📚 AQA Year 12 Economics: Formula & Theorem Quick Reference | AQA 12年级经济：公式定理速查手册
This handbook brings together all the key formulas, equations, and theoretical rules you need to master for AQA Year 12 Economics. From the microeconomic calculation of elasticities to the macroeconomic multiplier, every entry is designed for quick recall and accurate application during revision and exams. Use this resource to reinforce your quantitative skills and deepen your understanding of economic relationships.
本手册汇集了 AQA 12 年级经济学所需掌握的所有核心公式、方程式与理论规则。从微观弹性的计算到宏观乘数分析，每一项内容都旨在帮助你快速记忆并在复习与考试中准确运用。借助本手册，你可以强化定量分析能力，更深入地理解经济变量之间的内在联系。
1. Price Elasticity of Demand (PED) | 需求价格弹性
The price elasticity of demand measures how responsive the quantity demanded of a good is to a change in its price. The basic formula uses percentage changes:
需求价格弹性衡量的是商品需求量对其自身价格变化的反应程度。基本公式使用百分比变动：
PED = %ΔQd / %ΔP
Where %ΔQd is the percentage change in quantity demanded and %ΔP is the percentage change in price. Because demand curves slope downwards, PED values are usually negative, but the sign is often ignored and the absolute value is used.
其中 %ΔQd 是需求量的百分比变化，%ΔP 是价格的百分比变化。由于需求曲线向下倾斜，PED 值通常为负，但实际运用时常忽略负号，取绝对值。
For accuracy over a range, the midpoint (arc) formula is recommended:
若需计算一段价格区间的弹性，推荐使用中点（弧）公式：
PED = (ΔQd / average Qd) / (ΔP / average P)
Elasticity values are classified as follows:
弹性值可分为以下几类：
| Value | Classification |
|---|---|
| |PED| > 1 | Elastic (responsive) |
| |PED| < 1 | Inelastic (unresponsive) |
| |PED| = 1 | Unit elastic |
| |PED| = 0 | Perfectly inelastic |
| |PED| = ∞ | Perfectly elastic |
ic, a price reduction raises total revenue; if demand is inelastic, a price increase raises total revenue. Total revenue is maximised where PED is unit elastic.
一个关键定理将 PED 与总收入（TR = P × Q）联系起来。若需求富有弹性，降价会增加总收入；若需求缺乏弹性，提价会增加总收入。当 PED 为单位弹性时，总收入达到最大。
2. Income Elasticity of Demand (YED) | 需求收入弹性
Income elasticity measures how quantity demanded responds to a change in consumers' income.
收入弹性衡量需求量对消费者收入变化的反应程度。
YED = %ΔQd / %ΔY
Where %ΔY is the percentage change in income. A positive YED indicates a normal good; a negative YED indicates an inferior good. Among normal goods, a YED greater than 1 defines a luxury good, while a YED between 0 and 1 defines a necessity.
其中 %ΔY 为收入的百分比变动。YED 为正表示正常品；YED 为负表示劣质品。在正常品中，YED 大于 1 为奢侈品，YED 介于 0 与 1 之间为必需品。
Firms use YED forecasts to plan output as the economy grows or contracts. For instance, producers of luxury cars are more vulnerable during a recession (high positive YED), while producers of basic foods are relatively stable (low positive YED).
企业利用 YED 预测来规划经济扩张或收缩时的产出。例如，豪华汽车生产商在经济衰退时更易受损（高正 YED），而基本食品生产商则相对稳定（低正 YED）。
3. Cross Elasticity of Demand (XED) | 需求交叉弹性
Cross elasticity measures the responsiveness of demand for one good (A) to a change in the price of another good (B).
交叉弹性衡量一种商品（A）的需求量对另一种商品（B）价格变动的反应程度。
XED = %ΔQdA / %ΔPB
A positive XED indicates that goods A and B are substitutes; a negative XED indicates complements. A value close to zero suggests the two goods are independent. The magnitude of XED tells you how strong the relationship is – a large positive XED suggests very close substitutes.
XED 为正表明 A 与 B 互为替代品；为负表明互为互补品。数值接近零则说明两者为独立品。XED 的大小揭示了关连的紧密程度——一个较大的正 XED 意味着两者的替代性很强。
These values help businesses anticipate the impact of rivals' pricing strategies and identify merger risks.
