GCSE AQA Economics: Calculation Practice | GCSE AQA 经济：计算题专项训练

📚 GCSE AQA Economics: Calculation Practice | GCSE AQA 经济：计算题专项训练

Calculation questions form a significant part of the GCSE AQA Economics exam, testing your ability to apply formulas and interpret numerical data. Mastering these skills not only secures vital marks in Paper 1 and Paper 2 but also builds a strong foundation for understanding how businesses, consumers and governments make decisions. This revision guide covers all major calculation types you need to know, with clear formulas, worked examples and exam tips.

计算题在 GCSE AQA 经济考试中占有重要分量，考查你运用公式和解读数据的能力。掌握这些技能不仅能确保你在 Paper 1 和 Paper 2 中拿到关键分数，还能为理解企业、消费者和政府如何做决策打下坚实基础。本复习指南涵盖你需要掌握的所有主要计算类型，配有清晰的公式、例题和考试技巧。

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1. Understanding Percentage Changes | 理解百分比变化

Almost every economic calculation relies on percentage changes. The basic formula is: %Δ = (New Value − Original Value) ÷ Original Value × 100. A positive result indicates an increase, while a negative result shows a decrease.

几乎每个经济计算都依赖百分比变化。基本公式为：%Δ = (新值 − 原值) ÷ 原值 × 100。结果为正值表示增加，负值表示减少。

For instance, if the price of a cup of coffee rises from £2.50 to £3.00, the percentage change in price is: (3.00 − 2.50) ÷ 2.50 × 100 = 20%. This simple calculation is the building block for all elasticity measures.

例如，如果一杯咖啡的价格从 2.50 英镑涨到 3.00 英镑，价格百分比变化为：(3.00 − 2.50) ÷ 2.50 × 100 = 20%。这个简单的计算是所有弹性指标的基石。

When the original value is zero, the percentage change is mathematically undefined. In exam contexts, you will normally be given positive starting values, but always check that your denominator is not zero.

当原值为零时，百分比变化在数学上是无定义的。在考试情境下，你通常会得到正的初始值，但务必检查你的分母不为零。

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

Price elasticity of demand measures how responsive quantity demanded is to a change in price. The formula is:

需求价格弹性衡量需求量对价格变化的反应程度。其公式为：

PED = %Δ Quantity Demanded ÷ %Δ Price

Since price and quantity demanded move in opposite directions, PED is usually negative, but economists often ignore the minus sign and focus on the absolute value.

因为价格和需求量呈反向变动，PED 通常为负值，但经济学家通常忽略负号，关注其绝对值。

Example: A cinema reduces ticket price from £10 to £8, and daily ticket sales increase from 200 to 280. %Δ Price = (8−10)/10 × 100 = -20%. %Δ Qd = (280−200)/200 × 100 = 40%. Thus PED = 40% ÷ −20% = −2. The absolute value is 2, meaning demand is elastic.

例题：一家影院将票价从 10 英镑降至 8 英镑，日售票量从 200 张增至 280 张。%Δ 价格 = (8−10)/10 × 100 = −20%。%Δ Qd = (280−200)/200 × 100 = 40%。因此 PED = 40% ÷ −20% = −2。绝对值为 2，表明需求富有弹性。

The following table summarises how to interpret PED values:

下表总结了如何解读 PED 值：

PED Value (absolute)	Elasticity Type	中文解释
> 1	Elastic	富有弹性：需求量变动百分比大于价格变动百分比
< 1	Inelastic	缺乏弹性：需求量变动百分比小于价格变动百分比
= 1	Unitary elastic	单位弹性：需求量变动百分比等于价格变动百分比
= 0	Perfectly inelastic	完全无弹性：需求量完全不随价格变化
∞	Perfectly elastic	完全弹性：价格微小变化导致需求量骤变为零

Knowing the PED helps firms predict revenue changes. If demand is elastic, lowering price increases total revenue; if inelastic, raising price increases total revenue.

