📚 Year 9 CAIE Economics: Formula & Theorems Quick Reference Handbook | Year 9 CAIE 经济：公式定理速查手册
This quick reference handbook covers the essential formulas, theorems and key relationships you need to master for Year 9 CAIE Economics. Each entry is presented with clear definitions, notations and worked examples where appropriate, so you can revise efficiently and apply the concepts confidently in your exams.
本速查手册涵盖了 Year 9 CAIE 经济课程中必须掌握的核心公式、定理和关键关系。每一条目均配有清晰的定义、符号表示以及在适当情况下的计算示例，帮助你高效复习，并在考试中自信地运用相关概念。
1. The Basic Economic Problem: Scarcity and Opportunity Cost | 基本经济问题：稀缺性与机会成本
Scarcity is the condition that arises because resources are limited while human wants are unlimited. Because of scarcity, choices must be made, and every choice involves an opportunity cost — the value of the next best alternative forgone.
稀缺性是由于资源有限而人类欲望无限所产生的一种状况。由于稀缺性的存在，人们必须做出选择，而每一个选择都涉及机会成本——即所放弃的次优选择的价值。
tive sacrificed. For example, if a student spends one hour studying economics instead of playing video games (valued at £10 of enjoyment), the opportunity cost of studying is £10.
机会成本的概念并非由单一公式表示，但通常计算为：机会成本 = 所牺牲的次优选择的价值。例如，如果一名学生花一小时学习经济学，而不是玩电子游戏（享受价值 10 英镑），那么学习的机会成本就是 10 英镑。
2. Law of Demand | 需求定律
The law of demand states that, ceteris paribus (all other factors held constant), there is an inverse relationship between the price of a good and the quantity demanded. As price falls, quantity demanded rises; as price rises, quantity demanded falls.
需求定律指出，在其他条件不变（ceteris paribus）的前提下，商品的价格与需求量之间存在反向关系。价格下降，需求量上升；价格上升，需求量下降。
This relationship is driven by the income effect (a lower price increases consumers' real income) and the substitution effect (consumers switch from relatively more expensive alternatives). No formula is attached to the law itself, but the demand schedule and demand curve illustrate it graphically.
这一关系由收入效应（价格下降增加了消费者的实际收入）和替代效应（消费者转而购买相对更便宜的替代品）所驱动。需求定律本身没有附带的公式，但需求表与需求曲线以图形方式说明了这一关系。
3. Law of Supply | 供给定律
The law of supply states that, ceteris paribus, there is a direct relationship between the price of a good and the quantity supplied. As price rises, producers are willing to supply more; as price falls, the quantity supplied decreases.
供给定律指出，在其他条件不变的前提下，商品的价格与供给量之间存在正向关系。价格上升，生产者愿意供给更多；价格下降，供给量减少。
The rationale is that higher prices increase potential profit, incentivising existing firms to expand output and new firms to enter the market. Supply is typically represented by an upward-sloping supply curve.
其原理在于，较高的价格增加了潜在利润，激励现有企业扩大产量并吸引新企业进入市场。供给通常由一条向上倾斜的供给曲线来表示。
4. 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. The formula is:
需求价格弹性衡量需求量对价格变化的反应程度。计算公式为：
PED = % change in quantity demanded ÷ % change in price
is PED is always negative due to the law of demand, but the absolute value is usually considered. |PED| > 1 means demand is price elastic; |PED| < 1 means demand is price inelastic; |PED| c. Knowledge of PED helps businesses predict the effect of price changes on total revenue.
由于需求定律，PED 恒为负值，但通常考虑其绝对值。|PED| > 1 表示需求富有价格弹性；|PED| < 1 表示需求缺乏价格弹性；|PED| = 1 为单位弹性。掌握 PED 有助于企业预测价格变动对总收入的影响。
5. 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 price. The formula is:
供给价格弹性衡量供给量对价格变化的反应程度。计算公式为：
PES = % change in quantity supplied ÷ % change in price
ectly inelastic supply (fixed quantity). The key determinant of PES is the time period: supply tends to be more elastic in the long run as producers can adjust all inputs.
PES 通常为正值。PES > 1 表示供给富有弹性；PES < 1 表示供给缺乏弹性；PES = 0 表示供给完全无弹性（数量固定）。PES 的主要决定因素是时间周期：长期中，生产者能够调整所有投入，供给往往更具弹性。
6. Total Revenue (TR) | 总收入
Total revenue is the total income a firm receives from selling its output. The formula is:
总收入是企业通过销售其产品所获得的总收入。计算公式为：
TR = Price × Quantity sold
For example, if a bakery sells 500 loaves of bread at £2 each, TR = £2 × 500 = £ f demand is elastic, a price cut raises TR; if demand is inelastic, a price cut lowers TR.
