IB Economics Calculation Questions Drill | IB 经济计算题专项训练

📚 IB Economics Calculation Questions Drill | IB 经济计算题专项训练

Mastering calculation questions is essential for success in IB Economics. From elasticity to national income multipliers, these problems test both quantitative skills and economic reasoning. This guide provides a systematic drill covering the most common calculation topics across the syllabus.

掌握计算题对于 IB 经济学取得成功至关重要。从弹性到国民收入乘数，这些问题既考察数量技能，又考察经济推理。本指南提供一个系统性的训练，覆盖课程大纲中最常见的计算专题。

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

Price elasticity of demand measures the responsiveness of quantity demanded to a change in price. The midpoint formula is recommended for calculating arc elasticity as it gives a symmetric result regardless of direction.

需求价格弹性衡量需求量对价格变动的反应程度。建议使用中点公式计算弧弹性，因为无论变动方向如何，它都能给出对称的结果。

PED = %ΔQd / %ΔP = [(Q₂ – Q₁) / ((Q₁ + Q₂)/2)] ÷ [(P₂ – P₁) / ((P₁ + P₂)/2)]

Example: The price of a cinema ticket rises from $5 to $6, and tickets sold fall from 100 to 80 per day. Calculate PED and interpret the value.

例题：电影票价格从 5 美元上涨到 6 美元，每天售出的票数从 100 张减少到 80 张。计算 PED 并解释其数值。

%ΔQd = (80 – 100) ÷ ((100 + 80)/2) × 100 = -20/90 × 100 = -22.2%
%ΔP = (6 – 5) ÷ ((5 + 6)/2) × 100 = 1/5.5 × 100 = 18.2%
PED = -22.2% / 18.2% = -1.22. The absolute value is 1.22, which is greater than 1, so demand is price elastic. A 1% price increase leads to a 1.22% fall in quantity demanded.

%ΔQd = (80 – 100) ÷ ((100 + 80)/2) × 100 = -20/90 × 100 = -22.2%
%ΔP = (6 – 5) ÷ ((5 + 6)/2) × 100 = 1/5.5 × 100 = 18.2%
PED = -22.2% / 18.2% = -1.22。绝对值为 1.22，大于 1，因此需求是富有价格弹性的。价格上涨 1% 会导致需求量下降 1.22%。

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2. Cross-Price Elasticity of Demand (XED) and Income Elasticity of Demand (YED) | 交叉需求弹性和收入需求弹性

XED measures the responsiveness of demand for one good to a change in the price of another good. YED measures the responsiveness of demand to a change in income. These indicators classify goods as substitutes, complements, normal, or inferior.

交叉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。收入弹性衡量需求对收入变动的反应程度。这些指标将商品分类为替代品、互补品、正常品或劣质品。

XED = %ΔQd of good A / %ΔP of good B
YED = %ΔQd / %Δ income

Example (XED): The price of streaming service A rises by 10%, and the demand for streaming service B increases by 20%. Calculate XED and interpret.

例题（XED）：流媒体服务 A 的价格上涨 10%，流媒体服务 B 的需求增加了 20%。计算 XED 并解释。

XED = +20% / +10% = +2.0. A positive XED indicates that the two services are substitutes. Consumers switch from A to B.

XED = +20% / +10% = +2.0。正的交叉弹性表明这两种服务为替代品。消费者从 A 转向 B。

Example (YED): If income rises by 4% and demand for organic vegetables increases by 10%, YED = 10%/4% = +2.5. The good is a luxury normal good.

例题（YED）：如果收入增加 4%，有机蔬菜的需求增加 10%，则 YED = 10%/4% = +2.5。该商品为奢侈品正常品。

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

PES measures how responsive the quantity supplied is to a change in price. The formula mirrors PED but uses quantity supplied instead of demanded.

供给价格弹性衡量供给量对价格变动的反应程度。公式与 PED 相似，但使用供给量而非需求量。

PES = %ΔQs / %ΔP = [(Qs₂ – Qs₁) / ((Qs₁ + Qs₂)/2)] ÷ [(P₂ – P₁) / ((P₁ + P₂)/2)]

Example: The price of a good increases from $10 to $14, and firms raise output from 200 to 300 units. Calculate PES.

例题：某商品价格从 10 美元上涨至 14 美元，厂商将产量从 200 单位增加到 300 单位。计算 PES。

%ΔQs = (300-200) ÷ ((200+300)/2) × 100 = 100/250 × 100 = 40%
%ΔP = (14-10) ÷ ((10+14)/2) × 100 = 4/12 × 100 = 33.3%
PES = 40% / 33.3% = 1.2. Supply is elastic.

%ΔQs = (300-200) ÷ ((200+300)/2) × 100 = 100/250 × 100 = 40%
%ΔP = (14-10) ÷ ((10+14)/2) × 100 = 4/12 × 100 = 33.3%
PES = 40% / 33.3% = 1.2。供给富有弹性。

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4. Costs of Production: Total, Average, and Marginal | 生产成本：总成本、平均成本与边际成本

Firms use total cost (TC), average cost (AC), and marginal cost (MC) to make output decisions. MC is the extra cost of producing one more unit, while AC is total cost divided by output.

