📚 Year 9 Cambridge Economics: Formula & Theorem Quick Reference Handbook | Year 9 剑桥经济：公式定理速查手册
This handbook provides a concise summary of essential formulas and theorems for Year 9 Cambridge Economics. It is designed for quick revision and serves as a handy reference for students preparing for internal assessments or building a strong foundation for IGCSE. Use this guide to master the quantitative and theoretical tools needed to analyse economic problems effectively.
本手册为 Year 9 剑桥经济课程总结了必备的公式与定理，旨在帮助学生快速复习，并为 IGCSE 学习打下坚实基础。使用这本速查指南，你可以掌握分析经济问题所需的定量与理论工具。
1. Opportunity Cost & Production Possibility Frontier | 机会成本与生产可能性边界
Opportunity cost is defined as the value of the next best alternative that must be given up when making a choice. This concept lies at the heart of economics because scarcity forces individuals, firms and governments to make trade-offs. The true cost of any decision includes not only the monetary expense but also the forgone benefits of the next best option.
机会成本是指为了做出某一选择而必须放弃的次优选项的价值。由于资源稀缺，个人、企业和政府都需要进行权衡，因此这个概念是经济学的核心。任何决策的真正代价不仅包括货币支出，还包括所放弃的次佳选择的收益。
The Production Possibility Frontier (PPF) is a diagram that shows the maximum combinations of two goods or services an economy can produce when all resources are fully and efficiently used. Points on the PPF represent productive efficiency; points inside the curve represent inefficiency or unemployed resources; points outside are currently unattainable.
生产可能性边界（PPF）是展示一个经济体在资源充分且有效使用下能够生产的两种商品或服务的最大组合的示意图。曲线上的点代表生产效率；曲线内部的点代表低效或资源未充分利用；曲线外部的点则是目前无法达到的。
Opportunity Cost = Benefit of the Next Best Alternative Forgone
机会成本 = 放弃的次优选择的收益
te of transformation (MRT) = ΔY / ΔX shows how many units of Y are given up for one extra unit of X. In a concave (bowed-out) PPF, the law of increasing opportunity cost holds: as you produce more of one good, the opportunity cost in terms of the other good rises.
在 PPF 上，机会成本由斜率体现。沿着曲线移动，要获得更多的 X 商品就必须牺牲一部分 Y 商品。边际转换率（MRT）= ΔY / ΔX 表示每多生产一单位 X 需要放弃多少单位 Y。如果 PPF 是凹向原点的（向外弯曲），则递增机会成本定律成立：随着某种商品产量增加，以另一种商品计量的机会成本会上升。
2. Demand and Supply Functions | 需求与供给函数
The law of demand states that, ceteris paribus, as the price of a good rises, the quantity demanded falls. This inverse relationship is captured by a linear demand function: Qd = a – bP, where 'a' is the quantity demanded when the price is zero (the intercept), and 'b' represents the rate at which demand falls as price increases (the slope).
需求定律指出，在其他条件不变的情况下，商品价格上升，需求量下降。这种反向关系可以用线性需求函数表示：Qd = a – bP，其中 a 是价格为零时的需求量（截距），b 表示价格每上升一单位需求量的减少量（斜率）。
Qd = a – bP
The law of supply states that, ceteris paribus, as price increases, the quantity supplied increases. A typical linear supply function is Qs = c + dP, where 'c' pplied at zero price (usually negative or zero, indicating a minimum price is needed), and 'd' is the positive slope showing how much supply responds to a change in price.
供给定律指出，在其他条件不变的情况下，价格上升，供给量增加。典型的线性供给函数为 Qs = c + dP，其中 c 是价格为零时的供给量（通常为负或零，说明需要有一个最低价格才会开始供给），d 为正值斜率，反映供给对价格变化的反应程度。
Qs = c + dP
Changes in factors other than the good's own price shift the entire demand or supply curve. For demand, these non-price determinants include income, tastes, prices of substitutes and complements, and expectations. For supply, they include production costs, technology, taxes, subsidies and the number of sellers.
除了商品本身价格以外的因素变化会使整个需求曲线或供给曲线发生移动。需求的非价格决定因素包括收入、偏好、替代品和互补品的价格以及预期。供给的非价格决定因素包括生产成本、技术、税收、补贴和卖者数量。
3. Price Elasticity of Demand (PED) | 需求价格弹性
Price elasticity of demand measures the responsiveness of the quantity demanded of a good to a change in its price. The formula expresses this as the percentage change in quantity demanded divided by the percentage change in price. PED is almost always negative, but economists often ignore the minus sign and focus on its absolute value.
需求价格弹性衡量的是某种商品需求量对其价格变动的敏感程度。其公式为需求量的百分比变化除以价格的百分比变化。PED 通常为负值，但经济学家往往忽略负号而关注其绝对值。
PED = %ΔQd / %ΔP
PED = (ΔQd / Qd avg) ÷ (ΔP / Pavg)
ity demanded, so total revenue (P × Q) increases. If PED < 1, demand is price inelastic; a price decrease causes total revenue to fall. If PED = 1, demand is unit elastic and total revenue stays constant. Perfectly inelastic demand (PED = 0) means quantity demanded does not change with price, while perfectly elastic demand (PED = ∞) means any price increase causes quantity demanded to drop to zero.
若 PED > 1，需求富有价格弹性，消费者对价格变化非常敏感。价格下降会导致需求量以更大比例上升，因此总收入（P × Q）增加。若 PED < 1，需求缺乏价格弹性，降价会使总收入减少。若 PED = 1，需求为单位弹性，总收入保持不变。完全无弹性需求（PED = 0）表示需求量不随价格变化，而完全弹性需求（PED = ∞）表示任何涨价都会使需求量降至零。
The total revenue test is a quick way to check elasticity without calculating percentages. If a price cut raises total revenue, demand is elastic; if it lowers total revenue, demand is inelastic. This rule helps firms make pricing decisions.
