📚 Formula & Theorem Quick Reference Handbook | 公式定理速查手册
This handbook provides Year 10 CIE Economics students with a concise collection of the most important formulas, theorems and definitions. Use it as a daily revision tool to reinforce your understanding of microeconomics and macroeconomics. All expressions are presented using standard notation, with worked examples where helpful.
本书为 Year 10 CIE 经济学学子整理出最重要的公式、定理与定义，是一份便于查阅的速查手册。每天翻看几页，可以巩固你对微观与宏观经济的理解。所有表达式都使用标准符号，并附有用例以助记忆。
1. Core Concepts & Opportunity Cost | 核心概念与机会成本
Opportunity cost is the value of the next best alternative that must be sacrificed when a choice is made. It is the central concept that links scarcity and decision-making.
机会成本是指做出某种选择时所必须放弃的次优选项的价值。它是连接稀缺性与决策的核心概念。
On a Production Possibility Frontier (PPF), the opportunity cost of producing an extra unit of good X is the number of units of good Y that must be given up. When the PPF is a straight line, the opportunity cost is constant; when it is bowed outward, the opportunity cost increases.
在生产可能性边界（PPF）上，多生产一单位 X 产品的机会成本就是所必须放弃的 Y 产品的数量。如果 PPF 是一条直线，机会成本不变；如果 PPF 向外弯曲，机会成本递增。
Opportunity Cost = Units of Good Y Sacrificed / Units of Good X Gained
机会成本 = 放弃的 Y 产品数量 ÷ 增加获得的 X 产品数量
2. Demand, Supply & Market Equilibrium | 需求、供给与市场均衡
The law of demand states that, ceteris paribus, as the price of a good rises, the quantity demanded falls. The law of supply states that as price rises, the quantity supplied increases. Market equilibrium occurs where the demand and supply curves intersect.
需求法则指出，其他条件不变时，商品价格上升则需求量下降。供给法则指出，价格上升则供给量增加。市场均衡发生在需求曲线与供给曲线的交点。
where a, b, c and d are positive constants. Equilibrium price is found by setting Qd = Qs.
简单的线性需求函数可写为 Qd = a − bP，线性供给函数为 Qs = c + dP，其中 a、b、c、d 均为正数。令 Qd = Qs 即可求得均衡价格。
Equilibrium Condition: Qd = Qs
均衡条件：需求量 = 供给量
P* = (a − c) / (b + d)
均衡价格 P* = (a − c) / (b + d)
3. Price Elasticity of Demand (PED) | 需求价格弹性
PED measures the responsiveness of quantity demanded to a change in price. It is always negative, reflecting the law of demand, but we often use the absolute value to describe its magnitude.
需求价格弹性（PED）衡量需求量对价格变动的反应程度。由于需求法则，PED 恒为负值，但在描述其大小时我们常取绝对值。
PED = % Change in Quantity Demanded / % Change in Price
PED = 需求量的百分比变化 ÷ 价格的百分比变化
The midpoint formula gives a consistent measure regardless of the direction of the change.
中点公式可以避免因变动方向不同而得到不同的弹性值。
PED = [(Q₂ − Q₁) / ((Q₁ + Q₂)/2)] / [(P₂ − P₁) / ((P₁ + P₂)/2)]
PED = [(Q₂ − Q₁) ÷ 平均需求量] ÷ [(P₂ − P₁) ÷ 平均价格]
| PED Value (absolute) | Term | Meaning |
|---|---|---|
| |PED| > 1 | Elastic | %ΔQd > %ΔP; demand is responsive |
| |PED| = 1 | Unit elastic | %ΔQd = %ΔP |
| |PED| < 1 | Inelastic | %ΔQd < %ΔP; demand is unresponsive |
| |PED| = 0 | Perfectly inelastic | Qd does not change with price |
| |PED| → ∞ | Perfectly elastic | Any price rise reduces Qd to zero |
| PED 绝对值 | 术语 | 含义 |
|---|---|---|
| > 1 | 富有弹性 | 需求量变动幅度 > 价格变动幅度 |
| = 1 | 单位弹性 | 需求量与价格等比例变动 |
| < 1 | 缺乏弹性 | 需求量变动幅度 < 价格变动幅度 |
| = 0 | 完全无弹性 | 需求量不随价格变化 |
| →∞ | 完全有弹性 | 价格任何微小上升都会使需求量降为零 |
4. Other Elasticities: YED, XED & PES | 其他弹性：收入弹性、交叉弹性与供给弹性
Income elasticity of demand (YED) measures how quantity demanded responds to a change in consumers' income. Cross elasticity of demand (XED) measures the response of demand for one good to a change in the price of another. Price elasticity of supply (PES) measures the response of quantity supplied to a price change.
需求收入弹性（YED）衡量需求量对消费者收入变动的反应程度。需求交叉弹性（XED）衡量一种商品的需求量对另一种商品价格变动的反应。供给价格弹性（PES）衡量供给量对价格变动的反应程度。
YED = %Δ Quantity Demanded / %Δ Income
YED = 需求量的百分比变化 ÷ 收入的百分比变化
XED = %Δ Qd of Good A / %Δ Price of Good B
XED = A 商品需求量的百分比变化 ÷ B 商品价格的百分比变化
PES = %Δ Quantity Supplied / %Δ Price
PES = 供给量的百分比变化 ÷ 价格的百分比变化
Key interpretations: YED > 0 for normal goods, YED < 0 for inferior goods. XED > 0 for substitutes, XED < 0 for complements. PES is positive; supply is elastic when PES > 1 and inelastic when PES < 1.
