📚 Year 9 CCEA Economics: Formula & Theorem Quick Reference Handbook | Year 9 CCEA 经济：公式定理速查手册
This handbook provides a quick reference to essential formulas, theorems, and key economic principles for Year 9 students following the CCEA curriculum. Mastering these tools will strengthen your understanding and exam performance.
本手册为学习CCEA课程的九年级学生提供关键公式、定理和核心经济学原理的速查参考。掌握这些工具将加深你的理解并提升考试成绩。
1. Scarcity and Opportunity Cost | 稀缺性与机会成本
The fundamental economic problem is scarcity: limited resources but unlimited wants. This forces individuals, firms, and governments to make choices, and every choice has an opportunity cost.
根本的经济问题是稀缺性：有限的资源面对无限的欲望。这迫使个人、企业和政府做出选择，而每个选择都有机会成本。
Opportunity Cost = Value of the Next Best Alternative Forgone
The opportunity cost of a decision is the benefit lost from the second-best choice. It is not simply the money spent, but the next best use of resources.
一项决策的机会成本是放弃的次优选择带来的利益。它不仅仅是花费的金钱，而是资源的下一种最佳用途。
2. Law of Demand and Demand Curve | 需求定律与需求曲线
The law of demand states that, ceteris paribus (other things being equal), as the price of a good rises, the quantity demanded falls, and as the price falls, the quantity demanded rises.
需求定律指出，在其他条件不变的情况下，商品价格上升时需求量下降，价格下降时需求量上升。
A demand schedule shows the relationship between price and quantity demanded. A typical example:
需求表展示了价格与需求量之间的关系。一个典型示例：
| Price (£) per unit | Quantity Demanded (units per week) |
|---|---|
| 10 | 20 |
| 8 | 30 |
| 6 | 45 |
| 4 | 65 |
| 2 | 100 |
Plotting these points gives a downward-sloping demand curve. The inverse relationship between price and quantity demanded is a cornerstone of microeconomics.
将这些点描出即得到向下倾斜的需求曲线。价格与需求量之间的反向关系是微观经济学的基石。
3. Law of Supply and Supply Curve | 供给定律与供给曲线
The law of supply states that, ceteris paribus, as the price of a good rises, the quantity supplied increases, and as the price falls, the quantity supplied decreases.
供给定律指出，在其他条件不变的情况下，商品价格上升时供给量增加，价格下降时供给量减少。
A typical supply schedule:
一个典型的供给表：
| Price (£) per unit | Quantity Supplied (units per week) |
|---|---|
| 2 | 10 |
| 4 | 35 |
| 6 | 60 |
| 8 | 80 |
| 10 | 95 |
The supply curve slopes upward, reflecting that higher prices incentivise producers to supply more.
供给曲线向上倾斜，反映出更高的价格激励生产者提供更多产量。
4. Market Equilibrium | 市场均衡
Market equilibrium occurs at the price where quantity demanded equals quantity supplied. There is no shortage or surplus.
市场均衡出现在需求量等于供给量的价格水平上。此时没有短缺也没有过剩。
Equilibrium condition: Qd = Qs
At prices above equilibrium, a surplus exists, pushing price down. At prices below equilibrium, a shortage exists, pulling price up. The market automatically moves toward equilibrium.
在高于均衡的价格上，存在过剩，推动价格回落；在低于均衡的价格上，存在短缺，拉动价格上升。市场自动趋向均衡。
5. Total Revenue, Total Cost and Profit | 总收入、总成本与利润
These are fundamental business calculations. Total revenue is the income from selling goods or services.
这些是基础的商业计算。总收入是销售商品或服务带来的收入。
Total Revenue (TR) = Price (P) × Quantity Sold (Q)
Total cost is the sum of all expenses incurred in production. It can be split into fixed costs (do not change with output) and variable costs (change with output).
总成本是生产过程中产生的全部费用。它可分为固定成本（不随产量变化）和可变成本（随产量变化）。
Total Cost (TC) = Total Fixed Cost (TFC) + Total Variable Cost (TVC)
Profit is the reward for risk-taking; it is what remains after all costs have been covered.
利润是对承担风险的回报；它是覆盖所有成本后的剩余。
Profit (π) = Total Revenue (TR) − Total Cost (TC)
A business making a loss has TC greater than TR; a break-even situation occurs when TR equals TC.
当总成本大于总收入时企业亏损；当总收入等于总成本时，达到盈亏平衡。
6. Break-even Point | 盈亏平衡点
The break-even point is the level of sales at which a business covers all its costs, making neither a profit nor a loss. It is commonly calculated as a quantity of units.
盈亏平衡点是企业的销售收入刚好覆盖全部成本的业务量，此时既不盈利也不亏损。通常以销售量（单位数）来计量。
ntity = Total Fixed Costs ÷ (Selling Price per Unit − Variable Cost per Unit)
The denominator (Price minus Unit Variable Cost) is known as the contribution per unit — the amount each sale contributes towards fixed costs and then profit.
分母（单价减去单位可变成本）被称为单位贡献毛利——每卖出一件产品对固定成本和利润的贡献额。
For example, if fixed costs are £5,000, the selling price is £25 per unit, and variable cost is £15 per unit, then:
例如，若固定成本为5,000英镑，单价为25英镑，单位可变成本为15英镑，则：
Break-even Quantity = £5,000 ÷ (£25 − £15) = 500 units
7. Interest Calculation | 利息计算
Interest is the cost of borrowing money or the reward for saving. Simple interest is calculated on the original principal only.
