📚 Year 10 CCEA Economics Formula & Theorem Quick Reference Handbook | Year 10 CCEA 经济：公式定理速查手册
This handbook brings together the essential formulas, definitions and economic theorems you need for the Year 10 CCEA Economics course. Use it to revise relationships between variables, calculate key measures and understand the logic behind each concept. Each entry is paired with a Chinese explanation so you can switch between languages confidently.
本手册汇集了 Year 10 CCEA 经济课程中必备的公式、定义和经济定理。你可以用它来复习变量之间的关系、计算关键指标，并理解每个概念背后的逻辑。每条内容都配有中文解释，方便你在中英双语之间自如切换。
1. The Basic Economic Problem – Scarcity and Choice | 基本经济问题 – 稀缺与选择
The fundamental economic problem is scarcity: unlimited wants but limited resources. This forces individuals, firms and governments to make choices, each involving an opportunity cost.
基本的经济问题是稀缺性：无限的需求面对有限的资源。这迫使个人、企业和政府做出选择，每一次选择都涉及机会成本。
Opportunity cost ve forgone. There is no universal numerical formula because it depends on the alternatives available, but you can express it as the ratio of the benefit of the next best option given up.
机会成本 = 所放弃的次优选项的价值。由于机会成本取决于可用的替代方案，没有通用的数字公式，但你可以表示为所放弃的次优选项的利益之比。
When a student chooses to study economics for one hour instead of earning £8 at a part-time job, the opportunity cost is £8 (and the enjoyment forgone).
当一名学生选择学习经济一小时，而不是去做兼职赚8英镑时，机会成本就是8英镑（以及放弃的乐趣）。
2. Demand – Law and Function | 需求 – 定律与函数
The law of demand states that, ceteris paribus, as the price of a good rises, the quantity demanded falls. The opposite is true when the price falls.
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 basic demand function can be written as:
Qd = a – bP
其中 Qd = 需求量，P = 价格，a = 价格为零时的需求量（截距），b = 需求曲线的斜率（表示需求对价格的敏感度）。
Where Qd is quantity demanded, P is price, a is the quantity demanded when price is zero (the intercept), and b represents the slope of the demand curve (the responsiveness of quantity demanded to price changes).
Movements along the demand curve are caused only by a change in the good's own price. Shifts of the whole curve are caused by other factors such as income, tastes, prices of substitutes or complements.
沿着需求曲线的移动仅仅由商品自身价格的变化引起。整条曲线的位移则由其他因素引起，如收入、偏好、替代品或互补品的价格。
3. Supply – Law and Function | 供给 – 定律与函数
The law of supply: ceteris paribus, as the price of a good rises, the quantity supplied increases. A simple linear supply function is:
供给定律：在其他条件不变的情况下，商品价格上升，供给量增加。一个简单的线性供给函数为：
Qs = c + dP
Qs = 供给量，P = 价格，c = 价格为零时的供给量（通常为负或零），d = 供给曲线斜率（衡量供给对价格的反应程度）。
Qs is quantity supplied, P is price, c is the quantity supplied when price is zero (often negative or zero in practice), and d is the slope of the supply curve (how responsive supply is to price).
A movement along the supply curve is caused by a change in the good’s own price. A shift in the entire supply curve is caused by changes in costs of production, technology, indirect taxes, subsidies or the number of sellers.
沿着供给曲线的移动由商品自身价格的变化引起。整条供给曲线的位移则由生产成本变化、技术、间接税、补贴或卖者数量的变化引起。
4. Market Equilibrium | 市场均衡
Market equilibrium occurs where quantity demanded equals quantity supplied. At this point there is no tendency for price to change.
市场均衡出现在需求量等于供给量之处。在这个点上，价格没有变动的趋势。
Qd = Qs
Using the linear functions above:
a – bP = c + dP
Solve for equilibrium price P*:
P* = (a – c) / (b + d)
Then substitute P* into either Qd or Qs to find equilibrium quantity Q*.
