📚 KS3 WJEC Economics: Formula & Theorem Quick Reference Handbook | KS3 WJEC 经济：公式定理速查手册
This quick reference handbook is designed for KS3 students following the WJEC Economics specification. It collects all the essential formulas, key laws, and foundational theorems you need to master in one place. Use it to revise concepts like opportunity cost, demand and supply, elasticity, national income indicators, and basic financial calculations. Each tool is explained with clear examples, allowing you to apply economics confidently to real‑world contexts.
本速查手册专为学习 WJEC 经济学课程的 KS3 学生编写。它把必须掌握的所有核心公式、关键定律和基本定理汇集在一起。你可以用它复习机会成本、需求与供给、弹性、国民收入指标以及基础财务计算。每个工具都配有清晰的示例，帮助你自信地将经济学运用到实际情境中。
1. Opportunity Cost Formula | 机会成本公式
Opportunity cost is the value of the next best alternative that must be given up when a choice is made. It lies at the heart of economics because resources are scarce and every decision involves a trade‑off. The concept reminds us that the true cost of something is not just the money spent, but what we forgo.
机会成本是做出选择时必须放弃的下一个最佳替代方案的价值。它是经济学的核心，因为资源是稀缺的，每一个决策都涉及权衡。这一概念提醒我们，某物的真正成本不仅是所花的金钱，更是我们放弃的东西。
The opportunity cost can be written as a simple expression:
机会成本可用一个简单的表达式表示：
Opportunity Cost = Value of the Next Best Alternative Foregone
For example, if a government spends £10 million on building a new hospital instead of a school, the opportunity cost is the value of the school that could have been built. If a student spends two hours studying economics rather than working at a part‑time job that pays £9 per hour, the opportunity cost is £18 of lost earnings.
例如，如果政府花费 1000 万英镑修建一所新医院而不是一所学校，机会成本就是本来可以建成的那所学校的价值。如果一个学生花两个小时学习经济学，而不是去做每小时 9 英镑的兼职工作，机会成本就是损失的 18 英镑收入。
Opportunity cost applies to individuals, firms, and governments. It is not always measured in money; it can also be time, enjoyment, or any other benefit that is sacrificed. Understanding opportunity cost helps decision‑makers allocate resources more efficiently.
机会成本适用于个人、企业和政府。它并不总用货币衡量，也可以是被牺牲的时间、享乐或其他任何好处。理解机会成本有助于决策者更有效地配置资源。
2. The Law of Demand | 需求法则
The law of demand states that, ceteris paribus (all other things being equal), as the price of a good or service rises, the quantity demanded falls. Conversely, when the price falls, the quantity demanded rises. This inverse relationship is one of the most fundamental principles in economics and can be represented by a downward‑sloping demand curve.
需求法则指出，在其他条件不变的情况下，商品或服务的价格上升时，需求量下降。反之，价格下降时，需求量上升。这种反向关系是经济学最根本的原理之一，可以用一条向下倾斜的需求曲线来表示。
A simple linear demand function can summarise this relationship:
一个简单的线性需求函数可以概括这种关系：
Qd = a − bP
Here Qd is the quantity demanded, P is the price, 'a' represents the quantity demanded when the price is zero (the intercept), and 'b' ded to a change in price. For instance, Qd = 100 − 2P means that if the price increases by £1, quantity demanded decreases by 2 units.
其中 Qd 是需求量，P 是价格，‘a’ 表示价格为零时的需求量（截距），‘b’ 表示需求量对价格变动的反应程度。例如，Qd = 100 − 2P 意味着价格每上涨 1 英镑，需求量就减少 2 个单位。
The law of demand holds for most goods, known as normal goods. However, there are exceptions, such as Giffen goods or Veblen goods, where higher prices may increase demand because of perceived status or income effects. At KS3 level, you can safely assume the law of demand applies unless a question explicitly states otherwise.
需求法则适用于大多数商品，即正常品。但也有例外，如吉芬商品或韦伯伦商品，在这些情况下，更高的价格可能因为地位感知或收入效应而增加需求。在 KS3 阶段，除非题目明确说明，否则你可以放心地假定需求法则成立。
3. The Law of Supply | 供给法则
The law of supply describes a positive relationship between price and quantity supplied. If the price of a good rises, producers are generally willing to supply more of it, ceteris paribus. When the price falls, the quantity supplied tends to decrease. This is because higher prices make production more profitable and cover the rising marginal costs.
