📚 Year 12 CCEA Economics: Formula & Theorem Quick Reference Handbook | Year 12 CCEA 经济：公式定理速查手册
This handbook brings together the essential formulas, key theorems, and important relationships you need for the CCEA AS Economics course. It is designed as a quick revision tool covering microeconomics (Markets and Market Failure) and macroeconomics (Managing the National Economy). Every formula is presented with a clear definition, a worked-style notation, and a paired Chinese translation to support bilingual learners.
本手册汇集了 CCEA AS 经济课程中你必须掌握的核心公式、重要定理与关键关系。它以速查工具的形式覆盖微观经济学（市场与市场失灵）和宏观经济学（国民经济管理）。每个公式都配有清晰的定义、书写规范和对应的中文译文，方便双语学习者使用。
1. Price Elasticity of Demand (PED) | 需求价格弹性
PED measures the responsiveness of quantity demanded to a change in price. The standard formula is:
PED 衡量需求量对价格变动的反应程度，标准公式为：
PED = %ΔQd ÷ %ΔP
Because price and quantity demanded move in opposite directions, PED is always negative. Economists often ignore the minus sign and quote the absolute value.
由于价格与需求量反向变动，PED 恒为负值。经济学家通常忽略负号，使用绝对值进行讨论。
Use the midpoint (arc) formula to avoid inconsistency when moving up or down a demand curve:
为避免在需求曲线上移动方向不同带来的不一致，请使用中点（弧）弹性公式：
PED = [ (Q2 − Q1) ÷ ((Q1+Q2)/2) ] ÷ [ (P2 − P1) ÷ ((P1+P2)/2) ]
Interpretation: |PED| > 1 → elastic demand; |PED| < 1 → inelastic demand; |PED| tal revenue test states: raise price when demand is inelastic to increase TR; lower price when demand is elastic.
解读：|PED| > 1 为富有弹性；|PED| < 1 为缺乏弹性；|PED| = 1 为单位弹性。总收入检验定理：缺乏弹性时提价可增加总收入；富有弹性时降价可增加总收入。
2. Income Elasticity of Demand (YED) | 需求收入弹性
YED measures the responsiveness of demand to a change in consumers' income.
YED 衡量需求对消费者收入变化的反应程度。
YED = %ΔQd ÷ %ΔY
A positive YED indicates a normal good (YED > 0). A negative YED indicates an inferior good (YED < 0). Within normal goods, YED > 1 signals a luxury good, while 0 < YED < 1 signals a necessity.
YED 为正表明是正常品（YED > 0）；YED 为负表明是劣等品（YED < 0）。在正常品中，YED > 1 为奢侈品，0 < YED < 1 为必需品。
Businesses use YED forecasts to plan output during economic cycles and to adjust their product portfolios accordingly.
企业利用 YED 的预测来规划经济周期中的产量，并相应调整产品组合。
3. Cross Elasticity of Demand (XED) | 需求交叉弹性
XED measures the responsiveness of demand for good A when the price of good B changes.
XED 衡量 B 商品价格变动时，A 商品需求量的反应程度。
XED = %ΔQdA ÷ %ΔPB
If XED > 0, the two goods are substitutes (e.g. tea and coffee). If XED < 0, they are complements (e.g. printers and ink cartridges). XED near zero suggests unrelated goods. The sign matters and is never dropped.
若 XED > 0，两种商品互为替代品（如茶与咖啡）；若 XED < 0，则二者为互补品（如打印机与墨盒）。XED 接近零表示不相关商品。此处的符号含有经济含义，不可忽略。
4. Price Elasticity of Supply (PES) | 供给价格弹性
PES shows how responsive quantity supplied is to a change in the market price.
PES 表示供给量对市场价格变动的反应程度。
PES = %ΔQs ÷ %ΔP
upply; PES = 1: unit elastic supply. Key determinants include production time lags, spare capacity, and the ease of storing inventory.
PES 几乎总为正值，因为较高的价格会激励生产者增加供给。PES > 1 为供给富有弹性；PES < 1 为供给缺乏弹性；PES = 1 为单位弹性。主要决定因素包括生产时滞、闲置产能和库存难度。
5. Total, Average and Marginal Revenue | 总收益、平均收益与边际收益
Revenue concepts are fundamental for a firm's pricing and output decisions.
收益概念是企业定价和产量决策的基础。
Total Revenue (TR) = P × Q
Average Revenue (AR) = TR ÷ Q = P
Marginal Revenue (MR) = ΔTR ÷ ΔQ
and the demand curve faced by the firm is horizontal. In imperfectly competitive markets, the MR curve lies below the AR (demand) curve.
在完全竞争下，AR = MR = P，企业面对的需求曲线呈水平状。在不完全竞争市场中，边际收益曲线位于平均收益（需求）曲线之下。
6. Costs, Profit and Profit Maximisation | 成本、利润与利润最大化
A firm's cost structure determines its profitability. The key cost equations are:
企业的成本结构决定其盈利能力，关键成本公式如下：
Total Cost (TC) = Total Fixed Cost (TFC) + Total Variable Cost (TVC)
Average Total Cost (ATC) = TC ÷ Q
Average Variable Cost (AVC) = TVC ÷ Q
Marginal Cost (MC) = ΔTC ÷ ΔQ
The profit-maximising rule (theorem) states: a firm achieves maximum profit where MR = MC rom below. Normal profit occurs when AR = ATC; supernormal profit occurs when AR > ATC.
利润最大化定理：企业实现利润最大化的条件为 MR = MC，且边际成本从下方穿过边际收益。当 AR = ATC 时获得正常利润；当 AR > ATC 时获得超额利润。
7. Government Intervention: Indirect Tax and Subsidy | 政府干预：间接税与补贴
When an indirect tax is imposed, the tax burden is shared between consumers and producers.
