📚 Year 8 Cambridge Economics: Formula & Theorem Quick Reference | Year 8 剑桥经济：公式定理速查手册
This quick-reference handbook provides a concise summary of the essential formulas, theorems, and key concepts from the Year 8 Cambridge Economics syllabus. Use it alongside your class notes to reinforce your understanding and prepare for assessments.
本速查手册简明扼要地总结了 Year 8 剑桥经济课程中的基本公式、定理和关键概念。配合课堂笔记使用，可加深理解并高效备考。
1. Scarcity and Opportunity Cost | 稀缺性与机会成本
Scarcity is the fundamental economic problem: resources are limited, but human wants are unlimited. Because of this, every society and individual must make choices.
稀缺性是基本的经济问题：资源有限而人类的欲望无限。正因如此，每个社会和个人都必须做出选择。
Every choice involves an opportunity cost. Opportunity cost is the value of the next best alternative that is given up when a decision is made.
每个选择都存在机会成本。机会成本是指做出某个决定时所放弃的次优选项的价值。
Opportunity Cost = Value of Next Best Alternative Forgone
For example, if a government spends more on defence, the opportunity cost may be fewer resources for education.
例如，如果政府增加国防支出，机会成本可能是教育资源的减少。
2. Factors of Production | 生产要素
The four factors of production are the inputs used to produce goods and services: land, labour, capital and enterprise.
四大生产要素是用于生产商品和服务的投入：土地、劳动、资本和企业家才能。
Land includes all natural resources, such as water, minerals and forests. Labour refers to human effort, both physical and mental.
土地包括所有自然资源，如水、矿产和森林。劳动指人类体力和脑力的付出。
Capital consists of man-made goods used in production, such as machinery, tools and buildings. Enterprise is the skill of combining the other factors, taking risks and innovating.
资本包括用于生产的人造物品，如机器、工具和厂房。企业家才能指组合其他要素、承担风险并创新的能力。
3. Law of Demand | 需求定理
The law of demand states that, ceteris paribus (other things being equal), when the price of a good rises, the quantity demanded falls. Conversely, when the price falls, the quantity demanded rises.
需求定理指出，在其他条件不变的情况下，商品价格上升时，需求量下降；反之，价格下降时，需求量上升。
P ↑ → Qd ↓ | P ↓ → Qd ↑
This inverse relationship is represented by a downward-sloping demand curve. The quantity demanded (Qd) depends on price and other factors such as income and tastes.
这种反向关系表现为向下倾斜的需求曲线。需求量 (Qd) 取决于价格以及收入、偏好等其他因素。
4. Law of Supply | 供给定理
The law of supply says that, ceteris paribus, as the price of a good increases, the quantity supplied increases. If the price decreases, the quantity supplied decreases.
供给定理指出，条件不变时，商品价格上升，供给量增加；价格下降，供给量减少。
P ↑ → Qs ↑ | P ↓ → Qs ↓
Producers are willing to supply more at higher prices because higher prices can cover higher costs and generate greater profits.
生产者在价格较高时愿意提供更多产品，因为高价可以覆盖更高的成本并带来更大的利润。
5. Market Equilibrium | 市场均衡
Market equilibrium occurs at the price where quantity demanded equals quantity supplied. At this point, there is neither excess demand (shortage) nor excess supply (surplus).
市场均衡出现在需求量等于供给量的价格水平上。在这一点上，既无超额需求（短缺），也无超额供给（过剩）。
Qd = Qs
The equilibrium price (P*) and equilibrium quantity (Q*) are determined by the intersection of demand and supply curves. Any change in demand or supply will shift the curves and change the equilibrium.
均衡价格 (P*) 和均衡数量 (Q*) 由需求曲线和供给曲线的交点决定。需求或供给的任何变化都会移动曲线并改变均衡。
6. Price Elasticity of Demand (PED) | 需求价格弹性
Price elasticity of demand measures how responsive the quantity demanded is to a change in price. It helps firms predict the effect of price changes on their sales revenue.
需求价格弹性衡量需求量对价格变化的反应程度。它帮助企业预测价格变化对销售收入的影响。
PED = (%ΔQd) ÷ (%ΔP)
The value of PED is usually negative because of the law of demand, but we often compare elasticities using their absolute values (|PED|).