利息是借款的成本或储蓄的回报。单利仅以原始本金为基础计算。
terest (I) = Principal (P) × Rate of Interest per year (r) × Time in years (t)
In formula form: I = P × r × t. The total amount after t years = P + I.
公式形式为：I = P × r × t。t 年后的总金额 = P + I。
For instance, saving £200 at a 5% nnual simple interest rate for 3 years yields: I = 200 × 0.05 × 3 = £30.
例如，以年利率5%存入200英镑，存期3年，单利为：I = 200 × 0.05 × 3 = 30英镑。
Compound interest, where interest is earned on accumulated interest, is also important but follows a different formula not always required at Year 9.
复利（利息也生息）也很重要，但遵循不同的公式，九年级通常不作要求。
8. Price Elasticity of Demand | 需求价格弹性
Price elasticity of demand (PED) measures how responsive the quantity demanded is to a change in price. It is a numerical measure.
需求价格弹性（PED）衡量需求量对价格变化的反应程度，用数值表示。
PED = % Change in Quantity Demanded ÷ % Change in Price
Percentage changes are calculated as: (New Value - Original Value) / Original Value × 100. PED is usually negative, but economists often refer to its absolute value.
百分比变化的计算方式为：(新值 - 原值) / 原值 × 100。PED通常为负值，但经济学家常取其绝对值。
If |PED| > 1: demand is price elastic (responsive to price changes).
若 |PED| > 1：需求富有弹性（对价格变化敏感）。
If |PED| < 1: demand is price inelastic (unresponsive to price changes).
若 |PED| < 1：需求缺乏弹性（对价格变化不敏感）。
If |PED| = 1: demand is unit elastic.
若 |PED| = 1：需求具有单位弹性。
Knowing PED helps firms predict the effect of price changes on total revenue.
了解PED有助于企业预测价格变动对总收入的影响。
9. Average Costs | 平均成本
Average costs tell us the cost per unit of output. They are vital for pricing and efficiency analysis.
平均成本告诉我们每单位产出的成本。它对于定价和效率分析至关重要。
Average Total Cost (ATC) = Total Cost (TC) ÷ Quantity (Q)
Average Fixed Cost (AFC) = Total Fixed Cost (TFC) ÷ Quantity (Q)
Average Variable Cost (AVC) = Total Variable Cost (TVC) ÷ Quantity (Q)
As output rises, average fixed cost falls continuously (spreading overheads). Average variable cost typically falls initially due to efficiencies, then rises due to diminishing returns. The ATC curve is U-shaped.
随着产量增加，平均固定成本持续下降（分摊管理费）。平均可变成本通常先因效率提高而下降，后因收益递减而上升。ATC曲线呈U形。
10. Economic Systems and the Three Basic Questions | 经济体系与三个基本问题
Every economy must answer three fundamental questions because of scarcity: What to produce? How to produce? For whom to produce?
由于稀缺性，每个经济体都必须回答三个基本问题：生产什么？如何生产？为谁生产？
The way these questions are answered defines the economic system:
回答这些问题的方式决定了经济体系的类型：
In a market economy, decisions are driven by supply and demand, with minimal government intervention.
在市场经济中，决策由供求推动，政府干预极少。
In a command economy, the government makes all key decisions.
在指令经济中，政府制定所有关键决策。
Most real-world economies are mixed economies, combining market forces with government regulations.
大多数现实经济是混合经济，将市场力量与政府监管相结合。
This framework is not a formula but a theorem-like principle that structures all economic analysis.
这个框架虽非公式，但却是构建一切经济分析的基本定理式原则。
11. Shifts in Demand and Supply | 需求与供给的移动
A change in the price of the good itself causes a movement along the demand or supply curve. A change in any other factor causing a shift of the entire curve.
商品本身价格的变化引起沿需求曲线或供给曲线的移动。任何其他因素的变化则导致整条曲线的平移。
Factors shifting demand (mnemonic: TIPSY): Tastes, Income of consumers, Price of related goods (substitutes and complements), Special events, number of buyers.
影响需求移动的因素（助记：TIPSY）：消费者偏好、收入、相关商品价格（替代品和互补品）、特殊事件、买家数量。
Factors shifting supply (mnemonic: PESTC): Productivity, External shocks (weather), Subsidies and taxes, Technology, Costs of production.
影响供给移动的因素（助记：PESTC）：生产率、外部冲击（天气）、补贴与税收、技术、生产成本。
12. Inflation and its Measurement | 通货膨胀及其测量
Inflation is a sustained increase in the general price level. Deflation is a sustained decrease. The inflation rate is the percentage change in a price index, such as the Consumer Price Index (CPI).
通货膨胀是指总体价格水平的持续上升。通货紧缩是指总体价格水平的持续下降。通胀率是价格指数（如消费者价格指数CPI）的百分比变化。
nflation Rate = [(CPI this year − CPI last year) ÷ CPI last year] × 100
Mild inflation is common in growing economies, but very high or unpredictable inflation causes uncertainty and reduces the purchasing power of money.
温和通胀在经济增长期很常见，但过高或不可预测的通胀会引发不确定性并降低货币购买力。
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