A-Level AQA Economics: Calculation Practice | A-Level AQA 经济：计算题专项训练

📚 A-Level AQA Economics: Calculation Practice | A-Level AQA 经济：计算题专项训练

Mastering quantitative skills is essential for success in A-Level AQA Economics. From elasticities to national income multipliers, numerical questions appear across both Paper 1 (Markets and Market Failure) and Paper 2 (National and International Economy). This targeted workbook explains the key formulas, walks through step‑by‑step examples, and highlights common pitfalls. Use it to build confidence, speed, and accuracy before your exams.

掌握定量分析技能是 A-Level AQA 经济学考试成功的关键。从弹性到国民收入乘数，计算题分布在 Paper 1（市场与市场失灵）和 Paper 2（国民经济与国际经济）中。本文梳理核心公式，通过循序渐进的例题讲解，并提示常见易错点，帮助你提升解题信心、速度与准确率。

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

PED measures the responsiveness of quantity demanded to a change in price. AQA often expects you to use the midpoint method for percentage changes to avoid inconsistency.

PED 衡量需求量对价格变化的反应程度。AQA 通常要求使用中点法计算百分比变化，以避免方向不一致的问题。

PED = %ΔQd / %ΔP = (ΔQ / ((Q₁+Q₂)/2)) ÷ (ΔP / ((P₁+P₂)/2))

Example: A cinema increases ticket price from £8 to £10, and daily tickets sold fall from 500 to 400. Calculate PED and interpret the result.

例：电影院将票价从 8 英镑提高到 10 英镑，日售票量从 500 张降至 400 张。计算 PED 并解释结果。

ΔQ = 400 − 500 = −100; avg Q = (500+400)/2 = 450. ΔP = 10 − 8 = 2; avg P = (8+10)/2 = 9.

%ΔQd = −100/450 = −0.2222 (−22.22%); %ΔP = 2/9 = 0.2222 (22.22%).

PED = −22.22% / 22.22% = −1.0 (absolute value 1.0). Demand is unit elastic; total revenue stays unchanged (test: TR₁ = 8×500 = £4000; TR₂ = 10×400 = £4000).

PED 绝对值为 1.0，需求单位弹性；总收益不变（检验：TR₁ = £4000，TR₂ = £4000）。

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2. Income Elasticity of Demand (YED) | 需求收入弹性 (YED)

YED shows how demand changes as consumer income changes. The formula uses the midpoint method similarly.

YED 显示消费者收入变化如何影响需求，公式同样采用中点法。

YED = %ΔQd / %ΔY = (ΔQ / Q_avg) ÷ (ΔY / Y_avg)

Example: A household’s weekly supermarket spending rises from £80 to £92 when their disposable income increases from £500 to £550. Calculate YED and classify the good.

例：家庭周超市消费从 80 英镑升至 92 英镑，可支配收入从 500 英镑升至 550 英镑。计算 YED 并判断商品类型。

ΔQ = 12; avg Q = (80+92)/2 = 86. %ΔQ = 12/86 ≈ 0.1395. ΔY = 50; avg Y = (500+550)/2 = 525. %ΔY = 50/525 ≈ 0.0952.

YED = 0.1395 / 0.0952 ≈ +1.47. Positive and greater than 1, so it is a luxury good.

YED ≈ +1.47，为正且大于 1，属于奢侈品。

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3. Cross‑Price Elasticity of Demand (XED) | 需求交叉价格弹性 (XED)

XED reveals the relationship between two goods. Positive XED indicates substitutes; negative XED indicates complements. Midpoint bases are expected.

XED 揭示两种商品之间的关系。正值表示替代品，负值表示互补品。同样建议使用中点法。

XED = %ΔQd of good A / %ΔP of good B

Example: When the price of coffee rises from £3 to £3.60 per pack, the quantity demanded of tea increases from 200 to 260 packs. Calculate XED.

例：咖啡价格从每包 3 英镑升至 3.60 英镑，茶的需求量从 200 包升至 260 包。计算 XED。

%ΔQ tea = (60)/((200+260)/2) = 60/230 ≈ 0.2609. %ΔP coffee = (0.60)/((3+3.6)/2) = 0.60/3.30 ≈ 0.1818.

XED = 0.2609 / 0.1818 ≈ +1.43. Positive, so tea and coffee are substitutes.

XED ≈ +1.43，为正值，茶和咖啡为替代品。

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

PES measures how responsive quantity supplied is to a price change. The same midpoint method is preferred.

