📚 Formula & Theorems Quick Reference Handbook | 公式定理速查手册
This handbook brings together the essential formulas, definitions and theorems you need for the Year 10 Eduqas GCSE Economics course. Keep it close for quick revision – it covers the core microeconomic and macroeconomic tools that will help you explain how markets and economies work, and ace your assessments.
这本手册汇集了 Year 10 Eduqas GCSE 经济学课程中必备的公式、定义和定理。把它放在手边以便快速复习——它涵盖了有助于你解释市场和经济运行方式的核心微观与宏观经济工具，助你在测试中取得优异成绩。
1. The Economic Problem and Opportunity Cost | 经济问题与机会成本
The fundamental economic problem is scarcity: finite resources but infinite human wants force all economic agents to make choices. Every choice involves an opportunity cost.
基本经济问题是稀缺性：有限的资源与无限的人类欲望迫使所有经济主体做出选择。每一次选择都涉及机会成本。
Opportunity cost is defined as the value of the next best alternative forgone when a decision is made. It highlights the trade-off inherent in all resource allocations.
机会成本定义为做出决策时所放弃的次优选择的价值。它凸显了所有资源配置中固有的权衡取舍。
Theorem of rational choice: rational consumers and firms weigh marginal benefits against marginal costs to maximise utility or profit.
理性选择定理：理性的消费者和厂商会比较边际收益与边际成本，以最大化效用或利润。
Understanding opportunity cost is the bedrock of economic thinking – every time you say ‘yes’ to one option, you say ‘no’ to another.
理解机会成本是经济学思维的基石——每当你对一个选项说“是”时，你同时在对另一个选项说“否”。
2. Law of Demand and the Demand Curve | 需求定律与需求曲线
The law of demand states that, ceteris paribus, as the price of a good rises, the quantity demanded falls, and vice versa. This inverse relationship gives the demand curve its downward slope.
需求定律指出，在其他条件不变的情况下，商品价格上升则需求量下降，反之亦然。这种反向关系使需求曲线向下倾斜。
A simple linear demand function can be written as Qd = a – bP, where ‘a’ represents the quantity demanded when price is zero (the intercept), and ‘b’ measures the responsiveness of quantity demanded to a change in price (the gradient).
简单的线性需求函数可表示为 Qd = a – bP，其中“a”代表价格为零时的需求量（截距），“b”衡量需求量对价格变动的反应程度（斜率）。
A movement along the demand curve is caused solely by a change in the good’s own price. A shift of the whole curve is caused by changes in non-price determinants, such as income, tastes, prices of related goods (substitutes and complements), population and expectations.
沿需求曲线的移动仅由该商品自身价格的变化引起。整条曲线的平移则由非价格决定因素的变化引起，例如收入、偏好、相关商品（替代品和互补品）的价格、人口和预期。
Theorem of diminishing marginal utility: as a consumer consumes more units of a good, the additional satisfaction from each extra unit tends to decline, helping explain why demand curves slope downwards.
边际效用递减定理：随着消费者消费更多单位的商品，每额外一单位带来的额外满足感趋于下降，这有助于解释需求曲线向下倾斜的原因。
3. Law of Supply and the Supply Curve | 供给定律与供给曲线
The law of supply states that, ceteris paribus, as the price of a good rises, the quantity supplied rises, creating an upward-sloping supply curve. Producers are incentivised by higher prices to supply more because profit per unit increases.
供给定律指出，在其他条件不变的情况下，商品价格上升则供给量上升，形成一条向上倾斜的供给曲线。更高的价格激励生产者增加供应，因为单位利润上升。
A basic supply function is Qs = c + dP, where ‘c’ is the minimum price at which firms are willing to supply (intercept), and ‘d’ captures the responsiveness of quantity supplied to price changes.
