📚 Year 11 CCEA Economics Formulas and Theorems Quick Reference | CCEA 经济公式定理速查手册
This quick reference handbook compiles the essential formulas, theorems, and key concepts required for Year 11 CCEA Economics. It covers microeconomic fundamentals such as elasticity, utility, and production costs, as well as macroeconomic indicators and policy tools. Each section is designed for rapid revision, with bilingual explanations to reinforce understanding.
本速查手册汇总了Year 11 CCEA经济学所需的核心公式、定理及关键概念。内容涵盖需求弹性、效用、生产成本等微观基础，以及宏观经济指标与政策工具。每个小节均配有双语解说，方便快速复习，强化理解。
1. Scarcity and Opportunity Cost | 稀缺与机会成本
The fundamental economic problem states that resources are limited while human wants are infinite, leading to scarcity. Opportunity cost is defined as the value of the next best alternative forgone when a choice is made.
基本的经济学问题指出，资源是有限的而人的欲望是无限的，这就产生了稀缺性。机会成本是指做出某一选择时所放弃的次优替代方案的价值。
When calculating opportunity cost for two goods, the formula for the opportunity cost of one extra unit of Good X in terms of Good Y is:
计算两种商品的机会成本时，多获得一单位商品X所放弃的商品Y数量的公式为：
Opportunity Cost of 1 unit of X = ΔY / ΔX
This ratio shows how many units of Y must be given up to produce one more unit of X along a production possibility frontier (PPF).
该比率表示在生产可能性边界上，多生产一单位X必须放弃多少单位Y。
2. Demand and Supply | 需求与供给
The demand curve shows the quantity of a good consumers are willing and able to buy at different prices, normally downward sloping. The law of demand states that as price rises, quantity demanded falls, ceteris paribus.
需求曲线表示消费者在不同价格下愿意并能够购买的数量，通常向右下方倾斜。需求定律指出，在其他条件不变的情况下，价格上升，需求量下降。
The supply curve slopes upward, reflecting the law of supply: as price rises, quantity supplied increases. Market equilibrium occurs where quantity demanded equals quantity supplied.
供给曲线向右上方倾斜，反映供给定律：价格上升，供给量增加。市场均衡发生在需求量等于供给量的时候。
The basic linear demand and supply functions can be expressed as:
基本的线性需求函数和供给函数可表示为：
Qd = a − bP
Qs = c + dP
Where a, b, c, and d are constants. Equilibrium price is found by setting Qd = Qs.
其中a、b、c、d为常数。令Qd = Qs 可解出均衡价格。
3. Price Elasticity of Demand (PED) | 需求价格弹性
PED 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动的反应程度。公式为：
PED = %Δ Quantity Demanded / %Δ Price
Using the midpoint method for greater accuracy:
为提高准确性采用中点法计算：
PED = (ΔQ / Qₐᵥₑ) ÷ (ΔP / Pₐᵥₑ)
Values of PED indicate: perfectly inelastic (0), inelastic (0 to –1), unitary elastic (–1), elastic (less than – ectly elastic (∞). For CCEA, the absolute value is often used, ignoring the negative sign.
PED 的值表示：完全无弹性 (0)、缺乏弹性 (0 至 –1)、单位弹性 (–1)、富有弹性 (小于 –1) 和完全弹性 (∞)。CCEA 考试中常使用绝对值，忽略负号。
evenue; if inelastic, a price rise raises total revenue. Total revenue = Price × Quantity.
总收益检验：若需求富有弹性，降价会增加总收益；若缺乏弹性，提价会增加总收益。总收益 = 价格 × 数量。
4. Income and Cross Elasticities | 收入弹性与交叉弹性
Income elasticity of demand (YED) measures how quantity demanded responds to a change in consumers' income:
需求的收入弹性衡量需求量对消费者收入变动的反应程度：
YED = %Δ Quantity Demanded / %Δ Income
Positive YED indicates a normal good; negative YED indicates an inferior good. A YED greater than 1 suggests a luxury good.
YED 为正表示正常品；为负表示劣等品。YED 大于 1 则说明该商品为奢侈品。
Cross elasticity of demand (XED) measures how the demand for one good responds to a price change of another:
需求的交叉弹性衡量一种商品的需求对另一种商品价格变动的反应程度：
XED = %Δ Qd of Good A / %Δ Price of Good B
Positive XED means the two goods are substitutes; negative XED means they are complements. An XED close to zero indicates unrelated goods.
