AS OCR Economics: Formula & Theorem Quick Reference Handbook | AS OCR 经济：公式定理速查手册

📚 AS OCR Economics: Formula & Theorem Quick Reference Handbook | AS OCR 经济：公式定理速查手册

This handbook provides a concise summary of all essential formulas and key theorems required for the AS OCR Economics specification. Each section presents a formula or concept first in English and then its Chinese translation, ensuring you can quickly revisit the logic behind every calculation and theoretical proposition. Mastering these building blocks is critical for tackling data-response questions, multiple-choice items, and essays that demand precise economic terminology.

本手册汇总了AS OCR 经济学考试必需的核心公式与关键定理。每个小节先用英文呈现公式或概念，再配以中文解释，帮助你快速重温每一道计算和理论命题背后的逻辑。熟练掌握这些基础模块，对于应对数据分析题、选择题和要求精准专业术语的论述题至关重要。

1. Price Elasticity of Demand (PED) | 需求的价格弹性

Price elasticity of demand measures the responsiveness of quantity demanded to a change in price. The coefficient is calculated as the percentage change in quantity demanded divided by the percentage change in price, ignoring the sign (the absolute value is usually considered). The midpoint method can be used to avoid different results when moving up or down a demand curve:

需求的价格弹性衡量需求量对价格变动的反应程度。该系数等于需求量的变动百分比除以价格的变动百分比，通常取绝对值。为了避免沿需求曲线上移或下移时结果不一致，可以使用中点法计算：

PED = %ΔQd ÷ %ΔP

If PED > 1, demand is elastic; a price cut raises total revenue. If PED < 1, demand is inelastic; a price rise raises total revenue. If PED = 1, demand is unit elastic and total revenue is maximised. The determinants include the availability of close substitutes, the proportion of income spent on the good, whether it is a luxury or a necessity, and the time period considered.

若PED > 1，需求富有弹性，降价会使总收入增加；若PED < 1，需求缺乏弹性，提价会使总收入增加；若PED = 1，需求具有单位弹性，此时总收入达到最大。影响弹性的因素包括相近替代品的可获得性、商品支出占收入的比例、商品属于奢侈品还是必需品，以及考察的时间跨度。

PED Value	Classification	Effect on Total Revenue (Price ↓)
> 1	Elastic	Revenue increases
< 1	Inelastic	Revenue decreases
= 1	Unit elastic	Revenue unchanged
0	Perfectly inelastic	Qd stays constant
∞	Perfectly elastic	Infinite change in Qd

2. Income Elasticity of Demand (YED) | 需求的收入弹性

Income elasticity of demand captures the relationship between a change in consumers’ income and the demand for a good. The formula is:

需求的收入弹性反映消费者收入变化与商品需求之间的关系，公式为：

YED = %ΔQd ÷ %ΔY

Normal goods have a positive YED. If YED > 1, the good is a luxury (demand grows faster than income). If 0 < YED < 1, the good is a necessity. Inferior goods have a negative YED, meaning demand falls as income rises. For firms, YED helps forecast sales during economic booms or recessions, while governments use it to predict changes in tax revenue from different types of goods.

正常商品的YED为正；若YED > 1，该商品为奢侈品（需求增长快于收入）；若0 < YED < 1，则为必需品。劣质商品的YED为负，即收入上升时需求下降。对企业而言，YED有助于预测经济繁荣或萧条时的销售变化；政府则可借助它预估不同类别商品税收收入的变动。

3. Cross Elasticity of Demand (XED) | 需求的交叉弹性

Cross elasticity of demand measures the responsiveness of demand for one good (A) 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)价格变动的反应程度：

XED = %ΔQd of good A ÷ %ΔP of good B

A positive XED indicates substitutes (e.g. tea and coffee); a negative XED indicates complements (e.g. printers and ink cartridges). The magnitude shows the strength of the relationship. Strong substitutes will have a high positive XED, while strong complements will have a large negative value. Firms watch XED when setting prices to avoid cannibalising sales of related products.

