📚 Formula & Theorem Quick Reference Handbook | 公式定理速查手册
This quick-reference handbook compiles the essential formulas, conditions and theorems required for AQA A‑level Economics (Year 13). Each section presents the key relationships, definitions and worked interpretations that appear frequently in data‑response and essay questions. Mastering these tools will sharpen your quantitative analysis and help you build rigorous chains of reasoning in both microeconomic and macroeconomic contexts.
本速查手册整理了 AQA A‑level 经济（13年级）所必需的核心公式、条件和定理。每个小节都列出了在数据分析题和论文题中经常出现的关键关系、定义与操作解释。掌握这些工具将强化你的定量分析能力，并帮助你在微观和宏观经济情境中建立起严密的逻辑推理链条。
1. Costs, Revenues and Profits | 成本、收入与利润
A firm’s total cost is the sum of its fixed and variable components. Fixed costs do not change with output in the short run, while variable costs rise as output expands.
一家企业的总成本是其固定要素与可变要素之和。短期中，固定成本不随产量变化，而可变成本随着产量扩大而上升。
TC = TFC + TVC
Average total cost is obtained by dividing total cost by the quantity produced.
平均总成本由总成本除以产量得到。
ATC = TC ÷ Q
Marginal cost is the addition to total cost from producing one extra unit of output.
边际成本是额外生产一单位产量所导致的总成本增加量。
MC = ΔTC ÷ ΔQ
Total revenue is the price per unit multiplied by the quantity sold. In perfect competition, average revenue equals the market price.
总收入是单位价格乘以销售数量。在完全竞争市场中，平均收入等于市场价格。
TR = P × Q
AR = TR ÷ Q = P
Marginal revenue measures the change in total revenue when one more unit is sold. Under imperfect competition, MR lies below AR.
边际收入衡量的是多销售一单位产品所带来的总收入变化。在不完全竞争条件下，边际收入低于平均收入。
MR = ΔTR ÷ ΔQ
Profit is the difference between total revenue and total cost. Normal profit occurs when AR = ATC, implying zero supernormal profit but enough to keep resources in the industry.
利润是总收入与总成本之间的差额。正常利润出现在 AR = ATC 时，此时超常利润为零，但足以把资源留在该行业中。
Profit = TR − TC
Normal profit: AR = ATC
Supernormal profit: AR > ATC
2. Price Elasticity of Demand (PED) | 需求的价格弹性
PED measures the responsiveness of quantity demanded to a change in price. Its sign is negative, but by convention the absolute value is used.
需求的价格弹性衡量的是需求量对价格变化的反应程度。其符号为负，但习惯上使用绝对值。
PED = %ΔQd ÷ %ΔP
When using the midpoint (arc) method, the percentage changes are calculated from the average of the two observations to give a symmetric measure.
使用中点（弧）法计算时，百分比变化以两个观察值的平均值为基础，从而得到一个对称的弹性值。
%ΔQd = (Q₂ − Q₁) ÷ [(Q₁ + Q₂) ÷ 2] × 100%
%ΔP = (P₂ − P₁) ÷ [(P₁ + P₂) ÷ 2] × 100%
If |PED| > 1, demand is price‑elastic and a price cut raises total revenue. If |PED| < 1, demand is price‑inelastic and a price rise raises total revenue. Unit elastic demand (|PED| = 1) leaves total revenue unchanged when price changes.
若 |PED| > 1，需求富有价格弹性，降价会提高总收入；若 |PED| < 1，需求缺乏价格弹性，涨价会提高总收入；单位弹性时（|PED| = 1），价格变化不会改变总收入。
3. Income Elasticity of Demand (YED) and Cross‑Price Elasticity (XED) | 收入弹性与交叉弹性
YED indicates how demand responds to changes in real income. Normal goods have positive YED, luxury goods have YED > 1, and inferior goods have negative YED.
收入弹性表示需求如何对实际收入的变化作出反应。正常品的 YED 为正，奢侈品的 YED 大于 1，劣质品的 YED 为负。
YED = %ΔQd ÷ %ΔY
XED measures the effect of a change in the price of good B on the quantity demanded of good A. Complements yield negative XED, whereas substitutes yield positive XED.
