📚 IB AQA Economics: Formula Handbook | IB AQA 经济：公式汇总手册
This handbook brings together all the essential formulas you need to master both IB Economics and AQA A-level Economics. Whether you are tackling microeconomic elasticities, cost and revenue calculations, or macroeconomic multipliers and trade indicators, a clear understanding of these quantitative tools is vital for top marks in data response, multiple-choice, and paper 3 (IB) or context-based questions (AQA). Keep this reference handy as you revise.
本手册汇总了 IB 经济学与 AQA A-level 经济学所有必备公式。无论你正在学习微观弹性、成本收益计算，还是宏观经济乘数与贸易指标，清晰掌握这些量化工具对于在数据分析、选择题以及 IB 论文三或 AQA 情境题中取得高分至关重要。复习时请随身参阅本手册。
1. Percentage Change and Index Numbers | 百分比变化与指数计算
Many economic formulas start with a percentage change. This simple calculation allows you to compare the size of a change relative to the original value.
许多经济公式始于百分比变化。这一简单计算可用于比较变化相对于原始值的幅度。
%Δ = (New Value − Old Value) / Old Value × 100
Index numbers are widely used in both syllabi to simplify comparisons over time. The base year index always equals 100.
指数在 IB 和 AQA 课程中广泛用于简化跨时期比较。基年的指数始终等于 100。
Index = (Value in given year / Value in base year) × 100
When linking percentage changes, avoid the common mistake of adding percentages directly when the base changes. Always recount using the updated values.
当关联多个百分比变化时，避免在基数变化后直接相加这一常见错误。始终使用更新后的数值重新计算。
2. Price Elasticity of Demand (PED) | 需求的价格弹性 (PED)
PED measures the responsiveness of quantity demanded to a change in the good's own price. It is always negative due to the law of demand, but we usually consider the absolute value.
PED 衡量需求量对商品自身价格变化的反应程度。遵循需求定律，它始终为负值，但我们通常考虑其绝对值。
PED = %ΔQd / %ΔP
Using the standard formula with discrete data often gives different values depending on direction. The midpoint (arc) formula provides a consistent measure.
对离散数据使用标准公式常因变动方向不同而得到不同数值。中点（弧）公式提供了一致性度量。
PED = [(Q₂ − Q₁) / ((Q₁+Q₂)/2)] / [(P₂ − P₁) / ((P₁+P₂)/2)]
Interpretation of |PED|: if it is greater than 1, demand is price elastic; equal to 1, unit elastic; less than 1, price inelastic. Perfectly elastic demand gives |PED| tending to infinity, while perfectly inelastic yields zero.
|PED| 解读：若大于1，需求富有弹性；等于1，单位弹性；小于1，缺乏弹性。完全弹性需求的 |PED| 趋向无穷大，完全无弹性则为零。
3. Income Elasticity of Demand (YED) | 需求的收入弹性 (YED)
YED shows how demand for a good responds to changes in consumer income. It helps classify goods and predict shifts in demand as economies grow or contract.
YED 显示一种商品的需求如何随消费者收入变化而变动。它可用于划分商品类别，并预测经济增长或收缩时需求的移动。
YED = %ΔQd / %ΔY
A positive YED identifies a normal good, while a negative YED signals an inferior good. Among normal goods, YED > 1 suggests a luxury good, and 0 < YED < 1 points to a necessity. Firms use YED estimates to plan output and diversification.
正的 YED 表明正常品，负的 YED 则表明低档品。在正常品中，YED > 1 表现为奢侈品，0 < YED < 1 则为必需品。企业利用 YED 预估来规划产出与多元化经营。
4. Cross Elasticity of Demand (XED) | 需求的交叉弹性 (XED)
XED measures how the demand for one good reacts to a price change of another good. The sign and magnitude reveal the relationship between the two products.
XED 衡量一种商品的需求如何对另一商品的价格变化作出反应。其正负号与大小揭示了两种产品之间的关系。
XED = %ΔQd of good A / %ΔPof good B
A positive XED indicates substitute goods, while a negative XED signals complements. A value close to zero suggests independent goods. Strong substitution gives large positive values, giving firms insight into competitive threats and collaborative pricing strategies.
