IGCSE CIE Economics: Calculation Questions Intensive Practice | IGCSE CIE 经济：计算题专项训练

📚 IGCSE CIE Economics: Calculation Questions Intensive Practice | IGCSE CIE 经济：计算题专项训练

Calculation questions are a vital part of the CIE IGCSE Economics examination. They test your ability to apply formulas, interpret data, and make accurate economic decisions. This intensive practice guide covers the most common types of calculations you will face, from elasticity to taxation, providing step‑by‑step examples in both English and Chinese.

计算题是 CIE IGCSE 经济考试的重要组成部分。它们考查你运用公式、解读数据以及做出准确经济判断的能力。本专项训练指南覆盖了你将会遇到的最常见的计算题型，从弹性到税收，并提供了中英双语的逐步示例讲解。

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

Price elasticity of demand (PED) measures how responsive the quantity demanded is to a change in price. The basic formula is 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化的反应程度。基本公式是需求量变动的百分比除以价格变动的百分比。

PED = %ΔQd ÷ %ΔP

Example: A cinema raises its ticket price from $10 to $12. As a result, the number of tickets sold per week falls from 500 to 400. Calculate PED.

示例：某电影院将票价从 10 美元提高到 12 美元，导致每周售票数量从 500 张下降到 400 张。计算 PED。

Calculate the percentage change in price: (12 − 10) ÷ 10 × 100 = 20%. 计算价格变化百分比：(12−10) ÷ 10 × 100 = 20%。
Calculate the percentage change in quantity demanded: (400 − 500) ÷ 500 × 100 = −20%. 计算需求量变化百分比：(400−500) ÷ 500 × 100 = −20%。
Apply the formula: PED = −20% ÷ 20% = −1. The absolute value is 1. 应用公式：PED = −20% ÷ 20% = −1，绝对值为 1。

This means demand is unit elastic — the percentage change in quantity demanded is exactly equal to the percentage change in price.

这意味着需求是单位弹性的 — 需求量变动的百分比与价格变动的百分比完全相等。

If a firm lowers price from $8 to $7 and quantity demanded increases from 200 to 220 units, PED = (10% ÷ −12.5%) = −0.8. The absolute value 0.8 signals inelastic demand.

如果一家企业把价格从 8 美元降至 7 美元，需求量从 200 单位增至 220 单位，PED = (10% ÷ −12.5%) = −0.8。绝对值 0.8 表明需求缺乏弹性。

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

Price elasticity of supply (PES) measures how responsive quantity supplied is to a change in price. The formula is the percentage change in quantity supplied divided by the percentage change in price.

供给价格弹性（PES）衡量供给量对价格变化的反应程度。公式是供给量变动的百分比除以价格变动的百分比。

PES = %ΔQs ÷ %ΔP

Example: The price of a T‑shirt increases from $15 to $18, and monthly production rises from 1000 to 1300 units. Calculate PES.

示例：一件 T 恤的价格从 15 美元上涨到 18 美元，月产量从 1000 件上升到 1300 件。计算 PES。

%ΔP = (18−15) ÷ 15 × 100 = 20%. %ΔP = (18−15) ÷ 15 × 100 = 20%。
%ΔQs = (1300−1000) ÷ 1000 × 100 = 30%. %ΔQs = (1300−1000) ÷ 1000 × 100 = 30%。
PES = 30% ÷ 20% = 1.5. PES = 30% ÷ 20% = 1.5。

A PES value greater than 1 indicates supply is elastic; producers can increase output relatively easily when the price rises.

PES 值大于 1 说明供给富有弹性；当价格上升时，生产者能够相对容易地增加产出。

In another scenario, if price rises by 25% but quantity supplied only increases by 5%, PES = 5% ÷ 25% = 0.2, indicating highly inelastic supply.

在另一种情形下，若价格上升 25% 而供给量仅增加 5%，PES = 5% ÷ 25% = 0.2，表明供给极度缺乏弹性。

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

Income elasticity of demand (YED) shows how quantity demanded changes as consumer income changes. The formula is the percentage change in quantity demanded divided by the percentage change in income.

需求收入弹性（YED）反映需求数量如何随消费者收入变化。公式是需求量变动的百分比除以收入变动的百分比。

YED = %ΔQd ÷ %ΔY

Example: When average household income rises from $30,000 to $33,000, the demand for restaurant meals increases from 12 per month to 15 per month. Calculate YED.