PES 衡量供给量对价格变化的反应程度，同样推荐中点法。

PES = %ΔQs / %ΔP

Example: A farmer increases wheat supply from 10 tonnes to 13 tonnes when the price rises from £150 to £180 per tonne. Find PES.

例：小麦价格从每吨 150 英镑升至 180 英镑，农民供给量从 10 吨增至 13 吨。求 PES。

%ΔQs = 3/((10+13)/2) = 3/11.5 ≈ 0.2609. %ΔP = 30/((150+180)/2) = 30/165 ≈ 0.1818.

PES = 0.2609/0.1818 ≈ 1.43. Supply is elastic.

PES ≈ 1.43，供给富有弹性。

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5. Cost, Revenue and Profit | 成本、收益与利润

Firms’ short‑run decisions require calculations of total cost (TC), average total cost (ATC), total revenue (TR), and profit. Key relationships:

企业的短期决策需要计算总成本（TC）、平均总成本（ATC）、总收益（TR）和利润。核心关系如下：

TC = TFC + TVC

ATC = TC / Q

Profit = TR − TC

Example: A firm has fixed costs of £2000, variable cost per unit of £15, and sells 500 units at £25 each. Calculate profit.

例：某企业固定成本 2000 英镑，单位可变成本 15 英镑，销售 500 单位，单价 25 英镑。计算利润。

TVC = 15 × 500 = £7500; TC = 2000 + 7500 = £9500. TR = 25 × 500 = £12,500. Profit = 12,500 − 9500 = £3000.

利润 = £3000。

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6. Profit Maximisation Condition | 利润最大化条件

In standard theory, a firm maximises profit where marginal cost (MC) equals marginal revenue (MR). You may need to calculate these from a table of output, total cost, and price.

标准理论中，企业利润最大化出现在边际成本（MC）等于边际收益（MR）之处。你可能需要从产量、总成本和价格数据中推算。

MC = ΔTC / ΔQ , MR = ΔTR / ΔQ

Example: A firm can sell any quantity at £20. Given output and TC: Q=0 TC=50; Q=1 TC=64; Q=2 TC=72; Q=3 TC=85; Q=4 TC=104; Q=5 TC=130. Find profit‑maximising output.

例：企业可按每单位 20 英镑出售任意数量。已知产量 Q 和总成本 TC 如上。求利润最大化产量。

Since P is constant, MR = £20 for all units. MC between Q=0-1 is (64-50)=14; 1-2: 8; 2-3: 13; 3-4: 19; 4-5: 26. MC=MR at Q=4 where MC=19 just below MR=20 (next unit MC>MR). So produce 4 units.

利润最大化产量为 4 单位，此时 MC≈19，接近 MR=20，第 5 单位 MC>MR。

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7. Market Concentration Ratios | 市场集中度比率

Concentration ratios measure the combined market share of the largest firms. N‑firm concentration ratio = sum of market shares of top N firms. A high ratio suggests an oligopolistic or monopolistic market.

集中度比率衡量最大几家企业的合计市场份额。N 企业集中度比率 = 前 N 家企业市场份额之和。高比率暗示寡头或垄断市场。

Example: An industry has five firms with sales: £40m, £30m, £15m, £10m, £5m. Calculate the 3‑firm concentration ratio.

例：某行业五家企业销售额分别为 4000 万、3000 万、1500 万、1000 万、500 万英镑。计算 3 企业集中度比率。

Total market sales = 40+30+15+10+5 = £100m. Top 3 sales = 40+30+15 = £85m. CR3 = (85/100) × 100% = 85%.

CR3 = 85%，高度集中。

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8. The Multiplier Effect | 乘数效应

The multiplier quantifies how an initial injection into the circular flow leads to a larger final increase in national income. AQA may ask you to calculate either the simple multiplier or its effect on GDP.

乘数量化了初始注入如何导致国民收入的更大最终增长。AQA 题目可能要求计算简单乘数或其对 GDP 的影响。

Multiplier = 1 / (1 − MPC) or 1 / (MPW) where MPW = MPS + MPT + MPM

Example: In an economy, the marginal propensity to consume (MPC) is 0.75. The government increases spending by £20 billion. Calculate the final change in GDP.

例：某经济边际消费倾向（MPC）为 0.75。政府增加支出 200 亿英镑。计算 GDP 的最终变动。

Multiplier = 1/(1−0.75) = 1/0.25 = 4. ΔGDP = 4 × £20bn = £80bn.

