📚 IGCSE WJEC Economics: Calculation Practice | IGCSE WJEC 经济：计算题专项训练
Mastering quantitative skills is essential for success in WJEC IGCSE Economics. This guide walks you through the most common types of calculations that appear in the exam, from elasticities and costs to the multiplier and real GDP. Each section includes clear formulas, worked examples, and bilingual explanations to strengthen both your English and Economics understanding.
掌握定量技能对于 WJEC IGCSE 经济学的成功至关重要。本指南将带你逐一攻克考试中最常见的计算题型，从弹性、成本到乘数和实际 GDP。每个部分都包含清晰的公式、详细示例以及中英文双语解释，帮助你同时提升英语水平和经济学理解。
1. Percentage Changes and Index Numbers | 百分比变化与指数
Many economic calculations begin with the ability to compute a percentage change. The formula is: % change = (New Value – Old Value) / Old Value × 100. Always express the answer to one or two decimal places unless instructed otherwise. Index numbers simplify comparisons over time by setting a base year value to 100.
许多经济计算都始于计算百分比变化的能力。公式为：百分比变化 = (新值 – 旧值) / 旧值 × 100。除非另有要求，答案通常保留一或两位小数。指数通过将基年数值设定为 100 来简化跨时期比较。
Example: If the price of a good rises from £4.50 to £5.40, the percentage increase is (5.40 – 4.50) / 4.50 × 100 = 20.0%. For index numbers, if 2020 is the base year with a GDP of £800 billion, and 2023 GDP is £920 billion, the 2023 index number is (920 / 800) × 100 = 115.
示例：某商品价格从 4.50 英镑涨到 5.40 英镑，则上涨百分比为 (5.40 – 4.50) / 4.50 × 100 = 20.0%。在指数中，若 2020 年为基年，GDP 为 8000 亿英镑，2023 年 GDP 为 9200 亿英镑，则 2023 年指数为 (920 / 800) × 100 = 115。
2. 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:
PED 衡量的是需求量对价格变化的反应程度。公式为：
PED = %Δ Quantity Demanded / %Δ Price
Ignore the minus sign when interpreting the coefficient; we look at absolute value. If PED > 1, demand is elastic. If PED < 1, demand is inelastic. If PED = 1, demand is unit elastic.
解释系数时忽略负号，看绝对值。若 PED > 1，需求富有弹性；若 PED < 1，需求缺乏弹性；若 PED = 1，需求为单位弹性。
Worked example: A 10% rise in the price of cinema tickets causes a 25% fall in tickets sold. PED = –25% / 10% = –2.5. Absolute value is 2.5, so demand is elastic. If a cinema wants to increase total revenue, it should lower the price because demand is elastic.
计算示例：电影票价上涨 10% 导致售出数量下降 25%。PED = –25% / 10% = –2.5。绝对值为 2.5，因此需求富有弹性。影院若想增加总收入，应当降价，因为需求富有弹性。
3. Income Elasticity of Demand (YED) | 需求收入弹性
YED shows how demand changes with income. Formula:
YED 显示需求如何随收入变化。公式：
YED = %Δ Quantity Demanded / %Δ Income
A positive YED indicates a normal good; a negative YED indicates an inferior good. A YED greater than 1 identifies a luxury good. Exam questions often ask you to classify the good based on your calculation.
YED 为正表示正常商品；YED 为负表示低档商品。YED 大于 1 则属于奢侈品。考试常要求你根据计算结果对商品进行分类。
Example: When consumer income rises by 5%, demand for organic vegetables increases by 12%. YED = 12% / 5% = +2.4. This is a luxury normal good. If demand for own-brand bread falls by 3% when income rises by 5%, YED = –3% / 5% = –0.6, an inferior good.
示例：消费者收入上升 5%，有机蔬菜需求增加 12%。YED = 12% / 5% = +2.4，属于奢侈品（正常商品）。若收入上升 5% 导致自有品牌面包需求下降 3%，YED = –3% / 5% = –0.6，为低档商品。
4. Cross Elasticity of Demand (XED) | 需求交叉弹性
XED measures the responsiveness of demand for one good (A) to a change in the price of another (B).
XED 衡量一种商品 (A) 的需求对另一种商品 (B) 价格变化的反应程度。
XED = %Δ Quantity Demanded of Good A / %Δ Price of Good B
A positive XED signals substitutes; a negative XED signals complements. The larger the absolute value, the stronger the relationship.
XED 为正表示替代品；为负表示互补品。绝对值越大，关系越强。
Example: A 10% rise in the price of coffee leads to an 8% increase in demand for tea. XED = +8% / 10% = +0.8. These are substitutes. If a 5% drop in the price of printers raises demand for ink cartridges by 15%, XED = 15% / –5% = –3.0, which indicates strong complements.
