📚 Year 10 Edexcel Economics: Formula & Theorem Quick Reference | Year 10 Edexcel 经济：公式定理速查手册
This handbook compiles all essential formulas and theorems for Year 10 Edexcel Economics. Mastering these quantitative tools is crucial for analysing economic behaviour, market outcomes and macroeconomic performance. Use this guide to revise key equations, from elasticity calculations to profit-maximisation rules, and to make sure you can apply them confidently in exam-style scenarios.
本手册汇集了 Year 10 Edexcel 经济学科的核心公式与定理。掌握这些量化工具，对于分析经济行为、市场结果以及宏观经济表现至关重要。运用本指南复习从弹性计算到利润最大化法则的关键方程，确保你能自信地将其应用于考试风格的题目中。
1. Fundamental Concepts: Scarcity, Choice & Opportunity Cost | 基本概念：稀缺性、选择与机会成本
The economic problem arises because resources are limited, but human wants are infinite. Scarcity forces individuals, firms and governments to make choices, and every choice carries an opportunity cost - the value of the next best alternative forgone. The four factors of production are land, labour, capital and enterprise, and each of them earns a corresponding reward: rent, wages, interest and profit.
经济问题的根源在于资源有限而人类欲望无限。稀缺性迫使个人、企业和政府作出选择，而每一次选择都伴随着机会成本——即所放弃的次优选择的价值。四种生产要素是土地、劳动、资本和企业家才能，它们各自对应的报酬是地租、工资、利息和利润。
Opportunity cost is therefore best written as a simple ratio comparing what is sacrificed with what is gained.
因此，机会成本最适合写成一个简单的比率，用来比较被放弃之物与所得之物。
Opportunity cost = value of next best alternative forgone ÷ value of chosen option
The same idea is expressed graphically as the slope of the Production Possibility Frontier (PPF). A straight-line PPF implies constant opportunity cost, while a concave PPF (bowed outward from the origin) represents increasing opportunity cost. Points inside the frontier show productive inefficiency; points on the frontier show full and efficient use of resources; points beyond the frontier are currently unattainable.
同样的思想在生产可能性边界（PPF）上表现为斜率。直线型 PPF 意味着机会成本不变；而向外弯曲（凹向原点）的 PPF 则代表机会成本递增。边界内部的点表示生产效率低下；边界上的点表示资源已被充分且有效率地使用；边界以外的点在当前无法实现。
- Free goods have no opportunity cost (for example, air), while economic goods always do. | 自由物品没有机会成本（例如空气），而经济物品始终存在机会成本。
- Positive statements can be tested against evidence; normative statements contain value judgements. | 实证陈述可以用证据检验；规范陈述包含价值判断。
2. Production Possibility Frontier: Slope, Shape and Growth | 生产可能性边界：斜率、形状与增长
The PPF shows the maximum combinations of two goods an economy can produce using all its resources efficiently. Moving along the frontier, producing one more unit of Good X means giving up some units of Good Y, and that sacrifice is the opportunity cost of X. When a question asks for the opportunity cost of one unit, divide the change in the sacrificed good by the change in the gained good.
PPF 表示一个经济体在充分利用全部资源且有效率的情况下，所能生产的两种商品的最大组合。沿着边界移动，多生产一单位 X 就意味着放弃若干单位 Y，这个放弃量就是 X 的机会成本。当题目要求某一单位的机会成本时，用被放弃商品的变化量除以所获商品的变化量即可。
Opportunity cost of 1 unit of X = ΔY ÷ ΔX
A straight-line PPF is produced when the two goods use identical resources in identical proportions - the classic example being two goods that require the same labour skill. A concave (bowed) PPF appears when resources are not perfectly transferable between the two goods, so specialisation becomes progressively more costly and opportunity cost rises.
当两种商品以相同比例使用完全相同的资源时，PPF 为直线——经典例子是两种商品需要相同技能的劳动。当资源无法在两种商品之间完美转移时，PPF 呈凹形（向外弯曲），此时专业化生产的代价越来越大，机会成本随之递增。
Economic growth is shown by an outward shift of the PPF and is caused by an increase in the quantity or quality of factors of production, or by technological improvement. A movement from a point inside the frontier to a point on it represents a reduction in inefficiency (for example, falling unemployment) rather than growth.