关键解读：正常品的 YED > 0，低档品 YED < 0。替代品的 XED > 0，互补品的 XED < 0。供给价格弹性恒为正值：PES > 1 表示供给富有弹性，PES < 1 表示供给缺乏弹性。
5. Costs of Production | 生产成本
In the short run, a firm faces both fixed and variable costs. Understanding how these costs change with output is essential for pricing and output decisions.
在短期，企业面临固定成本与可变成本。理解这些成本如何随产量变化对定价和产量决策至关重要。
Total Cost (TC) = Total Fixed Cost (TFC) + Total Variable Cost (TVC)
总成本 = 总固定成本 + 总可变成本
Average Cost (AC) = TC / Quantity (Q)
平均成本 = 总成本 ÷ 产量 (Q)
Average Fixed Cost (AFC) = TFC / Q
平均固定成本 = 总固定成本 ÷ Q
Average Variable Cost (AVC) = TVC / Q
平均可变成本 = 总可变成本 ÷ Q
Marginal Cost (MC) = ΔTC / ΔQ
边际成本 = 总成本的变化量 ÷ 产量的变化量
(due to increasing returns) and then rises (due to diminishing returns). The AC curve is U‑shaped, and it is at its minimum when MC = AC.
边际成本曲线通常先降后升（受边际报酬递减影响）。平均成本曲线呈 U 形，当边际成本等于平均成本时平均成本最低。
6. Revenues & Profits | 收益与利润
Revenue is the income a firm receives from selling its output. Profit is the difference between total revenue and total cost, and it guides business decisions.
收益是企业出售产品所获得的收入。利润为总收益与总成本之差，指导着企业的决策。
Total Revenue (TR) = Price (P) × Quantity Sold (Q)
总收益 = 价格 × 销售量
Average Revenue (AR) = TR / Q = P
平均收益 = 总收益 ÷ Q = 价格
Marginal Revenue (MR) = ΔTR / ΔQ
边际收益 = 总收益的变化量 ÷ 产量的变化量
Profit (π) = TR − TC
利润 = 总收益 − 总成本
tion condition in the short run is to continue operating if P ≥ AVC; shut down if P < AVC.
当总收益等于总成本时，企业获得正常利润（盈亏平衡）。若总收益超过总成本，存在超额利润；反之则发生亏损。短期内的损失最小化原则为：只要价格不低于平均可变成本就继续生产，否则就关闭停产。
7. Market Structures & Profit Maximisation | 市场结构与利润最大化
All profit‑maximising firms, regardless of market structure, choose the output level where marginal cost equals marginal revenue. This is the golden rule of microeconomics.
无论市场结构如何，所有追求利润最大化的企业都会在边际成本等于边际收益的产量上生产。这是微观经济学的黄金法则。
Profit-Maximising Condition: MR = MC
利润最大化条件：边际收益 = 边际成本
In perfect competition, the firm is a price‑ acing the firm is perfectly elastic. In monopoly, the firm faces the market demand curve, so MR lies below AR and the firm can earn long‑run supernormal profits.
在完全竞争市场，企业是价格接受者，因此平均收益 = 边际收益 = 价格。企业面临的需求曲线完全弹性。在垄断市场，企业面对的是整个市场的需求曲线，边际收益低于平均收益，企业可在长期获得超额利润。
| Market Structure | Profit Maximisation Rule | Long-Run Outcome |
|---|---|---|
| Perfect Competition | P = MR = MC | Normal profit only |
| Monopoly | MR = MC (price > MC) | Supernormal profit possible |
| 市场结构 | 利润最大化规则 | 长期结果 |
|---|---|---|
| 完全竞争 | P = MR = MC | 仅获得正常利润 |
| 垄断 | MR = MC（价格>边际成本） | 可获得超额利润 |
8. Macroeconomic Indicators | 宏观经济指标
Macroeconomic indicators help economists evaluate the health of an economy. The most commonly examined are GDP, inflation, unemployment and their related formulas.
宏观经济指标帮助经济学家评估一国经济的健康状况。最常考察的是 GDP、通货膨胀和失业率及其相关公式。
GDP (Expenditure Approach) = C + I + G + (X − M)
支出法 GDP = 消费 + 投资 + 政府购买 + (出口 − 进口)
GDP per Capita = Nominal GDP / Total Population
人均 GDP = 名义 GDP ÷ 总人口
Inflation Rate = (CPI Current Year − CPI Previous Year) / CPI Previous Year × 100%
通货膨胀率 = (今年消费物价指数 − 去年消费物价指数) ÷ 去年消费物价指数 × 100%
Unemployment Rate = (Number of Unemployed / Labour Force) × 100%
失业率 = (失业人数 ÷ 劳动力总数) × 100%
Note that GDP measured at current prices is nominal GDP, while real GDP is adjusted for inflation to reflect the true volume of output. These indicators form the basis of most government policy targets.
注意，按当期价格计算的 GDP 是名义 GDP，而实际 GDP 经过通胀调整，反映真实的产出数量。这些指标是大多数政府政策目标的基础。
9. Aggregate Demand & the Multiplier | 总需求与乘数
Aggregate demand (AD) is the total demand for goods and services in an economy at a given price level. The multiplier effect shows how an initial change in spending can lead to a larger total change in national income.
总需求（AD）是指在某一价格水平下，经济体对所有商品与服务的需求总量。乘数效应表明，初始支出的变化会引发国民收入的更大总量变化。
AD = C + I + G + (X − M)
总需求 = 消费 + 投资 + 政府购买 + 净出口
ume (MPC) and the marginal propensity to save (MPS). Their sum is always 1: MPC + MPS = 1.
乘数 (k) 取决于边际消费倾向 (MPC) 和边际储蓄倾向 (MPS)，二者之和恒为 1：MPC + MPS = 1。
Multiplier (k) = 1 / (1 − MPC) = 1 / MPS
乘数
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