📚 IGCSE OCR Economics: Calculation Practice | IGCSE OCR 经济：计算题专项训练
Calculations form a vital part of IGCSE OCR Economics, testing your ability to apply formulas accurately and interpret numerical results. This article walks you through the core quantitative skills you need, with step‑by‑step examples and common pitfalls to avoid.
计算题是 IGCSE OCR 经济的重要组成部分，考查你对公式的准确运用与数字结果的解读能力。本文将通过分步例题和常见错误分析，带你掌握核心定量技能。
1. Price Elasticity of Demand (PED) | 需求价格弹性
PED measures the responsiveness of quantity demanded to a change in price. The formula is: Percentage change in quantity demanded divided by percentage change in price. If you are given raw data, always calculate the percentage change using the midpoint method unless specified otherwise.
PED 衡量需求量对价格变动的反应程度。公式为：需求量变动百分比除以价格变动百分比。如果题目给出原始数据，除非特别说明，否则一律用中点法计算百分比变动。
A product’s price rises from £10 to £12, and quantity demanded falls from 500 units to 400 units. The percentage change in price using midpoint = (12‑10) ÷ [(10+12)÷2] × 100 = 18.18%. The percentage change in quantity demanded = (400‑500) ÷ [(500+400)÷2] × 100 = −22.22%. PED = −22.22% ÷ 18.18% = −1.22. Ignore the minus sign; this good has elastic demand (|PED| > 1).
某商品价格从 10 英镑上涨至 12 英镑，需求量从 500 件降至 400 件。中点法计算价格变动百分比 = (12-10) ÷ [(10+12)÷2] × 100 = 18.18%。需求量变动百分比 = (400-500) ÷ [(500+400)÷2] × 100 = -22.22%。PED = -22.22% ÷ 18.18% = -1.22。忽略负号，该商品需求富有弹性 (|PED| > 1)。
Interpretation: A PED of 1.22 means a 1% price rise reduces quantity demanded by 1.22%. Total revenue would fall if price was increased.
解读：PED 为 1.22 意味着价格上涨 1%，需求量减少 1.22%。如果提价，总收入会下降。
2. Total Revenue and PED | 总收入与需求价格弹性
Total revenue (TR) = Price × Quantity. The relationship between TR and PED helps firms decide on pricing. When demand is elastic, lowering price raises TR; when inelastic, raising price raises TR.
总收入 (TR) = 价格 × 数量。TR 与 PED 的关系有助于企业定价：需求富有弹性时，降价能增加总收入；缺乏弹性时，提价能增加总收入。
Using the previous data, initial TR = £10 × 500 = £5,000. New TR = £12 × 400 = £4,800. TR fell by £200, confirming elastic demand: the price rise caused a proportionately larger fall in quantity demanded.
用前面数据，初始 TR = 10 × 500 = 5,000 英镑。新 TR = 12 × 400 = 4,800 英镑。TR 下降了 200 英镑，验证了需求富有弹性：价格上涨导致需求量以更大比例下降。
Always check the sign of the change in TR when analysing PED. A common mistake is to assume that higher price always brings higher revenue – this is only true for inelastic goods.
分析 PED 时务必检查 TR 变动的方向。常见错误是认为提价总能增收——这仅对缺乏弹性的商品成立。
3. Price Elasticity of Supply (PES) | 供给价格弹性
PES measures the responsiveness of quantity supplied to a price change. Formula: Percentage change in quantity supplied ÷ Percentage change in price. Use the midpoint method when raw figures are given.
PES 衡量供给量对价格变动的反应程度。公式：供给量变动百分比 ÷ 价格变动百分比。给定原始数据时使用中点法。
The price of a textbook increases from £25 to £30, and publishers increase output from 2,000 to 2,600 copies. Midpoint price change = (30‑25) ÷ [(25+30)÷2] × 100 = 18.18%. Midpoint quantity change = (2,600‑2,000) ÷ [(2,000+2,600)÷2] × 100 = 26.09%. PES = 26.09 ÷ 18.18 = 1.44, indicating elastic supply.
某教科书价格从 25 英镑涨到 30 英镑，出版商将产量从 2,000 本增加到 2,600 本。中点法价格变动百分比 = (30-25) ÷ [(25+30)÷2] × 100 = 18.18%。中点法数量变动百分比 = (2,600-2,000) ÷ [(2,000+2,600)÷2] × 100 = 26.09%。PES = 26.09 ÷ 18.18 = 1.44，表明供给富有弹性。
A value greater than 1 means supply is relatively responsive. Factors like time period, spare capacity, and stock levels affect PES.
数值大于 1 表示供给反应相对灵敏。时间长短、闲置产能和库存水平等因素都会影响 PES。
4. Income Elasticity of Demand (YED) | 收入需求弹性
YED measures the responsiveness of demand to a change in income. Formula: Percentage change in quantity demanded ÷ Percentage change in income. The result can be positive (normal goods) or negative (inferior goods).