经济增长表现为 PPF 向外移动，其成因是生产要素数量或质量的提高，或者技术进步。从边界内部一点移动到边界上一点，表示低效率的减少（例如失业率下降），而不是经济增长。
- Outward shift of the whole frontier = long-run growth in productive capacity. | 整条边界向外移动 = 生产能力的长期增长。
- Movement towards the frontier = better use of existing capacity. | 向边界靠近 = 对现有产能的更充分利用。
3. Demand, Supply and Market Equilibrium | 需求、供给与市场均衡
The law of demand states that, other things being equal (ceteris paribus), as the price of a good falls, the quantity demanded rises. The law of supply states that as as the price rises, the quantity supplied rises. Market equilibrium occurs where quantity demanded equals quantity supplied, so there is no tendency for price to change.
需求定律指出，在其他条件不变（ceteris paribus）的情况下，商品价格下降时需求量增加。供给定律指出，价格上升时供给量增加。市场均衡发生在需求量等于供给量之时，此时价格没有变动的趋势。
Equilibrium condition: Qd(P) = Qs(P)
Excess demand (a shortage) pushes prices up towards equilibrium; excess supply (a surplus) pushes prices down. It is essential to distinguish a movement along a curve (caused only by a price change) from a shift of the curve (caused by a change in a non-price determinant such as income, tastes, technology or the price of a related good).
超额需求（短缺）会把价格推高至均衡水平；超额供给（过剩）会把价格压低。必须区分沿曲线的移动（仅由价格变动引起）与曲线的整体移动（由非价格决定因素引起，如收入、偏好、技术或相关商品价格）。
| Curve | Key non-price determinants | 中文提示 |
| Demand (D) | Income, tastes, price of substitutes and complements, population, expectations | 收入、偏好、替代品与互补品价格、人口、预期 |
| Supply (S) | Costs of production, technology, taxes and subsidies, number of firms, weather | 生产成本、技术、税收与补贴、企业数量、天气 |
= 68. Always state both the equilibrium price and the equilibrium quantity in your answer.
例题：若 Qd = 100 - 2P、Qs = 20 + 3P，令二者相等得 100 - 2P = 20 + 3P，即 80 = 5P，P = 16。代回可得 Q = 100 - 32 = 68。答题时务必同时写出均衡价格与均衡数量。
4. Price Elasticity of Demand and Supply | 需求价格弹性与供给价格弹性
Price elasticity of demand (PED) measures the responsiveness of quantity demanded to a change in price. Price elasticity of supply (PES) measures the responsiveness of quantity supplied to a change in price. Both are calculated using percentage changes so that the result is independent of the units used.
需求价格弹性（PED）衡量需求量对价格变动的反应程度。供给价格弹性（PES）衡量供给量对价格变动的反应程度。两者都用百分比变化来计算，这样结果就不受计量单位影响。
PED = %ΔQd ÷ %ΔP PES = %ΔQs ÷ %ΔP
For a more accurate result across a range of prices, use the midpoint (arc) formula, which averages the initial and final values. This avoids the awkward situation where the elasticity differs depending on which point you treat as the starting point.
若要在一段价格区间上获得更精确的结果，可使用中点（弧弹性）公式，即取初始值与最终值的平均数。这可以避免因选择不同起点而得出不同弹性的尴尬情况。
PED = [ΔQ ÷ ((Q₁ + Q₂) ÷ 2)] ÷ [ΔP ÷ ((P₁ + P₂) ÷ 2)]
Remember that PED is conventionally written as a negative number because price and quantity move in opposite directions, but examiners usually accept the absolute value. PES is almost always positive because of the law of supply. The most useful application is the revenue rule: when demand is elastic (|PED| > 1), a price cut raises total revenue; when demand is inelastic (|PED| < 1), a price rise raises total revenue.
请注意，按惯例 PED 记为负数，因为价格与数量方向相反，但考官通常接受其绝对值。由于供给定律，PES 几乎总是正值。最实用的应用是收益法则：当需求富有弹性（|PED| > 1）时，降价会增加总收益；当需求缺乏弹性（|PED| < 1）时，涨价会增加总收益。
| Value | Interpretation | Revenue effect of a price cut |
| |PED| > 1 | Elastic | Total revenue rises |
| |PED| = 1 | Unit elastic | Total revenue unchanged |
| |PED| < 1 | Inelastic | Total revenue falls |
Determinants of PED include the availability of substitutes, the proportion of income spent on the good, whether the good is a necessity or a luxury, and the time period considered. Determinants of PES include spare capacity, the mobility of factors, the length of the production process and the ease of storing stock.
影响 PED 的因素包括替代品的可得性、该商品支出占收入的比重、商品是必需品还是奢侈品，以及所考虑的时间长短。影响 PES 的因素包括闲置产能、要素流动性、生产周期的长短以及存货储存的难易程度。
5. Income Elasticity and Cross Elasticity of Demand | 收入弹性与交叉弹性
Income elasticity of demand (YED) measures how quantity demanded responds to a change in consumer income. Cross elasticity of demand (XED) measures how the quantity demanded of Good A responds to a change in the price of Good B. Together with PED and PES, these four elasticities form the quantitative core of Year 10 microeconomics.
