📚 Year 7 Cambridge Business: Formula & Theorem Quick Reference Handbook | 剑桥七年级商务：公式定理速查手册
This handbook gathers the essential formulas, calculations and economic theorems that every Year 7 Cambridge Business student should know. Whether you are working through business cost problems, interpreting demand and supply diagrams or calculating profitability, these concise references will help you build a solid foundation. All formulas are presented using clear symbols and supported by practical examples, while key theorems are explained in a way that links directly to real-world business decisions. Use this guide alongside your class notes and revision activities to check your understanding quickly and accurately.
本手册汇集了每一位剑桥七年级商务学生都应掌握的核心公式、计算方法和经济学定理。无论你是在处理企业成本问题、解读需求与供给图表还是计算利润率，这些简明的参考内容都能帮助你打下扎实的基础。所有公式都使用清晰的符号呈现，并配有实际示例，而关键定理则与真实的商业决策相联系进行解释。请结合课堂笔记和复习活动使用本指南，以便快速、准确地检查你的理解。
1. The Profit Equation | 利润公式
Profit is the financial gain a business makes after subtracting all costs from its income. The fundamental formula used to measure a firm’s success is:
Profit = Total Revenue – Total Cost
利润是企业从收入中扣除所有成本之后获得的财务收益。衡量一家公司成功与否的基本公式为：
利润 = 总收入 – 总成本
If total revenue is greater than total cost, the business earns a profit. If total cost exceeds total revenue, the result is a loss. Managers use this equation not only to report performance but also to set sales targets and control spending. For example, if a bakery sells cakes earning £5,000 and its total costs amount to £3,200, the profit is £1,800.
如果总收入大于总成本，企业就获得利润；如果总成本超过总收入，结果就是亏损。管理者不仅用这一公式报告业绩，还用它来制定销售目标和控制支出。例如，一家面包店卖出蛋糕获得 5,000 英镑收入，总成本为 3,200 英镑，利润即为 1,800 英镑。
2. Total Revenue Formula | 总收入公式
Total revenue represents the money a business receives from selling its goods or services over a period. It is calculated using a simple multiplication:
Total Revenue = Price per unit × Quantity sold
总收入是指企业在一定时期内通过出售商品或服务而获得的资金总额。它通过一个简单的乘法公式计算得出：
总收入 = 每单位价格 × 销售数量
This formula helps firms predict income before they set production levels. If a stationery shop sells 300 notebooks at £2 each, total revenue equals £600. Understanding this relationship also allows businesses to see how changing the price or the number of units affects overall income, which is the first step in pricing strategy.
这个公式帮助企业在确定生产水平之前预测收入。如果一家文具店以每本 2 英镑的价格卖出 300 本笔记本，总收入就等于 600 英镑。理解这种关系还能让企业看清价格或销售数量的变化如何影响整体收入，这是定价策略的第一步。
3. Fixed and Variable Costs | 固定成本和可变成本
Costs are divided into two main types. Fixed costs remain unchanged regardless of output, while variable costs rise or fall directly with production volume. A clear classification is shown below:
成本主要分为两类。固定成本无论产量如何都保持不变，而可变成本则随生产量直接上升或下降。下面的表格清晰展示了分类：
| Cost Type 成本类别 | Examples 示例 |
|---|---|
| Fixed costs 固定成本 | Rent, insurance, manager salaries 租金、保险、经理薪酬 |
| Variable costs 可变成本 | Raw materials, packaging, piece-rate wages 原材料、包装、计件工资 |
Being able to separate fixed and variable costs is essential for budgeting and break‑even analysis. For instance, a pizzeria paying £800 monthly rent (fixed) and £2 for flour and toppings per pizza (variable) must cover both before generating profit.