YED 衡量需求对收入变动的反应程度。公式：需求量变动百分比 ÷ 收入变动百分比。结果可为正（正常品）或负（劣等品）。
Suppose income rises from £20,000 to £24,000 and demand for organic bread rises from 200 to 260 loaves. Income change midpoint = (24,000‑20,000) ÷ [(20,000+24,000)÷2] × 100 = 18.18%. Quantity change = (260‑200) ÷ [(200+260)÷2] × 100 = 26.09%. YED = 26.09 ÷ 18.18 = +1.44. The positive sign shows organic bread is a normal good, and its elasticity above 1 classifies it as a luxury.
假设收入从 20,000 英镑增至 24,000 英镑，有机面包需求量从 200 条增至 260 条。收入中点变动 = (24,000-20,000) ÷ [(20,000+24,000)÷2] × 100 = 18.18%。需求量变动 = (260-200) ÷ [(200+260)÷2] × 100 = 26.09%。YED = 26.09 ÷ 18.18 = +1.44。正号表明有机面包是正常品，弹性大于 1 意味着它是奢侈品。
For inferior goods like instant noodles, an income rise might cut demand from 500 to 400 packs. YED would be negative, e.g. (‑22.22% ÷ 18.18%) = −1.22.
对于方便面这样的劣等品，收入增加可能导致需求从 500 包降至 400 包。YED 为负值，比如 -22.22% ÷ 18.18% = -1.22。
5. Cross Elasticity of Demand (XED) | 交叉需求弹性
XED measures how the quantity demanded of one good responds to a price change of another good. Formula: Percentage change in quantity demanded of Good A ÷ Percentage change in price of Good B. Positive result → substitutes; negative → complements.
XED 衡量一种商品的需求量如何随另一种商品价格变动而变动。公式：商品 A 需求量变动百分比 ÷ 商品 B 价格变动百分比。结果为正 → 替代品；结果为负 → 互补品。
Coffee price rises from £3 to £3.60 per cup, and tea sales increase from 800 to 920 cups. Price change of coffee: (3.60‑3) ÷ [(3+3.60)÷2] × 100 = 18.18%. Tea quantity change: (920‑800) ÷ [(800+920)÷2] × 100 = 14.63%. XED = 14.63 ÷ 18.18 = +0.80. The positive value indicates tea and coffee are substitutes; the strength is moderate.
咖啡价格每杯从 3 英镑涨到 3.60 英镑，茶销量从 800 杯增至 920 杯。咖啡价格变动 = (3.60-3) ÷ [(3+3.60)÷2] × 100 = 18.18%。茶的数量变动 = (920-800) ÷ [(800+920)÷2] × 100 = 14.63%。XED = 14.63 ÷ 18.18 = +0.80。正值表明茶和咖啡互为替代品，替代强度中等。
A negative XED arises for complements: if a printer price rises by 10% and ink cartridge demand falls by 15%, XED = −1.5, showing strong complementarity.
互补品会得到负的 XED：假如打印机价格上涨 10%，墨盒需求下降 15%，XED = -1.5，表明强互补关系。
6. Costs: Total, Average and Marginal | 成本：总成本、平均成本与边际成本
Firms face various costs: Total Fixed Cost (TFC), Total Variable Cost (TVC), and Total Cost (TC = TFC + TVC). Average Cost (AC) = TC ÷ Output. Marginal Cost (MC) is the cost of producing one more unit: ΔTC ÷ ΔQ.
企业面临多种成本：总固定成本 (TFC)、总可变成本 (TVC) 和总成本 (TC = TFC + TVC)。平均成本 (AC) = TC ÷ 产量。边际成本 (MC) 是多生产一个单位所增加的成本：ΔTC ÷ ΔQ。
Example: A bakery has TFC = £1,000 per month. Producing 500 loaves incurs TVC = £400. TC = £1,400. AC = 1,400 ÷ 500 = £2.80 per loaf. If increasing output to 501 loaves raises TC to £1,402, MC = (1,402‑1,400) ÷ (501‑500) = £2.00. This shows MC can be below AC, pulling AC downwards.
例题：一家面包店每月 TFC = 1,000 英镑。生产 500 个面包的 TVC = 400 英镑，TC = 1,400 英镑。AC = 1,400 ÷ 500 = 2.80 英镑/个。若将产量提高到 501 个面包使得 TC 变为 1,402 英镑，MC = (1,402-1,400) ÷ (501-500) = 2.00 英镑。这体现了 MC 低于 AC 时会拉低平均成本。
Common pitfalls: confusing marginal and average costs, and forgetting that MC intersects AC at its minimum point. In OCR exams, you may be given a cost table to fill; always compute MC as the change in TC per extra unit.
