
PES = %ΔQs ÷ %ΔP
1. Key determinants include production time, spare capacity, and the level of inventories.
若 PES > 1，供给富有弹性；PES < 1 则缺乏弹性；PES = 1 为单位弹性。主要影响因素包括生产周期、闲置产能和库存水平。
Example: A firm increases its output from 500 to 700 units when the market price rises from $20 to $25. Calculate PES using the midpoint method.
例题：市场价格从 $20 升至 $25 时，某企业将产量从 500 单位提高到 700 单位。试用中点法计算 PES。
Solution: %ΔQs = (700 - 500) ÷ [(700 + 500) ÷ 2] × 100 = 200 ÷ 600 × 100 ≈ 33.33%.
%ΔP = (25 - 20) ÷ [(25 + 20) ÷ 2] × 100 = 5 ÷ 22.5 × 100 ≈ 22.22%.
PES ≈ 33.33% ÷ 22.22% ≈ 1.5. Supply is elastic in this range.
解答：%ΔQs ≈ 33.33%，%ΔP ≈ 22.22%。PES ≈ 1.5。在此价格区间供给富有弹性。
5. Total, Average and Marginal Costs & Revenues | 总成本、平均成本、边际成本与收益
Cost and revenue calculations form the backbone of the theory of the firm. You must be able to compute and interpret total cost (TC), fixed cost (FC), variable cost (VC), average total cost (ATC), average variable cost (AVC), marginal cost (MC), total revenue (TR), average revenue (AR) and marginal revenue (MR).
成本和收益计算是厂商理论的基础。你需熟练掌握总成本 (TC)、固定成本 (FC)、可变成本 (VC)、平均总成本 (ATC)、平均可变成本 (AVC)、边际成本 (MC)、总收益 (TR)、平均收益 (AR) 和边际收益 (MR) 的计算与解读。
Key formulae:
TC = FC + VC
ATC = TC ÷ Q
AVC = VC ÷ Q
MC = ΔTC ÷ ΔQ
TR = P × Q
AR = TR ÷ Q = P
MR = ΔTR ÷ ΔQ
关键公式：
TC = FC + VC；ATC = TC ÷ Q；AVC = VC ÷ Q；MC = ΔTC ÷ ΔQ；TR = P × Q；AR = TR ÷ Q = P；MR = ΔTR ÷ ΔQ。
Example: A firm produces 0 units with a total cost of $200 (all fixed). At Q = 10, total cost is $500. Assume the fixed cost remains at $200. Find VC at Q = 10, ATC, AVC and MC between Q = 0 and Q = 10.
例题：某企业产量为 0 时总成本为 $200（全部为固定成本）。产量为 10 时总成本为 $500，固定成本仍为 $200。求产量为 10 时的 VC、ATC、AVC 以及从 0 到 10 的 MC。
Solution: VC = TC - FC = 500 - 200 = $300. ATC = 500 ÷ 10 = $50. AVC = 300 ÷ 10 = $30. MC = ΔTC ÷ ΔQ = (500 - 200) ÷ (10 - 0) = $30 per unit.
解答：VC = TC − FC = $300。ATC = $500 ÷ 10 = $50。AVC = $300 ÷ 10 = $30。MC = ΔTC ÷ ΔQ = ($500 − $200) ÷ (10 − 0) = $30 / 单位。
6. Profit Maximisation and the Shut-down Point | 利润最大化与停业点
e (MC = MR), provided P > AVC. The profit or loss is then calculated as (AR - ATC) × Q.
当边际成本等于边际收益 (MC = MR) 且价格高于平均可变成本时，企业实现利润最大化。此时利润或亏损为 (AR − ATC) × Q。
ses. Its loss is then equal to total fixed cost. The break-even point occurs when P = ATC.
在短期，若价格低于最低 AVC，企业应停业以使亏损最小化，此时亏损等于全部固定成本。盈亏平衡点出现在价格等于平均总成本时。
Example: A perfectly competitive firm has a constant market price of $12. At the profit‑maximising output Q = 100, ATC = $10 and AVC = $8. Calculate total profit or loss.
例题：某完全竞争企业面对的市场价格恒为 $12。在利润最大化产量 Q = 100 时，ATC = $10，AVC = $8。计算总利润或亏损。
Solution: AR = P = $12. Profit per unit = AR - ATC = $12 - $10 = $2. Total profit = $2 × 100 = $200. Since P ($12) > AVC ($8), it is indeed worthwhile to produce.
解答：AR = P = $12。单位利润 = AR − ATC = $2。总利润 = $2 × 100 = $200。由于 P ($12) 高于 AVC ($8)，继续生产是正确的。
7. The National Income Multiplier | 国民收入乘数
The multiplier effect explains how an initial injection into the economy leads to a greater final increase in national income. The simple closed-economy multiplier is:
乘数效应解释了为何经济中的一笔初始注入会带来更大的国民收入最终增长。封闭经济中的简单乘数为：
k = 1 ÷ (1 - MPC) = 1 ÷ MPS
(MPS + MPT + MPM), where MPT is the marginal propensity to tax and MPM is the marginal propensity to import.