XED 为正表示两种商品为替代品；为负表示为互补品。XED 接近于零则说明两种商品不相关。
5. Price Elasticity of Supply (PES) | 供给价格弹性
PES measures the responsiveness of quantity supplied to a change in price:
供给价格弹性衡量供给量对价格变动的反应程度：
PES = %Δ Quantity Supplied / %Δ Price
The key determinants of PES include production time, spare capacity, and the ease of storing stock. A value above 1 indicates elastic supply; below 1 indicates inelastic supply.
决定 PES 的关键因素包括生产时间、闲置产能和库存存储的难易程度。PES 大于 1 表示供给富有弹性；小于 1 表示供给缺乏弹性。
In the long run, supply tends to be more elastic as firms can adjust all factors of production.
在长期内，企业可以调整所有生产要素，供给往往更具弹性。
6. Utility, Marginal Utility, and Consumer Equilibrium | 效用、边际效用与消费者均衡
Utility is the satisfaction derived from consuming a good. Total utility (TU) is the total satisfaction from all units consumed. Marginal utility (MU) is the additional satisfaction from consuming one more unit:
效用是消费者从商品消费中获得的满足感。总效用是消费所有单位获得的总满足，边际效用是多消费一单位商品所带来的额外满足：
MU = ΔTU / ΔQ
The law of diminishing marginal utility states that as more of a good is consumed, the extra satisfaction eventually declines.
边际效用递减规律指出，随着消费数量的增加，额外满足感最终会下降。
A rational consumer maximises utility when the marginal utility per pound spent is equal across all goods, subject to a budget constraint:
理性消费者会在预算约束下，使花在每种商品上的最后一英镑所带来的边际效用相等，从而实现效用最大化：
MUₐ / Pₐ = MUₙ / Pₙ
This is known as the equi-marginal principle or consumer equilibrium.
这被称为等边际原理或消费者均衡条件。
7. Costs of Production | 生产成本
Total cost (TC) is the sum of total fixed costs (TFC) and total variable costs (TVC):
总成本是总固定成本与总可变成本之和：
TC = TFC + TVC
Average total cost (ATC) is cost per unit of output:
平均总成本是每单位产出的成本：
ATC = TC / Q
milarly, average fixed cost and average variable cost are AFC = TFC / Q and AVC = TVC / Q.
同理，平均固定成本为 AFC = TFC / Q，平均可变成本为 AVC = TVC / Q。
Marginal cost (MC) is the change in total cost when output changes by one unit:
边际成本是产量变动一单位时总成本的变动量：
MC = ΔTC / ΔQ
Short-run costs feature diminishing marginal returns, causing MC to eventually rise. Long-run average cost curves can show economies and diseconomies of scale.
短期成本存在边际报酬递减，导致边际成本最终上升。长期平均成本曲线可体现规模经济与规模不经济。
8. Revenue and Profit | 收益与利润
Total revenue (TR) is the money received from selling a quantity of goods:
总收益是销售一定数量商品所获得的货币收入：
TR = Price × Quantity
Average revenue (AR) is revenue per unit sold, which equals the price if all units sell at the same price:
平均收益是每单位销售的收益，若所有商品以同一价格销售，则等于价格：
AR = TR / Q = P
Marginal revenue (MR) is the addition to total revenue from selling one more unit:
边际收益是增加销售一单位商品时总收益的增加量：
MR = ΔTR / ΔQ
Profit is total revenue minus total cost. A firm maximises profit where marginal cost equals marginal revenue:
利润等于总收益减总成本。企业实现利润最大化时满足边际成本等于边际收益：
Profit maximisation: MC = MR
Normal profit occurs when TR equals TC (including opportunity cost). Supernormal profit arises when TR exceeds TC.
当总收益等于总成本（包含机会成本）时获得正常利润；总收益超过总成本时获得超额利润。
9. Market Failure and Externalities | 市场失灵与外部性
Market failure occurs when the free market fails to allocate resources efficiently. Key sources include externalities, public goods, and information asymmetries.