交叉弹性衡量的是商品 B 的价格变化对商品 A 需求量的影响。互补品产生负的 XED，替代品产生正的 XED。
XED = %ΔQd of good A ÷ %ΔP of good B
4. Price Elasticity of Supply (PES) | 供给的价格弹性
PES captures the sensitivity of quantity supplied to price changes. A value greater than one indicates elastic supply; less than one indicates inelastic supply.
供给弹性衡量的是供给量对价格变化的敏感程度。数值大于 1 表示供给富有弹性，小于 1 表示供给缺乏弹性。
PES = %ΔQs ÷ %ΔP
The midpoint formula is also applied for arc‑elasticity calculations. The key determinants of PES include production time, spare capacity, and the ease with which factors can be reallocated.
中点公式同样可用于弧弹性计算。决定 PES 大小的关键因素包括生产周期、闲置产能以及生产要素是否容易被重新配置。
5. Market Structure: Concentration Ratios and the HHI | 市场结构：集中度比率与赫芬达尔指数
An n‑firm concentration ratio adds the market shares of the largest n firms. A high ratio (e.g. CR₃ > 70%) suggests an oligopolistic market structure.
n 企业集中度比率是将最大的 n 家企业的市场份额相加。高比率（例如 CR₃ > 70%）表明该市场为寡头垄断结构。
CRₙ = sum of market shares of top n firms (%)
The Herfindahl‑Hirschman Index (HHI) squares each firm’s market share (in percent) and then sums them. An HHI below 1,000 indicates a relatively unconcentrated market, while an HHI above 2,000 signals high concentration.
赫芬达尔‑赫希曼指数（HHI）先将每家企业的市场份额（以百分比计）平方，再求和。HHI 低于 1000 表示市场相对分散，高于 2000 则表示市场高度集中。
HHI = Σ (market share of each firm)²
6. Profit Maximisation and Shut‑Down Conditions | 利润最大化与停产条件
A firm maximises profit where marginal revenue equals marginal cost. This condition holds in all market structures, though the behaviour of MR differs.
任何市场结构中的企业都在边际收入等于边际成本时实现利润最大化，尽管 MR 的行为会因结构不同而存在差异。
Profit‑max condition: MR = MC
In perfect competition, P = MR = AR, so the profit‑maximising condition becomes P = MC. In monopoly, P > MR, leading to a higher price and lower output than perfect competition.
在完全竞争中，P = MR = AR，因此利润最大化条件变为 P = MC；在垄断中，P > MR，使得价格更高、产量更低。
A firm should continue operating in the short run if price covers average variable cost; otherwise it should shut down. In the long run, a firm exits the market if price falls below average total cost.
短期中，只要价格能够弥补平均可变成本，企业就应继续经营，否则应停产；长期中，若价格低于平均总成本，企业便会退出市场。
Short‑run shut‑down: P < AVC
Long‑run exit: P < ATC
7. Labour Market: Marginal Revenue Product | 劳动力市场：边际收益产品
Marginal revenue product of labour represents the extra revenue generated by hiring one more worker. It is computed by multiplying marginal physical product by marginal revenue.
劳动力的边际收益产品表示多雇佣一名工人所带来的额外收入，它等于边际实物产量乘以边际收入。
MRPL = MPP × MR
In a perfectly competitive product market, MR equals the product price, so MRPL = MPP × P. A profit‑maximising firm hires labour up to the point where MRPL equals the wage rate.
在完全竞争的产品市场中，MR 等于产品价格，故 MRPL = MPP × P。追求利润最大化的企业会把劳动力雇佣量确定在 MRPL 等于工资率的那一点上。
Optimal hiring: MRPL = Wage (MC of labour)
8. Macroeconomic Multipliers | 宏观乘数
The simple closed‑economy multiplier relates an initial change in autonomous spending to the final change in national income. It depends on the marginal propensity to consume and the marginal propensity to save.
简单的封闭经济乘数把自主性支出的初始变动与国民收入的最终变动联系起来，其大小取决于边际消费倾向和边际储蓄倾向。
k = 1 ÷ (1 − MPC) = 1 ÷ MPS
where MPS = 1 − MPC
In an open economy with taxation, leakages include savings, taxation and imports. The marginal rates of taxation and importation reduce the value of the multiplier.