供给法则描述了价格与供给量之间的正向关系。如果一种商品的价格上升，在其他条件不变的情况下，生产者通常愿意提供更多的该商品。当价格下降时，供给量趋于减少。这是因为更高的价格使生产更有利可图，并能覆盖上升的边际成本。
A typical supply function can be written as:
典型的供给函数可以写成：
Qs = c + dP
Here Qs is the quantity supplied, P is the price, 'c' quantity producers would supply even at a zero price (though rarely zero in practice), and 'd' indicates the change in quantity supplied for each unit change in price. For supply, 'd' is positive. For example, Qs = 20 + 3P tells us that a £1 price increase raises the quantity supplied by 3 units.
其中 Qs 是供给量，P 是价格，‘c’ 是生产者在价格为零时也会提供的最低数量（尽管实践中很少为零），‘d’ 表示价格每变动一单位所引起的供给量变动。对供给而言，‘d’ 为正值。例如，Qs = 20 + 3P 表明价格每上涨 1 英镑，供给量增加 3 个单位。
Supply is influenced by factors such as production costs, technology, taxes, and the number of sellers. A change in price causes a movement along the supply curve, while a change in other conditions causes the entire supply curve to shift. Recognising these shifts is crucial when analysing market outcomes.
供给受到生产成本、技术、税收和卖者数量等因素的影响。价格变动导致沿着供给曲线的移动，而其他条件的变化则导致整条供给曲线发生平移。分析市场结果时，识别这些平移至关重要。
4. Market Equilibrium Condition | 市场均衡条件
Market equilibrium occurs at the price where the quantity demanded by consumers equals the quantity supplied by producers. At this point, there is no tendency for the price to change unless an external factor disturbs the balance. The equilibrium price balances the plans of buyers and sellers, eliminating both excess demand and excess supply.
市场均衡出现在消费者需求量等于生产者供给量的那个价格上。在均衡点，除非有外部因素打破平衡，否则价格没有变动的趋势。均衡价格协调了买卖双方的计划，消除了超额需求和超额供给。
The core equilibrium condition is:
核心均衡条件为：
Qd = Qs
o either function to obtain Qe. For example, with Qd = 100 − 2P and Qs = 20 + 2P, setting 100 − 2P = 20 + 2P gives 80 = 4P, so Pe = £20. Substituting Pe into Qd yields Qe = 60 units.
为求得均衡价格与数量，令需求函数等于供给函数，解出 P，再将此价格代回任一函数求得 Qe。例如，已知 Qd = 100 − 2P，Qs = 20 + 2P，令 100 − 2P = 20 + 2P，得 80 = 4P，故 Pe = 20 英镑。把 Pe 代入 Qd 中得到 Qe = 60 单位。
If the market price is above equilibrium, a surplus exists and the price will tend to fall as sellers compete. If the price is below equilibrium, a shortage drives the price up. Understanding equilibrium helps economists predict how markets react to events like tax changes or technological improvements.
如果市场价格高于均衡水平，就会出现过剩，卖方竞争导致价格趋于下降。如果价格低于均衡水平，短缺会推动价格上升。理解均衡有助于经济学家预测市场对税收变化或技术改进等事件的反应。
5. Price Elasticity of Demand (PED) | 需求价格弹性
Price elasticity of demand measures how responsive the quantity demanded of a good is to a change in its price. It is a unit‑free ratio that allows us to compare the sensitivity of demand across different products. Firms and governments use PED to predict the impact of pricing decisions and tax policies.
需求价格弹性衡量一种商品的需求量对其价格变动的反应程度。它是一个无单位的比率，使我们能够比较不同产品需求的敏感度。企业和政府利用 PED 预测定价决策和税收政策的影响。
The basic PED formula is:
基本 PED 公式为：
PED = (% change in quantity demanded) / (% change in price)
To calculate percentage changes precisely, the midpoint (arc) method is often used:
为了精确计算百分比变化，常使用中点（弧）法：
PED = (ΔQ / Qavg) ÷ (ΔP / Pavg)
Where ΔQ and ΔP are the absolute changes, and Qavg and Pavg are the averages of the initial and final quantities and prices. In KS3, you will often be given two points and asked to calculate PED using the basic percentage change method, ignoring the midpoint unless instructed otherwise.