示例：当家庭平均收入从 30,000 美元上升到 33,000 美元时，餐馆用餐的需求从每月 12 次增加到 15 次。计算 YED。

%ΔY = (33,000−30,000) ÷ 30,000 × 100 = 10%. %ΔY = (33,000−30,000) ÷ 30,000 × 100 = 10%。
%ΔQd = (15−12) ÷ 12 × 100 = 25%. %ΔQd = (15−12) ÷ 12 × 100 = 25%。
YED = 25% ÷ 10% = 2.5. YED = 25% ÷ 10% = 2.5。

A positive YED greater than 1 means the good is a luxury item; demand grows faster than income. A YED between 0 and 1 indicates a necessity, while a negative YED signals an inferior good.

YED 为正且大于 1 意味着该商品是奢侈品，需求增长快于收入增长。YED 在 0 到 1 之间表示必需品，而 YED 为负则表示低档商品。

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

Cross elasticity of demand (XED) measures how the demand for one good responds to a change in the price of another good. The formula is the percentage change in quantity demanded of good A divided by the percentage change in price of good B.

需求交叉弹性（XED）衡量一种商品的需求对另一种商品价格变动的反应程度。公式是商品 A 需求数量变动的百分比除以商品 B 价格变动的百分比。

XED = %ΔQd(A) ÷ %ΔP(B)

Example: The price of bus tickets increases from $2 to $2.5, and the demand for train journeys rises from 800 to 1000 trips per day. Calculate XED.

示例：公交车票价从 2 美元涨到 2.5 美元，火车出行的需求从每天 800 次增至 1000 次。计算 XED。

%ΔP(B) = (2.5−2) ÷ 2 × 100 = 25%. %ΔP(B) = (2.5−2) ÷ 2 × 100 = 25%。
%ΔQd(A) = (1000−800) ÷ 800 × 100 = 25%. %ΔQd(A) = (1000−800) ÷ 800 × 100 = 25%。
XED = 25% ÷ 25% = +1. XED = 25% ÷ 25% = +1。

A positive XED indicates substitute goods. If the XED were negative, it would indicate complements. For instance, if the price of printers rose by 10% and the demand for ink cartridges fell by 8%, XED = −8% ÷ 10% = −0.8.

XED 为正表示替代品关系。如果 XED 为负值，则表示互补品。例如，若打印机价格上升 10%，墨盒需求下降 8%，则 XED = −8% ÷ 10% = −0.8。

5. Total Revenue and Elasticity | 总收益与弹性的关系

Total revenue (TR) is the amount a firm receives from sales, calculated as price multiplied by quantity sold. Understanding the link between PED and total revenue helps businesses set the right price.

总收益（TR）是企业从销售中获得的金额，用价格乘以销售量计算。理解 PED 与总收益之间的关系有助于企业设定正确的价格。

Example: A firm sells 300 units at $20 each, TR = $6000. It considers cutting the price to $18. Demand is price elastic (PED = −2). Quantity demanded increases by 20% to 360 units. New TR = 360 × $18 = $6480. Total revenue rises.

示例：某企业以单价 20 美元售出 300 单位，TR = 6000 美元。它考虑降为 18 美元。需求富有弹性（PED = −2），需求量增加 20% 至 360 单位。新的 TR = 360 × 18 = 6480 美元，总收益上升。

If demand were inelastic (PED = −0.5) and the same price cut caused quantity demanded to rise by only 5% (to 315 units), new TR = 315 × $18 = $5670. Total revenue would fall. So, when demand is elastic, cutting price raises revenue; when inelastic, raising price raises revenue.

若需求缺乏弹性（PED = −0.5），同样的降价只使需求量上升 5%（至 315 单位），新 TR = 315 × 18 = 5670 美元，总收益下降。因此，需求富有弹性时降价增加收益；缺乏弹性时提价增加收益。

Elastic PED (>1): Price ↓ → TR ↑; Price ↑ → TR ↓. 弹性 >1：降价 → 总收益↑；提价 → 总收益↓。
Inelastic PED (<1): Price ↓ → TR ↓; Price ↑ → TR ↑. 缺乏弹性 <1：降价 → 总收益↓；提价 → 总收益↑。

6. Cost, Revenue and Profit | 成本、收入与利润

Firms need to calculate total cost (TC), total revenue (TR) and profit to assess performance. TC = Total Fixed Cost (TFC) + Total Variable Cost (TVC). Profit = TR − TC.

企业需要计算总成本（TC）、总收益（TR）和利润来评估业绩。TC = 总固定成本（TFC）+ 总可变成本（TVC）。利润 = TR − TC。

Example: A bakery has fixed costs of $2000 per month. Each cake costs $3 in variable inputs, and it sells 800 cakes at $8 each.