常见错误：混淆边际成本与平均成本，忘记 MC 通过 AC 的最低点。OCR 考试可能提供一张成本表让你填写，务必按每增加一单位的 TC 变动来计算 MC。
7. Revenue and Profit Maximisation | 收益与利润最大化
Total Revenue (TR) = Price × Quantity. Profit = TR − TC. Profit maximisation occurs where the gap between TR and TC is greatest, or where Marginal Revenue (MR) equals Marginal Cost (MC), provided MC is rising.
总收入 (TR) = 价格 × 数量。利润 = TR − TC。利润最大化点出现在 TR 与 TC 差距最大之处，或者边际收益 (MR) 等于边际成本 (MC) 且 MC 呈上升趋势时。
Consider a firm selling at a constant price of £5. Output rises from 100 to 200 units, so TR rises from £500 to £1,000, giving MR = £5. If TC rises from £400 to £900, MC = (900‑400) ÷ (200‑100) = £5. Here MR = MC, but profit is unchanged because ATC might equal price. You must check profitability by computing TR‑TC at each output.
假设一家企业以恒定价格 5 英镑销售。产量从 100 增至 200 单位，TR 从 500 英镑升至 1,000 英镑，MR = 5 英镑。若 TC 从 400 英镑升至 900 英镑，MC = (900-400) ÷ (200-100) = 5 英镑。此时 MR = MC，但利润未变，因为平均总成本可能等于价格。你必须在每个产出水平下计算 TR‑TC 来检验盈利状况。
In a table format, compute profit at each quantity and select the highest. Do not assume MR = MC always yields maximum profit if MC is falling or if the firm can still increase profit by expanding further.
在表格形式中，计算每个数量对应的利润并选取最大值。不要在没有检查 MC 走势的情况下盲目认为 MR = MC 就是利润最大化点。
8. Break‑even Point | 盈亏平衡点
The break‑even point is where total revenue equals total cost (profit = 0). It can be calculated in units: Break‑even output = Total Fixed Cost ÷ (Selling Price per unit − Variable Cost per unit). The denominator is the contribution per unit.
盈亏平衡点是总收入等于总成本（利润为零）的产量。计算公式（单位数）：盈亏平衡产量 = 总固定成本 ÷ (单位售价 − 单位可变成本)。分母是单位贡献额。
Example: A firm has TFC = £10,000, selling price = £50 per unit, and variable cost = £30 per unit. Break‑even output = 10,000 ÷ (50‑30) = 500 units. Any sales above 500 contribute to profit.
例题：某企业 TFC = 10,000 英镑，售价 = 每单位 50 英镑，可变成本 = 每单位 30 英镑。盈亏平衡产量 = 10,000 ÷ (50-30) = 500 单位。销量超过 500 的部分将贡献利润。
You can also find break‑even in revenue terms: Break‑even revenue = Break‑even units × Price = 500 × £50 = £25,000. Make sure to correctly identify TFC – do not include variable costs as fixed.
你也可以用收入形式表示盈亏平衡点：盈亏平衡收入 = 盈亏平衡产量 × 价格 = 500 × 50 = 25,000 英镑。务必正确识别 TFC——不要把可变成本误算为固定成本。
9. Exchange Rates: Conversion Calculations | 汇率：货币换算计算
Exchange rates express the value of one currency in terms of another. To convert from one currency to another, multiply by the exchange rate if you are moving from the base currency; or divide if moving to the base. OCR questions often require converting prices and analysing appreciation/depreciation.
汇率表示一种货币以另一种货币衡量的价值。换算时，如果从基准货币转换为另一种货币，用乘法；反之用除法。OCR 考题常要求换算价格并分析升值和贬值。
If £1 = $1.25, a UK tourist wants $500. She needs £500 ÷ 1.25 = £400. Conversely, if she brings £400 to the US, she gets £400 × 1.25 = $500. An appreciation of the pound to £1 = $1.60 would give her more dollars for the same pounds – good for importers but bad for exporters.
若 1 英镑 = 1.25 美元，一位英国游客想要 500 美元。她需要 500 ÷ 1.25 = 400 英镑。反过来，如果她把 400 英镑带到美国，她会得到 400 × 1.25 = 500 美元。英镑升值到 1 英镑 = 1.60 美元，同样数额的英镑可兑换更多美元——这对进口商有利，对出口商不利。
A common mistake is to multiply when you should divide. Always ask: if I have the base currency (e.g. £) and want the foreign currency, I multiply by the foreign per unit of base; if I have foreign and want base, I divide.
