📚 CCEA Year 10 Economics Formula & Theorem Quick Reference Handbook | CCEA 十年级经济学公式定理速查手册
This quick reference handbook brings together all the essential formulae, definitions and key relationships you will encounter in the CCEA Year 10 Economics course. It is designed to support your revision by providing clear, concise statements of each concept, followed by worked examples or explanations. Whether you are memorising elasticity calculations, analysing market equilibrium or understanding macroeconomic indicators, this guide organises the material so you can find what you need quickly and reinforce your learning.
本速查手册汇集了 CCEA 十年级经济课程中所有重要的公式、定义和关键关系。它旨在通过为每个概念提供清晰、简明的表述，并辅以实例或解释来支持你的复习。无论是在记忆弹性计算、分析市场均衡，还是理解宏观经济指标，本指南都对知识点进行了系统整理，方便你快速查找所需内容，巩固学习成果。
1. The Law of Demand and Supply | 需求与供给定理
The law of demand states that, ceteris paribus, as the price of a good rises, the quantity demanded falls, and vice versa. This inverse relationship is shown by a downward‑sloping demand curve. The law of supply states that, ceteris paribus, as the price of a good rises, the quantity supplied rises, and vice versa. This direct relationship is shown by an upward‑sloping supply curve.
需求定理指出，在其他条件不变的情况下，商品价格上升，需求量下降，反之亦然。这种反向关系表现为一条向下倾斜的需求曲线。供给定理指出，在其他条件不变的情况下，商品价格上升，供给量上升，反之亦然。这种正向关系表现为一条向上倾斜的供给曲线。
Shifts in the demand curve are caused by changes in factors such as income, tastes, prices of substitutes and complements, advertising and population. Shifts in the supply curve are caused by changes in production costs, technology, indirect taxes, subsidies and the number of firms in the market.
需求曲线的移动由收入、偏好、替代品和互补品的价格、广告以及人口等因素的变化引起。供给曲线的移动由生产成本、技术、间接税、补贴和市场中企业数量的变化引起。
Demand: Qd = f(P) with dQd/dP < 0
Supply: Qs = f(P) with dQs/dP > 0
2. 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. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.
需求价格弹性衡量的是需求量对商品自身价格变化的反应程度。计算公式为需求量变化的百分比除以价格变化的百分比。
PED = %ΔQd / %ΔP
tly elastic, PED = ∞; when perfectly inelastic, PED = 0. Knowledge of PED helps firms set prices to maximise total revenue: if demand is elastic, a price cut raises total revenue; if inelastic, a price rise raises total revenue.
如果 PED > 1，需求富有弹性（消费者反应灵敏）。如果 PED < 1，需求缺乏弹性。如果 PED = 1，需求为单位弹性。需求完全弹性时，PED = ∞；完全无弹性时，PED = 0。了解 PED 有助于企业制定实现总收入最大化的价格：若需求富有弹性，降价能增加总收入；若需求缺乏弹性，提价能增加总收入。
3. Price Elasticity of Supply (PES) | 供给价格弹性
Price elasticity of supply measures how much the quantity supplied changes in response to a change in price. It is calculated as the percentage change in quantity supplied divided by the percentage change in price.
供给价格弹性衡量的是供给量对价格变化的反应程度。计算公式为供给量变化的百分比除以价格变化的百分比。
PES = %ΔQs / %ΔP
When PES > 1, supply is elastic; when PES < 1, supply is inelastic. The main determinants of PES are the time period (supply is more elastic in the long run), the availability of spare capacity, the ease of storing stock, the complexity of the production process and the mobility of factors of production.
当 PES > 1 时，供给富有弹性；当 PES < 1 时，供给缺乏弹性。决定 PES 的主要因素包括时间周期（长期内供给弹性更大）、闲置产能的可获得性、存货储存的难易程度、生产过程的复杂性以及生产要素的流动性。
4. Income Elasticity of Demand (YED) and Cross Elasticity of Demand (XED) | 收入弹性与交叉弹性
Income elasticity of demand measures the responsiveness of demand to a change in consumers' income. The formula is the percentage change in quantity demanded divided by the percentage change in income.
收入弹性衡量的是需求对消费者收入变化的反应程度。计算公式为需求量变化的百分比除以收入变化的百分比。
YED = %ΔQd / %ΔY
Normal goods have a positive YED (YED > 0). Luxury goods tend to have YED > 1, while necessities have 0 < YED < 1. Inferior goods have a negative YED. Cross elasticity of demand measures the responsiveness of demand for good A to a change in the price of good B.
正常商品的 YED 为正（YED > 0）。奢侈品的 YED 通常大于 1，而必需品的 YED 在 0 到 1 之间。低档商品的 YED 为负。交叉弹性衡量的是商品 A 的需求对商品 B 价格变化的反应程度。
XED = %ΔQd of good A / %ΔP of good B
A positive XED indicates substitute goods; a negative XED indicates complementary goods. An XED close to zero suggests the goods are unrelated.