基本的供给函数为 Qs = c + dP，其中“c”是企业愿意供给的最低价格（截距），“d”反映了供给量对价格变动的反应程度。
Shifts of the supply curve occur when conditions of production change: costs of inputs, technology, indirect taxes, subsidies, number of sellers, weather (for agricultural goods) and expectations about future prices.
当生产条件发生变化时，供给曲线发生平移：投入成本、技术、间接税、补贴、卖者数量、天气（对农产品而言）以及对未来价格的预期。
4. Market Equilibrium and Disequilibrium | 市场均衡与非均衡
Market equilibrium occurs at the price where quantity demanded equals quantity supplied: Qd = Qs. At this point, there is no tendency for price to change, and the market clears.
市场均衡出现在需求量等于供给量的价格水平：Qd = Qs。在此点上，价格没有变动的趋势，市场出清。
When the market price is above equilibrium, quantity supplied exceeds quantity demanded, creating a surplus (excess supply). This puts downward pressure on price as firms lower prices to clear unsold stock.
当市场价格高于均衡水平时，供给量超过需求量，产生过剩（超额供给）。企业为出清库存而降价，给价格带来下行压力。
When price is below equilibrium, quantity demanded exceeds quantity supplied, creating a shortage (excess demand). Consumers bid up the price, pulling it upwards until equilibrium is restored.
当价格低于均衡水平时，需求量超过供给量，产生短缺（超额需求）。消费者抬价竞购，推动价格上升直至恢复均衡。
Theorem of the invisible hand: in a free market, the self-interested actions of buyers and sellers guide resources towards their most valued uses through the price mechanism, achieving allocative efficiency.
“无形之手”定理：在自由市场中，买卖双方自利的行为通过价格机制引导资源流向其最有价值的用途，从而实现配置效率。
5. 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.
需求价格弹性衡量需求量对价格变动的反应程度。
PED = %Δ Qd / %Δ P
When using data between two points, the midpoint formula gives a more accurate measure by avoiding the problem of different starting points.
当使用两点间数据时，中点公式能避免不同起点带来的问题，从而给出更准确的度量。
PED = [(Q₂ – Q₁) / ((Q₁ + Q₂) / 2)] / [(P₂ – P₁) / ((P₁ + P₂) / 2)]
Interpret the absolute value: |PED| > 1 is price elastic (quantity is very responsive), |PED| < 1 is price inelastic (quantity is not very responsive), and |PED| = 1 is unit elastic. A straight vertical demand curve is perfectly inelastic (|PED| = 0), and a horizontal one is perfectly elastic (|PED| = ∞).
根据绝对值解读：|PED| > 1 为富有弹性（需求量非常敏感），|PED| < 1 为缺乏弹性（需求量不太敏感），|PED| = 1 为单位弹性。垂直的需求曲线完全无弹性（|PED| = 0），水平的则为完全弹性（|PED| = ∞）。
The relationship between PED and total revenue: if demand is elastic, a price cut raises total revenue; if inelastic, a price cut lowers total revenue. This theorem guides firms’ pricing strategies.
PED 与总收入的关系：若需求富有弹性，降价增加总收入；若缺乏弹性，降价减少总收入。这一定理指导着企业的定价策略。
6. Other Elasticities: PES, YED, XED | 其他弹性：供给弹性、收入弹性、交叉弹性
Price elasticity of supply (PES) measures how quantity supplied responds to a price change.
供给价格弹性（PES）衡量供给量对价格变动的反应程度。
PES = %Δ Qs / %Δ P
PES is usually positive. A value greater than 1 indicates elastic supply; less than 1 indicates inelastic supply. Supply tends to be more elastic when firms have spare capacity, high stock levels and can easily switch production.
PES 通常为正。数值大于1表示富有弹性；小于1表示缺乏弹性。当企业有闲置产能、高库存水平并能轻易转换生产时，供给往往更富有弹性。
Income elasticity of demand (YED) measures the responsiveness of demand to a change in consumer income.