市场失灵指自由市场无法有效配置资源。主要原因包括外部性、公共产品和信息不对称。
An externality is a cost or benefit experienced by a third party not directly involved in a transaction. The social cost equals private cost plus external cost:
外部性是指未直接参与交易的第三方所承受的成本或收益。社会成本等于私人成本加外部成本：
Social Cost = Private Cost + External Cost
benefit + external benefit. Negative production externalities lead to overproduction; positive consumption externalities lead to underconsumption.
同理，社会收益 = 私人收益 + 外部收益。负生产外部性导致过度生产，正消费外部性导致消费不足。
The deadweight welfare loss can be illustrated by the triangle between the marginal social cost and marginal social benefit curves at the free market quantity.
无谓福利损失可由市场产量处边际社会成本与边际社会收益曲线之间的三角形表示。
10. Macroeconomic Indicators | 宏观经济指标
Gross Domestic Product (GDP) measures the total value of final goods and services produced within an economy in a given period. The expenditure approach uses:
国内生产总值衡量一个经济体在一定时期内生产的最终商品与服务的总价值。支出法计算公式为：
GDP = C + I + G + (X − M)
Where C = consumption, I = investment, G = government spending, X = exports, M = imports.
其中 C = 消费，I = 投资，G = 政府支出，X = 出口，M = 进口。
The inflation rate is the percentage change in the average price level, commonly measured by the Consumer Price Index (CPI):
通货膨胀率是平均价格水平的百分比变动，通常用消费者价格指数衡量：
Inflation Rate = (CPIₙₑₓₜ − CPIₚᵣₑᵥ) / CPIₚᵣₑᵥ × 100%
The unemployment rate is the number of people actively seeking work as a percentage of the labour force:
失业率是积极寻找工作的人数占劳动力总数的百分比：
Unemployment Rate = (Number Unemployed / Labour Force) × 100%
Economic growth is usually measured as the percentage change in real GDP from one period to the next.
经济增长通常以实际GDP从一个时期到下一个时期的百分比变动来衡量。
11. Aggregate Demand and Aggregate Supply | 总需求与总供给
Aggregate demand (AD) is the total planned expenditure on an economy's goods and services at a given price level:
总需求是在给定价格水平下，对一国商品和服务的计划支出总额：
AD = C + I + G + (X − M)
The AD curve slopes downward due to the wealth effect, interest rate effect, and international trade effect.
由于财富效应、利率效应和国际贸易效应，AD曲线向右下方倾斜。
Short-run aggregate supply (SRAS) shows the total output firms will supply at different price levels, influenced by input costs. Long-run aggregate supply (LRAS) is determined by the quantity and productivity of factors of production and is often drawn as vertical at the full-employment level of output.
短期总供给反映企业在不同价格水平下愿意提供的总产出，受投入成本影响。长期总供给由生产要素的数量和生产率决定，通常画成一条位于充分就业产出水平的垂直线。
Macroeconomic equilibrium occurs where AD equals SRAS (and LRAS in the long run). Shifts in AD or SRAS can create inflationary or deflationary gaps.
宏观经济均衡发生在AD等于SRAS（长期则等于LRAS）之时。AD或SRAS的移动会造成通胀缺口或通缩缺口。
12. Government Policy Tools | 政府政策工具
Fiscal policy involves changes in government spending and taxation. The multiplier effect describes how an initial change in spending leads to a larger change in national income:
财政政策涉及政府支出和税收的变动。乘数效应描述了初始支出的变动如何导致国民收入发生更大的变动：
Multiplier = 1 / (1 − MPC)
MPC is the marginal propensity to consume, the fraction of additional income spent on consumption:
MPC 为边际消费倾向，即额外收入中用于消费的比例：
MPC = ΔC / ΔY
Monetary policy involves the central bank manipulating the interest rate or money supply to influence AD. A tightening policy raises interest rates to cool the economy; an expansionary policy lowers rates to stimulate spending.
货币政策指中央银行通过操控利率或货币供给来影响总需求。紧缩性政策提高利率以给经济降温；扩张性政策降低利率以刺激支出。
Supply-side policies aim to increase the productive capacity of the economy, shifting LRAS to the right. Examples include education, training, and tax reforms.
供给面政策旨在提高经济的生产能力，使LRAS右移。例子包括教育、培训及税制改革。
These tools are used to achieve macroeconomic objectives: low inflation, low unemployment, steady growth, and a satisfactory balance of payments.
这些工具用于实现宏观经济目标：低通胀、低失业、稳定增长及国际收支平衡。
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