正的 XED 表明替代品，负的 XED 则表明互补品。接近零的值表示独立品。强替代关系会产生较大的正值，帮助企业洞察竞争威胁与联合定价策略。
5. Price Elasticity of Supply (PES) | 供给的价格弹性 (PES)
PES captures the responsiveness of quantity supplied to price changes. Timeframe, production flexibility and spare capacity strongly influence its value.
PES 反映供给量对价格变化的反应程度。时间跨度、生产灵活性和闲置产能是影响其数值的关键因素。
PES = %ΔQs / %ΔP
supply can be considered infinite. In the momentary period supply is often highly inelastic, while in the long run it becomes more elastic.
当 PES > 1 时供给富有弹性，等于1时为单位弹性，<1 时缺乏弹性。完全无弹性供给的 PES = 0，完全弹性供给可视为无限大。在极短期，供给往往高度缺乏弹性，而在长期则更具弹性。
6. Total, Average and Marginal Revenue | 总收益、平均收益与边际收益
Revenue concepts are fundamental to understanding a firm's price-output decisions. Total revenue (TR) is the firm's income from sales.
收益概念是理解企业定价与产量决策的基础。总收益 (TR) 是企业销售所得的总收入。
TR = P × Q
mathematically identical to price: AR = TR / Q = P. The demand curve is therefore the firm's AR curve.
平均收益 (AR) 等于总收益除以产量，在数学上与价格恒等：AR = TR / Q = P。因此需求曲线即为企业的平均收益曲线。
Marginal revenue (MR) is the addition to total revenue from selling one more unit. Under perfect competition MR equals price; under imperfect competition MR lies below AR and can become negative.
边际收益 (MR) 是多售出一单位产品所带来的总收益增量。在完全竞争下 MR 等于价格；在不完全竞争下 MR 位于 AR 下方，且可能变为负值。
MR = ΔTR / ΔQ
7. Costs and Their Formulas | 成本及其计算公式
Total cost (TC) is the sum of all fixed and variable costs. Fixed costs (TFC) do not vary with output in the short run, while variable costs (TVC) change directly with output.
总成本 (TC) 是所有固定成本与可变成本之和。固定成本 (TFC) 在短期不随产量变化，可变成本 (TVC) 则直接随产量变化。
TC = TFC + TVC
Average costs show cost per unit. Average fixed cost (AFC) falls continuously as output rises; average variable cost (AVC) and average total cost (AC) tend to be U-shaped because of eventual diminishing returns.
平均成本反映单位成本。平均固定成本 (AFC) 随产量增加持续下降；平均可变成本 (AVC) 与平均总成本 (AC) 通常因边际报酬递减而呈 U 形。
AFC = TFC / Q
AVC = TVC / Q
AC = TC / Q = AFC + AVC
Marginal cost (MC) is the change in total cost when an additional unit is produced. The MC curve intersects AVC and AC at their minimum points, a key relationship used in both IB and AQA diagrams.
边际成本 (MC) 指多生产一单位产品所带来的总成本变动。MC 曲线分别交于 AVC 和 AC 的最低点，这一关键关系在 IB 和 AQA 图示中均有运用。
MC = ΔTC / ΔQ
8. Profit, Break-even and Shutdown Points | 利润、盈亏平衡点与停业点
Profit is the positive difference between total revenue and total cost. Economists distinguish between accounting and economic profit.
利润是总收益与总成本的正差额。经济学家区分会计利润与经济利润。
Accounting Profit = TR − Explicit Costs
Economic Profit = TR − (Explicit Costs + Implicit Costs)
Normal profit occurs when economic profit equals zero, meaning the firm is covering all opportunity costs. Supernormal profit exists when economic profit is positive.
