📚 Worked Examples for IB and AQA Economics | IB与AQA经济典型例题详解
Both IB and AQA Economics examinations reward students who can apply theoretical concepts to structured, real-world problems. This article provides ten worked examples spanning micro and macroeconomics, with step-by-step reasoning in both English and Chinese. Each example targets a typical question style found in IB Paper 1/2/3 or AQA Paper 1/2/3, helping you master analytical techniques and secure top marks.
IB 与 AQA 经济学考试都青睐能够将理论概念应用于结构化现实问题的学生。本文提供涵盖微观与宏观经济学的十道典型例题，每道均配有中英双语的逐步解析。这些例题针对 IB 试卷一/二/三及 AQA 试卷一/二/三中常见的题型，帮助你掌握分析技巧，稳拿高分。
1. Interpreting Demand and Supply Diagrams | 供求图解例题
Example: Analyse how an increase in consumers’ environmental awareness affects the market for petrol cars. Use a demand and supply diagram.
例题：分析消费者环保意识提高对燃油车市场的影响，并绘图说明。
Step 1: Identify the determinant. Greater environmental awareness shifts consumer preferences away from petrol cars, decreasing demand at every price. The demand curve shifts left (D₁ → D₂). The supply curve is unaffected as producers’ costs remain unchanged.
步骤一：确定影响因素。环保意识提高使消费者偏好偏离燃油车，导致每一价格水平下的需求量下降，需求曲线向左平移（D₁ → D₂）。供给曲线不受影响，因为厂商成本未变。
Step 2: Describe new equilibrium. The leftward demand shift lowers both the equilibrium price (P₁ ↓ P₂) and equilibrium quantity (Q₁ ↓ Q₂). Examiners expect clear labelling of axes, curves, and arrows showing the shift.
步骤二：描述新均衡。需求左移使均衡价格（P₁ ↓ P₂）和均衡数量（Q₁ ↓ Q₂）双双下降。阅卷人期望坐标轴、曲线及平移箭头标注清晰。
2. Calculating Price Elasticity of Demand | 需求价格弹性计算
Example: A cinema reduces ticket price from £12 to £9, and the quantity demanded rises from 200 to 280 tickets per day. Calculate PED and interpret the result.
例题：某影院将票价从12英镑降至9英镑，日需求量由200张增至280张。计算需求价格弹性并解释其含义。
Percentage change in price = [(9 − 12) ÷ 12] × 100 = −25%. Percentage change in quantity demanded = [(280 − 200) ÷ 200] × 100 = +40%. PED = +40% ÷ −25% = −1.6 (using absolute value 1.6).
价格变动百分比 = [(9 − 12) ÷ 12] × 100 = −25%。需求量变动百分比 = [(280 − 200) ÷ 200] × 100 = +40%。PED = +40% ÷ −25% = −1.6（取绝对值为1.6）。
Since PED > 1, demand is price elastic. The cinema’s total revenue changes from £12 × 200 = £2,400 to £9 × 280 = £2,520, confirming that a price cut raises total revenue when demand is elastic.
由于PED > 1，需求富有弹性。影院总收入从12 × 200 = 2400英镑变为9 × 280 = 2520英镑，证实弹性需求下降价会提高总收入。
3. Market Equilibrium and Government Price Controls | 市场均衡与政府价格调控
Example: The free-market equilibrium rent in a city is £800 per month. To protect tenants, the government imposes a rent ceiling of £600. Analyse the consequences.
例题：某城市租房市场的自由均衡月租金为800英镑。为保护租户，政府设定600英镑的租金上限。分析其后果。
A price ceiling set below equilibrium creates a binding constraint. At £600, the quantity of rental accommodation demanded exceeds the quantity supplied, resulting in a persistent housing shortage. The shortage is shown by the horizontal gap between demand and supply curves at the ceiling price.
设定在均衡价格下方的价格上限构成有效约束。在600英镑下，租房需求量超过供给量，产生持续性住房短缺。该短缺表现为上限价格处需求曲线与供给曲线之间的水平距离。
Additionally, falling rental income discourages landlords from maintaining properties, reducing quality. A black market may emerge where tenants pay under-the-table fees to secure a flat. IB/AQA candidates should mention efficiency loss and advocate alternative policies like housing subsidies.
此外，租金收入下降导致房东减少房屋维护，居住质量降低。可能催生黑市，租户为获得住房支付台底费。IB/AQA考生应提及效率损失，并主张住房补贴等替代政策。
4. Externalities: Identifying Social Optimum | 外部性：识别社会最优
Example: The production of steel generates air pollution. The private marginal cost (PMC) is given by PMC = 50 + 2Q, and the external marginal cost is constant at £20 per unit. The marginal social benefit (MSB) is MSB = 200 − 3Q. Find the socially optimal output and illustrate the welfare gain from internalising the externality.