示例：咖啡价格上升 10%，导致茶叶需求增加 8%。XED = +8% / 10% = +0.8，两者为替代品。若打印机价格下降 5%，墨盒需求增加 15%，XED = 15% / –5% = –3.0，说明是强互补品。
5. Price Elasticity of Supply (PES) | 供给价格弹性
PES captures how responsive quantity supplied is to a price change.
PES 反映供给量对价格变化的反应程度。
PES = %Δ Quantity Supplied / %Δ Price
PES is always positive because of the law of supply. Values above 1 are elastic (producers can expand output easily), below 1 are inelastic, and PES = 0 is perfectly inelastic (fixed supply). Key influences include production time and availability of spare capacity.
由于供给定律，PES 始终为正。大于 1 富有弹性（生产者能轻易扩大产出），小于 1 缺乏弹性，PES = 0 为完全无弹性（供给固定）。关键影响因素包括生产时间和闲置产能的可用性。
Example: The price of strawberries rises by 20%, enabling farmers to increase quantity supplied by 30% after one season. PES = 30% / 20% = 1.5. Supply is elastic. In contrast, a 15% rise in concert ticket prices may yield only a 2% increase in seats (fixed venue), giving PES = 2% / 15% ≈ 0.13, highly inelastic.
示例：草莓价格上涨 20%，农民在一季后将供给量提高 30%。PES = 30% / 20% = 1.5，供给富有弹性。相反，演唱会门票价格上涨 15% 可能只能增加 2% 座位（场地固定），PES = 2% / 15% ≈ 0.13，高度缺乏弹性。
6. Total, Average and Marginal Cost | 总成本、平均成本与边际成本
Cost calculations form a core part of firm behavior analysis. Total Cost (TC) = Total Fixed Cost (TFC) + Total Variable Cost (TVC). Average Cost (AC) or Average Total Cost (ATC) = TC / Output. Marginal Cost (MC) = Δ TC / Δ Output.
成本计算是企业行为分析的核心部分。总成本 (TC) = 总固定成本 (TFC) + 总变动成本 (TVC)。平均成本 (AC) 或平均总成本 (ATC) = TC / 产量。边际成本 (MC) = Δ TC / Δ 产量。
When marginal cost is below average cost, average cost falls. When marginal cost exceeds average cost, average cost rises. This relationship is crucial for understanding the shape of the cost curves.
当边际成本低于平均成本时，平均成本下降；当边际成本高于平均成本时，平均成本上升。这一关系对于理解成本曲线的形状至关重要。
Example: A bakery has fixed costs of £200 per day. Producing 50 loaves incurs variable costs of £50. TC = 200 + 50 = £250. AC = 250 / 50 = £5 per loaf. If producing the 51st loaf raises total cost to £253, then MC = (253 – 250) / (51 – 50) = £3. Since MC (£3) < AC (£5), average cost will decrease.
示例：一家面包店的固定成本为每天 200 英镑。生产 50 个面包的变动成本为 50 英镑。TC = 200 + 50 = 250 英镑。AC = 250 / 50 = 每个面包 5 英镑。若生产第 51 个面包使总成本升至 253 英镑，则 MC = (253 – 250) / (51 – 50) = 3 英镑。因为 MC (3) < AC (5)，平均成本将下降。
7. Revenue and Profit Calculations | 收入与利润计算
Total Revenue (TR) = Price × Quantity sold. Average Revenue (AR) = TR / Quantity = Price. Thus AR equals the demand curve. Marginal Revenue (MR) = Δ TR / Δ Quantity. Profit = TR – TC. You may be asked to find the profit-maximising output where MR = MC, or to calculate supernormal profit.
总收入 (TR) = 价格 × 销量。平均收入 (AR) = TR / 数量 = 价格，因此 AR 等于需求曲线。边际收入 (MR) = Δ TR / Δ 数量。利润 = TR – TC。考试可能要求你找到利润最大化的产量（MR = MC），或计算超额利润。
Example: A firm sells 200 units at £15 each. TR = 200 × 15 = £3 000. If total cost at this output is £2 400, profit = 3 000 – 2 400 = £600. If cutting price to £14 would sell 220 units, new TR = £3 080, and MR from the extra 20 units = (3 080 – 3 000) / (220 – 200) = £4 per unit. Because MR is below original price, the demand curve is downward sloping.