需求收入弹性（YED）衡量需求对消费者收入变动的反应程度。
YED = %Δ Qd / %Δ Income
Normal goods have a positive YED (YED > 0); luxury goods tend to have YED > 1. Inferior goods have a negative YED (YED < 0), as demand falls when income rises.
正常品的 YED 为正（YED > 0）；奢侈品通常的 YED > 1。低档品的 YED 为负（YED < 0），因为收入增加时需求下降。
Cross elasticity of demand (XED) measures how the demand for one good responds to a change in the price of another good.
需求交叉弹性（XED）衡量一种商品的需求对另一种商品价格变动的反应程度。
XED = %Δ Qd of good A / %Δ P of good B
Substitutes have a positive XED (e.g. tea and coffee). Complements have a negative XED (e.g. cars and petrol). The larger the absolute value, the stronger the relationship.
替代品的 XED 为正（如茶和咖啡）；互补品的 XED 为负（如汽车和汽油）。绝对值越大，关系越强。
7. Costs, Revenue and Profit | 成本、收入与利润
Firms use cost and revenue formulas to determine their profit-maximising output. Understanding these is essential for analysing producer behaviour.
厂商运用成本和收入公式来确定利润最大化的产量。理解这些概念对分析生产者行为至关重要。
Key cost formulas are summarised below:
关键成本公式总结如下：
| Formula in English | 中文公式 | Description |
|---|---|---|
| TC = TFC + TVC | 总成本 = 总固定成本 + 总可变成本 | Total cost is the sum of all costs |
| ATC = TC / Q | 平均总成本 = 总成本 / 产量 | Cost per unit of output |
| AFC = TFC / Q | 平均固定成本 = 总固定成本 / 产量 | Spreads fixed cost over output |
| AVC = TVC / Q | 平均可变成本 = 总可变成本 / 产量 | Variable cost per unit |
| MC = ΔTC / ΔQ | 边际成本 = 总成本变化量 / 产量变化量 | Cost of producing one extra unit |
Revenue and profit:
收入与利润：
Total Revenue (TR) = Price × Quantity (P × Q)
总收入 (TR) = 价格 × 数量 (P × Q)
Average Revenue (AR) = TR / Q = P — the demand curve is also the AR curve.
平均收入 (AR) = 总收入 / 数量 = P——需求曲线同时也是平均收入曲线。
Profit = TR – TC. Supernormal profit occurs when TR > TC; normal profit is when TR = TC (firm covers all opportunity costs).
利润 = 总收入 – 总成本。超额利润指当总收入大于总成本时；正常利润是当总收入等于总成本时（企业刚好覆盖所有机会成本）。
The profit-maximising condition under marginal analysis: produce where MC = MR, provided MC cuts MR from below.
边际分析下的利润最大化条件：在 边际成本 = 边际收入 处生产，前提是边际成本从下方与边际收入相交。
8. Market Failures and Externalities | 市场失灵与外部性
Market failure occurs when the free market, left to itself, fails to allocate resources efficiently. One main cause is externalities – costs or benefits that affect third parties not directly involved in the transaction.
当自由市场放任自流而无法有效配置资源时，便出现了市场失灵。一个主要原因是外部性——即影响到未直接参与交易的第三方的成本或收益。
A negative externality (e.g. pollution from a factory) means the social cost exceeds the private cost. The market overproduces because producers only consider their own costs, ignoring the external cost to society.
负外部性（如工厂污染）意味着社会成本大于私人成本。市场会过度生产，因为生产者只考虑自身成本，而忽略了给社会带来的外部成本。
A positive externality (e.g. education, vaccination) means the social benefit exceeds the private benefit. The market underproduces because the full value to society is not captured by private decision-makers.
正外部性（如教育、接种疫苗）意味着社会收益大于私人收益。市场会生产不足，因为私人决策者未能获取对社会的全部价值。
Theorem of the welfare loss: externalities create a deadweight loss – a loss of social welfare that no one gains from – because the equilibrium output is not at the socially optimal level where marginal social benefit equals marginal social cost.