例题：钢铁生产产生空气污染。私人边际成本为 PMC = 50 + 2Q，边际外部成本恒为每单位20英镑。边际社会收益为 MSB = 200 − 3Q。求社会最优产量，并说明外部性内部化带来的福利增益。
Social marginal cost: SMC = PMC + external cost = (50 + 2Q) + 20 = 70 + 2Q. Social optimum where MSB = SMC → 200 − 3Q = 70 + 2Q → 5Q = 130 → Q_social = 26 units. Free market equilibrium is where MSB = PMC: 200 − 3Q = 50 + 2Q → Q_market = 30 units.
社会边际成本：SMC = PMC + 外部成本 = (50 + 2Q) + 20 = 70 + 2Q。社会最优满足 MSB = SMC → 200 − 3Q = 70 + 2Q → Q_social = 26单位。自由市场均衡条件为 MSB = PMC：200 − 3Q = 50 + 2Q → Q_market = 30单位。
The overproduction of 4 units creates a deadweight loss, shown as the triangle between Q_social and Q_market where SMC > MSB. A Pigouvian tax of £20 per unit shifts PMC to align with SMC, achieving the socially optimal output and eliminating welfare loss.
超产4单位造成无谓损失，表现为 Q_social 与 Q_market 之间 SMC > MSB 的三角形区域。对每单位征收20英镑的庇古税可使 PMC 与 SMC 对齐，达到社会最优产量，消除福利损失。
5. Taxation and Incidence | 税收与税负归宿
Example: The government levies a £3 per unit specific tax on a good. The pre-tax equilibrium price is £10 and quantity is 1,000 units. After tax, consumer price rises to £12 and producer receives £9. Calculate the tax incidence on consumers and producers, and evaluate the significance of price elasticity.
例题：政府对某商品征收每单位3英镑的从量税。税前均衡价格为10英镑，数量为1000单位。税后消费者支付价为12英镑，生产者实收9英镑。计算消费者与生产者的税负分担，并评价价格弹性的重要性。
Incidence on consumers = (£12 − £10) × 1,000 = £2,000; incidence on producers = (£10 − £9) × 1,000 = £1,000. Tax revenue = £3 × 1,000 = £3,000. Consumers bear 2/3 of the tax burden.
消费者税负 = (12 − 10) × 1000 = 2000英镑；生产者税负 = (10 − 9) × 1000 = 1000英镑。政府税收 = 3 × 1000 = 3000英镑。消费者承担了三分之二的税负。
The relative burden depends on elasticities. Here, demand is relatively inelastic compared to supply, so consumers pay a larger share. If supply were perfectly inelastic, producers would bear the entire tax. IB/AQA students should always link incidence back to PED and PES.
相对负担取决于弹性。本题中需求相对供给缺乏弹性，故消费者承担较大份额。若供给完全无弹性，则生产者承担全部税收。IB/AQA 学生务必将税负归宿与需求价格弹性（PED）和供给价格弹性（PES）联系起来。
6. Costs, Revenues and Profit Maximisation | 成本、收益与利润最大化
Example: A firm faces the following total cost schedule: TC = 100 + 2Q², and the market price is £40 per unit. Determine the profit-maximising output and maximum profit.
例题：某企业总成本函数为 TC = 100 + 2Q²，市场单价为40英镑。求利润最大化产量及最大利润。
Total revenue: TR = P × Q = 40Q. Profit: π = TR − TC = 40Q − (100 + 2Q²). Profit maximising rule: produce where MR = MC. For a price-taking firm, MR = P = 40. MC is the derivative of TC: MC = 4Q. Set 40 = 4Q → Q* = 10 units.
总收入：TR = P × Q = 40Q。利润：π = TR − TC = 40Q − (100 + 2Q²)。利润最大化法则：MR = MC。对于价格接受者，MR = P = 40。MC 为 TC 的导数：MC = 4Q。令 40 = 4Q → Q* = 10 单位。
Maximum profit = 40×10 − (100 + 2×100) = 400 − 300 = £100. Candidates can verify that profit declines if Q ≠ 10. A diagram showing TR and TC curves, or MR=MC, earns additional marks.
最大利润 = 40×10 − (100 + 2×100) = 400 − 300 = 100英镑。考生可验证当 Q ≠ 10 时利润下降。绘出 TR 与 TC 曲线或 MR=MC 交点图可获额外加分。
7. Aggregate Demand and the Multiplier | 总需求与乘数效应
Example: In a closed economy, the marginal propensity to consume (MPC) is 0.8. The government increases its spending by £50 million. Calculate the final change in real GDP, and explain why the actual multiplier may be smaller than predicted.
例题：在一个封闭经济中，边际消费倾向为0.8。政府增加5000万英镑支出。计算实际GDP的最终变动额，并解释为何实际乘数可能小于理论值。
The simple multiplier k = 1/(1 − MPC) = 1/(1 − 0.8) = 5. Change in GDP = k × ΔG = 5 × £50m = £250 million. This assumes all induced income is spent domestically without any leakages.