能够区分固定成本和可变成本对于预算编制和盈亏平衡分析至关重要。例如，一家披萨店每月支付 800 英镑租金（固定成本），每张披萨的面粉和配料花费 2 英镑（可变成本），在产生利润之前必须覆盖这两类成本。
4. Total Cost Formula | 总成本公式
Total cost combines all expenses incurred in producing a given quantity of output. The formula builds directly on the fixed and variable cost concepts:
Total Cost = Fixed Cost + (Variable cost per unit × Quantity)
总成本包含生产给定数量产品所发生的全部费用。该公式直接建立在固定成本和可变成本概念之上：
总成本 = 固定成本 + (每单位可变成本 × 数量)
This calculation allows managers to estimate the full cost for any planned output. If a toy factory has fixed costs of £3,000 and each toy carries a variable cost of £5, producing 400 toys will lead to a total cost of £3,000 + (£5 × 400) = £5,000. Regularly updating total cost figures helps businesses set prices that ensure profitability.
这一计算方法让管理者能够估计任何计划产量的全部成本。如果一家玩具厂的固定成本为 3,000 英镑，每件玩具的可变成本为 5 英镑，那么生产 400 件玩具的总成本就是 3,000 + (5 × 400) = 5,000 英镑。定期更新总成本数据有助于企业制定确保盈利的价格。
5. Break‑even Point | 盈亏平衡点
The break‑even point shows the level of sales at which total revenue equals total cost, resulting in zero profit and zero loss. For a single product, the break‑even quantity is found with:
Break‑even Quantity = Fixed Cost ÷ (Selling price per unit – Variable cost per unit)
盈亏平衡点表示总收入等于总成本、利润为零且无亏损的销售水平。对于单一产品，盈亏平衡数量按下式求得：
盈亏平衡数量 = 固定成本 ÷ (单位售价 – 单位可变成本)
The denominator, selling price minus variable cost per unit, is called the contribution per unit. Every unit sold above the break‑even point generates profit. Consider a candle shop with £600 fixed costs, a selling price of £8 per candle and a variable cost of £3 per candle. The break‑even point is 600 ÷ (8 – 3) = 120 candles. Selling 150 candles would yield a profit of 30 × £5 = £150.
分母（单位售价减去单位可变成本）被称作每单位贡献毛利。每售出一件超出盈亏平衡点的产品都会产生利润。假设一家蜡烛店固定成本为 600 英镑，每支蜡烛售价 8 英镑，单位可变成本为 3 英镑。盈亏平衡点为 600 ÷ (8 – 3) = 120 支蜡烛。若售出 150 支，利润则为 30 × 5 = 150 英镑。
6. Profit Margin | 利润率
Profit margin measures how much of every pound of revenue becomes profit after costs are covered. It is expressed as a percentage and is a key indicator of efficiency:
Profit Margin = (Profit ÷ Total Revenue) × 100%
利润率衡量的是每一英镑收入中有多少在覆盖成本之后变为利润。它以百分比表示，是衡量效率的关键指标：
利润率 = (利润 ÷ 总收入) × 100%
A high profit margin suggests strong control over costs relative to sales, while a falling margin warns of rising expenses or pricing pressure. For example, if a café earns £12,000 revenue and records a profit of £2,400, its profit margin is (2,400 ÷ 12,000) × 100% = 20%. Comparing margins over time helps owners identify trends before profits are seriously affected.
高利润率表明相对于销售而言，成本控制良好；而利润率下降则预示着费用增加或定价压力。例如，一家咖啡馆获得 12,000 英镑收入并实现 2,400 英镑利润，其利润率为 (2,400 ÷ 12,000) × 100% = 20%。通过比较不同时期的利润率，经营者可以在利润受到严重影响之前察觉趋势。
7. Law of Demand | 需求定律
The law of demand describes the inverse relationship between the price of a good and the quantity consumers are willing to buy, assuming all other factors stay constant. The theorem can be stated simply:
Price ↑ → Quantity demanded ↓ (and vice versa, ceteris paribus)
需求定律描述了商品价格与消费者愿意购买的数量之间的反向关系，前提是所有其他因素保持不变。该定理可简述为：
价格 ↑ → 需求量 ↓（反之亦然，其他条件不变）
When prices rise, consumers typically seek substitutes or buy less, reducing the quantity demanded. When prices fall, the product becomes more affordable and demand usually expands. This principle underpins demand curves and helps firms predict how a price change might affect sales volume. A real‑world illustration is a cinema reducing ticket prices on weekdays to attract more viewers.
