📚 Cambridge IGCSE Economics: Quick Formula & Theorem Reference | 剑桥 IGCSE 经济公式定理速查手册
Welcome to your ultimate formula and theorem cheat sheet for Year 11 Cambridge IGCSE Economics. This handbook compiles the essential calculations, key relationships, and fundamental theorems you need to master for your exams. Each section provides a clear English explanation followed by its Chinese counterpart, ensuring you grasp both the concept and the terminology in both languages. Use this guide to revise efficiently and strengthen your economic reasoning.
欢迎使用 Year 11 剑桥 IGCSE 经济公式定理速查手册。本手册汇集了考试必备的核心计算、关键关系与基础定理。每个小节首先提供清晰的英文解释，紧接着是中文对照，帮助你同时掌握概念与双语术语。利用本指南高效复习，巩固你的经济学推理能力。
1. Price Elasticity of Demand (PED) | 需求价格弹性
Price elasticity of demand measures how responsive the quantity demanded of a good is to a change in its own price. The formula in its simplest form is:
需求价格弹性衡量商品需求量对其自身价格变化的反应程度。其最简公式为：
PED = %ΔQd / %ΔP
emand is perfectly inelastic; and if PED approaches infinity, demand is perfectly elastic.
若 PED > 1，需求富有弹性；若 PED < 1，需求缺乏弹性；若 PED = 1，需求为单位弹性；若 PED = 0，需求完全无弹性；若 PED 趋于无穷大，需求完全有弹性。
Key determinants include the availability of close substitutes, the proportion of income spent on the good, whether the good is a necessity or a luxury, and the time period considered.
主要决定因素包括：相近替代品的可获得性、该商品占收入的比例、该商品是必需品还是奢侈品，以及所考虑的时间周期。
2. Price Elasticity of Supply (PES) | 供给价格弹性
Price elasticity of supply measures the responsiveness of quantity supplied to a change in the product's own price. The formula is:
供给价格弹性衡量供给量对产品自身价格变化的反应程度。其公式为：
PES = %ΔQs / %ΔP
main factors influencing PES are production time lags, availability of spare capacity, ease of storing inventory, and the mobility of factors of production.
供给可以是弹性的 (PES > 1)、缺乏弹性的 (PES < 1)、单位弹性的 (PES = 1)、完全无弹性的 (PES = 0) 或完全有弹性的 (PES = 无穷大)。影响 PES 的主要因素包括：生产时滞、闲置产能的可获得性、库存储存的难易度，以及生产要素的流动性。
In the short run, supply tends to be more price inelastic because firms cannot easily change all factor inputs; in the long run, supply becomes more price elastic.
在短期内，供给往往更缺乏弹性，因为企业难以迅速改变所有要素投入；在长期内，供给变得更加富有弹性。
3. Income Elasticity of Demand (YED) | 需求收入弹性
Income elasticity of demand measures how quantity demanded responds to a change in consumers' income. The formula is:
需求收入弹性衡量需求量对消费者收入变化的反应程度。其公式为：
YED = %ΔQd / %ΔY
Where Y represents income. For normal goods, YED is positive. For inferior goods, YED is negative. Within normal goods, necessities have a YED between 0 and 1, while luxury goods have a YED greater than 1.
其中 Y 表示收入。对于正常商品，YED 为正；对于劣质商品，YED 为负。在正常商品中，必需品的 YED 介于 0 与 1 之间，而奢侈品的 YED 大于 1。
Firms use YED to forecast demand growth during economic expansion and to adjust their product portfolios accordingly.
企业利用 YED 来预测经济扩张期间的需求增长，并据此调整产品组合。
4. Cross Elasticity of Demand (XED) | 需求交叉弹性
Cross elasticity of demand measures the responsiveness of demand for one good (A) to a change in the price of another good (B). The formula is:
需求交叉弹性衡量一种商品 (A) 的需求量对另一种商品 (B) 价格变化的反应程度。其公式为：
XED = %ΔQdA / %ΔPB
he goods are independent. The magnitude of XED indicates the strength of the relationship.
若 XED > 0，两种商品互为替代品（如茶与咖啡）；若 XED < 0，它们互为互补品（如打印机与墨盒）；若 XED ≈ 0，两种商品相互独立。XED 的绝对值大小表明了关系的强弱。
This concept helps firms anticipate the impact of competitors' pricing strategies and complements' price changes on their own sales.
