📚 Year 9 CIE Economics Formula & Theorem Quick Reference Handbook | Year 9 CIE 经济：公式定理速查手册
This handbook provides a concise summary of the essential formulas and theorems you will encounter in the Year 9 CIE Economics course. Each concept is presented with its core logic, mathematical expression (where applicable), and illustrative notes to reinforce your understanding for classwork, homework, and exam preparation.
本手册简洁地汇总了 Year 9 CIE 经济课程中会接触到的核心公式与定理。每个概念都配有核心逻辑、数学表达式（如适用）和解释性说明，帮助你在课堂练习、作业和备考中巩固理解。
1. The Basic Economic Problem | 基本经济问题
Economics studies how people make choices under conditions of scarcity. Scarcity means that resources are limited while human wants are unlimited, forcing societies and individuals to decide what to produce, how to produce, and for whom to produce.
经济学研究的是人们如何在稀缺条件下做出选择。稀缺性是指资源有限而人的欲望无限，这迫使社会和个人必须决定生产什么、如何生产以及为谁生产。
Opportunity cost is the next best alternative forgone when an economic decision is made. It is a key concept that reminds us every choice involves a trade-off.
机会成本是指做出经济决策时所放弃的次优选择。这个概念提醒我们，每一个选择都包含取舍。
Fundamental economic questions: What to produce? How to produce? For whom to produce? All answers hinge on the allocation of scarce resources.
基本经济问题：生产什么？如何生产？为谁生产？所有回答都取决于稀缺资源的配置。
2. Demand | 需求
The law of demand states that, ceteris paribus, as the price of a good rises, the quantity demanded falls, and as price falls, the quantity demanded rises. This inverse relationship is shown by a downward-sloping demand curve.
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；价格下降，需求量上升。这种反向关系表现为一条向下倾斜的需求曲线。
A linear demand function can be written as: Qd = a − bP, where Qd is quantity demanded, P is price, a is the intercept (quantity demanded when price is zero), and b is the slope (change in Qd per unit change in P).
线性需求函数可表示为：Qd = a − bP，其中 Qd 为需求量，P 为价格，a 为截距（价格为零时的需求量），b 为斜率（每单位价格变化引起的 Qd 变化量）。
Movements along the demand curve are caused by a change in the good's own price, while shifts of the entire curve result from changes in other factors such as income, tastes, prices of related goods, and expectations.
需求量沿着需求曲线的移动是由商品自身价格变化引起的，而整条曲线的平移则由收入、偏好、相关商品价格和预期等因素变化所致。
3. Supply | 供给
The law of supply states that, ceteris paribus, as the price of a good increases, the quantity supplied increases, and as price decreases, the quantity supplied decreases. This positive relationship is represented by an upward-sloping supply curve.
供给定律指出，在其他条件不变的情况下，商品价格上升，供给量增加；价格下降，供给量减少。这种正向关系表现为一条向上倾斜的供给曲线。
A linear supply function can be expressed as: Qs = c + dP, where Qs is quantity supplied, P is price, c is the intercept (minimum price at which supply begins), and d is the slope (responsiveness of Qs to P).
线性供给函数可表达为：Qs = c + dP，其中 Qs 为供给量，P 为价格，c 为截距（供给开始的最低价格），d 为斜率（Qs 对 P 的反应程度）。
Shifts in the supply curve are driven by changes in production costs, technology, taxes and subsidies, number of sellers, and expectations. A movement along the curve reflects a change in the own price of the good.
供给曲线的平移由生产成本、技术、税收与补贴、卖者数量和预期等因素的变化驱动。沿着曲线的移动反映的则是商品自身价格的变化。
4. Market Equilibrium | 市场均衡
Market equilibrium occurs when quantity demanded equals quantity supplied at a particular price. There is no tendency for change as long as external factors remain constant.
当某一价格水平下需求量等于供给量时，市场达到均衡。只要外部因素保持不变，市场就没有变化的趋势。
Equilibrium condition: Qd = Qs. Solve for P to find the equilibrium price, then substitute into either function to obtain the equilibrium quantity.
均衡条件：Qd = Qs。求解 P 得到均衡价格，再将其代入任一函数得到均衡数量。
Excess demand (shortage) exists when market price is below equilibrium, pushing prices upward. Excess supply (surplus) exists when market price is above equilibrium, pulling prices downward.
当市场价格低于均衡价格时，存在超额需求（短缺），推动价格上升。当市场价格高于均衡价格时，存在超额供给（过剩），拉动价格下降。
These price adjustment mechanisms illustrate the "invisible hand" of the market, restoring equilibrium without central direction.
这些价格调整机制体现了市场的“看不见的手”，无需中央指令即可恢复均衡。
5. 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 the good's own price. Formula: PED = % ΔQd / % ΔP.
需求价格弹性衡量需求量对该商品自身价格变化的反应程度。公式：PED = % ΔQd / % ΔP。
are usually negative because of the law of demand, but we commonly use the absolute value |PED|. If |PED| > 1, demand is price elastic (responsive to price changes); if |PED| < 1, demand is price inelastic; if |PED| = 1, it is unit elastic.
