📚 Year 7 CAIE Business: Formula & Theorem Quick Reference Handbook | Year 7 CAIE 商务：公式定理速查手册
Welcome to your ultimate quick-reference guide for Year 7 CAIE Business! This handbook brings together all the essential formulas and key economic principles (theorems) you need to master at this level. From calculating profit and break-even points to understanding demand and supply laws, each section is designed for quick revision and deep understanding.
欢迎阅读Year 7 CAIE商务终极速查手册！本手册汇总了你需要掌握的Year 7核心公式和关键经济学原理（定理）。从计算利润和盈亏平衡点到理解需求与供给定律，每个部分都旨在帮助你快速复习和深刻理解。
1. Profit and Loss Formulas | 利润与损失公式
The most fundamental concept in business is profit. Profit is the positive difference between total revenue and total costs. If costs exceed revenue, the business makes a loss.
商业中最基本的概念是利润。利润是总收入减去总成本后的正差值。如果成本大于收入，企业就会出现亏损。
Profit = Total Revenue – Total Costs
利润 = 总收入 – 总成本
Total Revenue (TR) is the money a business earns from selling goods or services. Total Costs (TC) include all expenses, such as rent, wages, and raw materials.
总收入（TR）是企业通过销售商品或服务获得的钱。总成本（TC）包括所有费用，如租金、工资和原材料。
If the result is negative, it is a loss: Loss = Total Costs – Total Revenue.
如果结果是负数，就是亏损：亏损 = 总成本 – 总收入。
2. Profit Margins | 利润率
Profit margin shows profitability as a percentage of revenue. Two common margins are gross profit margin and net profit margin. Gross profit is revenue minus cost of goods sold (COGS). Net profit is gross profit minus all other expenses.
利润率用收入百分比来表示盈利水平。常见的两个利润率是毛利率和净利率。毛利是收入减去销货成本（COGS）。净利润是毛利减去所有其他费用。
Gross Profit Margin = (Gross Profit / Revenue) x 100%
毛利率 = (毛利 / 收入) x 100%
Net Profit Margin = (Net Profit / Revenue) x 100%
净利率 = (净利润 / 收入) x 100%
A higher margin means the business keeps more of each dollar earned as profit. Monitoring margins over time helps identify cost control or pricing issues.
利润率越高，企业从每一元收入中留存的利润就越多。长期监测利润率有助于发现成本控制或定价方面的问题。
3. Break-even Analysis | 盈亏平衡分析
The break-even point is where total revenue equals total costs, so the business makes neither profit nor loss. It is a vital planning tool for new and existing businesses.
盈亏平衡点是总收入等于总成本的点，此时企业不赚不赔。它是新老企业进行规划的重要工具。
Break-even Point (units) = Fixed Costs / (Selling Price per Unit – Variable Cost per Unit)
盈亏平衡点（单位） = 固定成本 / (每单位售价 – 每单位变动成本)
Fixed costs (FC) stay the same regardless of output, e.g., rent. Variable costs (VC) change with output, e.g., raw materials. The denominator (Selling price – VC) is called contribution per unit.
固定成本（FC）不随产量变化，例如租金。变动成本（VC）随产量变化，例如原材料。分母（售价 – VC）称为单位边际贡献。
You can also calculate break-even revenue: Break-even Revenue = Break-even units x Selling Price.
你也可以计算盈亏平衡收入：盈亏平衡收入 = 盈亏平衡单位数 x 售价。
4. Total, Fixed, Variable and Average Costs | 总成本、固定成本、变动成本及平均成本
Understanding cost structures helps businesses make pricing and production decisions. Total Cost (TC) = Fixed Costs (FC) + Variable Costs (VC).
理解成本结构有助于企业做出定价和生产决策。总成本（TC）= 固定成本（FC）+ 变动成本（VC）。
TC = FC + VC
Average cost (or unit cost) is the cost per unit of output:
平均成本（或单位成本）是每单位产出的成本：
Average Cost = Total Cost / Quantity of Output
平均成本 = 总成本 / 产出数量
When output increases, average costs may fall due to economies of scale (see Section 10). Fixed costs are spread over more units, reducing the average fixed cost per unit.
当产出增加时，平均成本可能因规模经济而下降（见第10节）。固定成本分摊到更多单位上，降低了每单位的平均固定成本。
5. Revenue Formulas | 收入公式
Total Revenue (TR) is the income from sales. It is calculated as:
Total Revenue = Selling Price per Unit x Quantity Sold
总收入（TR）是销售收入，计算公式为：
总收入 = 每单位售价 x 销售数量
Average Revenue (AR) is the revenue per unit, which is the same as price if all units are sold at the same price: AR = TR / Q = Price.
平均收入（AR）是每单位收入，如果所有单位都以相同价格售出，则等于价格：AR = TR / Q = 价格。
Revenue can be affected by changes in price or quantity demanded, linking back to demand elasticity.
收入会受到价格或需求量变化的影响，这与需求弹性有关。
6. The Law of Demand | 需求定律
The law of demand states that, ceteris paribus (all else equal), as the price of a good increases, the quantity demanded decreases, and vice versa. There is an inverse relationship.
需求定律指出，在其他条件不变的情况下，当商品价格上升时，需求量下降，反之亦然。两者存在反向关系。
Demand curve slope: downwards from left to right.