其中 ΔQ 和 ΔP 是绝对变化量，Qavg 和 Pavg 是初始与最终数量和价格的平均值。在 KS3 阶段，通常会给出两个点并要求使用基本百分比变化法计算 PED，除非另有说明，否则可忽略中点法。
The value of PED can be classified as follows:
PED 值可按如下分类：
| PED Value | Description |
|---|---|
| |PED| > 1 | Elastic demand: quantity is very responsive to price changes |
| |PED| < 1 | Inelastic demand: quantity is not very responsive |
| |PED| = 1 | Unit elastic: percentage changes are equal |
| |PED| = 0 | Perfectly inelastic: quantity does not change at all |
| |PED| = ∞ | Perfectly elastic: any price rise will reduce quantity demanded to zero |
If a product has elastic demand, a price cut will increase total revenue. If demand is inelastic, raising the price will increase total revenue. This relationship is key to business pricing strategies.
如果某种产品的需求富有弹性，降价会增加总收益。如果需求缺乏弹性，提价会增加总收益。这一关系是企业定价策略的关键。
6. Revenue, Cost and Profit Formulas | 收益、成本与利润公式
A firm's financial performance is captured by three fundamental equations: total revenue (TR), total cost (TC), and profit. These measures allow a business to understand whether it is covering its costs and making a return. Even at KS3, you should be able to calculate simple profit and loss.
企业的财务表现可用三个基本方程刻画：总收益 (TR)、总成本 (TC) 和利润。这些量度使企业能够了解自己是否覆盖成本并获得回报。即使在 KS3，你也应能计算简单的利润与亏损。
Total revenue is the money coming in from sales:
总收益是销售带来的收入：
TR = P × Q
Total cost is the sum of all fixed costs (TFC) — which do not vary with output — and total variable costs (TVC) — which change as production changes:
总成本是所有固定成本 (TFC) 与总可变成本 (TVC) 之和：固定成本不随产量变动，可变成本随产量变化而变化：
TC = TFC + TVC
Profit, or net income, is simply the difference between revenue and total costs:
利润，即净收入，就是收益与总成本之差：
Profit = TR − TC
profit. If TC is larger, the firm makes a loss. For example, a bakery sells 500 loaves at £2 each, giving TR = £1,000. Fixed costs are £400 and variable costs are £350, so TC = £750. Profit = £1,000 − £750 = £250.
若 TR 大于 TC，企业盈利；若 TC 更大，企业亏损。例如，一家面包店以 2 英镑单价售出 500 条面包，TR = 1000 英镑。固定成本为 400 英镑，可变成本为 350 英镑，因此 TC = 750 英镑。利润 = 1000 − 750 = 250 英镑。
alysing these relationships helps managers decide whether to expand production, change prices, or cut costs.
企业常常在 TR = TC 时实现盈亏平衡。分析这些关系有助于管理者决定是扩大生产、调整价格还是削减成本。
7. Average and Marginal Values | 平均值与边际值
To understand how efficiently a firm is producing, economists look at average and marginal costs and revenues. Average cost tells us the cost per unit, while marginal cost reveals the extra cost of producing one more unit. These concepts are vital for determining the optimal level of output.
为了理解企业生产的效率，经济学家会考察平均成本和收益以及边际成本和收益。平均成本告诉我们每单位产品的成本，而边际成本揭示了多生产一单位产品所带来的额外成本。这些概念对于确定最优产量水平至关重要。
Average total cost is calculated as:
平均总成本的计算公式为：
ATC = TC ÷ Q
Marginal cost is the change in total cost when output increases by one unit:
MC = ΔTC ÷ ΔQ
Similarly, average revenue (AR) is TR ÷ Q, which equals the price if all units are sold at the same price. Marginal revenue (MR) is the change in total revenue from selling one more unit.