这一概念有助于企业预判竞争对手定价策略以及互补品价格变化对自身销量的影响。
5. Total, Average and Marginal Product | 总产量、平均产量与边际产量
In the short run, when at least one factor input is fixed, output can be analysed through three related concepts:
在短期内，当至少一种要素投入固定时，可以通过三个相关概念分析产出：
- Total product (TP) – total output produced. | 总产量 (TP) – 生产的总产出。
- Average product (AP) = TP / quantity of variable input (e.g., labour). | 平均产量 (AP) = TP / 可变投入量（如劳动力）。
- Marginal product (MP) = ΔTP / ΔQ of variable input. | 边际产量 (MP) = ΔTP / 可变投入量的变化。
The law of diminishing marginal returns states that as more units of a variable input are added to a fixed input, MP will eventually fall. Initially, MP may rise due to specialisation and division of labour, but beyond a certain point, MP declines.
边际报酬递减规律指出，随着越来越多的可变投入被追加到固定投入上，边际产量最终会下降。最初，由于专业化和分工，边际产量可能上升，但超过某一点后，边际产量便开始下降。
fter this point, AP also declines. This relationship governs the shape of the cost curves.
当 AP = MP 时，平均产量达到最大值。此后，平均产量也随之下降。这一关系决定了成本曲线的形状。
6. Costs of Production: Total, Average and Marginal Costs | 生产成本：总成本、平均成本与边际成本
Firms incur various costs that can be categorised into total, average and marginal costs. Key formulas include:
企业承担各种成本，可分为总成本、平均成本和边际成本。关键公式包括：
| Total Fixed Cost (TFC) | Costs that do not vary with output in the short run. | 总固定成本 (TFC) – 短期内不随产量变化的成本。 |
| Total Variable Cost (TVC) | Costs that vary directly with output. | 总可变成本 (TVC) – 直接随产量变化的成本。 |
| Total Cost (TC) | TC = TFC + TVC | 总成本 (TC) = TFC + TVC |
| Average Fixed Cost (AFC) | AFC = TFC / Q | 平均固定成本 (AFC) = TFC / Q |
| Average Variable Cost (AVC) | AVC = TVC / Q | 平均可变成本 (AVC) = TVC / Q |
| Average Total Cost (AC or ATC) | AC = TC / Q = AFC + AVC | 平均总成本 (AC 或 ATC) = TC / Q = AFC + AVC |
| Marginal Cost (MC) | MC = ΔTC / ΔQ = ΔTVC / ΔQ | 边际成本 (MC) = ΔTC / ΔQ = ΔTVC / ΔQ |
The MC curve intersects both AVC and AC at their minimum points. This is because when the marginal is below the average, the average falls; when the marginal is above the average, the average rises.
边际成本曲线在 AVC 和 AC 的最低点与两者相交。这是因为当边际量低于平均量时，平均量下降；当边际量高于平均量时，平均量上升。
7. Revenue Concepts: Total, Average and Marginal Revenue | 收益概念：总收益、平均收益与边际收益
Revenue is the income a firm receives from selling its output. The three fundamental measures are:
收益是企业从销售产出中获得的收入。三个基本衡量指标是：
- Total Revenue (TR) = Price × Quantity sold. | 总收益 (TR) = 价格 × 销售量。
- Average Revenue (AR) = TR / Q = Price. AR is the demand curve for the firm. | 平均收益 (AR) = TR / Q = 价格。AR 就是企业的需求曲线。
- Marginal Revenue (MR) = ΔTR / ΔQ. | 边际收益 (MR) = ΔTR / ΔQ。
e, and the demand curve is perfectly elastic. In imperfect markets (e.g., monopoly), the demand curve slopes downwards, meaning MR lies below AR because the firm must lower price to sell additional units.
在完全竞争市场中，AR = MR = 价格，需求曲线完全有弹性。在不完全竞争市场（如垄断）中，需求曲线向右下方倾斜，边际收益曲线位于平均收益曲线之下，因为企业必须降低价格以出售更多单位。
8. Profit Maximisation: MC = MR | 利润最大化：边际成本等于边际收益
). At this output, the additional cost of producing one more unit is exactly equal to the additional revenue generated from selling it.
任何企业的利润最大化产量发生在边际成本等于边际收益 (MC = MR) 之处。在这一产出水平上，多生产一单位所带来的额外成本恰好等于销售该单位所产生的额外收益。
= MR is profit maximised (or loss minimised). This rule applies to all market structures.
若 MR > MC，企业可以通过扩大产量增加利润；若 MC > MR，企业应减少产量。只有当 MC = MR 时，利润达到最大（或亏损最小）。这一规则适用于所有市场结构。
fit (AR > AC). The shutdown point, discussed next, occurs when the firm cannot even cover its average variable costs.