征收间接税时，税负由消费者和生产者共同分担。
Consumer tax burden = Pc − Pe
Producer tax burden = Pe − Pp
where Pe is the original equilibrium price, Pc is the higher price paid by consumers, and Pp is the net price received by producers. The more inelastic side of the market bears a larger share of the tax.
其中 Pe 为原均衡价格，Pc 为消费者支付的更高价格，Pp 为生产者实际得到的净价格。市场越缺乏弹性的一方承担越大的税负比例。
A subsidy shifts the supply curve rightwards, lowering the price for consumers and raising the effective price for producers. The welfare gain from a subsidy can be measured by the rise in consumer and producer surplus, net of the government cost.
补贴使供给曲线右移，降低消费者价格并提高生产者的实际所得。补贴带来的福利增益可通过消费者剩余和生产者剩余的增加减去政府支出计算。
8. Market Failure: Externalities and Deadweight Loss | 市场失灵：外部性与无谓损失
When external costs or benefits exist, the free market fails to deliver allocative efficiency. The key relationships are:
当存在外部成本或外部收益时，自由市场无法实现配置效率。核心关系如下：
Social Cost (SC) = Private Cost (PC) + External Cost (EC)
Social Benefit (SB) = Private Benefit (PB) + External Benefit (EB)
The socially optimal output occurs where MSB = MSC. A negative externality causes overproduction and a deadweight loss (welfare triangle). A positive externality leads to underproduction and a similar deadweight loss. The Pigouvian tax equals the value of the marginal external cost at the socially efficient quantity.
社会最优产量出现在 MSB = MSC 处。负外部性导致过度生产和无谓损失（福利三角形）；正外部性导致生产不足，同样造成无谓损失。庇古税等于在社会有效产量处的边际外部成本值。
9. Aggregate Demand and the Multiplier | 总需求与乘数
Aggregate demand (AD) is the total planned spending on domestic output.
总需求（AD）是对国内产出的计划支出总额。
AD = C + I + G + (X − M)
The multiplier (k) measures the magnification of an initial injection into national income.
乘数（k）衡量初始注入对国民收入的放大效应。
k = 1 ÷ (1 − MPC) = 1 ÷ MPS
ginal propensity to save (MPC + MPS = 1). An initial injection ΔJ raises real GDP by ΔY = k × ΔJ. The multiplier also works in reverse if withdrawals rise.
其中 MPC 为边际消费倾向，MPS 为边际储蓄倾向（MPC + MPS = 1）。初始注入 ΔJ 将使实际 GDP 增加 ΔY = k × ΔJ。若漏出增加，乘数也会反向起作用。
10. Macroeconomic Indicators and Key Relationships | 宏观经济指标与关键关系
The headline indicators for economic performance are calculated as follows:
衡量经济表现的主要指标计算公式如下：
Inflation Rate = (CPIcurrent − CPIprevious) ÷ CPIprevious × 100
Unemployment Rate = (Number of unemployed ÷ Labour force) × 100
The circular flow of income emphasises the equivalence: National Income ≡ National Output ≡ National Expenditure al . Real GDP is nominal GDP adjusted for inflation: Real GDP = (Nominal GDP ÷ GDP Deflator) × 100.
收入循环流转强调恒等式：国民收入 ≡ 国民产出 ≡ 国民支出。实际 GDP 是剔除通胀后的名义 GDP，计算公式为：实际 GDP =（名义 GDP ÷ GDP 平减指数）× 100。
11. The Phillips Curve and Policy Trade-offs | 菲利普斯曲线与政策权衡
The original short-run Phillips Curve illustrates an inverse relationship between inflation and unemployment. The modern version links the inflation rate to the gap between actual unemployment and the non-accelerating inflation rate of unemployment (NAIRU).
最初版的短期菲利普斯曲线描述了通货膨胀与失业之间的反向关系。现代版本则将通胀率与实际失业率和非加速通胀失业率（NAIRU）之间的缺口联系起来。
π = πe − β(u − un) + ε
where π is actual inflation, πe is expected inflation, u is actual unemployment, un is the natural rate of unemployment, and ε captures supply shocks. In the long run, the Phillips Curve is vertical at un, meaning there is no trade-off between inflation and unemployment.
其中 π 表示实际通胀，πe 为预期通胀，u 为实际失业率，un 为自然失业率，ε 代表供给冲击。长期来看，菲利普斯曲线在 un 处呈现垂直线，意味着通胀与失业之间不存在权衡取舍。
12. Key Economic Relationships and Theorems | 重要经济关系与定理
Several foundational relationships underpin the Year 12 CCEA syllabus. They are not always expressed as single formulas but as cause-effect chains that shape policy analysis.
数条基础性关系构成了 Year 12 CCEA 课程大纲的支柱。它们未必总以单一公式呈现，而是体现为影响政策分析的因果链条。
The law of diminishing marginal utility: as a consumer increases consumption of a good, the additional satisfaction (MU) eventually falls. This explains the downward-sloping demand curve. The law of diminishing returns: in the short run, when one factor is fixed, adding variable factor units eventually yields smaller additions to output, causing MC to rise.
边际效用递减规律：消费者增加对某商品的消费时，额外满足感（MU）最终会下降，这解释了下倾的需求曲线。收益递减规律：短期内当某要素固定时，增加可变要素投入最终导致边际产出递减，从而边际成本上升。
ductive efficiency occurs at the minimum point of the ATC curve. Both concepts feature heavily in CCEA exam explanations.
配置效率在价格等于边际成本（P = MC）时实现；生产效率在平均总成本曲线最低点实现。这两个概念在 CCEA 考试的解释题中出现频率很高。
Published by TutorHao | Economics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图