福利损失定理：外部性造成了无谓损失——一种无人从中受益的社会福利损失——因为均衡产量并非处于边际社会收益等于边际社会成本的社会最优水平。
Government intervention, such as taxation, subsidies, regulation and tradable permits, can help correct these market failures.
政府干预措施，如税收、补贴、监管和可交易许可证，有助于纠正这些市场失灵。
9. Macroeconomic Indicators: GDP, Unemployment and Inflation | 宏观经济指标：GDP、失业与通货膨胀
A country’s economic performance is measured using key indicators. Gross Domestic Product (GDP) measures the total value of output produced within an economy in a given period. The expenditure approach is:
一个国家的经济表现使用关键指标来衡量。国内生产总值（GDP）衡量一定时期内一国境内生产的产出总价值。支出法公式为：
GDP = C + I + G + (X − M)
where C = consumption, I = investment, G = government spending, X = exports, M = imports.
其中，C = 消费，I = 投资，G = 政府支出，X = 出口，M = 进口。
GDP per capita = GDP / population, used to compare living standards. Economic growth rate is calculated as:
人均 GDP = GDP / 人口，用于比较生活水平。经济增长率计算公式为：
Growth Rate = [(GDP₁ − GDP₀) / GDP₀] × 100
where GDP₁ is the current year and GDP₀ is the base year.
其中，GDP₁ 为当年值，GDP₀ 为基年值。
The unemployment rate measures the percentage of the labour force that is actively seeking work but cannot find a job.
失业率衡量的是正在积极寻找工作但无法就业的劳动力所占百分比。
Unemployment Rate = (Number of Unemployed / Labour Force) × 100
The labour force includes all those in work plus the unemployed who are actively seeking work.
劳动力包括所有有工作的人加上正在积极寻找工作的失业者。
Inflation is a sustained increase in the general price level. It is commonly measured using the Consumer Price Index (CPI). The inflation rate is:
通货膨胀是指一般物价水平的持续上升。通常使用消费者价格指数（CPI）来衡量。通货膨胀率为：
Inflation Rate = [(CPI₁ − CPI₀) / CPI₀] × 100%
where CPI₁ is the current-period index and CPI₀ is the base-period index.
其中，CPI₁ 为现期指数，CPI₀ 为基期指数。
10. Multiplier Effect and Fiscal Policy | 乘数效应与财政政策
The multiplier effect explains how an initial injection into the circular flow of income can lead to a larger final increase in national income. The simple multiplier (k) depends on the marginal propensity to withdraw (MPW) or the marginal propensity to consume (MPC).
乘数效应解释了为何对收入循环流的一次初始注入能导致国民收入出现更大幅度的最终增长。简单乘数（k）取决于边际漏出倾向（MPW）或边际消费倾向（MPC）。
Multiplier (k) = 1 / (1 − MPC) = 1 / MPW
where MPW = MPS + MPT + MPM (marginal propensities to save, tax and import).
其中，MPW = 边际储蓄倾向(MPS) + 边际税收倾向(MPT) + 边际进口倾向(MPM)。
A higher MPC (and lower withdrawals) produces a larger multiplier. If the government increases spending by $10 billion and the multiplier is 1.5, national income rises by $15 billion.
MPC 越高（即漏出越少），乘数越大。如果政府增加支出 100 亿美元，乘数为 1.5，国民收入将增加 150 亿美元。
Fiscal policy involves changes in government spending and taxation to influence the level of aggregate demand. The multiplier is a key concept behind fiscal stimulus: during a recession, a government may cut taxes or increase spending, relying on the multiplier to amplify the impact on GDP.
财政政策涉及改变政府支出和税收以影响总需求水平。乘数是财政刺激政策背后的关键概念：在经济衰退期间，政府可能减税或增加支出，依靠乘数效应放大对 GDP 的影响。
The reverse effect also works:
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