需要区分正常利润（零经济利润，AR = AC）与超常利润（AR > AC）。接下来讨论的停产点发生在企业连平均可变成本都无法弥补之时。
9. Breakeven and Shutdown Points in Perfect Competition | 完全竞争下的盈亏平衡点与停产点
In the short run, a perfectly competitive firm can make supernormal profits, normal profits, or losses. Two critical reference points exist:
在短期内，完全竞争企业可能获得超常利润、正常利润或亏损。存在两个关键的参照点：
- Breakeven point – es normal profit (zero economic profit). This occurs at the minimum point of the AC curve. | 盈亏平衡点 – 当 AR = AC 时，企业获得正常利润（零经济利润）。这发生在 AC 曲线的最低点。
- Shutdown point – C, the firm will shut down in the short run because it cannot cover its variable costs. The firm's short-run supply curve is the portion of its MC curve that lies above the AVC curve. | 停产点 – 当 AR = AVC 时。若价格低于 AVC，企业在短期内将停产，因为它无法弥补可变成本。企业的短期供给曲线是其边际成本曲线位于 AVC 曲线之上的部分。
If AR > AC, supernormal profits attract new firms in the long run, shifting industry supply to the right until only normal profit remains. If AR < AC but > AVC, the firm continues producing in the short run to minimise losses, covering some of its fixed costs.
若 AR > AC，超常利润在长期会吸引新企业进入，使行业供给右移，直至只留下正常利润。若 AR < AC 但 > AVC，企业在短期内会继续生产以最小化亏损，弥补部分固定成本。
10. Comparative Advantage and Terms of Trade | 比较优势与贸易条件
Comparative advantage exists when a country can produce a good at a lower opportunity cost than another country. It is the basis for mutually beneficial trade, even if one country has an absolute advantage in all goods.
比较优势是指一国生产某种商品的机会成本低于另一国。它构成了互利贸易的基础，即使一国在所有商品上都具有绝对优势。
To determine comparative advantage, calculate the opportunity cost of producing one unit of a good in each country. Each country should specialise in the good for which it has the lower opportunity cost.
确定比较优势时，需计算各国生产一单位某种商品的机会成本。各国应专门生产其机会成本较低的商品。
The terms of trade (ToT) is the ratio at which goods are exchanged between countries. To be mutually beneficial, the ToT must lie between the two countries' opportunity cost ratios:
贸易条件 (ToT) 是两国交换商品时的比率。要使双方均受益，贸易条件必须处于两国机会成本比率之间：
Country A's opportunity cost < ToT < Country B's opportunity cost
For example, if country X gives up 2 units of wheat for 1 unit of steel, and country Y gives up 3 units of wheat for 1 unit of steel, the terms of trade for steel must be between 2 and 3 units of wheat.
例如，若 X 国放弃 2 单位小麦获得 1 单位钢铁，Y 国放弃 3 单位小麦获得 1 单位钢铁，那么钢铁的贸易条件必须介于 2 至 3 单位小麦之间。
11. Multiplier Effect | 乘数效应
The multiplier effect explains how an initial change in aggregate demand can lead to a larger final change in national income. The simple multiplier (k) in a closed economy with no government is:
乘数效应解释了总需求的初始变动如何导致国民收入最终产生更大的变动。在一个无政府的封闭经济中，简单乘数 (k) 为：
k = 1 / (1 - MPC) = 1 / MPS
/ ΔY), with MPC + MPS = 1. The change in national income = k × initial change in spending.
其中 MPC 为边际消费倾向 (ΔC / ΔY)，MPS 为边际储蓄倾向 (ΔS / ΔY)，且 MPC + MPS = 1。国民收入的变化 = k × 支出的初始变化。
A higher MPC (or lower MPS) leads to a larger multiplier because more of any additional income is re-spent in the economy. The multiplier can also be dampened by leakages such as taxation, savings and imports.
较高的 MPC（或较低的 MPS）会带来更大的乘数，因为额外收入中有更多会在经济体内被重新消费。乘数效应也可能因税收、储蓄和进口等漏出项而被削弱。
12. Marginal Utility and Consumer Equilibrium | 边际效用与消费者均衡
Marginal utility (MU) is the additional satisfaction gained from consuming one more unit of a good. The law of diminishing marginal utility states that as a person consumes more units of a good, the additional satisfaction from each extra unit eventually decreases.
边际效用 (MU) 是指多消费一单位商品所带来的额外满足感。边际效用递减规律指出，随着一个人消费某种商品的单位数增加，每多消费一单位带来的额外满足感最终会下降。
A consumer maximises total utility when the marginal utility per pound (or dollar) spent is equal across all goods, given a fixed budget:
在预算固定的情况下，当花费在每一种商品上的最后一镑（或一美元）所带来的边际效用相等时，消费者实现总效用最大化：
MUA / PA = MUB / PB = ... = MUN / PN
If the ratio is higher for good A, the consumer should buy more of A and less of other goods until the equal marginal principle is restored. This is the consumer equilibrium condition, also known as the equi-marginal principle.
如果商品 A 的该比率更高，消费者应增加 A 的购买并减少其他商品的购买，直至等边际原则恢复。这就是消费者均衡条件，又称等边际原则。
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