总收入测试是一种无需计算百分比即可快速判断弹性的方法。如果降价使总收入上升，则需求有弹性；如果降价使总收入下降，则需求缺乏弹性。这一规则有助于企业制定定价策略。
4. Price Elasticity of Supply (PES) | 供给价格弹性
Price elasticity of supply measures how responsive the quantity supplied of a good is to a change in its price. It is calculated as the percentage change in quantity supplied divided by the percentage change in price. Unlike PED, PES is usually positive because higher prices generally encourage producers to supply more.
供给价格弹性衡量商品供给量对价格变动的反应程度。其计算方式为供给量的百分比变化除以价格的百分比变化。与 PED 不同，PES 通常为正值，因为价格提高一般会激励生产者增加供给。
PES = %ΔQs / %ΔP
PES = (ΔQs / Qs avg) ÷ (ΔP / Pavg)
When PES > 1, supply is elastic and producers can adjust output quickly without a large increase in cost. When PES < 1, supply is inelastic and firms find it difficult to change production in the short run. The main factors determining supply elasticity are the time period, availability of raw materials, complexity of production, spare capacity and the perishability of the product.
当 PES > 1 时，供给有弹性，生产者能够在不显著增加成本的情况下快速调整产量。当 PES < 1 时，供给缺乏弹性，企业短期内难以改变产量。决定供给弹性的主要因素包括时间周期、原材料的可获得性、生产复杂性、闲置产能以及产品是否易腐烂。
5. Market Equilibrium and the Price Mechanism | 市场均衡与价格机制
Market equilibrium occurs when the quantity demanded equals the quantity supplied at a particular price. This is where the demand and supply curves intersect. The equilibrium price (Pe) and equilibrium quantity (Qe) clear the market, meaning there is no tendency for change.
市场均衡出现在某一价格下需求量等于供给量时，即需求曲线与供给曲线相交之处。均衡价格（Pe）和均衡数量（Qe）使市场出清，没有变动的趋势。
Qd = Qs at equilibrium
均衡时 Qd = Qs
If the market price is above equilibrium, excess supply (surplus) results, pushing the price down as sellers compete. If the price is below equilibrium, excess demand (shortage) occurs, pulling the price up as buyers compete. The price mechanism – sometimes called the invisible hand – describes how prices adjust to allocate scarce resources efficiently without any central planning.
若市场价格高于均衡水平，会出现超额供给（过剩），促使卖方竞争压价。若价格低于均衡，则出现超额需求（短缺），买方竞争抬价。价格机制——有时被称为“看不见的手”——描述了价格如何在没有任何中央计划的情况下自行调整，从而有效配置稀缺资源。
Shifts in demand or supply disrupt equilibrium and lead to a new equilibrium price and quantity. For example, an increase in demand (rightward shift) raises both equilibrium price and quantity, while an increase in supply (rightward shift) lowers equilibrium price and raises equilibrium quantity.
需求或供给的移动会打破均衡，导致新的均衡价格与数量。例如，需求增加（向右移动）会同时提高均衡价格和数量；而供给增加（向右移动）则会降低均衡价格并提高均衡数量。
6. Costs, Revenue and Profit | 成本、收益与利润
In economics, firms face various types of costs. Total fixed costs (TFC) do not vary with output in the short run (e.g. rent), while total variable costs (TVC) change directly with the level of production (e.g. raw materials). Total cost (TC) is the sum of fixed and variable costs. Average total cost (ATC or AC) is the cost per unit of output.
在经济学中，企业面临各类成本。总固定成本（TFC）在短期内不随产量变动（如租金），总可变成本（TVC）则直接随产量变化（如原材料）。总成本（TC）是固定成本与可变成本之和。平均总成本（ATC 或 AC）是每单位产出的成本。
TC = TFC + TVC
ATC = TC ÷ Q (Q = quantity of output / 产量)
Total revenue (TR) is the income a firm receives from selling its output. It is calculated by multiplying the price per unit by the quantity sold. Average revenue (AR) is TR divided by Q, which is equal to the price. Profit is what remains after all costs are subtracted from total revenue.
总收入（TR）是企业销售产品所得的收入，即单位售价乘以销售数量。平均收入（AR）为 TR 除以 Q，等同于价格。利润是总收入扣除所有成本后的剩余部分。
TR = P × Q
Profit / 利润 = TR – TC
neither a profit nor a loss. If TR > TC, the firm earns supernormal profit; if TR < TC, it makes a loss. Understanding cost and revenue structures helps businesses decide how much to produce.
当 TR = TC 时，企业盈亏平衡，既无盈利也无亏损；若 TR > TC，企业获得超额利润；若 TR < TC，则出现亏损。理解成本与收益结构有助于企业决定产量水平。
7. Productivity and Efficiency | 生产率与效率
Productivity measures how efficiently inputs are converted into outputs. Labour productivity, the most common measure, is defined as total output divided by the number of workers (or total hours worked). Higher labour productivity means that each worker produces more, which can lower costs and increase living standards over time.
生产率衡量的是投入转化为产出的效率。最常用的衡量标准是劳动生产率，即总产量除以工人数量（或总工作小时数）。劳动生产率提高意味着每个工人产出更多，可以降低成本并逐步提高生活水平。
Labour Productivity = Total Output ÷ Number of Workers
劳动生产率 = 总产量 ÷ 工人数量
Capital productivity is total output divided by the amount of capital employed. Factors that boost productivity include investment in new technology, better education and training, improved management practices and infrastructure development. Productivity growth is a key driver of economic growth.
资本生产率是总产量除以所使用的资本量。提高生产率的
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