了解 PED 有助于企业预测收入变化。如果需求富有弹性，降价会增加总收入；如果缺乏弹性，提价会增加总收入。

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

Price elasticity of supply indicates how much quantity supplied changes in response to a price change. The formula is:

供给价格弹性表示供给量对价格变化的反应程度。公式如下：

PES = %Δ Quantity Supplied ÷ %Δ Price

Unlike PED, PES is always positive because price and quantity supplied usually move in the same direction.

与 PED 不同，PES 恒为正，因为价格和供给量通常同向变动。

Example: A baker raises the price of sourdough loaves from £3.50 to £4.20, and weekly supply expands from 500 to 650 loaves. %Δ Price = (4.20−3.50)/3.50 × 100 = 20%. %Δ Qs = (650−500)/500 × 100 = 30%. PES = 30% ÷ 20% = 1.5, indicating elastic supply.

例题：面包师将酸面包价格从 3.50 英镑提高到 4.20 英镑，每周供给量从 500 个增至 650 个。%Δ 价格 = (4.20−3.50)/3.50 × 100 = 20%。%Δ Qs = (650−500)/500 × 100 = 30%。PES = 30% ÷ 20% = 1.5，表明供给富有弹性。

Supply is more elastic when firms can increase output quickly (e.g., manufactured goods) and more inelastic when production capacity is fixed in the short run (e.g., agriculture). Time period is a key determinant of PES.

当企业能够迅速扩大产出时（如制成品），供给弹性较大；当短期产能固定时（如农业），供给缺乏弹性。时间是 PES 的关键决定因素。

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4. Income Elasticity of Demand (YED) | 收入需求弹性

Income elasticity of demand measures how demand responds to changes in consumers’ income. The formula is:

收入需求弹性衡量需求量对消费者收入变化的反应程度。公式为：

YED = %Δ Quantity Demanded ÷ %Δ Income

A positive YED indicates a normal good; a negative YED indicates an inferior good. For normal goods, YED > 1 signifies a luxury good, while YED between 0 and 1 signifies a necessity.

正值 YED 表示正常品；负值 YED 表示劣等品。对于正常品，YED > 1 代表奢侈品，YED 介于 0 和 1 之间代表必需品。

Example: Average incomes in a town rise by 5%, and demand for bus journeys falls by 2%. YED = −2% ÷ 5% = −0.4. The negative sign tells us bus journeys are an inferior good. When people become wealthier, they switch to cars or taxis.

例题：某镇平均收入上升 5%，公交车出行需求下降 2%。YED = −2% ÷ 5% = −0.4。负号表明公交车出行是劣等品。当人们变得更富裕时，他们会转向汽车或出租车。

Firms use YED to forecast sales. Producers of luxury goods benefit most in an economic boom, while makers of inferior goods may thrive during a recession.

企业用 YED 预测销售。奢侈品生产商在经济繁荣时获益最多，而劣等品制造商在经济衰退期间可能发展良好。

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5. Cross Elasticity of Demand (XED) | 交叉需求弹性

Cross elasticity of demand measures the responsiveness of demand for one good to a change in the price of another good. The formula is:

交叉需求弹性衡量一种商品的需求对另一种商品价格变动的反应程度。公式如下：

XED = %Δ Quantity Demanded of Good A ÷ %Δ Price of Good B

If XED is positive, the two goods are substitutes (e.g., tea and coffee). If XED is negative, they are complements (e.g., printers and ink cartridges). A value close to zero suggests the goods are unrelated.

如果 XED 为正，两种商品互为替代品（如茶和咖啡）。如果 XED 为负，它们互为互补品（如打印机和墨盒）。数值接近零则表明商品不相关。

Example: The price of margarine rises by 10%, and the quantity demanded of butter increases by 8%. XED = 8% ÷ 10% = +0.8. The positive sign shows that margarine and butter are substitutes; consumers switch to butter as margarine becomes more expensive.

例题：人造黄油价格上涨 10%，黄油需求量增加 8%。XED = 8% ÷ 10% = +0.8。正号表明人造黄油和黄油互为替代品；随着人造黄油变得更贵，消费者转向黄油。

Businesses use XED to assess the impact of competitors’ pricing strategies and to plan product portfolios. Strong complements might be bundled together in promotions.