依据需求定律，PED 通常为负值，但我们常取其绝对值 |PED|。若 |PED| > 1，需求富有价格弹性（对价格变化反应灵敏）；|PED| < 1，需求缺乏弹性；|PED| = 1，则为单位弹性。
Key determinants: availability of substitutes, necessity vs luxury, proportion of income spent, time period. Elastic demand affects total revenue: if P rises, TR falls; if P falls, TR rises. Inelastic demand: if P rises, TR rises.
关键决定因素：替代品的可获得性、必需品还是奢侈品、支出占收入的比例、时间长短。弹性需求对总收益的影响是：价格上升则 TR 下降，价格下降则 TR 上升。缺乏弹性的需求则相反：价格上升，TR 上升。
6. 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. Formula: PES = % ΔQs / % ΔP.
供给价格弹性衡量供给量对价格变化的反应程度。公式：PES = % ΔQs / % ΔP。
S = 0, supply is perfectly inelastic; if PES approaches infinity, it is perfectly elastic.
PES 通常为正值。若 PES > 1，供给富有弹性；PES < 1，供给缺乏弹性；PES = 0，供给完全无弹性；PES 趋于无穷大，则为完全弹性。
Determinants of PES include production time, availability of spare capacity, storage possibilities, and complexity of the production process. Longer time frames usually allow more elastic supply.
决定供给弹性的因素包括生产时间、剩余产能的可用性、存储可能性以及生产过程的复杂性。时间越长，供给通常越富有弹性。
7. Income Elasticity of Demand (YED) & Cross Elasticity (XED) | 收入弹性与交叉弹性
Income elasticity of demand measures how quantity demanded responds to a change in consumer income. Formula: YED = % ΔQd / % ΔY, where Y is income.
收入弹性衡量需求量对消费者收入变化的反应。公式：YED = % ΔQd / % ΔY，其中 Y 表示收入。
Goods with YED > 0 are normal goods (demand rises as income rises). For YED > 1, they are luxury goods; for 0 < YED < 1, they are necessities. Goods with YED < 0 are inferior goods (demand falls as income rises).
YED > 0 的商品为正常品（收入增加，需求增加）。YED > 1 为奢侈品；0 < YED < 1 为必需品。YED < 0 的商品为低档品（收入增加，需求减少）。
Cross elasticity of demand measures the responsiveness of demand for good A to a change in the price of good B. Formula: XED = % ΔQd of A / % ΔP of B.
交叉弹性衡量商品 A 的需求量对商品 B 价格变化的反应。公式：XED = % ΔQd of A / % ΔP of B。
If XED > 0, the goods are substitutes (e.g. tea and coffee); if XED < 0, they are complements (e.g. printers and ink cartridges).
若 XED > 0，这两种商品互为替代品（如茶与咖啡）；若 XED < 0，则互为互补品（如打印机与墨盒）。
8. Costs of Production | 生产成本
Total cost (TC) is the sum of total fixed costs (TFC) and total variable costs (TVC): TC = TFC + TVC. Fixed costs do not change with output in the short run; variable costs change with output.
总成本（TC）是总固定成本（TFC）与总可变成本（TVC）之和：TC = TFC + TVC。短期内固定成本不随产量变化，可变成本则随产量变化。
Average total cost: ATC = TC / Q. Average fixed cost: AFC = TFC / Q. Average variable cost: AVC = TVC / Q.
平均总成本：ATC = TC / Q。平均固定成本：AFC = TFC / Q。平均可变成本：AVC = TVC / Q。
Marginal cost is the additional cost of producing one more unit of output: MC = ΔTC / ΔQ. MC often declines initially due to rising marginal returns, then rises due to the law of diminishing marginal returns.
边际成本是多生产一单位产品所增加的成本：MC = ΔTC / ΔQ。由于边际报酬递增，MC 最初往往下降，但随后因边际报酬递减规律转而上升。
The short-run cost curves are U-shaped because of these productivity patterns. Understanding cost relationships helps firms make output and pricing decisions.
短期成本曲线因上述生产率模式而呈 U 形。理解成本关系有助于企业做出产量和定价决策。
9. Revenue | 收益
Total revenue (TR) is the income a firm receives from selling its goods: TR = P × Q, where P is the selling price per unit and Q is the quantity sold.
总收益（TR）是企业销售商品所获得的收入：TR = P × Q，其中 P 为单价，Q 为销量。
Average revenue (AR) is revenue per unit sold: AR = TR / Q = P. For a firm facing a downward-sloping demand curve, AR equals the price that consumers are willing to pay at each quantity.
平均收益（AR）是每单位销量带来的收益：AR = TR / Q = P。对于面临向下倾斜需求曲线的企业，AR 等于消费者在每一数量下愿意支付的价格。
Marginal revenue (MR) is the additional revenue gained from selling one more unit: MR = ΔTR / ΔQ = P; under monopoly or imperfect competition, MR is less than AR and can become negative.