在有税收的开放经济中，漏出项包括储蓄、税收和进口。边际税率和边际进口倾向会降低乘数的数值。
Open‑economy multiplier: k = 1 ÷ (MPS + MPT + MPM)
where MPT is the marginal propensity to tax and MPM is the marginal propensity to import
Government purchases and lump‑sum transfers have different multiplier effects. The balanced‑budget multiplier equals one: an equal increase in government spending and taxation raises GDP by the same amount.
政府采购与一次性转移支付的乘数效应不同。平衡预算乘数等于 1：等额增加政府支出与税收会使 GDP 增加同样数额。
9. Unemployment and Inflation Measures | 失业与通货膨胀指标
The unemployment rate is the percentage of the labour force that is actively seeking work but unable to find employment.
失业率是劳动力中积极寻找工作但无法就业的人所占的百分比。
Unemployment rate = (Number of unemployed ÷ Labour force) × 100%
Inflation is measured by the annual percentage change in a price index such as the Consumer Price Index (CPI). The CPI is constructed from a representative basket of goods and services.
通货膨胀通过价格指数的年度百分比变化来衡量，例如消费者价格指数（CPI）。CPI 由一篮子具有代表性的商品和服务构成。
Inflation rate = [(CPIₜ − CPIₜ₋₁) ÷ CPIₜ₋₁] × 100%
The Retail Price Index (RPI) includes housing costs such as mortgage interest payments, which often make RPI higher than CPI. Both indices can be used to deflate nominal data into real figures.
零售价格指数（RPI）包含抵押贷款利息支付等住房成本，这通常使 RPI 高于 CPI。两种指数都可用于将名义数据平减为实际数值。
Real value = (Nominal value ÷ Price index) × 100
10. Exchange Rates and the Marshall‑Lerner Condition | 汇率与马歇尔‑勒纳条件
The real exchange rate adjusts the nominal exchange rate for differences in price levels between two countries. A depreciation makes exports cheaper and imports dearer in domestic‑currency terms, while an appreciation does the opposite.
实际汇率根据两国价格水平的差异调整名义汇率。本币贬值使出口以外币计价更便宜、进口以本币计价更昂贵，升值则相反。
Real exchange rate = Nominal exchange rate × (Domestic price level ÷ Foreign price level)
The Marshall‑Lerner condition states that a currency depreciation will improve the trade balance only if the sum of the price elasticities of demand for exports and imports (in absolute values) exceeds one.
马歇尔‑勒纳条件指出，只有当进出口需求的价格弹性绝对值之和大于 1 时，本币贬值才会改善贸易收支。
│PED exports│ + │PED imports│ > 1
11. Economic Growth and Development Indicators | 经济增长与发展指标
Economic growth is measured by the annual percentage change in real Gross Domestic Product (GDP). Real GDP strips out the effects of inflation, allowing comparison over time.
经济增长以实际国内生产总值（GDP）的年度百分比变化来衡量。实际 GDP 剔除了通货膨胀的影响，因此可以进行跨期比较。
Growth rate = [(Real GDPₜ − Real GDPₜ₋₁) ÷ Real GDPₜ₋₁] × 100%
Purchasing Power Parity (PPP) exchange rates adjust GDP figures for differences in the cost of living, providing a more accurate comparison of living standards across countries.
购买力平价（PPP）汇率根据生活成本的差异调整 GDP 数据，从而能更准确地比较不同国家的生活水平。
The Human Development Index (HDI) combines life expectancy, education (mean and expected years of schooling) and gross national income per capita into a single indicator. It runs on a scale from 0 to 1 and offers a broader measure of development than GDP alone.
人类发展指数（HDI）将预期寿命、教育（平均和预期受教育年限）以及人均国民总收入合并为一个综合指标。其取值介于 0 到 1 之间，比单独使用 GDP 提供了更广泛的发展衡量标准。
HDI = (I health × I education × I income)^(1/3)
Each dimension index is calculated as (actual value − minimum) ÷ (maximum − minimum). This normalisation allows diverse indicators to be combined.
各维度的指数均通过（实际值 − 最小值）÷（最大值 − 最小值）计算得出，这种标准化处理使得不同的指标能够被综合成单一指数。
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