常见错误是该除时用了乘法。始终自问：如果我持有基准货币（如英镑）并想兑换外币，乘以单位基准货币对应的外币数；如果持有外币想换回基准货币，则用除法。
10. National Income: Expenditure and Output Approaches | 国民收入：支出法与产出法
IGCSE students need to understand that GDP can be measured via expenditure (C + I + G + (X − M)) or by summing the value of output. Calculations may involve finding GDP from a table or computing real GDP using a price index.
IGCSE 学生需要理解 GDP 既可用支出法（C + I + G + (X – M)）衡量，也可通过产出价值加总计算。考题可能要求根据表格求 GDP，或使用价格指数计算实际 GDP。
Given: Consumption = £800bn, Investment = £200bn, Government spending = £300bn, Exports = £150bn, Imports = £100bn. GDP = 800 + 200 + 300 + (150 − 100) = £1,350bn. This is nominal GDP.
假设：消费 = 8000 亿英镑，投资 = 2000 亿英镑，政府支出 = 3000 亿英镑，出口 = 1500 亿英镑，进口 = 1000 亿英镑。GDP = 800 + 200 + 300 + (150 – 100) = 1,3500 亿英镑。这是名义 GDP。
Real GDP adjusts for inflation: Real GDP = (Nominal GDP ÷ Price Index) × 100. If the GDP deflator is 120, real GDP = (1,350 ÷ 120) × 100 = £1,125bn. Always interpret the deflator: a value above 100 means prices have risen since the base year.
实际 GDP 剔除了通胀影响：实际 GDP = (名义 GDP ÷ 价格指数) × 100。若 GDP 平减指数为 120，实际 GDP = (1,350 ÷ 120) × 100 = 1,1250 亿英镑。解读平减指数时：数值高于 100 意味着价格自基年以来上涨了。
11. Index Numbers and Percentage Changes | 指数与百分比变动
Index numbers simplify the comparison of data over time. To construct an index, choose a base year (value = 100) and calculate: (Value in Current Year ÷ Value in Base Year) × 100. They are used for prices, wages, output, etc.
指数简化了跨时期数据的比较。构建指数时，选择基年（值=100）并按如下公式计算：(当年数值 ÷ 基年数值) × 100。指数可用于价格、工资、产出等方面。
In 2015, a basket of goods cost £200; in 2020, it cost £260. Take 2015 as base: 2020 index = (260 ÷ 200) × 100 = 130. The inflation rate over the period = (130‑100) ÷ 100 × 100 = 30%.
2015 年，一篮子商品价格为 200 英镑；2020 年已是 260 英镑。以 2015 年为基年：2020 年指数 = (260 ÷ 200) × 100 = 130。该期间通胀率 = (130-100) ÷ 100 × 100 = 30%。
When comparing two index numbers, remember the percentage change is simply the difference in index values because the base is 100. For instance, an index rising from 110 to 121 represents a (121‑110) ÷ 110 × 100 = 10% increase, not a rise of ’11 per cent’ in absolute terms.
比较两个指数时，注意百分比变动等于指数值之差除以初期指数，而不是指数的直接差值。例如，指数从 110 升至 121，上涨幅度为 (121-110) ÷ 110 × 100 = 10%，而非 11 个百分点。
12. Common Mistakes and Exam Tips | 常见错误与应试技巧
Always show your working; even if the final answer is wrong, you may earn method marks. Write the formula first, substitute the numbers, and then compute. Pay attention to the direction of change: for elasticities, the sign matters – give the sign, then interpret absolute value when discussing elasticity strength.
始终展示计算过程；即使最终答案错误，也可能得到过程分。先写公式，再代入数字，最后计算。注意变动的方向：弹性的正负号很重要——写出符号，然后在讨论弹性大小时再用绝对值解释。
Use the midpoint method for elasticity calculations unless the question specifies ‘simple percentage change’. In OCR, both methods may be accepted but stick to midpoint when raw data is given. When interpreting results, link your answer clearly to the question: e.g., ‘As PED is 1.22, demand is elastic, so a price cut would increase total revenue.’
弹性计算中，除非题目明确要求“简易百分比变动”，否则使用中点法。OCR 考试两种方法可能都接受，但在给定原始数据时坚持中点法。解读结果时，务必与题目明确关联：例如，“因为 PED 为 1.22，需求富有弹性，所以降价将增加总收入。”
Practise filling tables: cost, revenue, and profit tables appear regularly. Double‑check that MC refers to the change in TC when output rises by exactly one unit. For exchange rates, remember: ‘foreign per home’ means multiply home to get foreign; divide foreign to get home. These small checks can save precious marks.
练习填写表格：成本、收益和利润表格经常出现。再三检查 MC 是否对应产量恰好增加一单位时 TC 的变动。对于汇率，记住：“每单位本币折合外币”意味着本币乘汇率得外币，外币除以汇率得本币。这些小检查能帮你保住宝贵分数。
Published by TutorHao | Economics Revision Series | aleveler.com
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