📚 Year 11 CCEA Economics: Quick Reference Handbook of Formulas and Theorems | Year 11 CCEA 经济：公式定理速查手册
This handbook brings together the essential formulas, definitions, and quantitative tools you need for the Year 11 CCEA Economics course. Each section presents the core relationship in a clear, exam-friendly way, followed by its Chinese equivalent to support bilingual learning.
本手册汇集了 Year 11 CCEA 经济学课程所需的关键公式、定义和定量工具。每一节都以清晰、适合考试的方式呈现核心关系，并附有中文对应内容，以支持双语学习。
1. Price Elasticity of Demand (PED) | 需求的价格弹性
Price elasticity of demand measures how responsive the quantity demanded of a good is to a change in its price. The basic formula uses percentage changes.
PED = %Δ Quantity Demanded / %Δ Price
需求的价格弹性衡量一种商品的需求量对其价格变化的反应程度。基本公式采用百分比变化。
PED = %Δ Qd / %Δ P
A PED value greater than 1 indicates elastic demand (consumers are sensitive to price changes), a value less than 1 indicates inelastic demand, and a value of exactly 1 is unit elastic. The sign is normally ignored because the relationship is inverse, so PED is treated as a positive number.
PED 值大于 1 表示富有弹性（消费者对价格变化敏感），小于 1 表示缺乏弹性，等于 1 则表示单位弹性。由于需求量与价格呈反向关系，符号通常忽略不计，PED 被当作正数处理。
Knowledge of PED helps firms predict the effect of price changes on total revenue. If demand is elastic, a price cut raises total revenue; if demand is inelastic, a price rise increases total revenue.
掌握 PED 有助于企业预测价格变化对总收入的影响。若需求富有弹性，降价会增加总收入；若需求缺乏弹性，提价则会增加总收入。
2. Income and Cross Elasticities of Demand (YED & XED) | 需求的收入弹性与交叉弹性
Income elasticity of demand (YED) measures the responsiveness of demand to a change in consumers' income.
YED = %Δ Quantity Demanded / %Δ Income
需求的收入弹性（YED）衡量需求对消费者收入变化的反应程度。
YED = %Δ Qd / %Δ Y
YED is positive for normal goods and negative for inferior goods. A YED greater than 1 suggests a luxury good, while a YED between 0 and 1 indicates a necessity.
正常商品的 YED 为正，劣质品的 YED 为负。YED 大于 1 通常为奢侈品，介于 0 到 1 之间则为必需品。
Cross elasticity of demand (XED) measures the responsiveness of demand for one good when the price of another good changes.
XED = %Δ Quantity Demanded of Good A / %Δ Price of Good B
需求的交叉弹性（XED）衡量一种商品的需求对另一种商品价格变化的反应程度。
XED = %Δ Qd(A) / %Δ P(B)
XED is positive for substitute goods and negative for complementary goods. The larger the absolute value, the stronger the relationship.
替代品的 XED 为正，互补品的 XED 为负。绝对值越大，两种商品的关系越密切。
3. Price Elasticity of Supply (PES) | 供给的价格弹性
Price elasticity of supply measures how responsive the quantity supplied is to a change in price.
PES = %Δ Quantity Supplied / %Δ Price
供给的价格弹性衡量供给量对价格变化的反应程度。
PES = %Δ Qs / %Δ P
PES is always positive due to the law of supply. A value greater than 1 shows elastic supply, less than 1 shows inelastic supply, and equal to 1 is unit elastic. The key determinants include production time, spare capacity, and the availability of stocks.
由于供给定律，PES 始终为正。大于 1 表示供给富有弹性，小于 1 表示供给缺乏弹性，等于 1 为单位弹性。关键决定因素包括生产周期、闲置产能和库存的可获得性。
4. Revenue Concepts: Total, Average & Marginal | 收入概念：总收入、平均收入与边际收入
Total revenue (TR) is the income a firm receives from selling its output. It is calculated as price multiplied by quantity sold.
TR = Price × Quantity
总收入（TR）是企业销售产品所获得的收入，计算公式为价格乘以销售量。
TR = P × Q
Average revenue (AR) is revenue per unit sold and is equal to the price of the good. Marginal revenue (MR) is the change in total revenue from selling one additional unit.