乘数 = 4，ΔGDP = 800 亿英镑。

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9. Equilibrium National Income (AD=AS) | 均衡国民收入 (AD=AS)

You may be given consumption and investment functions and asked to find equilibrium Y where aggregate demand equals income. Assume simple economy: Y = C + I.

题目可能给出消费函数和投资函数，要求计算均衡国民收入 Y，使得总需求等于收入。假设简单经济：Y = C + I。

C = a + bY ; Y = a + bY + I → Y = (a + I) / (1 − b)

Example: C = 200 + 0.8Y, planned investment I = 300. Find equilibrium national income.

例：C = 200 + 0.8Y，计划投资 I = 300。求均衡国民收入。

Y = 200 + 0.8Y + 300 → Y − 0.8Y = 500 → 0.2Y = 500 → Y = 2500.

均衡 Y = 2500。

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10. Inflation and Index Numbers | 通货膨胀与指数

AQA may ask you to calculate a consumer price index (CPI) change or the inflation rate using a basket of goods. Weighted average price changes are common.

AQA 可能要求计算消费者价格指数（CPI）变动或通货膨胀率，通常涉及一篮子商品的加权平均价格变化。

Inflation rate = (CPI_current − CPI_previous) / CPI_previous × 100

Example: A simple basket with two goods: bread (weight 60%) price rises from £1.00 to £1.10; milk (weight 40%) rises from £0.80 to £0.96. Calculate the weighted inflation rate.

例：简化篮子包括面包（权重 60%）价格从 1.00 英镑升至 1.10 英镑；牛奶（权重 40%）从 0.80 英镑升至 0.96 英镑。计算加权通货膨胀率。

Bread %Δ = (0.10/1.00)×100 = 10%; Milk %Δ = (0.16/0.80)×100 = 20%. Weighted inflation = (0.6×10) + (0.4×20) = 6 + 8 = 14%.

加权通货膨胀率 = 14%。

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11. Comparative Advantage and Trade | 比较优势与贸易

To determine who specialises in what, calculate opportunity cost ratios. The country with the lower opportunity cost for a good has a comparative advantage. Output per unit of input is often given.

要确定分工，需计算机会成本比率。某商品机会成本较低的国家拥有比较优势。通常给出单位投入的产出量。

Example: Country X can produce 20 units of wheat or 10 units of cloth per labour hour. Country Y can produce 15 wheat or 5 cloth. Determine comparative advantage.

例：X 国每小时劳动可生产 20 单位小麦或 10 单位布。Y 国每小时可生产 15 小麦或 5 布。判断比较优势。

For X: 1 wheat costs 10/20 = 0.5 cloth; 1 cloth costs 20/10 = 2 wheat. For Y: 1 wheat costs 5/15 = 0.33 cloth; 1 cloth costs 15/5 = 3 wheat. X has lower opportunity cost in cloth (2 < 3) → comparative advantage in cloth. Y has lower opportunity cost in wheat (0.33 < 0.5) → comparative advantage in wheat.

X 国在布上机会成本更低（2 < 3），比较优势在布。Y 国在小麦上机会成本更低（0.33 < 0.5），比较优势在小麦。

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12. Exchange Rates and Conversion | 汇率与换算

Exchange rate calculations test your ability to convert currencies and calculate percentage changes in the value of a currency. A rise in £/$ (more $ per £) means an appreciation of the pound.

汇率计算测试货币换算和货币价值百分比变化的能力。£/$ 上升（1 英镑兑换更多美元）表示英镑升值。

Example: Initial exchange rate: £1 = $1.25. New rate: £1 = $1.30. Calculate the percentage change in the value of the pound against the dollar.

例：初始汇率 £1 = $1.25，新汇率 £1 = $1.30。计算英镑对美元的价值百分比变化。

Change = (1.30 − 1.25) / 1.25 × 100 = 0.05/1.25 × 100 = 4%. The pound appreciated by 4% against the dollar.

英镑对美元升值 4%。

If a UK importer buys $100,000 of goods when £1 = $1.20, the cost in pounds is 100,000 / 1.20 = £83,333.33. At a rate of £1 = $1.15, the cost would be 100,000 / 1.15 = £86,956.52, making imports more expensive.

若英国进口商购买 10 万美元货物，汇率为 £1 = $1.20，则英镑成本为 100,000/1.20 = £83,333.33。若汇率变为 £1 = $1.15，成本为 100,000/1.15 = £86,956.52，进口变得更贵。

Published by TutorHao | Economics Revision Series | aleveler.com

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