示例：一家面包店每月固定成本为 2000 美元。每个蛋糕的可变投入成本为 3 美元，它以 8 美元的单价售出 800 个蛋糕。

TFC = $2000; TVC = 800 × $3 = $2400. TFC = 2000 美元；TVC = 800 × 3 = 2400 美元。
TC = $2000 + $2400 = $4400. TC = 2000 + 2400 = 4400 美元。
Average Cost (AC) = TC ÷ Q = $4400 ÷ 800 = $5.5. 平均成本 AC = 4400 ÷ 800 = 5.5 美元。
TR = 800 × $8 = $6400. TR = 800 × 8 = 6400 美元。
Profit = $6400 − $4400 = $2000. 利润 = 6400 − 4400 = 2000 美元。

The firm makes a profit because price ($8) exceeds average cost ($5.5). If price fell below average cost, the firm would make a loss.

该企业实现了盈利，因为价格（8 美元）高于平均成本（5.5 美元）。如果价格降至平均成本以下，企业就会亏损。

7. Indirect Tax and Price Impact | 间接税与价格影响

An indirect tax, such as a specific tax per unit, shifts the supply curve vertically upwards by the amount of the tax. The new equilibrium price paid by consumers and the price received by producers need to be calculated.

间接税，比如每单位从量税，会使供给曲线垂直上移一个税额。需要计算消费者支付的新均衡价格以及生产者实际获得的价格。

Example: The pre‑tax equilibrium price is $15 and quantity is 600 units. A $4 specific tax is imposed. The new consumer price is $18, and the new quantity is 500 units.

示例：税前均衡价格为 15 美元，数量为 600 单位。征收 4 美元的从量税后，新的消费者价格为 18 美元，新的数量为 500 单位。

Consumer burden per unit = new price − old price = $18 − $15 = $3. 消费者每单位负担 = 新价格 − 旧价格 = 18−15 = 3 美元。
Producer receives = new price − tax = $18 − $4 = $14. Producer burden = $15 − $14 = $1. 生产者实际得到 = 新价格 − 税额 = 18−4 = 14 美元。生产者负担 = 15−14 = 1 美元。
Government tax revenue = tax per unit × new quantity = $4 × 500 = $2000. 政府税收收入 = 每单位税额 × 新数量 = 4 × 500 = 2000 美元。

The burden of the tax is shared: consumers pay $3 more, while producers receive $1 less per unit. The more inelastic the demand, the larger the consumer’s share.

税收负担由双方分担：消费者每单位多付 3 美元，生产者少得 1 美元。需求越缺乏弹性，消费者承担的份额就越大。

8. Subsidy and Price Impact | 补贴与价格影响

A government subsidy lowers production costs and shifts the supply curve vertically downwards. This reduces the price consumers pay and increases the price producers receive.

政府补贴降低了生产成本，使供给曲线垂直下移。这会降低消费者支付的价格并提高生产者获得的价格。

Example: Before subsidy, equilibrium price is $20 and quantity is 400 units. A subsidy of $5 per unit is granted. The new consumer price falls to $17, and quantity rises to 480 units.

示例：补贴前，均衡价格为 20 美元，数量 400 单位。政府给予每单位 5 美元的补贴。新的消费者价格降至 17 美元，数量升至 480 单位。

Consumer benefit per unit = old price − new price = $20 − $17 = $3. 消费者每单位受益 = 旧价格 − 新价格 = 20−17 = 3 美元。
Producer receives = new price + subsidy = $17 + $5 = $22. Producer benefit = $22 − $20 = $2. 生产者实际得到 = 新价格 + 补贴 = 17+5 = 22 美元。生产者受益 = 22−20 = 2 美元。
Total subsidy cost to government = subsidy per unit × new quantity = $5 × 480 = $2400. 政府补贴总支出 = 每单位补贴 × 新数量 = 5 × 480 = 2400 美元。

Again, the benefit is split, and the more inelastic the demand, the greater the proportion of the subsidy that goes to consumers.

同样，利益由双方分享，需求越缺乏弹性，消费者获得的补贴比例就越大。

9. Unemployment Rate Calculation | 失业率计算

The unemployment rate is a key macroeconomic indicator. It is calculated as the number of unemployed people divided by the total labour force, multiplied by 100.

失业率是一个关键的宏观经济指标。它是失业人数除以

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IGCSE CIE Economics: Calculation Questions Intensive Practice | IGCSE CIE 经济：计算题专项训练