IB & OCR Economics Calculation Questions Mastery | IB与OCR经济计算题专项训练

📚 IB & OCR Economics Calculation Questions Mastery | IB与OCR经济计算题专项训练

Mastering calculation questions is essential for scoring high marks in both IB and OCR Economics. Whether you are working through elasticities, market equilibria, national income accounts, or exchange rate arithmetic, precision with formulas and step-by-step logic can transform a tricky quantitative task into guaranteed marks. This guide brings together the most frequently examined calculation techniques, enriched with worked examples, so you can confidently tackle any numerical problem on Paper 2, Paper 3 (IB HL), or the OCR quantitative components.

无论是 IB 还是 OCR 经济，计算题都是得分的重头戏。从弹性、市场均衡到国民收入核算和汇率计算，熟练掌握公式与推导步骤，就能把看似复杂的数字题变成稳拿的分数。这篇文章汇总了两个考试局最高频的计算题型，配合详细演算，帮助你彻底攻克计算难关。

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

PED measures the responsiveness of quantity demanded to a change in price. For discrete data, IB and OCR both favour the midpoint (arc) formula to avoid inconsistency depending on the direction of change.

PED 衡量需求量对价格变化的反应程度。在处理离散数据时，IB 和 OCR 均推荐使用中点（弧弹性）公式，以消除变化方向带来的偏差。

PED = [(Q₂ − Q₁) / ((Q₁ + Q₂)/2)] ÷ [(P₂ − P₁) / ((P₁ + P₂)/2)]

Worked example: The price of a cinema ticket rises from $10 to $12, and the quantity sold falls from 100 to 80 per day. Calculate PED, state whether demand is elastic or inelastic, and explain the impact on total revenue.

例题：电影票价从 10 美元涨到 12 美元，日销量从 100 张降至 80 张。计算 PED，判断需求弹性类型，并解释对总收入的影响。

Q₁ = 100, Q₂ = 80, P₁ = 10, P₂ = 12
ΔQ = 80 − 100 = −20; ΔP = 12 − 10 = 2
Average Q = (100+80)/2 = 90; Average P = (10+12)/2 = 11
PED = (−20/90) ÷ (2/11) = (−0.2222) / 0.1818 ≈ −1.22
Ignoring the negative sign, |PED| = 1.22 > 1 → demand is price elastic.
Total revenue before = $10 × 100 = $1000; after = $12 × 80 = $960. Revenue falls, which is consistent with elastic demand: the percentage drop in quantity (22.2%) outweighs the percentage rise in price (18.2%).

|PED| = 1.22 > 1，需求富有弹性。总收入从 1000 美元降至 960 美元，符合弹性需求特征——需求量下降幅度超过价格上涨幅度。

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

YED quantifies how demand shifts when consumer income changes. It is pivotal for classifying goods as normal (YED > 0), inferior (YED < 0), and luxury or necessity within normal goods.

YED 反映需求对消费者收入变动的敏感度，可用于区分正常品（YED > 0）、劣等品（YED < 0）以及正常品中的奢侈品与必需品。

YED = [(Q₂ − Q₁) / ((Q₁ + Q₂)/2)] ÷ [(Y₂ − Y₁) / ((Y₁ + Y₂)/2)]

Example: When average household income grows from $40,000 to $44,000, demand for organic vegetables increases from 200 kg to 240 kg per week. Compute YED and interpret.

例题：家庭平均收入从 40,000 美元增至 44,000 美元，有机蔬菜周需求量从 200 kg 升至 240 kg。计算 YED 并解释。

Y₁ = 40000, Y₂ = 44000, Q₁ = 200, Q₂ = 240
ΔQ = 40, ΔY = 4000; avg Q = 220, avg Y = 42000
YED = (40/220) ÷ (4000/42000) = 0.1818 / 0.09524 ≈ +1.91

YED ≈ +1.91, which is positive and greater than 1, indicating that organic vegetables are a luxury normal good for these consumers.