XED 为正时表示替代品；为负时表示互补品。XED 接近于零则表示商品不相关。
5. Market Equilibrium and Disequilibrium | 市场均衡与不均衡
s no inherent tendency for change. Algebraically, equilibrium is found by setting Qd = Qs.
市场均衡出现在需求量等于供给量的价格水平上。此时不存在内在的变化趋势。从代数角度看，均衡可通过令 Qd = Qs 求得。
Equilibrium condition: Qd = Qs
Example: suppose the demand function is Qd = 100 – 2P and the supply function is Qs = –20 + 4P. Equating: 100 – 2P = –20 + 4P → 120 = 6P → P* = £20. Substituting P* into either function gives Q* = 100 – 2(20) = 60 units.
示例：假设需求函数为 Qd = 100 – 2P，供给函数为 Qs = –20 + 4P。令两者相等：100 – 2P = –20 + 4P → 120 = 6P → P* = 20 英镑。将 P* 代入任一函数可得 Q* = 100 – 2×20 = 60 单位。
Disequilibrium arises when the market price is above or below the equilibrium price. A price above equilibrium creates excess supply (a surplus), putting downward pressure on price. A price below equilibrium creates excess demand (a shortage), putting upward pressure on price. These forces push the market back toward equilibrium.
当市场价格高于或低于均衡价格时，就会出现非均衡状态。价格高于均衡导致超额供给（过剩），对价格形成下行压力。价格低于均衡导致超额需求（短缺），对价格形成上行压力。这些力量会将市场推回均衡状态。
6. Consumer 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. It is measured as the area below the demand curve and above the market price. Producer surplus is the difference between the price producers actually receive and the minimum price they are willing to accept. It is the area above the supply curve and below the market price.
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。它用需求曲线之下、市场价格之上的面积来衡量。生产者剩余是生产者实际收到的价格与愿意接受的最低价格之间的差额。它是供给曲线之上、市场价格之下的面积。
For a linear demand curve P = a – and a given market price P*, consumer surplus can be calculated as the area of a triangle:
对于线性需求曲线 P = a – bQ 和给定的市场价格 P*，消费者剩余可按三角形面积计算：
Consumer surplus = ½ × (a – P*) × Q*
Similarly, for a linear supply curve, producer surplus is ½ × (P* – e concepts are used to evaluate the welfare effects of price changes, taxes and subsidies.
类似地，对于线性供给曲线，生产者剩余为 ½ × (P* – c) × Q*，其中 c 是供给曲线的纵截距。这些概念用于评估价格变化、税收和补贴的福利效应。
7. Costs, Revenue and Profit | 成本、收入与利润
Total cost (TC) is the sum of total fixed cost (TFC) and total variable cost (TVC). Total revenue (TR) is price multiplied by quantity sold. Profit is total revenue minus total cost.
总成本 (TC) 是总固定成本 (TFC) 与总可变成本 (TVC) 之和。总收入 (TR) 等于价格乘以销售量。利润等于总收入减去总成本。
TC = TFC + TVC
TR = P × Q
Profit = TR – TC
cost (AVC) = TVC / Q. Marginal cost (MC) is the additional cost of producing one more unit: MC = ΔTC / ΔQ. Profit maximisation occurs where marginal cost equals marginal revenue (MR = MC).
平均成本由总成本除以产量得出。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。边际成本 (MC) 是多生产一单位产品所增加的成本：MC = ΔTC / ΔQ。利润最大化出现在边际成本等于边际收益时 (MR = MC)。
Profit maximisation rule: MR = MC
8. Market Structures – Perfect Competition to Monopoly | 市场结构：完全竞争与垄断
y buyers and sellers, homogeneous products, free entry and exit, and perfect information. Firms are price‑takers and in the long run earn only normal profit. The profit‑ ince the demand curve facing the firm is perfectly elastic, price equals marginal revenue.
在完全竞争市场中，买卖双方众多，产品同质，进入和退出自由，信息完全。企业是价格接受者，长期内只能获得正常利润。利润最大化条件是 MR = MC，但由于企业面临的需求曲线完全弹性，价格等于边际收益。
For a perfectly competitive firm: P = MR = AR = MC (in equilibrium)
. Profit is maximised where MR = MC, but the price is found on the demand curve above that quantity, leading to supernormal profits in the long run and a deadweight loss to society.
垄断指市场中只有一个卖者，且存在显著的进入壁垒。垄断者面临整个市场的需求曲线，可设定高于边际成本的价格。利润最大化仍遵循 MR = MC，但价格位于该产量需求曲线上方，从而在长期内获得超额利润，并给社会带来无谓损失。
Other market structures include monopolistic competition (many firms, differentiated products, low barriers) and oligopoly (few dominant firms, interdependence, potential for collusion). The concentration ratio and game theory pricing models are often used to analyse oligopolistic behaviour.