在存在税收和进口的开放经济中，乘数变小：k = 1 ÷ (MPS + MPT + MPM)，其中 MPT 为边际税收倾向，MPM 为边际进口倾向。
Example: The marginal propensity to consume is 0.75, and the government increases spending by $40 billion. Calculate the simple multiplier and the total increase in national income.
例题：边际消费倾向为 0.75，政府支出增加 $400 亿。计算简单乘数及国民收入的最终增量。
olution: k = 1 ÷ (1 - 0.75) = 1 ÷ 0.25 = 4. Total change in national income = k × ΔG = 4 × $40 bn = $160 billion.
解答：k = 1 ÷ (1 − 0.75) = 4。国民收入总变动 = k × ΔG = 4 × $400 亿 = $1600 亿。
8. Comparative Advantage and Terms of Trade | 比较优势与贸易条件
Comparative advantage is determined by comparing opportunity costs. The country with the lower opportunity cost in producing a good has the comparative advantage in that good.
比较优势通过比较机会成本来确定。一国生产某种商品的机会成本较低，即在该商品上具有比较优势。
Example: In one hour, Country X can produce either 10 units of rice or 5 units of cars. Country Y can produce either 6 units of rice or 3 units of cars. Calculate opportunity costs and identify comparative advantages.
例题：Country X 在一小时内可生产 10 单位大米或 5 单位汽车。Country Y 可生产 6 单位大米或 3 单位汽车。计算机会成本并指出比较优势。
he same opportunity cost, so no comparative advantage exists; nevertheless, if a country specialises based on absolute advantage, gains from trade require mutually beneficial terms of trade. For a case with differences, if Country X: 1 rice = 0.5 cars, Country Z: 1 rice = 1 car, X has comparative advantage in rice, Z in cars, and the terms of trade for 1 car must lie between 1 and 2 rice.
解答：X 国 1 大米的机会成本为 0.5 汽车，1 汽车为 2 大米；Y 国 1 大米的机会成本也是 0.5 汽车，1 汽车为 2 大米。机会成本相同，无比较优势；但若有差异，如 X 国 1 大米 = 0.5 汽车，Z 国 1 大米 = 1 汽车，则 X 在大米上有比较优势，Z 在汽车上有比较优势，1 辆汽车的贸易条件应介于 1 至 2 单位大米之间。
Mutually beneficial terms of trade lie between the opportunity cost ratios of the two countries.
互利的贸易条件介于两国机会成本比率之间。
9. Exchange Rate Calculations | 汇率计算
. You may need to calculate percentage appreciation or depreciation, or convert between currencies.
汇率可采用直接标价（如 1 GBP = 1.25 USD）或间接标价（如 1 USD = 0.80 GBP）。你可能需要计算货币升值或贬值的百分比，或在不同货币间进行换算。
e - Old rate) ÷ Old rate × 100. A positive change means the base currency has appreciated.
汇率变动百分比 = (新汇率 − 旧汇率) ÷ 旧汇率 × 100。正值表示基础货币升值。
Example: The GBP/USD exchange rate moves from 1.3000 to 1.3650. Calculate the percentage change in the value of the pound.
例题：GBP/USD 汇率从 1.3000 变为 1.3650。计算英镑价值的变动百分比。
Solution: % change = (1.3650 - 1.3000) ÷ 1.3000 × 100 ≈ +5.00%. The pound has appreciated by 5% against the dollar.
解答：% 变动 = (1.3650 − 1.3000) ÷ 1.3000 × 100 ≈ +5.00%。英镑对美元升值了 5%。
UR = 1.10 and USD/GBP = 1.30, then EUR/GBP = (USD/GBP) ÷ (USD/EUR) = 1.30 ÷ 1.10 ≈ 1.1818.
交叉汇率：若 USD/EUR = 1.10，USD/GBP = 1.30，则 EUR/GBP = 1.30 ÷ 1.10 ≈ 1.1818。
10. Inflation and Index Numbers | 通胀与指数
Inflation is typically measured by the Consumer Price Index (CPI). The CPI is calculated as the cost of a fixed basket of goods in the current year divided by the cost in the base year, multiplied by 100.
通货膨胀通常用消费者价格指数 (CPI) 衡量。CPI = (当年固定一篮子商品成本 ÷ 基年成本) × 100。
The annual inflation rate is the percentage change in the CPI:
年通胀率即 CPI 变动的百分比：
Inflation rate = (CPIt - CPIt-1) ÷ CPIt-1 × 100
Example: The basket of goods costs $850 in the base year. In 2023 it costs $1,020, and in 2024 it costs $1,071. Calculate the CPI for both years (base year = 100) and the inflation rate for 2024.
例题：一篮子商品在基年成本为 $850，2023 年成本为 $1,020，2024 年为 $1,071。计算两年各自的 CPI（基年 = 100）及 2024 年的通胀率。
Solution: CPI2023 = (1,
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