利用上述线性函数，令 a – bP = c + dP，解出均衡价格 P* = (a – c) / (b + d)，然后将 P* 代入 Qd 或 Qs 求出均衡数量 Q*。
When price is above equilibrium, a surplus exists (excess supply). When price is below equilibrium, a shortage exists (excess demand). Free market forces push the price towards equilibrium.
当价格高于均衡价格时，存在过剩（超额供给）。当价格低于均衡价格时，存在短缺（超额需求）。自由市场力量会推动价格趋向均衡。
5. Price Elasticity of Demand (PED) | 需求的价格弹性
PED measures the responsiveness of quantity demanded to a change in the good's own price. The basic formula is:
需求的价格弹性衡量需求量对商品自身价格变化的反应程度。基本公式为：
PED = % change in quantity demanded / % change in price
Using the midpoint (arc) method for accuracy:
PED = (ΔQd / Qd average) ÷ (ΔP / P average)
其中 Δ 表示变化量，平均值取起点和终点的中位数。
Where Δ means change, and the averages are the midpoints between the old and new values.
- |PED| > 1: elastic (responsive) demand
- |PED| = 1: unit elastic
- |PED| < 1: inelastic (less responsive) demand
- |PED| = ∞: perfectly elastic; |PED| = 0: perfectly inelastic
- |PED| > 1：富有弹性（敏感）
- |PED| = 1：单位弹性
- |PED| < 1：缺乏弹性（不敏感）
- |PED| = ∞：完全弹性；|PED| = 0：完全无弹性
If demand is elastic, a price decrease raises TR; if inelastic, a price decrease lowers TR.
PED 影响总收益（TR = P × Q）。如果需求富有弹性，降价会使总收益增加；若缺乏弹性，降价反而使总收益减少。
6. Price Elasticity of Supply (PES) | 供给的价格弹性
PES measures how much quantity supplied changes in response to a change in price. Formula:
供给的价格弹性衡量供给量对价格变化的反应程度。公式：
PES = % change in quantity supplied / % change in price
Again the midpoint method may be used:
PES = (ΔQs / Qs average) ÷ (ΔP / P average)
7. Income Elasticity of Demand (YED) | 需求的收入弹性
YED measures the responsiveness of demand to a change in consumers’ income. The formula is:
需求的收入弹性衡量需求量对消费者收入变化的反应程度。公式：
YED = % change in quantity demanded / % change in income
YED > 0: normal good (demand rises when income rises).
YED > 0：正常品（收入增加，需求增加）。
YED > 1: luxury good (demand rises faster than income).
YED > 1：奢侈品（需求增长快于收入增长）。
YED between 0 and 1: necessity.
0 < YED < 1：必需品。
YED < 0: inferior good (demand falls when income rises).
YED < 0：劣质品（收入增加，需求减少）。
8. Cross Elasticity of Demand (XED) | 需求的交叉弹性
XED measures how the demand for one good (A) responds to a change in the price of another good (B).
需求的交叉弹性衡量一种商品 (A) 的需求量对另一种商品 (B) 价格变化的反应程度。
XED = % change in Qd of good A / % change in price of good B
XED > 0: substitute goods (goods can replace each other).
XED > 0：替代品（两种商品可以互相替换）。
XED < 0: complement goods (goods are used together).
XED < 0：互补品（两种商品一起使用）。
XED = 0: unrelated goods.
XED = 0：不相关商品。
9. Costs of Production – Short Run | 生产成本 – 短期
In the short run at least one factor of production is fixed. Key cost concepts:
在短期，至少有一种生产要素是固定的。主要成本概念：
- Total Fixed Cost (TFC): costs that do not vary with output, e.g. rent.
- Total Variable Cost (TVC): costs that vary directly with output, e.g. raw materials.