AR = TR / Q = P
MR = ΔTR / ΔQ
平均收入（AR）是每单位销售的收入，等于商品价格。边际收入（MR）是多销售一单位产品所带来的总收入变化。
AR = TR / Q = P；MR = ΔTR / ΔQ
In perfect competition AR and MR are constant and equal to price. In other market structures MR slopes downward and lies below the AR curve.
在完全竞争市场中，AR 和 MR 保持不变且等于价格。在其他市场结构中，MR 向下倾斜且位于 AR 曲线下方。
5. Costs of Production: Total, Average & Marginal | 生产成本：总成本、平均成本与边际成本
Total cost (TC) is the sum of total fixed costs (TFC) and total variable costs (TVC). Fixed costs do not vary with output, while variable costs do.
TC = TFC + TVC
总成本（TC）是总固定成本（TFC）与总可变成本（TVC）之和。固定成本不随产量变化，可变成本则随产量变化。
TC = TFC + TVC
Average total cost (ATC or AC) is total cost divided by output. It can also be split into average fixed cost (AFC) and average variable cost (AVC).
AC = TC / Q = AFC + AVC
平均总成本（ATC 或 AC）是总成本除以产量。它也可分为平均固定成本（AFC）和平均可变成本（AVC）。
AC = TC / Q = AFC + AVC
Marginal cost (MC) is the additional cost of producing one more unit of output.
MC = ΔTC / ΔQ
边际成本（MC）是额外生产一单位产品所增加的成本。
MC = ΔTC / ΔQ
As output increases AFC falls continuously because fixed costs are spread over more units. MC eventually rises due to the law of diminishing returns.
随着产量增加，AFC 持续下降，因为固定成本被分摊到更多的产品上。由于边际报酬递减规律，MC 最终会上升。
6. Break-even Analysis | 收支平衡分析
The break-even point occurs where total revenue equals total costs, so the firm makes neither profit nor loss. It is also the output level where average revenue equals average total cost.
ven output (units) = Total Fixed Costs / (Selling Price per unit − Variable Cost per unit)
收支平衡点出现在总收入等于总成本时，企业既不盈利也不亏损。这也是平均收入等于平均总成本的产量水平。
收支平衡产量（单位）= 总固定成本 / (单位售价 − 单位可变成本)
The contribution per unit is the selling price minus the variable cost per unit. Every unit sold beyond the break-even point generates profit equal to the contribution.
单位贡献毛利等于单位售价减去单位可变成本。超出收支平衡点的每一单位销售都会产生相当于贡献毛利的利润。
Break-even analysis helps firms set targets, assess risk, and evaluate the impact of changes in costs or prices.
收支平衡分析有助于企业设定目标、评估风险并评价成本或价格变化的影响。
7. Productivity and Efficiency Measures | 生产率与效率衡量
Labour productivity measures output per worker or per hour worked. Higher labour productivity lowers unit labour costs and can improve competitiveness.
Labour productivity = Total Output / Number of Workers (or Hours Worked)
劳动生产率衡量每名工人或每工时的产出。劳动生产率越高，单位劳动力成本越低，可提高竞争力。
劳动生产率 = 总产出 / 工人数（或工时数）
Capital productivity can be measured as output per unit of capital employed. Efficiency is about making the best use of scarce resources; productive efficiency occurs when a firm operates at the lowest point on its average cost curve.
资本生产率可以用每单位资本的产出来衡量。效率指充分利用稀缺资源；当企业在平均成本曲线的最低点运营时，即实现了生产效率。
Allocative efficiency is achieved when resources are distributed to produce the mix of goods and services consumers most value, where price equals marginal cost.
配置效率在资源被分配以生产消费者最看重的商品和服务组合时实现，此时价格等于边际成本。
8. Unemployment Rate | 失业率
The unemployment rate is a key macroeconomic indicator showing the percentage of the labour force that is without work but actively seeking employment.
Unemployment rate = (Number of Unemployed / Labour Force) × 100
失业率是一个关键的宏观经济指标，显示劳动力中没有工作但正在积极求职的人口所占的百分比。
失业率 = (失业人数 / 劳动力) × 100
The labour force consists of all people who are either employed or unemployed and actively looking for work. People not actively seeking work are not counted in the labour force.
劳动力包括所有就业或失业并积极寻找工作的人。不积极求职的人不计入劳动力。
Changes in the unemployment rate can reflect the health of the economy and influence government policy decisions.