由于需求定理，PED 通常为负值，但我们常用其绝对值 (|PED|) 来比较弹性大小。
If |PED| > 1, demand is elastic (quantity changes by a larger percentage than price). If |PED| < 1, demand is inelastic. If |PED| = 1, demand is unit elastic.
若 |PED| > 1，需求富有弹性（数量变化百分比大于价格变化百分比）；若 |PED| < 1，需求缺乏弹性；若 |PED| = 1，则为单位弹性。
Example: A 10% rise in the price of cinema tickets leads to a 25% fall in the number of tickets sold. PED = -25% / 10% = -2.5, so demand is elastic.
例：电影票价上涨 10% 导致售票量下跌 25%。PED = -25% / 10% = -2.5，因此需求富有弹性。
7. Price Elasticity of Supply (PES) | 供给价格弹性
Price elasticity of supply measures how responsive quantity supplied is to a change in price. It reflects how easily producers can increase output when prices rise.
供给价格弹性衡量供给量对价格变化的反应程度。它反映了价格上涨时生产者扩大产出的难易程度。
PES = (%ΔQs) ÷ (%ΔP)
PES is typically positive. If PES > 1, supply is elastic; if PES < 1, supply is inelastic. A PES of zero means supply is perfectly inelastic (fixed quantity).
PES 通常为正值。若 PES > 1，供给富有弹性；若 PES < 1，供给缺乏弹性。PES 为零时供给完全无弹性（数量固定）。
Factors such as time, spare capacity and ease of storage influence supply elasticity. Supply tends to be more elastic in the long run.
时间、闲置产能和储存难易等因素影响供给弹性。长期中供给往往更有弹性。
8. Costs of Production | 生产成本
Total cost is the sum of all costs a firm incurs to produce a given level of output. It is divided into fixed costs and variable costs.
总成本是企业为生产一定产出所承担的全部成本之和，分为固定成本和可变成本。
TC = TFC + TVC
Total fixed cost (TFC) does not vary with output (e.g., rent, insurance). Total variable cost (TVC) changes with output (e.g., raw materials, energy).
总固定成本 (TFC) 不随产量变化（如租金、保险费）。总可变成本 (TVC) 随产量变化（如原材料、能源）。
Average total cost (ATC) is the cost per unit of output. It is calculated by dividing total cost by quantity.
平均总成本 (ATC) 是每单位产出的成本，由总成本除以产量得到。
ATC = TC ÷ Q
9. Revenue and Profit | 收益与利润
Total revenue is the income a firm receives from selling its goods or services. It is calculated by multiplying price by quantity sold.
总收益是企业销售商品或服务所获得的收入，由价格乘以销售量计算得出。
TR = P × Q
Average revenue (AR) is revenue per unit sold. For a firm that charges a single price, AR equals the price.
平均收益 (AR) 是每单位产品的收益。对于制定单一价格的企业，AR 等于价格。
AR = TR ÷ Q = P
Profit is the difference between total revenue and total cost. It is the reward for risk-taking and innovation.
利润是总收益与总成本之差，是对承担风险和创新的回报。
Profit = TR − TC
firm makes a profit; if TC exceeds TR, it makes a loss. Breaking even occurs when TR = TC.
若 TR 大于 TC，企业盈利；若 TC 大于 TR，企业亏损。当 TR = TC 时，企业实现盈亏平衡。
10. Economic Systems and Basic Questions | 经济体系与基本问题
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 method used to answer these questions defines the type of economic system: traditional, command, market or mixed. In a market economy, prices and competition guide decisions; in a command economy, the government plans output.
回答这些问题的机制决定了经济体系的类型：传统经济、指令经济、市场经济或混合经济。在市场经济中，价格和竞争引导决策；在指令经济中，政府计划产出。
While not a mathematical formula, the concept of resource allocation is central to understanding how different systems work.
虽不是数学公式，但资源配置的概念对于理解不同体系的运作至关重要。
11. Budget Constraints and Saving | 预算约束与储蓄
Individuals and households face a budget constraint: their income must be allocated between consumption and saving.
个人和家庭面临预算约束：收入必须在消费和储蓄之间分配。
Y = C + S
Here Y represents disposable income, C is consumption spending on goods and services,
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