📚 Year 12 OCR Economics: Essential Formula & Theorem Quick Reference | 12年级 OCR 经济：公式定理速查手册
This quick reference handbook compiles the key formulas, definitions, and theorems you need to master for the Year 12 OCR Economics course. Understanding these building blocks is crucial for analysing markets, evaluating policy, and scoring high marks on your assessments.
本速查手册汇编了 12 年级 OCR 经济学课程所需掌握的关键公式、定义和定理。理解这些基本要素对于分析市场、评估政策以及在考试中取得高分至关重要。
1. Price Elasticity of Demand (PED) | 需求价格弹性（PED）
Price elasticity of demand (PED) measures the responsiveness of the quantity demanded of a good to a change in its price, ceteris paribus.
需求价格弹性（PED）衡量的是在其他条件不变的情况下，一种商品的需求量对其自身价格变动的反应程度。
The basic formula uses percentage changes:
PED = %Δ in Quantity Demanded / %Δ in Price
基本公式使用百分比变化：PED = 需求量变动的百分比 / 价格变动的百分比。
To avoid asymmetry when moving between two points on a demand curve, the midpoint (arc) formula is often used:
PED = [(Q₂ − Q₁) / ((Q₁ + Q₂) ÷ 2)] ÷ [(P₂ − P₁) / ((P₁ + P₂) ÷ 2)]
为避免在需求曲线上两点间移动时出现不对称，常使用中点（弧）公式：PED = [(Q₂ − Q₁) / ((Q₁ + Q₂) ÷ 2)] ÷ [(P₂ − P₁) / ((P₁ + P₂) ÷ 2)]。
hough PED is always negative due to the law of demand, we interpret its absolute value. If |PED| > 1, demand is elastic; if |PED| < 1, demand is inelastic; and if |PED| = 1, demand is unit elastic.
尽管根据需求定律，PED 总是为负值，但我们取其绝对值进行解释。如果 |PED| > 1，需求富有弹性；如果 |PED| < 1，需求缺乏弹性；如果 |PED| = 1，需求具有单位弹性。
The law of demand itself states: as the price of a good rises, the quantity demanded falls, ceteris paribus. PED quantifies by how much.
需求定律本身表明：在其他条件不变的情况下，一种商品的价格上升，其需求量就会下降。PED 则量化了下降的程度。
Key determinants of PED include the number and closeness of substitutes, the proportion of income spent on the good, and the time period under consideration.
PED 的关键决定因素包括替代品的数量与相近程度、该商品支出占收入的比例，以及所考虑的时间长短。
2. Income Elasticity of Demand (YED) | 需求收入弹性（YED）
Income elasticity of demand (YED) measures the responsiveness of demand for a good to a change in consumers' real income.
需求收入弹性（YED）衡量的是消费者实际收入变动时，对一种商品需求量的反应程度。
YED = %Δ in Quantity Demanded / %Δ in Real Income
公式为：YED = 需求量变动的百分比 / 实际收入变动的百分比。
Normal goods have a positive YED (YED > 0). For necessities, 0 < YED < 1; for luxuries, YED > 1. Inferior goods have a negative YED (YED < 0).
正常品的 YED 为正（YED > 0）。必需品的 YED 在 0 到 1 之间；奢侈品的 YED 大于 1。低档品的 YED 为负（YED < 0）。
Engel's law is an important theorem: as income rises, the proportion of income spent on food falls, meaning food has a YED less than 1.
恩格尔定律是一项重要定理：随着收入增加，用于食品的支出比例下降，这意味着食品的收入弹性小于 1。
Firms use YED to forecast the impact of economic growth on demand for their products and to plan output accordingly.
企业利用 YED 来预测经济增长对其产品需求的影响，并据此规划产量。
3. Cross Elasticity of Demand (XED) | 需求交叉弹性（XED）
Cross elasticity of demand (XED) measures the responsiveness of demand for one good (A) to a change in the price of another good (B).
需求交叉弹性（XED）衡量的是商品 A 的需求量对商品 B 价格变动的反应程度。
XED = %Δ in Quantity Demanded of Good A / %Δ in Price of Good B
公式：XED = 商品 A 需求量变动的百分比 / 商品 B 价格变动的百分比。
are complements (e.g., printers and ink cartridges). If XED ≈ 0, the goods are unrelated.
如果 XED > 0，则两种商品为替代品（例如茶和咖啡）。如果 XED < 0，则为互补品（例如打印机和墨盒）。如果 XED 接近 0，则两者不相关。
The magnitude of XED indicates the strength of the relationship: a large positive XED implies very close substitutes, while a large negative XED implies strong complements.