YED 为正且大于 1，说明有机蔬菜对该消费群体属于奢侈正常品。

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

XED captures the relationship between two goods. A positive XED signals substitutes, a negative XED indicates complements, and a near‑zero value suggests independent goods.

XED 衡量一种商品需求对另一种商品价格变化的反应。正值表示替代品，负值为互补品，接近零则是独立品。

XED = [(Qₐ₂ − Qₐ₁) / ((Qₐ₁ + Qₐ₂)/2)] ÷ [(P_b₂ − P_b₁) / ((P_b₁ + P_b₂)/2)]

Worked scenario: The price of coffee increases from $5 to $6 per pack, and the demand for tea rises from 80 boxes to 100 boxes. Find XED and classify the relationship.

案例：咖啡每包从 5 美元涨到 6 美元，茶叶需求量从 80 盒上升到 100 盒。求 XED 并判断关系。

P_b1 = 5, P_b2 = 6, Q_a1 = 80, Q_a2 = 100
Avg P_b = 5.5, Avg Q_a = 90
XED = (20/90) ÷ (1/5.5) = 0.2222 / 0.1818 ≈ +1.22

XED > 0 confirms that tea and coffee are substitutes. A 1% rise in coffee price leads to a 1.22% increase in quantity demanded for tea.

XED 正 ≈1.22，说明茶与咖啡互为替代品：咖啡价格每上涨 1%，茶叶需求量增加 1.22%。

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

PES measures how responsive quantity supplied is to price changes. The arc formula is identical in structure but focuses on quantity supplied. Key determinants include production time, spare capacity, and storability.

PES 测度供给量对价格变化的反应程度，弧弹性公式结构相同但关注供给量。主要决定因素有生产周期、闲置产能和存储能力。

Practice example: A furniture maker supplies 50 tables at $200 each. When the price increases to $240, the quantity supplied rises to 70 tables. Compute PES using the midpoint method.

练习：一个家具厂商在单价 200 美元时供给 50 张桌子，价格涨至 240 美元时供给 70 张。用中点法求 PES。

P₁=200, P₂=240, Q₁=50, Q₂=70
ΔQ=20, ΔP=40; Avg Q=60, Avg P=220
PES = (20/60) ÷ (40/220) = 0.3333 / 0.1818 ≈ 1.83

PES > 1 signals elastic supply — the firm can respond strongly to price incentives, likely due to spare capacity or flexible production.

PES ≈1.83，供给富有弹性，表明该厂商能够灵活扩大产出，可能拥有闲置产能。

5. Market Equilibrium and Surplus | 市场均衡与剩余

Linear demand and supply functions are staples of IB HL Paper 3 and OCR quantitative sections. You must be able to find equilibrium price and quantity, then calculate consumer surplus (CS) and producer surplus (PS) using triangular areas.

线性供需函数是 IB HL Paper 3 和 OCR 计算题的常客。需要能求解均衡价格与数量，再用三角形面积计算消费者剩余和生产者剩余。

Let Qd = 100 − 2P and Qs = −20 + 4P.

Set Qd = Qs: 100 − 2P = −20 + 4P → 120 = 6P → Pₑ = 20, Qₑ = 100 − 2×20 = 60.
Demand choke price (Qd=0): 0 = 100 − 2P → P = 50.
Supply intercept (Qs=0): 0 = −20 + 4P → P = 5.
CS = ½ × (50 − 20) × 60 = ½ × 30 × 60 = 900.
PS = ½ × (20 − 5) × 60 = ½ × 15 × 60 = 450.

设 Qd = 100 − 2P，Qs = −20 + 4P。令 Qd = Qs 得均衡价格 Pₑ = 20，均衡数量 60。需求纵截距 50，供给纵截距 5。CS = 0.5×(50−20)×60 = 900；PS = 0.5×(20−5)×60 = 450。

Total welfare = CS + PS = 1350. A government-imposed price ceiling at $15 would create a shortage, reducing total surplus. The ability to compute these areas is frequently tested.