企业利用 XED 评估竞争对手定价策略的影响，并规划产品组合。强互补品可能会捆绑促销。

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6. Total Revenue and Its Relationship with PED | 总收入及其与 PED 的关系

Total revenue (TR) is the income a firm receives from selling its products. It is calculated simply as:

总收入（TR）是企业销售产品所获得的收入。其计算公式简单：

TR = Price × Quantity Sold

Example: A stall sells 150 handmade bracelets at £4 each. TR = £4 × 150 = £600. If the price is cut to £3 and sales rise to 250, the new TR = £3 × 250 = £750.

例题：一个摊位以每条 4 英镑的价格售出 150 条手工手链。TR = £4 × 150 = £600。如果价格降至 3 英镑，销量升至 250，新的 TR = £3 × 250 = £750。

The direction of the revenue change depends on the price elasticity of demand. With elastic demand, a price cut raises total revenue because the % increase in quantity demanded outweighs the % decrease in price. With inelastic demand, a price rise boosts total revenue.

收入的变化方向取决于需求价格弹性。需求富有弹性时，降价会增加总收入，因为需求量增加的百分比超过价格下降的百分比。需求缺乏弹性时，提价会增加总收入。

Calculations: % Change in TR = (New TR − Original TR) / Original TR × 100. In the bracelet example, %Δ TR = (750 − 600) / 600 × 100 = 25%.

计算方法：%Δ TR = (新 TR − 原 TR) / 原 TR × 100。在手链例子中，%Δ TR = (750 − 600) / 600 × 100 = 25%。

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7. Costs of Production | 生产成本

Understanding costs is essential for calculating profit. Key cost concepts include:

理解成本对于计算利润至关重要。关键成本概念包括：

Total Fixed Costs (TFC) are costs that do not vary with output, such as rent and insurance. Total Variable Costs (TVC) change directly with the level of output, like raw materials and energy. Total Cost (TC) is the sum of both:

总固定成本（TFC）是不随产量变动的成本，如租金和保险。总可变成本（TVC）直接随产量水平变化，如原材料和能源。总成本（TC）是两者之和：

TC = TFC + TVC

Average cost (AC) or unit cost is the cost per unit of output:

平均成本（AC）或单位成本是每单位产出的成本：

AC = TC ÷ Quantity (Q)

Example: A bakery has TFC of £2,000 per month and TVC of £1.50 per loaf. If it produces 4,000 loaves, TVC = £1.50 × 4,000 = £6,000. TC = £2,000 + £6,000 = £8,000. AC = £8,000 ÷ 4,000 = £2.00 per loaf.

例题：一家面包店每月 TFC 为 2,000 英镑，每条面包的 TVC 为 1.50 英镑。如果生产 4,000 条面包，TVC = £1.50 × 4,000 = £6,000。TC = £2,000 + £6,000 = £8,000。AC = £8,000 ÷ 4,000 = 每条 2.00 英镑。

Average fixed cost (AFC) = TFC ÷ Q, and average variable cost (AVC) = TVC ÷ Q. As output rises, AFC falls continuously, spreading the fixed costs over more units.

平均固定成本 (AFC) = TFC ÷ Q，平均可变成本 (AVC) = TVC ÷ Q。随着产量增加，AFC 持续下降，将固定成本摊薄在更多单位上。

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8. Profit and Loss | 利润与亏损

Profit is the reward for risk-taking and is calculated by subtracting total costs from total revenue:

利润是对承担风险的回报，通过从总收入中减去总成本来计算：

Profit = Total Revenue − Total Cost

If the result is positive, the firm earns a profit; if negative, it makes a loss.

如果结果为正，企业盈利；如果为负，企业亏损。

Example: A t-shirt business sells 500 shirts at £12 each. TR = £6,000. Total costs are £4,500. Profit = £6,000 − £4,500 = £1,500.

例题：一家 T 恤店以每件 12 英镑售出 500 件。TR = £6,000。总成本为 £4,500。利润 = £6,000 − £4,500 = £1,500。

Profit margin can be expressed as a percentage: (Profit ÷ Total Revenue) × 100. Here, profit margin = (£1,500 ÷ £6,000) × 100 = 25%.