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）衡量商品 A 的需求量对商品 B 价格变动的反应程度。与 PED 和 PES 一起，这四个弹性构成了 Year 10 微观经济学的量化核心。
YED = %ΔQd ÷ %ΔY XED = %ΔQd of A ÷ %ΔP of B
The sign of YED tells you what kind of good you are dealing with. A positive YED indicates a normal good; a negative YED indicates an inferior good. If YED is greater than 1, the good is a luxury whose demand grows faster than income. The sign of XED reveals the relationship between two goods: a positive XED means they are substitutes, and a negative XED means they are complements.
YED 的符号告诉你面对的是何种商品。YED 为正表示正常品；YED 为负表示劣等品。若 YED 大于 1，该商品属于奢侈品，其需求增长快于收入增长。XED 的符号揭示两种商品之间的关系：XED 为正表示二者是替代品，XED 为负表示二者是互补品。
- YED > 1: luxury good - demand is highly sensitive to income. | YED > 1：奢侈品——需求对收入高度敏感。
- 0 < YED < 1: normal necessity - demand rises with income but less than proportionately. | 0 < YED < 1：正常必需品——需求随收入上升，但幅度小于收入增幅。
- YED < 0: inferior good - demand falls as income rises. | YED < 0：劣等品——收入上升时需求下降。
- XED > 0: substitutes; XED < 0: complements; XED = 0: unrelated goods. | XED > 0：替代品；XED < 0：互补品；XED = 0：无关商品。
n of reasoning is: falling income, then a proportionally larger fall in quantity demanded, then lower total revenue if price is held constant. Always link the numerical elasticity to a real-world consequence.
常见考题是：若某企业产品的 YED = +2.5，经济衰退会带来什么影响？正确的推理链条是：收入下降，进而需求量以更大比例下降，在价格不变的情况下总收益减少。务必把弹性数值与现实后果联系起来。
6. Revenue, Costs and Profit | 收益、成本与利润
Cost and revenue formulas allow you to translate a firm's production data into conclusions about its profitability. Total revenue is price multiplied by quantity sold, and average revenue is simply the price of the good under normal market conditions. Marginal values are always calculated as the change in the total divided by the change in quantity.
成本与收益公式可以帮助你根据企业的生产数据判断其盈利状况。总收益等于价格乘以销售量；在正常市场条件下，平均收益就等于商品价格。边际值始终用总量的变化量除以数量的变化量来计算。
| Concept | Formula | 中文 |
| Total revenue | TR = P × Q | 总收益 |
| Average revenue | AR = TR ÷ Q = P | 平均收益 |
| Marginal revenue | MR = ΔTR ÷ ΔQ | 边际收益 |
| Total cost | TC = TFC + TVC | 总成本 |
| Average cost | AC = TC ÷ Q | 平均成本 |
| Marginal cost | MC = ΔTC ÷ ΔQ | 边际成本 |
| Profit | Profit = TR - TC | 利润 |
tput rises - this is the source of economies of scale in the short run. Note that MC intersects AC at the minimum point of AC; this relationship is frequently tested in multiple-choice questions.
固定成本在短期内不随产量变动，因此平均固定成本（AFC = TFC ÷ Q）随着产量上升而持续下降——这正是短期规模经济的来源。请注意，MC 曲线在 AC 的最低点与之相交；这一关系在选择题中经常被考查。
if TR = 600 and TC = 480, then profit is 120 and the profit margin is 120 ÷ 600 × 100 = 20% then AR = 600 ÷ 60 = 10 and AC = 480 ÷ 60 = 8, confirming a profit of 10 - 8 = 2 per unit.
例题：若 TR = 600、TC = 480，则利润为 120，利润率为 120 ÷ 600 × 100 = 20%。若产量为 60 单位，则 AR = 600 ÷ 60 = 10，AC = 480 ÷ 60 = 8，验证出单位利润为 10 - 8 = 2。
7. Profit Maximisation and Market Structure Theorems | 利润最大化与市场结构定理
The central theorem of firm behaviour is that profit is maximised where marginal revenue equals marginal cost. At any output below that point, each extra unit adds more to revenue than to cost, so profit is still rising; beyond that point, each extra unit costs more than it earns.
企业行为理论的核心定理是：当边际收益等于边际成本时，利润达到最大。在该产量之前，每多生产一单位带来的收益大于成本，利润仍在上升；超过该点之后，每多生产一单位所耗成本大于所获收益。
Profit maximisation condition: MR = MC
ales volume may produce more than the profit-maximising output. Sales maximisation, in the Baumol model, occurs where AR = AC, that is, where the firm just earns normal profit while producing the greatest possible quantity.