XED为正表明是替代品（如茶与咖啡），为负则表明是互补品（如打印机与墨盒）。数值大小反映关联强度：强替代品的XED为正且较大，强互补品的XED为负且绝对值较大。企业在定价时会关注交叉弹性，以避免挤占自身相关产品的销售。

4. Price Elasticity of Supply (PES) | 供给的价格弹性

Price elasticity of supply measures how much the quantity supplied responds to a change in price. The standard formula is:

供给的价格弹性衡量供给量对价格变动的反应程度，标准公式为：

PES = %ΔQs ÷ %ΔP

PES is positive because the supply curve generally slopes upward. Values greater than 1 indicate elastic supply (firms can easily increase output), less than 1 indicate inelastic supply (output is difficult to expand quickly). Determinants include time period (short-run supply is typically more inelastic), availability of spare capacity, complexity of the production process, and the ease of storing stock. In the momentary period, supply is often perfectly inelastic (PES = 0), while in the long run PES can become very high.

由于供给曲线通常向右上方倾斜，PES为正值。数值大于1表示供给富有弹性（企业可轻易增产），小于1表示缺乏弹性（短期内难以迅速扩大产量）。影响供给弹性的因素包括时间跨度（短期供给通常更缺乏弹性）、闲置产能的可获得性、生产流程的复杂程度，以及存货储存的难易程度。在瞬时期内，供给往往完全无弹性（PES = 0），而在长期，PES可能很高。

5. Total, Average and Marginal Revenue | 总收入、平均收入与边际收入

Revenue concepts lie at the heart of a firm’s decision-making. Total revenue (TR) is the money received from sales, average revenue (AR) is revenue per unit sold, and marginal revenue (MR) is the additional revenue from selling one more unit:

收入概念是厂商决策的核心。总收入(TR)是销售收入，平均收入(AR)是单位销售收入，边际收入(MR)则是多销售一单位产品所带来的额外收入：

TR = P × Q

AR = TR ÷ Q = P

MR = ΔTR ÷ ΔQ

Under perfect competition, the firm is a price taker, so P = AR = MR (horizontal demand curve). In imperfect competition, the demand curve is downward sloping; to sell more the firm must lower the price, making MR lie below AR. The relationship is essential for understanding profit maximisation and for illustrating the shape of revenue curves.

在完全竞争下，厂商是价格接受者，因此P = AR = MR（需求曲线为水平）。在不完全竞争下，需求曲线向右下方倾斜，厂商为增加销售必须降价，因此MR低于AR。这一关系对于理解利润最大化和绘制收入曲线至关重要。

6. Short-Run Cost Structures | 短期成本结构

In the short run, at least one factor of production is fixed. Costs are split into total fixed cost (TFC) and total variable cost (TVC). The key unit-cost formulas are:

短期中至少有一种生产要素固定不变。成本分为总固定成本(TFC)和总可变成本(TVC)。核心的单位成本公式如下：

TC = TFC + TVC

ATC (or AC) = TC ÷ Q

AFC = TFC ÷ Q

AVC = TVC ÷ Q

MC = ΔTC ÷ ΔQ

The law of diminishing marginal returns explains the U-shape of the marginal cost curve and the average cost curves. Initially, adding variable factors to fixed factors raises productivity, so MC falls. Eventually, the fixed factor becomes overcrowded, productivity drops, and MC rises. The MC curve intersects both AVC and ATC at their minimum points.

边际报酬递减规律解释了边际成本和平均成本曲线呈U型的原因。起初，向固定要素追加可变要素会提高生产率，MC下降；最终固定要素过度拥挤，生产率下降，MC随之上升。MC曲线与AVC、ATC曲线相交于后两者的最低点。

7. Profit Maximisation and Objectives | 利润最大化与企业目标

The standard profit-maximising condition for any firm is where marginal cost equals marginal revenue. Profit is maximised when the gap between total revenue and total cost is greatest, which mathematically corresponds to the equality of MC and MR:

任何厂商利润最大化的标准条件是边际成本等于边际收入。当总收入与总成本之间的差距最大时利润达到最大，从数学上看，这相当于MC = MR：

Profit maximisation: MC = MR

Normal profit occurs when TR = TC (AR = ATC), meaning the firm is covering all its opportunity costs. Supernormal (abnormal) profit exists when TR > TC (AR > ATC). In the short run, supernormal profits can persist, but they attract new entrants in the long run under perfect competition, driving profit back to normal. Firms may also pursue other objectives such as revenue maximisation (MR = 0) or sales maximisation (AC = AR).