总福利 = 1350。若政府设定价格上限 15 美元，将导致短缺并造成无谓损失，这类面积计算常见于考试。

6. Costs, Revenue, and Profit | 成本、收益与利润

Firms’ cost and revenue calculations lie at the heart of the Theory of the Firm. You must confidently derive total fixed cost (TFC), total variable cost (TVC), average total cost (ATC), marginal cost (MC), and profit-maximising output under perfect competition.

成本与收益计算是企业理论的核心。需要熟练推导总固定成本、总可变成本、平均总成本、边际成本，并掌握完全竞争下的利润最大化产量。

Given: TC = 100 + 2Q², and market price P = $40.

TFC = 100 (the constant term). TVC = 2Q².
ATC = TC/Q = (100/Q) + 2Q. MC = ΔTC/ΔQ = 4Q (differentiating).
For perfect competition, profit max occurs at P = MC: 40 = 4Q → Q* = 10.
TR = 40 × 10 = 400. TC = 100 + 2×(10)² = 100 + 200 = 300.
Profit (π) = 400 − 300 = 100.

已知总成本函数 TC = 100 + 2Q²，市场价格 P = 40 美元。固定成本 TFC = 100，总可变成本 TVC = 2Q²。ATC = 100/Q + 2Q，MC = 4Q。完全竞争下利润最大化条件 P = MC → 40 = 4Q，得 Q* = 10。总收入 TR = 400，总成本 TC = 300，利润 π = 100。

When drawing diagrams, remember that MC intersects ATC at its minimum. Incorporating these values into accurate graphs is essential for full marks.

作图时需注意 MC 穿过 ATC 最低点，将计算结果准确标注在图形上才能拿到全部分数。

7. National Income Accounting | 国民收入核算

Both IB and OCR require the expenditure approach to GDP: GDP = C + I + G + (X − M). You may also need to adjust for net factor income from abroad to obtain GNI, or convert nominal to real values.

IB 和 OCR 均要求掌握支出法 GDP：GDP = C + I + G + (X − M)。有时还需调整国外净要素收入获得 GNI，或进行名义值与实际值的换算。

Component	Amount ($bn)
Household consumption (C)	850
Gross investment (I)	230
Government spending (G)	310
Exports (X)	180
Imports (M)	210
Net income from abroad	+15

GDP = 850 + 230 + 310 + (180 − 210) = 1360. GNI = GDP + net income from abroad = 1360 + 15 = 1375.

GDP = 850+230+310+(180−210) = 1360 亿美元。加上国外净收入 15 得 GNI = 1375 亿美元。

If the GDP deflator is 108, real GDP = (Nominal GDP / Deflator) × 100 = (1360 / 108) × 100 ≈ 1259.26. Always remember to multiply by 100 when the deflator is given as an index.

若 GDP 平减指数为 108，实际 GDP = (1360/108)×100 ≈ 1259.26 亿美元。务必在指数形式平减指数下乘以 100。

8. The Multiplier Effect | 乘数效应

The Keynesian multiplier magnifies the impact of an initial injection into the circular flow. The simple multiplier k = 1 / (1 − MPC) or 1 / MPS. You must also handle tax and import leakages in more advanced models.

凯恩斯乘数放大初始注入对经济的影响。简单乘数 k = 1/(1−MPC) = 1/MPS。更高要求下还需处理税收和进口的漏出。

Given MPC = 0.75:

k = 1 / (1 − 0.75) = 4.
A $20 billion increase in government spending ultimately raises real GDP by ΔY = k × ΔG = 4 × 20 = $80 billion.
Tax multiplier (lump sum) = −MPC / (1−MPC) = −0.75 / 0.25 = −3.