利润率可以表示为百分比：(利润 ÷ 总收入) × 100。此处，利润率 = (£1,500 ÷ £6,000) × 100 = 25%。

In economics, normal profit is the minimum reward required to keep an entrepreneur in the industry; it is already included in total costs. Supernormal profit (or abnormal profit) is any profit above normal profit.

在经济学中，正常利润是使企业家留在该行业的最低报酬；它已包含在总成本中。超常利润（或超额利润）是高于正常利润的任何利润。

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9. Average, Marginal and Total Values | 平均、边际与总量

Working with totals and averages is a core numerical skill. The relationships are straightforward:

处理总量和平均值是一项核心数字技能。它们的关系很简单：

Average = Total ÷ Quantity

Marginal cost (MC) is the additional cost of producing one more unit:

边际成本（MC）是额外生产一单位所带来的成本增加：

MC = Change in Total Cost ÷ Change in Quantity

Example: If TC for 10 units is £200 and TC for 11 units is £215, then MC = (£215 − £200) ÷ (11 − 10) = £15.

例题：如果 10 单位产品的 TC 为 £200，11 单位产品的 TC 为 £215，则 MC = (£215 − £200) ÷ (11 − 10) = £15。

Similarly, marginal revenue (MR) is the extra revenue from selling one additional unit. When data is provided in a table, always look at the changes row by row.

类似地，边际收入（MR）是额外销售一单位所带来的额外收入。当数据以表格形式给出时，务必逐行观察变化。

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10. Index Numbers and Real Values | 指数与实际值

Index numbers simplify comparisons over time by setting a base year value to 100. The formula is:

指数通过将基年值设为 100 来简化时间维度的比较。公式为：

Index Number = (Value in Current Year ÷ Value in Base Year) × 100

For example, if the price of a basket of goods was £60 in 2015 (base year) and £72 in 2023, the price index for 2023 = (72 ÷ 60) × 100 = 120. This means prices have risen by 20% relative to the base year.

例如，如果一篮子商品在 2015 年（基年）的价格为 60 英镑，2023 年为 72 英镑，则 2023 年的价格指数 = (72 ÷ 60) × 100 = 120。这意味着相对于基年，价格上涨了 20%。

To find a real value (adjusted for inflation), use:

Real Value = (Nominal Value ÷ Price Index) × 100

Example: A worker’s nominal wage in 2023 is £30,000 and the price index is 120. Real wage = (£30,000 ÷ 120) × 100 = £25,000. This shows the purchasing power of the wage compared to the base year.

要求出实际值（经通胀调整），使用：实际值 = (名义值 ÷ 价格指数) × 100。例如，某工人 2023 年的名义工资为 £30,000，价格指数为 120。实际工资 = (£30,000 ÷ 120) × 100 = £25,000。这显示了该工资相对于基年的购买力。

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11. Unemployment Rate and GDP per Capita | 失业率与人均 GDP

Two common macroeconomic indicators require simple calculations. The unemployment rate is:

两个常见的宏观经济指标需要简单的计算。失业率为：

Unemployment Rate = (Number of Unemployed ÷ Labour Force) × 100

The labour force includes all people who are employed or actively seeking work. Example: If an economy has 1.5 million unemployed and a labour force of 25 million, the unemployment rate = (1.5m ÷ 25m) × 100 = 6%.

劳动力包括所有就业或正在积极寻找工作的人。例题：如果一个经济体有 150 万失业人口，劳动力为 2,500 万，则失业率 = (1.5m ÷ 25m) × 100 = 6%。

GDP per capita measures average output per person and is a proxy for living standards:

人均 GDP 衡量人均平均产出，是生活水平的近似指标：

GDP per Capita = Total GDP ÷ Population

For instance, a country with a GDP of £2,000 billion and a population of 50 million has GDP per capita = £2,000bn ÷ 50m = £40,000.

例如，一个 GDP 为 2 万亿英镑、人口为 5,000 万的国家，人均 GDP = £2,0000 亿 ÷ 5,000 万 = £40,000。

These indicators are often used in data-response questions. Make sure

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