在同一框架下还可以推出其他几条决策法则。收益最大化发生在 MR = 0 时，这也是为什么薪酬与销售额挂钩的管理者可能生产超过利润最大化产量的原因。在鲍莫尔模型中，销售最大化发生在 AR = AC 时，即企业在只获得正常利润的条件下生产尽可能多的产量。
- Perfect competition: P = AR = MR = MC at equilibrium in the long run. | 完全竞争：长期均衡时 P = AR = MR = MC。
- s a downward-sloping AR curve and sets MC = MR, then reads the price off the demand curve. | 垄断：企业面对向右下方倾斜的 AR 曲线，令 MC = MR，再从需求曲线上读取价格。
- Shut-down point: a firm closes in the short run if price falls below average variable cost (P < AVC). | 停产点：若价格低于平均可变成本（P < AVC），企业在短期内会选择停产。
- Break-even point: normal profit is earned where AR = AC. | 盈亏平衡点：当 AR = AC 时，企业获得正常利润。
uctive efficiency at the minimum of AC, while monopoly typically produces at a higher price and lower output, generating a deadweight loss of welfare. These theorems should be quoted with the correct diagram labels: AR, MR, MC, AC and the profit rectangle.
效率方面的结论同样重要。完全竞争在 P = MC 处实现配置效率，并在 AC 最低点实现生产效率；而垄断通常以更高价格、更低产量进行生产，造成福利净损失。引用这些定理时应配合正确的图形标注：AR、MR、MC、AC 以及利润矩形。
8. Market Failure, Externalities and Government Intervention | 市场失灵、外部性与政府干预
Market failure occurs when the free market produces a quantity that does not maximise social welfare. The standard cause in Year 10 is an externality - a third-party effect not reflected in market prices. Social cost equals private cost plus external cost, and social benefit equals private benefit plus external benefit.
市场失灵是指自由市场所生产的数量未能实现社会福利最大化。Year 10 涉及的标准成因是外部性——一种未反映在市场交易价格中的第三方效应。社会成本等于私人成本加外部成本，社会收益等于私人收益加外部收益。
MSC = MPC + external cost MSB = MPB + external benefit
ive externality exists, such as pollution, the free market produces too much and creates a deadweight loss triangle between the market output and the social optimum. Where a positive externality exists, such as education, the free market produces too little.
社会最优解发生在边际社会收益等于边际社会成本之时（MSB = MSC）。当存在负外部性（如污染）时，自由市场产量过多，在市场产量与社会最优产量之间形成净损失三角形。当存在正外部性（如教育）时，自由市场产量过少。
- Pigouvian tax: set the tax equal to the external marginal cost at the social optimum. | 庇古税：税额应等于社会最优产量处的边际外部成本。
- Subsidy: used to correct positive externalities by shifting supply, or demand, to the social optimum. | 补贴：通过移动供给或需求曲线来纠正正外部性，使之达到社会最优。
- Regulation, tradable permits and information provision are alternatives with different strengths. | 管制、可交易许可证和信息披露是各有优劣的替代手段。
Elasticity matters for policy outcomes. If demand for the taxed good is inelastic, the tax burden falls mainly on consumers; if demand is elastic, producers bear more of the burden. In addition, the effectiveness of a subsidy depends on PES: a subsidy raises producer revenue most when supply is inelastic.
弹性会影响政策效果。若被征税商品的需求缺乏弹性，税负主要落在消费者身上；若需求富有弹性，生产者则承担更多税负。此外，补贴的效果取决于 PES：当供给缺乏弹性时，补贴最能提高生产者收益。
9. Macroeconomic Indicators: Output, Inflation and Unemployment | 宏观指标：产出、通胀与失业
Gross Domestic Product measures the total value of final goods and services produced in an economy in a given period. The expenditure approach is the version required at Year 10, and it decomposes GDP into four components.
国内生产总值衡量一个经济体在特定时期内所生产的最终商品与服务的总价值。Year 10 要求掌握的是支出法，它把 GDP 分解为四个组成部分。
GDP = C + I + G + (X - M)
Nominal GDP is measured at current prices, while real GDP is adjusted for inflation; real GDP is the appropriate measure for comparing living standards over time. The GDP deflator converts one into the other, and the inflation rate is calculated from the consumer price index.
名义 GDP 按当期价格计量，实际 GDP 则剔除了通胀因素；比较不同时期的生活水平时应使用实际 GDP。GDP 平减指数可用于两者之间的换算，而通胀率则由消费者价格指数（CPI）计算得出。
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