Year 10 CAIE Economics: Formula & Theorem Quick-Reference Handbook | Year 10 CAIE 经济：公式定理速查手册

📚 Year 10 CAIE Economics: Formula & Theorem Quick-Reference Handbook | Year 10 CAIE 经济：公式定理速查手册

This handbook brings together the essential definitions, formulas, and core theorems needed for Year 10 CAIE Economics. It is designed to help you revise the quantitative and qualitative principles that underpin the syllabus, from scarcity and opportunity cost to elasticity and government intervention. Use it as a quick-look guide to cement your understanding before exams.

本手册汇总了 Year 10 CAIE 经济课程所需的定义、公式和核心定理。它旨在帮助你复习支撑考纲的数理与概念原理，从稀缺性、机会成本到弹性及政府干预。考试前可将它作为快速查阅指南，巩固理解。

1. Scarcity and the Basic Economic Problem | 稀缺性与基本经济问题

Scarcity arises because human wants are unlimited while the resources available to satisfy them are finite. This fundamental condition forces every economy to answer three questions: What to produce? How to produce? For whom to produce?

稀缺性源于人类欲望的无限性与满足这些欲望的资源有限性之间的矛盾。这一根本条件迫使每个经济体回答三个问题：生产什么？如何生产？为谁生产？

All economic models assume rational choice under scarcity. The concept is not just about physical shortage; it is the inescapable reality that choices must be made and trade-offs accepted.

所有经济模型都假设在稀缺条件下进行理性选择。这一概念不仅关乎物质短缺，更是必须做出选择和接受权衡的不可逃避的现实。

Scarcity → Choice → Opportunity Cost

2. Factors of Production and Their Rewards | 生产要素及其报酬

Resources are categorised into four factors of production. Each factor earns a corresponding reward.

资源被划分为四种生产要素，每种要素获得相应的报酬。

Factor of Production	Reward	Example
Land (natural resources)	Rent	Oil, forests
Labour (human effort)	Wages / Salaries	Factory workers
Capital (man-made aids)	Interest	Machinery
Enterprise (risk-taking)	Profit	Entrepreneurs

Enterprise organises the other three factors and bears the risk of business failure. The mobility of each factor – both geographical and occupational – influences how easily resources can be reallocated.

企业组织另外三种要素并承担经营失败的风险。每种要素的流动性——包括地理流动性和职业流动性——影响着资源配置的难易程度。

3. Opportunity Cost and the Production Possibility Curve (PPC) | 机会成本与生产可能性曲线

Opportunity cost is the value of the next best alternative foregone. When a choice is made, the sacrifice is measured against what could have been chosen instead.

机会成本是所放弃的次优替代品的价值。做出选择时，牺牲量用原本可选的方案来衡量。

Opportunity Cost = Sacrifice / Gain

A Production Possibility Curve (PPC) illustrates the maximum combinations of two goods an economy can produce with existing resources and technology. Points on the curve are efficient; points inside show unemployment or inefficiency; points outside are unattainable.

生产可能性曲线（PPC）展示了一个经济体在现有资源和技术下能生产的两种商品的最大组合。曲线上的点代表有效率的生产；曲线内的点表示失业或低效率；曲线外的点无法企及。

The slope of the PPC is the marginal rate of transformation (MRT), which equals the opportunity cost of producing one more unit of the good on the horizontal axis. A straight-line PPC implies constant opportunity cost; a concave PPC (bowed outward) indicates increasing opportunity cost.

PPC 的斜率即边际转换率（MRT），等于多生产一单位横轴商品的机会成本。直线型 PPC 意味着机会成本不变；凹向原点的 PPC（向外弯曲）表明机会成本递增。

MRT = ΔY / ΔX

4. Demand and the Law of Demand | 需求与需求定律

Demand is the quantity of a good that consumers are willing and able to buy at a given price over a period of time. The law of demand states that, ceteris paribus, as price falls, quantity demanded rises, and vice versa. This inverse relationship creates a downward-sloping demand curve.

需求是在一段时期内，消费者在给定价格下愿意且能够购买的商品数量。需求定律指出，在其他条件不变的情况下，价格下降则需求量上升，反之亦然。这种反向关系形成了一条向下倾斜的需求曲线。

A movement along the demand curve is caused solely by a change in the good’s own price. A shift of the entire demand curve is caused by changes in non-price determinants: income, tastes, prices of related goods (substitutes and complements), population size, and expectations.

沿着需求曲线的移动仅由商品自身价格变化引起。整条需求曲线的平移则由非价格决定因素的变化导致：收入、偏好、相关商品（替代品和互补品）的价格、人口规模以及预期。

5. Supply and the Law of Supply | 供给与供给定律

Supply is the quantity of a good that producers are willing and able to sell at a given price over a period of time. The law of supply states that, ceteris paribus, as price rises, quantity supplied rises. The supply curve slopes upward.