当经济利润为零时，即为正常利润，表明企业恰好覆盖了全部机会成本。经济利润为正时则存在超常利润。
The break-even level of output is found where total revenue equals total cost, or where price covers average total cost. Using contribution, the break-even point can be expressed as:
盈亏平衡产量是总收益等于总成本时的产出水平，或价格等于平均总成本时的产出。运用单位贡献毛益，盈亏平衡点可表示为：
Break-even output = TFC / (Price − AVC)
The shutdown point in the short run occurs when the firm cannot cover its variable costs. If P < AVC, the loss from producing exceeds fixed costs, so the firm should temporarily shut down.
短期停业点出现在企业无法覆盖可变成本时。若 P < AVC，生产的亏损将超过固定成本，企业应暂时停业。
9. Macroeconomic Multipliers | 宏观经济乘数
The multiplier quantifies how an initial injection into the circular flow leads to a larger final change in national income. The simple closed-economy multiplier without government and trade is based solely on the marginal propensity to consume (MPC) and marginal propensity to save (MPS).
乘数量化了初始注入如何引发国民收入更大规模的最终变动。无政府和国际贸易的简单封闭经济乘数仅基于边际消费倾向 (MPC) 与边际储蓄倾向 (MPS)。
k = 1 / (1 − MPC) = 1 / MPS
In an open economy with government, withdrawals include saving, taxation and imports. The marginal propensity to withdraw (MPW) is the sum of MPS, MPT and MPM, giving a more realistic multiplier.
在包含政府部门的开放经济中，漏出包括储蓄、税收与进口。边际漏出倾向 (MPW) 等于 MPS、MPT 与 MPM 之和，由此得出更贴近现实的乘数。
k = 1 / (MPS + MPT + MPM) = 1 / MPW
−MPC / (1 − MPC) or −MPC / MPS. AQA typically focuses on the expenditure multiplier, but the concept of the tax multiplier can still deepen your analysis.
对 IB HL 学生而言，税收乘数同样重要。一次性税收的变化将使消费函数移动 MPC × ΔT，因此税收乘数为 −MPC / (1 − MPC) 或 −MPC / MPS。AQA 通常侧重支出乘数，但理解税收乘数仍能深化你的分析。
10. Propensities to Consume and Save | 消费与储蓄倾向
Average propensities tell us the fraction of total income that is spent or saved. The average propensity to consume (APC) plus the average propensity to save (APS) always equals one for any given level of national income.
平均倾向表示总收入中被用于消费或储蓄的比例。在任一给定国民收入水平下，平均消费倾向 (APC) 与平均储蓄倾向 (APS) 之和恒等于一。
APC = C / Y
APS = S / Y
Marginal propensities measure the change in consumption or saving as income changes. They are crucial for determining the multiplier and the slope of aggregate expenditure functions.
边际倾向衡量消费或储蓄随收入变化而变动的量。它们是决定乘数和总支出函数斜率的关键。
MPC = ΔC / ΔY
MPS = ΔS / ΔY
MPT = ΔT / ΔY
MPM = ΔM / ΔY
wals-based marginal condition is MPC + MPS + MPT + MPM = 1, or equivalently MPC + MPW = 1.
注意，在不含税收与进口的模型中 MPC + MPS = 1。基于漏出的完整边际等式为 MPC + MPS + MPT + MPM = 1，或者等同于 MPC + MPW = 1。
11. Terms of Trade | 贸易条件
Terms of trade reflect a country's export prices relative to its import prices. An improvement means the country can buy more imports for a given volume of exports.
贸易条件反映一国出口价格相对于进口价格的水平。贸易条件改善意味着给定出口量可以换回更多的进口品。
Terms of Trade = (Index of export prices / Index of import prices) × 100
When the index rises, the terms of trade improve; when it falls, they deteriorate. IB HL candidates frequently use this formula in international economics, while AQA also expects you to calculate and interpret changes in the terms of trade.
指数上升时贸易条件改善，下降时则恶化。IB HL 考生常在讨论国际经济学时运用此公式，AQA 同样要求你计算并解读贸易条件的变化。
12. Exchange Rates, Inflation and Unemployment Indicators | 汇率、通胀与失业指标
Consumer price index (CPI) measures the cost of
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