简单乘数 k = 1/(1 − 0.8) = 5。GDP 变动额 = 5 × 5000万 = 2.5亿英镑。前提是所有引致收入均用于国内消费，无任何漏出。
In reality, the multiplier is dampened by taxation, imports, and saving that are not reinvested domestically. For IB/AQA, mention that income taxes reduce disposable income growth, and higher imports (M) mean spending leaks abroad. Thus the real-world multiplier is lower, e.g., 1.5–2.5.
现实中，税收、进口及未再投资于国内的储蓄会削弱乘数效应。IB/AQA 考试中需提及所得税降低可支配收入增长，进口增加意味着支出漏出至国外。因此现实乘数较小，如1.5至2.5之间。
8. Inflation and Unemployment Trade-off | 通货膨胀与失业的权衡
Example: Using the Phillips curve, assess the short-run and long-run effects of expansionary monetary policy on inflation and unemployment.
例题：运用菲利普斯曲线，评价扩张性货币政策在短期和长期对通货膨胀与失业的影响。
Short-run: Lower interest rates boost AD, shifting the economy along a downward-sloping Phillips curve, so unemployment falls (U₁ → U₂) but inflation rises (π₁ → π₂). There is a trade-off.
短期：降低利率刺激总需求，经济沿向下倾斜的短期菲利普斯曲线移动，失业率下降（U₁ → U₂）而通胀上升（π₁ → π₂）。存在权衡取舍。
Long-run: As inflation expectations adjust, workers demand higher wages, shifting the short-run Phillips curve rightwards. The economy returns to the natural rate of unemployment (NAIRU) at a permanently higher inflation rate. The long-run Phillips curve is vertical, meaning no trade-off. AQA and IB both expect the accelerationist hypothesis.
长期：随着通胀预期调整，工人要求更高工资，短期菲利普斯曲线右移。经济回到自然失业率（NAIRU），但通胀率永久性更高。长期菲利普斯曲线垂直，意味着不存在权衡。AQA 与 IB 均预期考生提及加速主义假说。
9. Exchange Rate Determination | 汇率决定
Example: A country experiences a fall in exports due to a global recession. Using a demand and supply diagram for the currency, explain the likely effect on its exchange rate.
例题：某国因全球衰退导致出口下降。运用货币供求图，解释对该国汇率可能产生的影响。
Exports generate demand for the domestic currency by foreign buyers. A fall in exports reduces the demand for the currency, shifting the demand curve leftwards (D₁ → D₂). Supply of the currency (from importers and capital outflows) is unchanged initially.
出口为外币持有者创造对本币的需求。出口下降减少对本币的需求，需求曲线向左平移（D₁ → D₂）。本币供给（来自进口商和资本外流）暂时不变。
Result: the exchange rate depreciates (e.g., £1 = $1.40 → $1.30). A weaker currency may restore competitiveness by making exports cheaper, partially offsetting the initial shock. Examiners like to see the flow link: trade balance → currency demand → exchange rate.
结果：汇率贬值（例如，1英镑兑1.40美元跌至1.30美元）。本币贬值使出口更便宜，可能恢复竞争力，部分抵消初始冲击。阅卷人乐于看到链条：贸易差额 → 货币需求 → 汇率。
10. Comparative Advantage and Trade | 比较优势与贸易
Example: Country A can produce 12 units of wheat or 6 units of cloth per worker; country B can produce 8 units of wheat or 8 units of cloth. Determine the pattern of specialisation and gains from trade if the terms of trade settle at 1 wheat = 0.8 cloth.
例题：A国每工人可生产12单位小麦或6单位布；B国每工人可生产8单位小麦或8单位布。若贸易条件为1小麦兑0.8布，确定专业化模式及贸易所得。
Opportunity cost: For country A, 1 wheat costs 0.5 cloth (6/12); 1 cloth costs 2 wheat. For country B, 1 wheat costs 1 cloth (8/8); 1 cloth costs 1 wheat. A has comparative advantage in wheat (lower opportunity cost 0.5 < 1), B in cloth (1 < 2).
机会成本：A国，1小麦成本为0.5布（6/12），1布成本为2小麦。B国，1小麦成本为1布，1布成本为1小麦。A国在小麦上有比较优势（0.5 < 1），B国在布上有比较优势（1 < 2）。
Specialisation: A produces only wheat (12 units), B produces only cloth (8 units). Without trade, assume each splits labour equally: A gets 6W and 3C, B gets 4W and 4C. With trade, if A exports 5W for 4C (at 1:0.8), A ends with 7W and 4C, B with 5W and 4C. Both consume beyond their PPFs.
专业化：A 专产小麦（12单位），B 专产布（8单位）。若无贸易，假设均分劳动：A 获得 6W 和 3C，B 获得 4W 和 4C。贸易后，若 A 出口5W换4C（按1:0.8），A 最终得 7W 和 4C，B 得 5W 和 4C。双方消费均超出其生产可能性边界。
Published by TutorHao | Economics Revision Series | aleveler.com
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