示例：某公司以单价 15 英镑出售 200 单位商品。TR = 200 × 15 = 3 000 英镑。若该产量下的总成本为 2 400 英镑，则利润 = 3 000 – 2 400 = 600 英镑。若降价到 14 英镑能卖出 220 单位，新 TR = 3 080 英镑，额外 20 单位的 MR = (3 080 – 3 000) / (220 – 200) = 每单位 4 英镑。MR 低于原价格，表明需求曲线向下倾斜。
8. The Multiplier Effect | 乘数效应
The multiplier quantifies the magnified impact of an injection into the circular flow. Basic multiplier = 1 / (1 – MPC) or 1 / MPS. Here MPC is the marginal propensity to consume, and MPS = 1 – MPC. The change in national income = multiplier × initial injection.
乘数量化了注入资金对循环流的放大效应。基本乘数 = 1 / (1 – MPC) 或 1 / MPS。其中 MPC 是边际消费倾向，MPS = 1 – MPC。国民收入变动 = 乘数 × 初始注入。
You can also calculate the multiplier from the marginal propensity to withdraw (MPW), which includes savings, taxes, and imports: multiplier = 1 / MPW. Exam data may give you a change in consumption for a given change in income, from which you derive MPC.
你也可以通过边际漏出倾向 (MPW)，包括储蓄、税收和进口来计算乘数：乘数 = 1 / MPW。考试数据可能会给出给定收入变化下的消费变化，由此得出 MPC。
Example: Households spend £80 million of a £100 million increase in income. MPC = 80/100 = 0.8. MPS = 0.2. Multiplier = 1 / 0.2 = 5. If the government increases spending by £200 million, total final increase in national income = 5 × £200m = £1 000 million. This chain explains how small injections can produce significant economic growth.
示例：家庭在收入增加 1 亿英镑时消费增加 8 000 万英镑。MPC = 80/100 = 0.8，MPS = 0.2。乘数 = 1 / 0.2 = 5。若政府增加支出 2 亿英镑，国民收入的最终总增加 = 5 × 2 亿 = 10 亿英镑。这个链条解释了小额注入何以带来显著经济增长。
9. Real GDP and Inflation | 实际 GDP 与通货膨胀
Nominal GDP is measured at current prices; Real GDP strips out the effect of inflation using a price index. Real GDP = (Nominal GDP / Price Index) × 100. The inflation rate itself is the percentage change in the price index, typically the Consumer Price Index (CPI).
名义 GDP 按现价计量；实际 GDP 用价格指数剔除通货膨胀影响。实际 GDP = (名义 GDP / 价格指数) × 100。通货膨胀率本身是价格指数（通常是消费者价格指数 CPI）的百分比变化。
Example: In 2023, nominal GDP is £1 200 billion; the GDP deflator index is 120 (base year = 100). Real GDP = (1 200 / 120) × 100 = £1 000 billion. If last year’s CPI was 105 and this year’s CPI is 108, inflation rate = (108 – 105) / 105 × 100 ≈ 2.86%. This allows economists to compare living standards accurately over time.
示例：2023 年名义 GDP 为 12 000 亿英镑，GDP 平减指数为 120（基年 = 100）。实际 GDP = (1 200 / 120) × 100 = 10 000 亿英镑。若去年 CPI 为 105，今年为 108，通货膨胀率 = (108 – 105) / 105 × 100 ≈ 2.86%。这使经济学家能够准确比较各时期的生活水平。
10. Unemployment Rate Calculation | 失业率计算
The unemployment rate is the percentage of the labour force that is actively seeking work but cannot find it. Labour force = employed + unemployed. Unemployment rate = (Number of unemployed / Labour force) × 100.
失业率是指积极寻找工作但未能找到的劳动力所占的百分比。劳动力 = 就业者 + 失业者。失业率 = (失业人数 / 劳动力) × 100。
You must be careful to exclude the economically inactive (students, retirees, full-time carers) from the labour force. Exam data often requires you to identify the denominator correctly before applying the formula.
你必须注意将非经济活动人口（学生、退休人员、全职照顾者）排除在劳动力之外。考试数据常需要你在应用公式前正确确定分母。
Example: In a country with 25 million employed, 3 million unemployed, and 12 million economically inactive, the labour force is 25 + 3 = 28 million. Unemployment rate = (3 / 28) × 100 ≈ 10.71%. Always show your working and interpret the result: a rate above 5–6% may indicate cyclical unemployment needing stimulus.
示例：某国就业人口 2 500 万，失业人口 300 万，非经济活动人口 1 200 万，则劳动力为 2 500 + 300 = 2 800 万。失业率 = (300 / 2 800) × 100 ≈ 10.71%。务必展示计算过程并解释结果：高于 5–6% 的失业率可能表明需要刺激的周期性失业。
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