企业利用总成本（TC）、平均成本（AC）和边际成本（MC）做出产量决策。MC 是多生产一单位产品所增加的额外成本，而 AC 是总成本除以产量。

AC = TC / Q
MC = ΔTC / ΔQ

Example: A firm’s costs are shown in the table below. Complete AC and MC.

例题：某企业的成本如下表所示。计算 AC 和 MC。

Q (units)	TC ($)	AC ($)	MC ($)
0	50	–	–
1	90	90	40
2	120	60	30
3	140	46.7	20
4	180	45	40

AC is obtained by TC/Q. MC is ΔTC/ΔQ. For example, moving from Q=1 to Q=2, MC = (120-90)/(2-1) = 30. Note how AC falls and then rises – the U-shaped cost curve.

AC 通过 TC/Q 计算。MC 通过 ΔTC/ΔQ 计算。例如，产量从 1 增至 2 时，MC = (120-90)/(2-1) = 30。注意 AC 先降后升 —— U 形成本曲线。

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5. Revenue and Profit Maximization | 收益与利润最大化

Total revenue (TR) = Price × Quantity. Average revenue (AR) = TR/Q = Price. Marginal revenue (MR) = ΔTR/ΔQ. Profit is maximized where MR = MC, provided price covers average variable cost.

总收益 (TR) = 价格 × 数量。平均收益 (AR) = TR/Q = 价格。边际收益 (MR) = ΔTR/ΔQ。当 MR = MC 且价格覆盖平均可变成本时，利润达到最大化。

Example: A firm can sell output at a constant price of $10. Output and total cost data are given. Determine the profit-maximizing level of output.

例题：某企业可以按固定价格 10 美元出售产品。已知产量和总成本数据，确定利润最大化的产量水平。

Q	P ($)	TR ($)	TC ($)	MR ($)	MC ($)	Profit ($)
0	10	0	20	–	–	-20
1	10	10	25	10	5	-15
2	10	20	28	10	3	-8
3	10	30	30	10	2	0
4	10	40	33	10	3	7
5	10	50	38	10	5	12

MR is constant at $10 because price is fixed (perfect competition). MC is calculated as ΔTC/ΔQ. Profit peaks where MR exceeds MC by the smallest margin. At Q=4, MR (10) > MC(3) and profit begins rising sharply. But the best choice is Q=5, where profit is highest ($12) and MR still covers MC. In competitive markets, produce up to where MR=MC; here Q=5 yields the maximum total profit.

MR 因价格固定（完全竞争）恒定在 10 美元。MC 通过 ΔTC/ΔQ 计算。利润在 MR 超出 MC 最小的产量处达到顶峰。在 Q=4 时，MR (10) > MC (3) 且利润明显上升。但最佳产量为 Q=5，此时利润最高（12 美元）且 MR 仍覆盖 MC。在竞争市场中，应生产至 MR=MC 处；此处 Q=5 实现最大总利润。

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6. Calculating the National Income Multiplier | 国民收入乘数计算

The multiplier (k) shows the magnified impact of an initial change in spending on aggregate demand and real GDP. The formula uses the marginal propensity to consume (MPC) or the marginal propensity to save (MPS).

乘数 (k) 显示了初始支出变动对总需求和实际 GDP 的放大影响。公式利用边际消费倾向 (MPC) 或边际储蓄倾向 (MPS)。

k = 1 / (1 – MPC) = 1 / MPS
ΔGDP = k × Δinjection

Example: In an economy, households spend $0.75 out of every additional dollar earned. The government increases infrastructure spending by $40 million. Calculate the multiplier and the total change in equilibrium real GDP.

例题：某经济体中，家庭每增加 1 美元收入就会消费 0.75 美元。政府将基础设施支出增加 4000 万美元。计算乘数和均衡实际 GDP 的总变动。

MPC = 0.75, so MPS = 1 – 0.75 = 0.25.
k = 1 / 0.25 = 4.
ΔGDP = 4 × $40 million = $160 million.
The final increase in GDP is four times the initial injection, highlighting the multiplier effect.

MPC = 0.75，故 MPS = 1 – 0.75 = 0.25。
k = 1 / 0.25 = 4。
ΔGDP = 4 × 4000 万美元 = 1.6 亿美元。
GDP 的最终增量是最初注入的四倍，体现了乘数效应。

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7. Inflation Rate and Price Index Calculations | 通货膨胀率与价格指数计算

The inflation rate is the percentage change in a price index, typically the Consumer Price Index (CPI). The GDP deflator can also be used to convert nominal to real GDP.

通货膨胀率是价格指数（通常是消费者价格指数 CPI）变动的百分比。GDP 平减指数也可用于将名义

Published by TutorHao | IB Economics Revision Series | aleveler.com

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