这些数值有助于企业预判竞争对手定价策略的影响，并识别并购风险。
4. Price Elasticity of Supply (PES) | 供给价格弹性
Price elasticity of supply measures how responsive quantity supplied is to a change in price.
供给价格弹性衡量供给量对价格变动的反应程度。
PES = %ΔQs / %ΔP
Unlike demand, PES is typically positive. The key determinants include the length of the production period, spare capacity, ease of storing inventory, and the availability of resources. Over longer time periods, supply becomes more elastic because firms can adjust all inputs.
与需求弹性不同，PES 通常为正。主要决定因素包括生产周期的长短、闲置产能、库存储存的难易程度以及资源的可获得性。时间越长，供给弹性越大，因为企业可以调整所有生产要素。
tic (PES = ∞). A PES of less than 1 is inelastic supply; greater than 1 is elastic supply.
弹性值范围从完全无弹性（PES = 0）到完全弹性（PES = ∞）。PES 小于 1 为缺乏弹性的供给，大于 1 为富有弹性的供给。
5. Market Equilibrium and Intervention | 市场均衡与政策干预
Market equilibrium occurs where quantity demanded equals quantity supplied: Qd = Qs. At this point there is no tendency for price to change. When governments impose an indirect tax or grant a subsidy, a wedge is created between the price consumers pay (Pc) and the price producers receive (Ps).
市场均衡出现在需求量等于供给量之处：Qd = Qs。此时价格没有变动的趋势。当政府征收间接税或给予补贴时，消费者支付的价格（Pc）与生产者收到的价格（Ps）之间会出现一个楔子。
For a tax of t per unit:
对于每单位税收 t：
t = Pc − Ps
The burden of a tax falls more heavily on the side of the market that is less elastic. The shares can be approximated as:
税收负担更多地落在市场中弹性较小的一方。分担比例可近似表示为：
Consumer burden = (PES / (PES + |PED|)) × t
Producer burden = (|PED| / (PES + |PED|)) × t
A subsidy shifts the supply curve vertically downwards and increases both consumer and producer surplus. The deadweight loss from a tax (or inefficient subsidy) is the triangle formed by the reduction in quantity, with area:
补贴会使供给曲线垂直下移，同时增加消费者剩余和生产者剩余。税收（或无效率补贴）造成的无谓损失是产量减少形成的三角形区域，面积为：
DWL = 0.5 × t × (Qe − Q1)
where Qe is the free‑market equilibrium quantity and Q1 is the quantity after intervention.
其中 Qe 为自由市场均衡数量，Q1 为干预后的数量。
6. Consumer and Producer Surplus | 消费者剩余与生产者剩余
Consumer surplus is the difference between what consumers are willing to pay and what they actually pay, summed across all units purchased. Producer surplus is the difference between the market price and the minimum price at which producers are willing to supply.
消费者剩余是消费者愿意支付的最高价格与实际支付价格之差的总和。生产者剩余是市场价格与生产者愿意供给的最低价格之差的总和。
With linear demand and supply curves, these surpluses are triangles:
在线性需求与供给曲线下，这些剩余表现为三角形区域：
CS = 0.5 × (Pmax − Pe) × Qe
PS = 0.5 × (Pe − Pmin) × Qe
t is allocatively efficient when marginal social benefit (MSB) equals marginal social cost (MSC). Any divergence from this equilibrium reduces total surplus, creating a deadweight loss.
社会总剩余 = CS + PS。当边际社会收益 (MSB) 等于边际社会成本 (MSC) 时，市场达到配置效率。任何偏离此均衡的情况都会减少总剩余，形成无谓损失。
7. Costs of Production | 生产成本
Firm cost structures are fundamental to supply decisions. Total cost (TC) combines fixed and variable costs:
企业的成本结构是供给决策的基础。总成本 (TC) 由固定成本与可变成本构成：
TC = TFC + TVC
Average and marginal cost measures are derived as:
平均成本与边际成本指标由以下公式得出：
AFC = TFC / Q AVC = TVC / Q
AC = TC / Q MC = ΔTC / ΔQ
A key theorem of cost curves: the marginal cost curve always intersects both the average variable cost and average total cost curves at their minimum points. When MC is below AC, AC falls; when MC is above AC, AC rises. The same relationship holds for AVC. The law of diminishing marginal returns ensures that eventually MC increases as more variable factors are added to fixed factors in the short run.