正常利润出现在TR = TC（即AR = ATC）时，意味着厂商恰好覆盖了全部机会成本。超常利润（超额利润）则出现在TR > TC（AR > ATC）时。短期内，超常利润可以持续，但在完全竞争下长期会吸引新厂商进入，最终利润回归正常。企业也可能追求收入最大化（MR = 0）或销售额最大化（AC = AR）等目标。

8. Aggregate Demand and the Multiplier | 总需求与乘数

Aggregate demand (AD) is the total planned expenditure on domestically produced goods and services at a given price level. Its components are consumption (C), investment (I), government spending (G), and net exports (X − M):

总需求(AD)是在既定价格水平下，对国内生产的产品和服务的计划支出总额，由消费(C)、投资(I)、政府支出(G)和净出口(X − M)构成：

AD = C + I + G + (X − M)

The multiplier effect describes how an initial injection into the circular flow leads to a larger final increase in national income. The simple Keynesian multiplier, assuming no government or foreign sector, depends on the marginal propensity to consume (MPC) and the marginal propensity to save (MPS):

乘数效应描述经济循环流量中一笔初始注入如何导致国民收入出现更大的最终增长。简化的凯恩斯乘数（假设无政府部门和对外贸易）取决于边际消费倾向(MPC)和边际储蓄倾向(MPS)：

Multiplier (k) = 1 ÷ (1 − MPC) = 1 ÷ MPS

The larger the MPC, the greater the multiplier. In an open economy with taxes and imports, the multiplier shrinks because of leakages. The formula becomes 1 ÷ (MPS + MPT + MPM), where MPT is the marginal propensity to tax and MPM is the marginal propensity to import. Knowing the multiplier helps evaluate the effectiveness of fiscal policy.

MPC越大，乘数效应越强。在包含税收和进口的开放经济中，由于漏出项的存在，乘数会变小，公式变为 1 ÷ (MPS + MPT + MPM)，其中MPT是边际税收倾向，MPM是边际进口倾向。理解乘数有助于评估财政政策的有效性。

9. Key Macroeconomic Indicators | 关键宏观经济指标

OCR AS Economics requires students to calculate and interpret inflation, unemployment, and growth rates. The consumer price index (CPI) is used to measure the rate of inflation:

OCR AS经济学要求学生能计算并解读通胀率、失业率和经济增长率。消费物价指数(CPI)用来衡量通胀率：

Inflation rate = (CPIₜ − CPIₜ₋₁) ÷ CPIₜ₋₁ × 100

The unemployment rate is the percentage of the labour force that is actively seeking work but unable to find employment. The labour force includes those in employment plus the unemployed; discouraged workers and students are excluded. The formula is:

失业率是劳动力中积极寻找工作但无法找到工作的人所占的百分比。劳动力包括就业者加上失业者；丧失信心的劳动者和全日制学生不计入内。公式为：

Unemployment rate = (Number of unemployed ÷ Labour force) × 100

Economic growth is typically measured by the percentage change in real GDP. Real GDP is calculated by adjusting nominal GDP for inflation using the GDP deflator:

经济增长通常用实际GDP的百分比变动来衡量。实际GDP通过用GDP平减指数调整名义GDP得出：

Real GDP = Nominal GDP ÷ (GDP deflator ÷ 100)

Alternatively, real GDP per capita can be found by dividing real GDP by the population. These indicators are often presented in index-number form, with a base year set to 100, to facilitate comparisons over time.

人均实际GDP可以用实际GDP除以人口计算。这些指标常以指数形式呈现，基年设为100，以便进行跨期比较。

10. Fundamental Economic Theorems | 基本经济定理

The production possibility frontier (PPF) illustrates the maximum combinations of two goods an economy can produce given its resources. The slope of the PPF reflects the opportunity cost. Moving along the frontier, the law of increasing opportunity cost states that as more of one good is produced, ever-increasing amounts of the other good must be sacrificed because resources are not equally efficient in all uses. The PPF shifts outward when the quantity or quality of resources improves.

生产可能性边界(PPF)显示了一个经济体在既定资源条件下所能生产的两种产品的最大组合。PPF的斜率反映了机会成本。沿边界移动时，机会成本递增规律指出，随着一种产品产量增加，需要牺牲越来越多的另一种产品，因为资源在不同用途上的效率并不相同。当资源数量增加或质量提高时，PPF会向外移动。

The law of demand states that, ceteris paribus, there is an inverse relationship between price and quantity demanded. The law of supply states a direct relationship between price and quantity supplied. The equilibrium price clears the market where Qd = Qs. When the market is not in equilibrium, price adjusts to eliminate shortages (excess demand) or surpluses (excess supply).