例如，如果一家面包店以每只 2 英镑的价格售出 500 只面包，TR = 2 英镑 × 500 = 1,000 英镑。理解 TR 至关重要，结合需求价格弹性可以分析价格变动的影响：如果需求富有弹性，降价会增加总收入；如果需求缺乏弹性，降价会减少总收入。
7. Costs of Production: Total Cost, Average Cost and Marginal Cost | 生产成本：总成本、平均成本与边际成本
Cost analysis is fundamental for firms. The key formulas are:
成本分析对企业至关重要。关键公式如下：
Total Cost (TC) = Total Fixed Cost (TFC) + Total Variable Cost (TVC)
Average Cost (AC) = TC ÷ Quantity (Q)
Marginal Cost (MC) = Change in TC ÷ Change in Q
Fixed costs (e.g. rent) do not vary with output in the short run, while variable costs (e.g. raw materials) change with output. AC and MC typically form U-shaped curves due to the law of diminishing returns.
固定成本（如租金）在短期内不随产量变化，而可变成本（如原材料）随产量变化。由于边际报酬递减规律，平均成本和边际成本通常呈 U 形曲线。
8. Profit Maximisation Condition | 利润最大化条件
A firm maximises profit by producing the output level at which marginal cost equals marginal revenue. The profit-maximising rule is:
企业通过生产边际成本等于边际收益的产量水平来实现利润最大化。利润最大化法则为：
Profit is maximised where MC = MR
If MC < MR, the firm can increase profit by producing more. If MC > MR, producing an additional unit would reduce profit, so the firm should cut output. Total profit is calculated as TR − TC.
如果 MC < MR，企业增加产量可以增加利润。如果 MC > MR，增产一个单位会减少利润，因此企业应减产。总利润计算为 TR − TC。
9. Productivity | 生产力
Productivity measures the efficiency of a firm or economy. Labour productivity is a common measure:
生产力衡量企业或经济体的效率。劳动生产率是一个常用指标：
Labour Productivity = Total Output ÷ Number of Workers
or equivalently, output per worker per time period. Higher productivity reduces average costs and can raise living standards. Factors such as technology, training and specialisation improve productivity.
或者等价地，单位时间内每名工人的产出。更高的生产力能降低平均成本并提高生活水平。技术、培训和专业化等因素会提高生产力。
10. Market Equilibrium | 市场均衡
Market equilibrium occurs where quantity demanded equals quantity supplied. At the equilibrium price, there is no tendency for change — the market clears. The condition can be written as:
市场均衡发生在需求量等于供给量时。在均衡价格下，不存在变动的趋势——市场出清。这一条件可写为：
Qd = Qs at the equilibrium price (P*)
If the price is above equilibrium, a surplus exists (Qs > Qd), putting downward pressure on price. If the price is below equilibrium, a shortage exists (Qd > Qs), pushing price upward. The market mechanism moves price towards equilibrium without central planning.
如果价格高于均衡水平，就会出现过剩（Qs > Qd），价格面临下行压力。如果价格低于均衡水平，就会出现短缺（Qd > Qs），推动价格上升。在没有中央计划的情况下，市场机制会使价格趋向均衡。
11. Consumer Surplus and Producer Surplus | 消费者剩余与生产者剩余
Consumer surplus is the difference between what consumers are willing to pay and what they actually pay. Producer surplus is the difference between the market price and the minimum price at which producers are willing to supply. There is no single formula, but the concepts are essential for welfare analysis:
消费者剩余是消费者愿意支付的最高价格与实际支付价格之间的差额。生产者剩余是市场价格与生产者愿意供给的最低价格之间的差额。虽然没有单一公式，但这些概念对于福利分析至关重要：
Consumer Surplus = Willingness to Pay − Market Price (summed over all units bought)
Producer Surplus = Market Price − Minimum Supply Price (summed over all units sold)
Total welfare in a market is the sum of consumer and producer surplus. At the free-market equilibrium, total welfare is maximised; any price control, tax or subsidy can create a deadweight loss.
市场中的总福利是消费者剩余与生产者剩余之和。在自由市场均衡下，总福利达到最大；任何价格管制、税收或补贴都可能产生无谓损失。
12. Incidence of Taxation and Subsidies | 税收与补贴的归宿
When a tax is imposed, the burden is shared between consumers and producers depending on the relative elasticities of demand and supply. The more inelastic side of the market bears a larger share of the tax. The tax wedge is given by:
征收税收时，负担根据需求与供给的相对弹性在消费者与生产者之间分摊。市场中更缺乏弹性的一方承担较大比例的税负。税收楔子表示为：
Tax per unit = Price paid by consumers − Price received by producers
nd increasing the effective price for producers. The subsidy per unit = Price received by producers − Price paid by consumers.
对于补贴，收益同样根据弹性进行分配。补贴使供给曲线向下移动，降低消费者支付的价格并提高生产者实际得到的价格。每单位补贴 = 生产者获得的价格 − 消费者支付的价格。
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