成本曲线的一个重要定理：边际成本曲线总是在平均可变成本曲线和平均总成本曲线的最低点与之相交。当 MC 低于 AC 时，AC 下降；当 MC 高于 AC 时，AC 上升。AVC 也有同样的规律。在短期，边际报酬递减规律使得增加可变要素时，边际成本最终会上升。
8. Revenue and Profit Maximisation | 收入与利润最大化
A firm's revenue concepts are tightly linked to the demand curve it faces. Total revenue (TR), average revenue (AR), and marginal revenue (MR) are defined as:
企业的收入概念与其面临的需求曲线密切相关。总收入（TR）、平均收入（AR）和边际收入（MR）的定义如下：
TR = P × Q AR = TR / Q = P MR = ΔTR / ΔQ
The profit‑ MC, increasing output adds more to revenue than to cost, raising profit. If MR < MC, reducing output improves profit.
利润最大化的通用规则是：在 MR = MC 的产量上进行生产。若 MR > MC，增加产出带来的收入大于成本，利润上升；若 MR < MC，减少产出可改善利润。
= AC. Supernormal profit exists when AR > AC. In perfect competition, the firm is a price‑taker, so P = AR = MR, and the profit‑maximising condition becomes P = MC. For a monopolist or any firm with a downward‑sloping demand curve, MR always lies below AR, so price exceeds marginal revenue.
正常利润是指总收益等于总成本（包括机会成本），即 AR = AC。超常利润则出现在 AR > AC 时。在完全竞争市场，企业是价格接受者，因此 P = AR = MR，利润最大化条件转化为 P = MC。对于垄断者或任何面临向下倾斜需求曲线的企业，MR 始终低于 AR，因此价格高于边际收入。
9. Labour Market & Marginal Revenue Product | 劳动力市场与边际收入产品
The demand for labour is a derived demand. A firm's optimal employment level is found where the marginal cost of hiring an extra worker equals the extra revenue that worker generates. The marginal revenue product of labour (MRP) is the key formula:
劳动力需求是一种派生需求。企业的最优雇用量出现在雇佣额外一名工人的边际成本等于该工人带来的额外收入时。劳动的边际收入产品（MRP）是核心公式：
MRP = MPP × MR
arket, MR equals price, so MRP = MPP × P (also called the value of the marginal product, VMP). The firm will hire labour up to the point where MRP equals the wage rate (W). The demand curve for labour is therefore the downward‑sloping MRP curve, reflecting diminishing marginal returns to labour.
MPP（边际实物产品）是多雇佣一单位劳动所带来的额外产出。若企业在完全竞争的产品市场上销售，MR 等于价格，因此 MRP = MPP × P（亦称边际产品价值，VMP）。企业雇佣劳动力的数量将达到 MRP 等于工资率（W）的水平。因此，劳动的需求曲线即为向下倾斜的 MRP 曲线，反映了劳动的边际收益递减。
10. Macroeconomic Indicators and the Multiplier | 宏观经济指标与乘数
AQA Year 12 macroeconomics introduces essential aggregate measures. Gross domestic product (GDP) can be calculated via the expenditure approach:
AQA 12 年级宏观经济学引入了基本的加总指标。国内生产总值（GDP）可通过支出法计算：
GDP = C + I + G + (X − M)
To strip out the effect of inflation, convert nominal GDP to real GDP:
为消除通胀影响，需将名义 GDP 转换为实际 GDP：
Real GDP = (Nominal GDP / GDP deflator) × 100
Key labour market indicators include:
关键的劳动力市场指标包括：
Unemployment rate = (Unemployed / Labour force) × 100
Labour force participation rate = (Labour force / Working‑age population) × 100
Inflation is measured using the consumer price index (CPI):
通胀通过消费价格指数（CPI）来衡量：
CPI = (Cost of basket in current year / Cost of basket in base year) × 100
Inflation rate = [(CPIt − CPIt−1) / CPIt−1] ×
Published by TutorHao | Year 12 Economics Revision Series | aleveler.com 更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图