- Total Cost (TC) = TFC + TVC
- Average Fixed Cost (AFC) = TFC ÷ Q
- Average Variable Cost (AVC) = TVC ÷ Q
- Average Total Cost (ATC or AC) = TC ÷ Q = AFC + AVC
- Marginal Cost (MC) = change in TC ÷ change in Q
- 总固定成本 (TFC)：不随产量变化的成本，如租金。
- 总可变成本 (TVC)：直接随产量变化的成本，如原材料。
- 总成本 (TC) = TFC + TVC
- 平均固定成本 (AFC) = TFC ÷ Q
- 平均可变成本 (AVC) = TVC ÷ Q
- 平均总成本 (ATC 或 AC) = TC ÷ Q = AFC + AVC
- 边际成本 (MC) = 总成本变化量 ÷ 产量变化量
MC typically falls at first due to increasing returns, then rises due to diminishing marginal returns.
边际成本起初因报酬递增而下降，然后因边际报酬递减而上升。
10. Revenue and Profit Maximisation | 收益与利润最大化
Total Revenue (TR) = Price (P) × Quantity sold (Q).
总收益 (TR) = 价格 (P) × 销售量 (Q)。
Average Revenue (AR) = TR ÷ Q = P (if all units sold at same price).
平均收益 (AR) = TR ÷ Q = P（如果所有单位按同一价格出售）。
Marginal Revenue (MR) = change in TR ÷ change in Q.
边际收益 (MR) = 总收益变化量 ÷ 销售量变化量。
Profit (π) = TR – TC.
利润 (π) = TR – TC。
produces where MR = MC, provided that price covers average variable cost in the short run.
追求利润最大化的企业会在 MR = MC 的产量处生产，前提是在短期价格至少能够覆盖平均可变成本。
al profit occurs when TR = TC (including opportunity cost). Supernormal profit is TR > TC.
正常利润出现在 TR = TC（包括机会成本）时。超额利润则是 TR > TC。
11. Market Structures – Key Characteristics | 市场结构 – 关键特征
| Structure / 结构 | Number of firms / 企业数量 | Barriers to entry / 进入壁垒 | Product differentiation / 产品差异 | LR profit / 长期利润 |
|---|---|---|---|---|
| Perfect competition / 完全竞争 | Very many / 非常多 | None / 无 | Homogeneous / 同质 | Normal / 正常 |
| Monopolistic competition / 垄断竞争 | Many / 很多 | Low / 低 | Differentiated / 有差异 | Normal / 正常 |
| Oligopoly / 寡头垄断 | Few dominant / 少数主导 | High / 高 | Can be differentiated or homogeneous / 可差异或同质 | Potential supernormal / 潜在超额 |
| Monopoly / 垄断 | One / 一家 | Very high / 非常高 | Unique, no close substitutes / 独特，无相近替代品 | Supernormal possible / 可能超额 |
In perfect competition, firms are 'price takers' and demand = AR = MR is perfectly elastic. In monopoly, the firm is a 'price maker' with a downward-sloping demand curve.
在完全竞争中，企业是“价格接受者”，需求 = AR = MR 完全弹性。在垄断中，企业是“价格制定者”，面临向下倾斜的需求曲线。
12. Key Graphs – Quick Reference to Axes | 关键图表 – 坐标轴速查
- Demand and supply diagram: vertical axis = Price; horizontal axis = Quantity.
- 需求与供给图：纵轴 = 价格；横轴 = 数量。
- Cost curves: vertical axis = Cost (£); horizontal axis = Output (Q). MC, ATC, AVC typically shown.
- 成本曲线图：纵轴 = 成本（£）；横轴 = 产量（Q）。通常显示 MC、ATC、AVC。
- Revenue curves: vertical axis = Revenue, Price (£); horizontal axis = Quantity.
- 收益曲线图：纵轴 = 收益、价格（£）；横轴 = 数量。
- PED diagram: can be shown on demand and supply axes, often illustrating changes in TR with price changes.
- PED 图：可在需求与供给轴上显示，通常用来说明价格变化对总收益的影响。
Always label equilibrium, surplus and shortage areas clearly. Shifts of curves versus movements along curves are a common exam focus.
始终清晰地标注均衡、过剩和短缺区域。曲线的位移与沿着曲线的移动是常见的考试重点。
Published by TutorHao | Economics Revision Series | aleveler.com
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