需求定律指出，在其余条件不变的情况下，价格与需求量呈反向关系。供给定律指出，价格与供给量呈正向关系。均衡价格是指在Qd = Qs时市场出清的价格。当市场不均衡时，价格会进行调整以消除短缺（超额需求）或过剩（超额供给）。

Diminishing marginal utility explains why demand curves slope downward: as a consumer consumes additional units of a good, the extra satisfaction gained from each successive unit falls, so they are only willing to buy more if the price drops. On the production side, diminishing marginal returns sets in when adding more of a variable factor to a fixed factor eventually yields smaller increments in output.

边际效用递减解释了需求曲线向下倾斜的原因：随着消费者消费更多单位的商品，每增加一单位所获得的额外满足感下降，因此只有在价格降低时才愿意购买更多。在生产方面，当向固定要素持续追加可变要素时，最终每追加一单位可变要素带来的产量增量会减少，即出现边际报酬递减。

11. Elasticity and Tax Incidence | 弹性与税收归宿

When an indirect tax is imposed, the burden is shared between consumers and producers, and the division depends on the relative elasticities of demand and supply. If demand is more inelastic than supply, consumers bear a larger share of the tax (greater incidence), and vice versa. The consumer burden per unit can be calculated as the increase in the price paid by consumers, while the producer burden is the reduction in the price received by producers after taxation.

征收间接税时，税负由消费者和生产者共同分担，分担的比例取决于需求与供给的相对弹性。若需求比供给更缺乏弹性，消费者承担的税负更大；反之亦然。每单位商品消费者的税负可用消费者支付价格的上升幅度来衡量，生产者的税负则是税后生产者实际收入价格的下降幅度。

The subsidy counterpart works similarly: a per-unit subsidy shifts the supply curve downward/rightward by the amount of the subsidy. The benefit is split between consumers (lower price) and producers (higher received price), again in inverse proportion to the elasticities. The total cost to the government is the per-unit subsidy multiplied by the new equilibrium quantity.

补贴的情况与之类似：每单位补贴使得供给曲线向下/向右垂直移动，移动幅度等于补贴金额。补贴带来的好处由消费者（支付更低价格）和生产者（获得更高价格）分享，其分配比例同样与弹性呈反向关系。政府补贴的总成本等于每单位补贴额乘以新的均衡数量。

12. Market Failure and Welfare Calculations | 市场失灵与福利计算

Market failure arises when the free market misallocates resources. Externalities are a key cause. The formula for the social cost (or benefit) helps quantify the divergence between private and social outcomes:

当自由市场错误配置资源时，就会发生市场失灵。外部性是主要原因之一。社会成本（或社会效益）的计算公式有助于量化私人结果与社会结果之间的偏离：

Social cost = Private cost + External cost

Social benefit = Private benefit + External benefit

Where external costs (negative externalities) or external benefits (positive externalities) exist, the free-market equilibrium output differs from the socially optimal level (where MSC = MSB). The welfare loss (deadweight loss) triangle area can be estimated as ½ × (external cost per unit) × (change in quantity). For policy evaluation, the Pigouvian tax should be set equal to the marginal external cost at the socially optimal output.

当存在外部成本（负外部性）或外部效益（正外部性）时，自由市场均衡产量会偏离社会最优水平（即MSC = MSB处）。无谓损失三角形可以用 ½ ×（每单位外部成本）×（产量变动量）来估算。在政策评估中，庇古税应设定为等于社会最优产量处的边际外部成本。

Public goods are defined by non-rivalry and non-excludability; their optimal provision occurs where the sum of individual marginal benefits equals marginal provision cost. Common access resources suffer from the tragedy of the commons due to lack of well-defined property rights. For all these failures, drawing accurate cost-benefit diagrams and labelling the welfare triangle is essential for achieving high marks.

公共物品具有非竞争性和非排他性，其最优提供量出现在个人边际收益之和等于边际提供成本之时。公共池塘资源因产权界定不清而遭受“公地悲剧”。对于所有这些失灵情形，准确绘制成本-收益图形并标出无谓损失三角，是获取高分的关键。

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AS OCR Economics: Formula & Theorem Quick Reference Handbook | AS OCR 经济：公式定理速查手册