XED 的大小表明了相关程度：一个较大的正 XED 意味着高度替代，一个较大的负 XED 意味着强互补。
4. Price Elasticity of Supply (PES) | 供给价格弹性（PES）
Price elasticity of supply (PES) measures the responsiveness of the quantity supplied of a good to a change in its price.
供给价格弹性（PES）衡量的是商品供给量对其自身价格变动的反应程度。
PES = %Δ in Quantity Supplied / %Δ in Price
公式：PES = 供给量变动的百分比 / 价格变动的百分比。
ly is unit elastic. The law of supply states that, ceteris paribus, as price increases, quantity supplied increases.
若 PES > 1，供给富有弹性；若 PES < 1，供给缺乏弹性；若 PES = 1，供给具有单位弹性。供给定律指出，在其他条件不变的情况下，价格上升，供给量增加。
The main determinants of PES are the time period, the availability of spare production capacity, the ease of storing inventories, and the complexity of the production process.
PES 的主要决定因素包括时间长短、闲置生产能力、库存储存的难易程度，以及生产过程的复杂程度。
); in the short run, it is relatively inelastic; in the long run, it becomes more elastic.
在瞬时阶段，供给通常完全无弹性（PES = 0）；在短期，供给相对缺乏弹性；在长期，供给变得更具弹性。
5. Total Revenue Test and PED | 总收益检验与 PED
Total revenue (TR) is the money a firm receives from selling its output. It is calculated as:
总收益（TR）是企业销售产品所获得的货币收入，计算公式为：
TR = Price × Quantity Sold
总收益 = 价格 × 销售量。
The relationship between TR and PED gives the total revenue test: if demand is elastic (|PED| > 1), a price cut raises TR; if demand is inelastic (|PED| < 1), a price rise raises TR. When demand is unit elastic, TR is maximised.
TR 与 PED 之间的关系构成了总收益检验：如果需求富有弹性（|PED| > 1），降价会增加总收益；如果需求缺乏弹性（|PED| < 1），提价会增加总收益。当需求为单位弹性时，总收益达到最大。
This theorem helps firms set prices strategically, since the impact on revenue depends on whether consumers are price-sensitive or not.
这一原理有助于企业制定战略价格，因为对收入的影响取决于消费者对价格是否敏感。
6. Consumer Surplus and Producer Surplus | 消费者剩余与生产者剩余
Consumer surplus (CS) is the difference between what consumers are willing to pay and what they actually pay. On a demand-supply diagram, it is the area below the demand curve and above the market price.
消费者剩余（CS）是消费者愿意支付的最高价格与实际支付价格之间的差额。在供需图上，它是需求曲线以下、市场价格以上的区域。
CS = ½ × (Maximum Price − Equilibrium Price) × Equilibrium Quantity
PS = ½ × (Equilibrium Price − Minimum Acceptable Price) × Equilibrium Quantity
消费者剩余可用三角形面积计算：CS = ½ ×（最高价格 − 均衡价格）× 均衡数量；生产者剩余：PS = ½ ×（均衡价格 − 最低可接受价格）× 均衡数量。
oducers receive and the minimum price they are willing to accept. Total welfare = CS + PS.
生产者剩余（PS）是生产者实际得到的价格与其愿意接受的最低价格之间的差额。社会总福利 = CS + PS。
A competitive market in equilibrium maximises the sum of consumer and producer surplus, according to the theorem of allocative efficiency.
根据配置效率定理，处于均衡状态的竞争性市场使消费者剩余和生产者剩余之和最大化。
7. The Multiplier Effect | 乘数效应
The multiplier effect explains how an initial injection into the circular flow of income leads to a more than proportionate increase in national income.
乘数效应解释了向收入循环流注入的初始支出如何导致国民收入发生更大幅度的增长。
The simple closed-economy multiplier (k) depends on the marginal propensity to consume (MPC):
k = 1 / (1 − MPC) or k = 1 / MPS
简单的封闭经济乘数（k）取决于边际消费倾向（MPC）：k = 1 / (1 − MPC) 或 k = 1 / 边际储蓄倾向（MPS）。
where MPT is the marginal propensity to tax and MPM is the marginal propensity to import.
MPC = ΔC / ΔY，MPS = ΔS / ΔY，且 MPC + MPS = 1。在有税收和进口的开放经济中，乘数更小：k = 1 / (MPS + MPT + MPM)，其中 MPT 是边际税率倾向，MPM 是边际进口倾向。
The change in national income is then given by:
ΔY = k × ΔJ
国民收入的变动量为：ΔY = k × ΔJ（注入量的变动）。
8. Aggregate Demand (AD) Components | 总需求（AD）的构成
Aggregate demand is the total spending on goods and services produced in an economy at a given price level. Its formula is the sum of four components:
总需求是在一个给定价格水平下，经济中对所生产的商品和服务的总支出。其公式为四个组成部分之和：
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