其他市场结构还包括垄断竞争（企业众多，产品有差异，壁垒较低）和寡头垄断（几家主导企业，相互依存，存在合谋可能）。集中度和博弈论定价模型常被用来分析寡头垄断行为。
9. Macroeconomic Indicators – GDP, Unemployment, Inflation | 宏观经济指标：GDP、失业、通胀
Gross Domestic Product (GDP) is the total value of all final goods and services produced within a country in a given period. The three methods of measuring GDP are expenditure, income and output. The expenditure approach is summarised by the equation:
国内生产总值 (GDP) 是指一国在一定时期内生产的所有最终产品和服务的总价值。衡量 GDP 的三种方法是支出法、收入法和产出法。支出法可由以下等式概括：
GDP = C + I + G + (X – M)
where C is consumption, I is investment, G is government spending, X is exports and M is imports. Nominal GDP is measured at current prices, while real GDP is adjusted for inflation to reflect true volume changes.
其中 C 为消费，I 为投资，G 为政府支出，X 为出口，M 为进口。名义 GDP 按当期价格计算，而实际 GDP 经过通货膨胀调整，以反映真实的物量变动。
The unemployment rate is the percentage of the labour force that is actively seeking work but unable to find a job. The inflation rate is the annual percentage change in the general price level, commonly measured by the Consumer Price Index (CPI).
失业率是指劳动力中积极寻找工作但未能就业的人所占的百分比。通胀率是指一般物价水平的年度百分比变动，通常用消费者价格指数 (CPI) 来衡量。
Unemployment rate = (Number of unemployed / Labour force) × 100%
Inflation rate = (CPI this year – CPI last year) / CPI last year × 100%
Understanding these indicators helps governments and central banks formulate appropriate economic policies.
理解这些指标有助于政府和中央银行制定适当的经济政策。
10. The Multiplier Effect | 乘数效应
The multiplier effect describes how an initial injection of spending into the economy leads to a larger final increase in national income. This occurs because one person's spending becomes another's income, which in turn is partly spent again. The size of the multiplier depends on the marginal propensity to consume (MPC) – the fraction of extra income that households spend.
乘数效应描述了一笔初始注入经济的支出如何导致国民收入出现更大的最终增长。其原因在于，一个人的支出成为另一个人的收入，然后这部分收入又会被部分地再次支出。乘数的大小取决于边际消费倾向 (MPC)，即家庭将额外收入用于消费的比例。
Multiplier (k) = 1 / (1 – MPC) = 1 / MPS
MPC leads to a larger multiplier. For example, if the MPC is 0.8, the multiplier is 1 / (1 – 0.8) = 5. This means that an initial injection of £100 million could eventually raise national income by £500 million, assuming sufficient spare capacity exists in the economy.
MPS（边际储蓄倾向）是额外收入中用于储蓄的比例。MPC 越高，乘数越大。例如，如果 MPC 为 0.8，乘数为 1 / (1 – 0.8) = 5。这意味着，若经济中存在足够的闲置产能，1 亿英镑的初始注入最终可使国民收入增加 5 亿英镑。
When the government increases its spending, the impact on national income is magnified by the multiplier. Conversely, withdrawing spending reduces income by a multiplied amount. This principle underpins fiscal policy decisions.
当政府增加支出时，通过乘数效应会放大对国民收入的影响。反之，减少支出则会使收入成倍地下降。这一原理是财政政策决策的基础。
11. Monetary and Fiscal Policy Tools | 货币政策与财政政策工具
Monetary policy involves the central bank controlling the money supply and interest rates to influence economic activity. A lower policy interest rate encourages borrowing and investment, boosting aggregate demand and helping to close a recessionary gap. Raising the rate can dampen inflationary pressures by curbing spending.
货币政策指中央银行通过控制货币供给和利率来影响经济活动。降低政策利率会鼓励借贷和投资，从而增加总需求，有助于消除衰退缺口。提高利率则可通过抑制支出来缓解通胀压力。
Fiscal policy involves the government adjusting its spending (G) and taxation (T) to influence the economy. Expansionary fiscal policy – either increasing G or cutting T – can stimulate demand during a downturn, while contractionary fiscal policy – reducing G or raising T – can cool an overheating economy.
财政政策是指政府通过调整支出 (G) 和税收 (T) 来影响经济。扩张性财政政策——要么增加政府支出，要么减税——可在经济低迷时期刺激需求；而紧缩性财政政策——减少政府支出或增税——则可为过热的经济降温。
The government's budget balance is the difference between its total revenue and its spending. A budget deficit occurs when G > T, requiring borrowing. A budget surplus occurs when T > G, allowing debt repayment. Automatic stabilisers, such as progressive taxation and unemployment benefits, help to smooth economic cycles without active policy changes.
政府的预算平衡是其总收入与总支出之间的差额。当政府支出大于税收 (G > T) 时出现财政赤字，需要借款弥补。当税收大于政府支出 (T > G) 时出现财政盈余，可用于偿还债务。自动稳定器，如累进税制和失业救济，无需主动调整政策即可起到熨平经济周期的作用。
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