需求曲线斜率：从左到右向下倾斜。
Factors that shift the demand curve (non-price determinants):
- Changes in consumer income (normal vs. inferior goods)
- Changes in tastes and preferences
- Prices of substitutes and complements
- Advertising and branding
- Population size and demographics
导致需求曲线移动的因素（非价格决定因素）：
- 消费者收入变化（正常品与低档品）
- 口味和偏好的变化
- 替代品和互补品的价格
- 广告和品牌
- 人口规模与人口结构
Remember: a change in price causes movement along the demand curve; a change in other factors causes the entire curve to shift.
记住：价格变动导致沿需求曲线移动；其他因素变动导致整条曲线平移。
7. The Law of Supply | 供给定律
The law of supply states that, ceteris paribus, as the price of a good increases, the quantity supplied increases, and vice versa. There is a direct relationship.
供给定律指出，在其他条件不变的情况下，当商品价格上升时，供给量增加，反之亦然。两者存在正向关系。
Supply curve slope: upwards from left to right.
供给曲线斜率：从左到右向上倾斜。
Factors that shift the supply curve:
- Changes in production costs (e.g., raw materials, wages)
- Technological advancements
- Taxes and subsidies
- Number of sellers in the market
- Weather and natural conditions
导致供给曲线移动的因素：
- 生产成本变化（如原材料、工资）
- 技术进步
- 税收与补贴
- 市场中卖家的数量
- 天气与自然条件
8. Market Equilibrium | 市场均衡
Equilibrium occurs where quantity demanded equals quantity supplied. The market-clearing price and quantity are determined by the intersection of demand and supply curves.
均衡发生在需求量等于供给量时。市场出清价格和数量由需求曲线和供给曲线的交点决定。
If the market price is above equilibrium, there is excess supply (surplus), pushing prices down. If price is below equilibrium, there is excess demand (shortage), pushing prices up.
如果市场价格高于均衡水平，出现超额供给（过剩），价格会下降；如果价格低于均衡，出现超额需求（短缺），价格会上升。
Market forces will always push the price towards equilibrium in a free market.
在自由市场中，市场力量总会推动价格趋向均衡。
9. Price Elasticity of Demand (PED) – Basic Concept | 需求价格弹性（基本概念）
PED measures how responsive quantity demanded is to a change in price. Although full calculation often appears in higher years, Year 7 students can grasp the core idea:
PED = % Change in Quantity Demanded / % Change in Price
需求价格弹性衡量需求量对价格变化的反应程度。虽然完整计算常在更高年级出现，但Year 7学生可以掌握核心概念：
需求价格弹性 = 需求量变动百分比 / 价格变动百分比
If PED > 1, demand is elastic (consumers are very responsive to price changes). If PED < 1, demand is inelastic (consumers are less responsive). Goods with many substitutes tend to have elastic demand; necessities tend to have inelastic demand.
如果 PED > 1，需求富有弹性（消费者对价格变化非常敏感）；如果 PED < 1，需求缺乏弹性（消费者不太敏感）。替代品多的商品往往富有弹性；必需品往往缺乏弹性。
Revenue rule: when demand is elastic, a decrease in price will increase total revenue. When demand is inelastic, an increase in price may increase total revenue.
收入规律：当需求富有弹性时，降价会增加总收入；当需求缺乏弹性时，提价可能增加总收入。
10. Economies of Scale and Key Business Objectives | 规模经济与主要商业目标
As a business grows, average costs can fall – this is economies of scale. Internal economies include technical, purchasing, managerial, financial and marketing advantages. External economies arise from industry growth, such as a skilled local workforce.
当企业规模扩大时，平均成本会下降——这就是规模经济。内部规模经济包括技术、采购、管理、财务和营销方面的优势。外部规模经济源于行业增长，例如当地熟练劳动力。
Diseconomies of scale occur when a firm becomes too large and average costs rise due to communication problems, bureaucracy, or coordination issues.
规模不经济发生在企业过大时，由于沟通问题、官僚主义或协调问题导致平均成本上升。
Common business objectives (theorems/goals): profit maximisation, survival, growth, increasing market share, and providing a service (social enterprises).
常见的商业目标（定理/目标）：利润最大化、生存、成长、提高市场份额以及提供服务（社会企业）。
Market Share (%) = (Company’s Sales / Total Market Sales) x 100%
市场份额 (%) = (公司销售额 / 市场总销售额) x 100%
11. Cash Flow and Working Capital | 现金流与营运资金
Cash flow is the movement of money into and out of a business. Positive cash flow means more money is coming in than going out. Net Cash Flow is a simple formula:
Net Cash Flow = Total Cash Inflows – Total Cash Outflows
现金流是资金流入和流出企业的运动。正现金流意味着流入资金多于流出。净现金流有一个简单公式：
净现金流 = 总现金流入 – 总现金流出
Working capital measures a firm’s short-term financial health. It shows the ability to pay short-term debts.
Working Capital = Current Assets – Current Liabilities
营运资金衡量企业的短期财务健康状况，显示其偿还短期债务的能力。
营运资金 = 流动资产 – 流动负债
Maintaining a positive working capital is crucial to avoid liquidity problems.
保持正营运资金对于避免流动性问题至关重要。
12. Key Formula Summary Table | 核心公式汇总表
Use this handy table to review all the essential formulas at a glance. Each formula is paired with its core use.
使用这个便捷的表格快速回顾所有核心公式。每个公式都注明了主要用途。
| Formula (English) | 中文公式 | Purpose / 用途 |
|---|---|---|
| Profit = Total Revenue – Total Costs | 利润 = 总收入 – 总成本 | Measure profitability / 衡量盈利 |
| Gross Profit Margin = (Gross Profit / Revenue) x 100% | 毛利率 = (毛利 / 收入) x 100%
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