若 MPC = 0.75，简单乘数 k = 4。政府支出增加 200 亿美元，最终 GDP 增加 800 亿美元。定额税收乘数 = −0.75/0.25 = −3。

When both government spending and lump-sum taxes increase by the same amount, the balanced-budget multiplier equals 1. This means GDP rises exactly by the amount of the spending and tax increase, a subtle point frequently tested in multiple-choice and short-answer questions.

平衡预算乘数为 1：政府支出和定额税同增等量，GDP 恰好增加同等数额，这一细节常在选择题和简答题中考察。

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

Comparative advantage is determined by comparing opportunity costs. The country with the lower opportunity cost in producing a good should specialise in it. You must calculate opportunity cost in terms of the other good forgone.

比较优势通过机会成本判定，机会成本低的国家应专业生产该商品。计算时需以放弃的另一种商品数量表示机会成本。

Country / Goods	Cloth (units per day)	Wine (units per day)
England	20	10
Portugal	12	8

Opportunity cost of 1 unit of cloth:

England: 10 wine / 20 cloth = 0.5 wine per cloth.
Portugal: 8 wine / 12 cloth = 2/3 ≈ 0.67 wine per cloth.

Opportunity cost of 1 unit of wine:

England: 20 cloth / 10 wine = 2 cloth per wine.
Portugal: 12 cloth / 8 wine = 1.5 cloth per wine.

England has a lower opportunity cost for cloth (0.5 < 0.67), so comparative advantage in cloth. Portugal has a lower opportunity cost for wine (1.5 < 2), so comparative advantage in wine. With specialisation and trade, both can consume beyond their PPF.

英国生产布的机会成本（0.5 酒）低于葡萄牙（0.67 酒），英国在布上有比较优势；葡萄牙酒的机会成本（1.5 布）低于英国（2 布），葡萄牙在酒上有比较优势。通过专业化与贸易，两国消费可突破各自的生产可能性边界。

10. Exchange Rates | 汇率计算

Candidates must convert currencies and compute percentage appreciation or depreciation. A rise in the value of a currency is an appreciation; a fall is a depreciation.

考生需会货币换算，并计算货币升/贬值百分比。货币价值上升为升值，下降为贬值。

Scenario: Initially £1 = $1.30. Later, £1 = $1.35.

Percentage change in the value of the pound: [(1.35 − 1.30) / 1.30] × 100 ≈ 3.85% appreciation.
When converting $650 into pounds at the new rate: £ received = 650 / 1.35 ≈ £481.48. At the old rate, £500 would have been received, illustrating that a stronger pound means fewer pounds per dollar for British exporters receiving dollar revenues.

场景：初始 £1 = $1.30，随后 £1 = $1.35。英镑升值幅度 = [(1.35−1.30)/1.30]×100 ≈ 3.85%。按新汇率将 650 美元兑换为英镑：650/1.35≈481.48 英镑，而旧汇率下可得 500 英镑，表明英镑升值不利于英国出口商将美元收入换回本币。

Weighted exchange rate indices and real effective exchange rate calculations may appear in OCR papers, combining trade-weighted baskets with relative inflation differentials.

权重汇率指数和实际有效汇率可能出现在 OCR 试卷中，需要结合贸易加权篮子与相对通胀差异计算。

11. Inflation, Unemployment, and Real GDP | 通胀、失业与实际 GDP

Inflation is typically measured via a consumer price index (CPI). The annual inflation rate is the percentage change in the CPI from one year to the next. Unemployment rate is the number of unemployed divided by the labour force, expressed as a percentage.

通胀通常用消费者价格指数（CPI）衡量，年通胀率即 CPI 的年度百分比变化。失业率 = 失业人数 ÷ 劳动力总数 × 100%。

CPI example: CPI in 2023 = 124, CPI in 2024 = 130. Inflation rate = [(130 − 124) / 124] × 100 ≈

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IB & OCR Economics Calculation Questions Mastery | IB与OCR经济计算题专项训练