供给是在一段时期内，生产者在给定价格下愿意且能够出售的商品数量。供给定律指出，在其他条件不变的情况下，价格上升则供给量上升。供给曲线向上倾斜。

A movement along the supply curve reflects a change in the good’s own price. Shifts in supply occur when any other determinant changes: costs of production, technology, taxes/subsidies, number of sellers, weather (for agricultural goods), and producer expectations.

沿着供给曲线的移动反映商品自身价格的变化。当任何其他决定因素发生变化时，供给曲线就会平移：生产成本、技术、税收/补贴、卖者数量、天气（对农产品）以及生产者预期。

6. Market Equilibrium | 市场均衡

Equilibrium occurs where quantity demanded equals quantity supplied. At this intersection, there is no tendency for price to change. The equilibrium price (Pₑ) and equilibrium quantity (Qₑ) are determined simultaneously.

均衡发生在需求量等于供给量之处。在这个交点上，价格没有变动的趋势。均衡价格（Pₑ）和均衡数量（Qₑ）同时被决定。

Qd = Qs at equilibrium

If the market price is above equilibrium, there is excess supply (a surplus), causing price to fall. If the price is below equilibrium, excess demand (a shortage) pushes price upward. These market forces drive the system back to equilibrium, a concept known as the price mechanism.

若市场价格高于均衡水平，就会出现超额供给（过剩），导致价格下降。若价格低于均衡水平，超额需求（短缺）将推高价格。这些市场力量驱使系统回归均衡，这便是价格机制的概念。

7. Price Elasticity of Demand (PED) | 需求的价格弹性（PED）

PED measures the responsiveness of quantity demanded to a change in the good’s own price. It is calculated as:

PED 衡量需求量对商品自身价格变化的反应程度。其计算公式为：

PED = (% change in quantity demanded) ÷ (% change in price)

The standard formula for percentage change is: (New – Original) / Original × 100. PED values are treated as absolute numbers, though the raw result is usually negative because of the law of demand.

百分比变化的标准公式为：（新值 – 原值）÷ 原值 × 100。尽管由于需求定律原始结果通常为负数，但 PED 值按绝对值处理。

If PED > 1, demand is elastic (revenue rises when price falls).

若 PED > 1，需求富有弹性（价格下降时总收入增加）。
If PED < 1, demand is inelastic (revenue falls when price falls).

若 PED < 1，需求缺乏弹性（价格下降时总收入减少）。
If PED = 1, demand is unit elastic (revenue stays constant).

若 PED = 1，需求单位弹性（总收入不变）。
If PED = 0, demand is perfectly inelastic.

若 PED = 0，需求完全无弹性。
If PED = ∞, demand is perfectly elastic.

若 PED = ∞，需求完全弹性。

Determinants of PED include the number and closeness of substitutes, the proportion of income spent on the good, whether the good is a necessity or a luxury, and the time period considered.

PED 的决定因素包括替代品的数量和密切程度、购买该商品占收入的比例、商品属于必需品还是奢侈品，以及所考虑的时间跨度。

8. Price Elasticity of Supply (PES) | 供给的价格弹性（PES）

PES measures how responsive quantity supplied is to a change in price.

PES 衡量供给量对价格变化的反应程度。

PES = (% change in quantity supplied) ÷ (% change in price)

If PES > 1, supply is elastic.

若 PES > 1，供给富有弹性。
If PES < 1, supply is inelastic.

若 PES < 1，供给缺乏弹性。
If PES = 1, supply is unit elastic.

若 PES = 1，供给单位弹性。
If PES = 0, supply is perfectly inelastic (momentary supply).

若 PES = 0，供给完全无弹性（瞬间供给）。

Key determinants of PES are the length of the production period, the availability of spare capacity, the ease of storing stocks, and the mobility of factors of production. In the short run, supply tends to be more inelastic; in the long run, it becomes more elastic.

PES 的主要决定因素包括生产周期的长度、闲置产能的可用性、库存储存的难易程度以及生产要素的流动性。短期中供给往往更缺乏弹性，长期中则变得更具弹性。

9. Income Elasticity of Demand (YED) | 需求的收入弹性（YED）

YED measures the responsiveness of demand to a change in consumers’ income.

YED 衡量需求对消费者收入变化的反应程度。

YED = (% change in quantity demanded) ÷ (% change in income)

If YED > 0, the good is a normal good (demand rises as income rises).

若 YED > 0，商品为正常品（收入上升需求上升）。
If YED > 1, it is a luxury good (income-elastic).