类似地，平均收益 (AR) 等于 TR ÷ Q，若所有单位以相同价格出售，它就等于价格。边际收益 (MR) 是多售出一单位产品所带来的总收益变动。
A profit‑ nsures that the last unit produced adds exactly as much to revenue as to cost. If MR > MC, the firm can increase profit by expanding output; if MR < MC, it should reduce output.
追求利润最大化的企业会在 MR = MC 处生产。这一条件确保最后一单位产品带来的收益增量恰好等于其成本增量。若 MR > MC，企业可通过扩大产量增加利润；若 MR < MC，则应减少产量。
8. Inflation Rate Calculation | 通货膨胀率计算
Inflation measures the general rise in the price level of goods and services over time. A low and stable inflation rate is a common macroeconomic objective. The most common way to measure inflation is through the Consumer Price Index (CPI), which tracks the price of a basket of typical household purchases.
通货膨胀衡量一段时间内商品与服务总体价格水平的普遍上涨。保持低且稳定的通胀率是一个常见的宏观经济目标。衡量通胀最常见的方法是消费者价格指数 (CPI)，它追踪一篮子典型家庭购买商品的价格。
The inflation rate is the percentage change in the CPI from one period to the next:
Inflation Rate (%) = [(CPI in current year − CPI in previous year) ÷ CPI in previous year] × 100
105 last year and is 110 this year, the inflation rate = [(110 − 105) ÷ 105] × 100 = 4.76%. This means the general price level has risen by about 4.8%.
例如，若去年 CPI 为 105，今年为 110，则通胀率 = [(110 − 105) ÷ 105] × 100 = 4.76%。这意味着总体价格水平上涨了约 4.8%。
High inflation erodes purchasing power and savings, whereas deflation (negative inflation) can discourage spending. Governments and central banks use inflation data to set interest rates and other policies. In your exam, you may be expected to calculate the inflation rate and comment on its likely economic effects.
高通胀侵蚀购买力和储蓄，而通缩（负通胀）则可能抑制消费。政府和央行利用通胀数据制订利率和其他政策。考试中，你可能需要计算通胀率并评论其可能的经济影响。
9. Unemployment Rate Formula | 失业率公式
The unemployment rate is a key indicator of labour market health. It tells us the percentage of the labour force that is actively seeking work but unable to find employment. Monitoring unemployment helps policymakers assess the need for intervention.
失业率是衡量劳动力市场健康程度的关键指标。它告诉我们劳动力中积极寻找工作却无法获得就业的人数所占的百分比。监测失业率有助于决策者评估干预的必要性。
The formula is straightforward:
Unemployment Rate = (Number of Unemployed ÷ Labour Force) × 100
Here, the labour force includes both employed and unemployed people who are available for work and actively seeking a job. Students, retirees, and those not seeking work are not part of the labour force.
在这里，劳动力包括已就业和失业但能够工作并积极寻找工作的人。学生、退休人员以及不寻找工作的人不属于劳动力。
oyed people and a labour force of 25 million. The unemployment rate = (1.5 ÷ 25) × 100 = 6%. A rate around 4–5% is often considered close to full employment in developed economies, though this can vary.
假设某国有 150 万失业者，劳动力为 2500 万，则失业率 = (1.5 ÷ 25) × 100 = 6%。在发达经济体中，4–5% 左右的失业率通常被视为接近充分就业，尽管这一标准可能有所变化。
Different types of unemployment exist: cyclical (due to recession), structural (mismatch of skills), and frictional (people between jobs). While the formula stays the same, understanding the causes helps explain why the rate changes over time.
失业存在不同类型：周期性失业（由衰退引起）、结构性失业（技能不匹配）和摩擦性失业（人们在换工作间隙）。尽管公式不变，理解其成因有助于解释失业率随时间变化的原因。
10. Economic Growth Rate | 经济增长率
Economic growth refers to an increase in the production of goods and services in an economy over a period. It is commonly measured by the percentage change in real Gross Domestic Product (GDP), which adjusts for inflation. Sustained growth is associated with rising living standards.
经济增长指一段时期内一个经济体商品与服务产出的增加。它通常用实际国内生产总值 (GDP) 的百分比变化来衡量，该指标剔除了通胀因素。持续的增长与生活水平提高
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