边际收益（MR）是多销售一单位产品所带来的额外收益：MR = ΔTR / ΔQ。在完全竞争市场中，MR = AR = P；而在垄断或不完全竞争下，MR 小于 AR，甚至可能为负。
The relationship between elasticity and revenue is crucial: where demand is elastic, lowering price increases TR; where demand is inelastic, raising price increases TR.
弹性与收益的关系至关重要：在需求富有弹性处，降低价格可增加 TR；在需求缺乏弹性处，提高价格可增加 TR。
10. Profit | 利润
Profit is the difference between total revenue and total cost: Profit = TR − TC im to maximise profit, which occurs where marginal cost equals marginal revenue (MC = MR).
利润是总收益与总成本之间的差额：利润 = TR − TC。企业追求利润最大化，达到这一目标的产量水平位于边际成本等于边际收益处（MC = MR）。
Normal profit is the minimum return required to keep a firm in business; it is included as part of the firm's costs of production. Supernormal (abnormal) profit is any profit above normal profit.
正常利润是维持企业运营所需的最低回报，它已被包含在生产成本之中。超常利润（或异常利润）是指超出正常利润的任何利润。
ernormal profit arises when TR > TC. In the long run, competitive markets drive supernormal profit towards zero, while monopolies may sustain it.
正常利润出现于 TR = TC 时。超常利润出现于 TR > TC 时。在完全竞争市场中，长期内超常利润会趋于零，而垄断企业可能持续获得超常利润。
Profit provides signals for resource allocation. High profits attract new firms into an industry, while persistent losses encourage exit.
利润为资源配置提供信号。高利润吸引新企业进入行业，持续亏损则促使企业退出。
11. Production Possibility Frontier (PPF) | 生产可能性边界
A production possibility frontier shows the maximum combinations of two goods that an economy can produce given its resources and technology, under full and efficient use.
生产可能性边界展示了一个经济体在资源和技术水平给定，且充分高效利用的情况下，所能生产的两种商品的最大数量组合。
Points on the PPF curve are efficient and attainable; points inside the curve are inefficient (unemployment or underemployment of resources); points outside are unattainable with current resources.
位于 PPF 曲线上的点是有效率且可实现的；曲线内部的点表示无效率（资源未充分或未被利用）；曲线外部的点在当前资源下无法实现。
Moving along the PPF illustrates opportunity cost: to produce more of one good, some output of the other must be sacrificed. The slope of the PPF reflects the marginal rate of transformation.
沿着 PPF 移动体现了机会成本：要多生产一种商品，就必须牺牲另一种商品的部分产出。PPF 的斜率反映了边际转换率。
Economic growth shifts the PPF outward, allowing a country to produce more of both goods. This growth can result from increases in resources or improvements in technology.
经济增长使 PPF 曲线向外平移，让国家能够生产更多的两种商品。这种增长可能源于资源的增加或技术的进步。
12. Market Structures Overview | 市场结构概览
Market structure describes the key characteristics of a market, including the number of firms, type of product, freedom of entry and exit, and degree of control over price. The main types are: perfect competition, monopoly, oligopoly, and monopolistic competition.
市场结构描述的是一个市场的主要特征，包括企业数量、产品类型、进出市场的自由度以及企业控制价格的程度。主要类型包括：完全竞争、垄断、寡头和垄断竞争。
ms are price takers. P = MC = AR = MR in the long run, and only normal profits are earned.
完全竞争市场：众多小企业，同质产品，无进入或退出壁垒，企业是价格接受者。长期中 P = MC = AR = MR，企业仅能获得正常利润。
Monopoly: a single seller, unique product with no close substitutes, high barriers to entry. The monopolist is a price maker and can earn long-run supernormal profits. MR is below price.
垄断：单一卖者，产品独一无二且无相近替代品，进入壁垒高。垄断者是价格制定者，可长期获得超常利润。边际收益低于价格。
Oligopoly: a few large firms dominate the market, products may be homogeneous or differentiated, high barriers, firms are interdependent and may compete on non-price factors. Collusion can lead to cartel behaviour.
寡头：少数大企业占据市场主导，产品可同质也可差异化，进入壁垒高，企业之间互相依赖，可能在非价格因素上竞争。合谋可能导致卡特尔行为。
Monopolistic competition: many firms, product differentiation, low barriers. In the short run firms can earn supernormal profit; in the long run, free entry erodes supernormal profit to normal profit.
垄断竞争：众多企业，产品存在差异，进入壁垒较低。短期内企业可获得超常利润，长期内自由进入会将超常利润压缩至正常利润水平。
These structures determine pricing, output, and efficiency outcomes. The comparison provides a framework for evaluating real-world markets.
这些结构决定了定价、产量和效率结果。对不同市场结构的比较为评价现实市场提供了一个分析框架。
Published by TutorHao | Economics Revision Series | aleveler.com
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