失业率的变化可以反映经济健康状况并影响政府的政策决策。
9. Inflation and Consumer Price Index (CPI) | 通货膨胀与消费者价格指数
Inflation is a sustained increase in the general price level. The Consumer Price Index (CPI) is the main measure used in the UK. It tracks the change in the cost of a representative basket of goods and services.
CPI = (Cost of basket in current year / Cost of basket in base year) × 100
通货膨胀是指一般物价水平的持续上涨。消费者价格指数（CPI）是英国使用的主要衡量指标，它追踪一揽子代表性商品和服务成本的变化。
CPI = (当年一揽子商品成本 / 基年一揽子商品成本) × 100
The inflation rate is the percentage change in the CPI from one period to the next.
Inflation rate = (CPI this year − CPI last year) / CPI last year × 100
通货膨胀率是CPI从一期到下一期的百分比变化。
通货膨胀率 = (今年CPI − 去年CPI) / 去年CPI × 100
Low and stable inflation is a common macroeconomic objective. High inflation erodes purchasing power and can create uncertainty.
低而稳定的通货膨胀是一个常见的宏观经济目标。高通胀会侵蚀购买力并制造不确定性。
10. Economic Growth and Real GDP | 经济增长与实际GDP
Economic growth is measured by the percentage change in real Gross Domestic Product (GDP). Real GDP adjusts for inflation, showing the true increase in the value of output.
Real GDP growth rate = (Real GDP year 2 − Real GDP year 1) / Real GDP year 1 × 100
经济增长以实际国内生产总值（GDP）的百分比变化来衡量。实际GDP剔除了通胀影响，显示产出价值的真实增长。
实际GDP增长率 = (第2年实际GDP − 第1年实际GDP) / 第1年实际GDP × 100
Nominal GDP is measured at current prices, while real GDP is measured at constant prices. GDP per capita divides total GDP by the population, giving an indication of average living standards.
名义GDP按当前价格计算，实际GDP则按不变价格计算。人均GDP是GDP总额除以人口，反映平均生活水准。
Sustained economic growth is a key government aim because it can lead to higher employment and improved public services.
持续的经济增长是政府的一个重要目标，因为它可以带来更高的就业率和更好的公共服务。
11. The Multiplier Effect and Marginal Propensities | 乘数效应与边际倾向
The multiplier effect occurs when an initial injection into the circular flow leads to a larger final increase in national income. The size of the multiplier depends on how much of extra income is spent domestically.
Multiplier (k) = 1 / (1 − MPC) or k = 1 / MPW
乘数效应是指一笔初始注入国民收入循环流后，会导致国民收入最终出现更大幅度的增加。乘数的大小取决于额外收入中有多少被花在国内。
乘数 (k) = 1 / (1 − MPC) 或 k = 1 / MPW
The marginal propensity to consume (MPC) is the proportion of additional income that is spent on consumption. The marginal propensity to save (MPS) is the proportion saved. They must sum to 1.
MPC = ΔC / ΔY, MPS = ΔS / ΔY, MPC + MPS = 1
边际消费倾向（MPC）是额外收入中用于消费的比例。边际储蓄倾向（MPS）是用于储蓄的比例。两者之和必须为 1。
MPC = ΔC / ΔY, MPS = ΔS / ΔY, MPC + MPS = 1
The marginal propensity to withdraw (MPW) includes savings, taxes and imports. A higher MPW makes the multiplier smaller. Governments can use the multiplier to estimate the impact of fiscal policy changes.
边际撤出倾向（MPW）包括储蓄、税收和进口。MPW 越高，乘数越小。政府可利用乘数估算财政政策变化的影响。
12. Exchange Rates and the Balance of Payments | 汇率与国际收支
An exchange rate is the price of one currency in terms of another. Appreciation means a currency becomes stronger (buys more of the other currency), while depreciation means it becomes weaker.
汇率是一种货币以另一种货币表示的价格。升值意味着货币走强（能兑换更多外币），贬值意味着货币走弱。
Exchange rate changes can be shown by calculating the new value. For example, if £1 = $1.25 and the pound appreciates to £1 = $1.30, the percentage appreciation is [(1.30 - 1.25) / 1.25] × 100 = 4%.
汇率变动可通过计算新值来展示。例如，若 1 英镑 = 1.25 美元，英镑升值到 1 英镑 = 1.30 美元，升值幅度为 [(1.30 - 1.25) / 1.25] × 100 = 4%。
The balance of payments records all transactions between a country and the rest of
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