当价格上涨时，消费者通常会寻找替代品或减少购买，从而降低需求量。当价格下降时，产品变得更实惠，需求通常会扩大。这一原理是需求曲线的基础，并能帮助企业预测价格变动如何影响销量。现实中的一个例子是电影院在工作日降低票价以吸引更多观众。
8. Law of Supply | 供给定律
The law of supply states that, ceteris paribus, producers are willing to offer more of a good for sale as its price increases. The theorem is summarised as:
Price ↑ → Quantity supplied ↑ (ceteris paribus)
供给定律指出，在其他条件不变的情况下，生产者愿意在商品价格上升时提供更多的商品以供出售。该定理总结为：
价格 ↑ → 供给量 ↑（其他条件不变）
Higher prices signal higher potential profit, encouraging firms to expand output. If the selling price of handmade bracelets rises significantly, craft businesses may hire extra workers or buy more materials to increase supply. Understanding the supply relationship is vital for production planning and for anticipating how markets respond to changes in demand.
更高的价格意味着更高的潜在利润，从而鼓励企业扩大产出。如果手工手链的售价大幅上涨，手工艺企业可能会雇佣额外员工或购买更多材料来增加供给。理解供给关系对生产计划以及预测市场如何响应需求变化至关重要。
9. Market Equilibrium | 市场均衡
Market equilibrium occurs at the price where the quantity consumers want to buy exactly matches the quantity producers want to sell. The balancing condition is expressed as:
Quantity demanded = Quantity supplied (at the equilibrium price)
市场均衡出现在消费者想购买的数量恰好等于生产者想出售的数量的那个价格点上。这一平衡条件可表示为：
需求量 = 供给量（在均衡价格时）
At any price above equilibrium, a surplus drives prices down; at any price below, a shortage pushes prices up until the market clears. For example, a farmers’ market selling strawberries might find that at £3 per punnet demand and supply both equal 200 punnets. That £3 is the equilibrium price, and the 200 punnets represent the equilibrium quantity. Governments and businesses watch this balance closely when setting policies or launching new products.
当价格高于均衡价格时，过剩会推动价格下降；当价格低于均衡价格时，短缺会推动价格上升，直至市场出清。例如，一个农贸市场的草莓售价若为每盒 3 英镑时需求和供给都等于 200 盒，那么 3 英镑就是均衡价格，200 盒就是均衡数量。政府和企业制定政策或推出新产品时都会密切关注这种平衡。
10. The Principle of Opportunity Cost | 机会成本原理
Opportunity cost is the value of the next best alternative that must be given up when a choice is made. It is a fundamental concept that shapes all business decisions, even though it does not appear on an accounting statement:
Opportunity cost = value of the next best alternative foregone
机会成本是为了做出某一选择而必须放弃的次优方案的价值。虽然它不会出现在财务报表上，但却是影响所有商业决策的基本概念：
机会成本 = 被放弃的次优选择的价值
If a teenager uses £50 savings to buy business equipment instead of keeping the money in a savings account earning 2% interest, the opportunity cost includes the lost interest and the next best item they could have purchased. In a business, choosing to invest in robotics rather than in staff training carries an opportunity cost equal to the benefits the foregone training would have generated. Recognising this hidden cost helps entrepreneurs allocate resources more wisely.
如果一位少年用 50 英镑积蓄购买了企业设备，而不是将钱存入年利率 2% 的储蓄账户，机会成本就包括损失的利息以及本可购买的次优物品。在一家企业中，选择投资机器人而非员工培训，其机会成本等于被放弃的培训本可带来的收益。认识到这种隐性成本有助于企业家更明智地配置资源。
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