若 YED > 1，属奢侈品（收入弹性大）。
If 0 < YED < 1, it is a necessity (income-inelastic).

若 0 < YED < 1，属必需品（收入缺乏弹性）。
If YED < 0, the good is an inferior good (demand falls as income rises).

若 YED < 0，商品为劣质品（收入上升需求下降）。

YED helps firms plan output during economic booms and recessions. It also explains the changing pattern of consumer spending as an economy grows.

YED 帮助企业根据经济繁荣或衰退来规划产量，也解释了随着经济增长消费者支出模式的变化。

10. Cross Elasticity of Demand (XED) | 需求的交叉弹性（XED）

XED measures the responsiveness of demand for one good (A) to a change in the price of another good (B).

XED 衡量一种商品（A）的需求对另一种商品（B）价格变化的反应程度。

XED = (% change in Qd of good A) ÷ (% change in price of good B)

If XED > 0, the goods are substitutes (e.g. tea and coffee).

若 XED > 0，两商品互为替代品（如茶和咖啡）。
If XED < 0, the goods are complements (e.g. cars and petrol).

若 XED < 0，两商品互为互补品（如汽车和汽油）。
If XED = 0, the goods are unrelated.

若 XED = 0，两商品不相关。

The magnitude of XED indicates the strength of the relationship. A high positive XED means the two goods are very close substitutes. Businesses use XED to anticipate how a competitor’s pricing decision might affect their own sales.

XED 的数值大小反映了关系的强弱。较高的正 XED 值意味着两者是非常近似的替代品。企业利用 XED 预测竞争对手的定价决策将如何影响自身销量。

11. Total Revenue and the Relationship with PED | 总收益及其与 PED 的关系

Total revenue (TR) is the money a firm receives from selling its output.

总收益（TR）是企业销售产品所获得的货币收入。

TR = Price × Quantity

When demand is elastic (PED > 1), a price cut raises total revenue because the percentage increase in quantity demanded outweighs the percentage decrease in price. Conversely, a price rise reduces total revenue.

当需求富有弹性（PED > 1）时，降价会提高总收益，因为需求量增加的百分比超过了价格下降的百分比。反之，提价则会减少总收益。

When demand is inelastic (PED < 1), a price rise increases total revenue, while a price cut decreases it. For unit elastic demand (PED = 1), total revenue remains constant when price changes.

当需求缺乏弹性（PED < 1）时，提价会增加总收益，而降价会减少总收益。对于单位弹性需求（PED = 1），价格变动时总收益保持不变。

This relationship is critical for firms when deciding pricing strategy. Understanding the elasticity of their product helps managers forecast the revenue impact of price changes.

这种关系对企业制定定价策略至关重要。了解产品的弹性有助于管理者预测价格变动对收入的影响。

12. Government Intervention: Indirect Taxes and Subsidies | 政府干预：间接税与补贴

An indirect tax is a charge levied on goods and services, which shifts the supply curve vertically upward by the amount of the tax. A subsidy is a payment by the government to producers, which shifts the supply curve vertically downward.

间接税是对商品和服务征收的费用，使供给曲线按税额向上平移。补贴是政府向生产者支付的款项，使供给曲线向下平移。

When a per-unit tax is imposed, the new equilibrium price paid by consumers (Pc) is higher than the pre-tax equilibrium, while the price received by producers (Pp) is lower. The tax burden is shared, and the proportion borne by each side depends on the relative elasticities of demand and supply.

征收单位税时，新的消费者支付价格（Pc）高于税前均衡，而生产者收到的价格（Pp）则较低。税收负担由双方分担，各自承担的比例取决于需求与供给的相对弹性。

If demand is more inelastic than supply, consumers bear a larger share of the tax.

若需求比供给更缺乏弹性，消费者承担更大份额的税收。
If supply is more inelastic than demand, producers bear a larger share.

若供给比需求更缺乏弹性，生产者承担更大份额。

The amount of the tax is Pc – Pp. The government’s tax revenue equals the per-unit tax multiplied by the post-tax quantity traded (Qt).

税额为 Pc – Pp。政府税收收入等于单位税额乘以税后的交易数量（Qt）。

For subsidies, the benefit is also split. The consumer pays a lower price while the producer receives a higher effective price. The cost of the subsidy to the government is the per-unit subsidy multiplied by the new quantity.

对于补贴，利益同样被分割。消费者支付更低的价格，而生产者获得更高的实际价格。政府的补贴成本等于单位补贴额乘以新交易量。

Government spending on subsidy = Subsidy per unit × Qs

Published by TutorHao | Economics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

Year 10 CAIE Economics: Formula & Theorem Quick-Reference Handbook | Year 10 CAIE 经济：公式定理速查手册