Year 12 CAIE Economics Formula & Theorem Quick Reference Handbook | CAIE 经济：公式定理速查手册

📚 Year 12 CAIE Economics Formula & Theorem Quick Reference Handbook | CAIE 经济：公式定理速查手册

Welcome to your essential quick-reference guide for Year 12 CAIE Economics. This handbook distills the key formulas, theorems, and graphical relationships you will encounter across the AS Level syllabus. From the fundamental mechanics of price elasticity to the macroeconomic dynamics of the multiplier effect, each concept is presented in a clear, exam-focused format. Whether you are revising for a mock examination or consolidating classroom learning, keep this handbook close at hand to sharpen your analytical precision and calculation speed. Remember, in CAIE Economics, showing the correct formula alongside accurate numerical working is often the difference between a good answer and an excellent one.

欢迎使用这份为你精心整理的 Year 12 CAIE 经济速查手册。本手册浓缩了 AS 阶段课程中你将遇到的所有核心公式、定理与图形关系。从需求价格弹性的基本机制到乘数效应的宏观动态，每个概念都以清晰、聚焦考试的形式呈现。无论你是在准备模拟考试还是巩固课堂所学，随身携带这份手册都能帮助你提高分析精确度与计算速度。请记住，在 CAIE 经济学考试中，写出正确的公式并展示准确的运算过程，往往是优秀答案与良好答案之间的关键分水岭。

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

The standard formula for PED measures the responsiveness of quantity demanded to a change in price. It is always expressed as a negative value due to the inverse relationship between price and quantity, though the negative sign is often dropped when interpreting magnitude.

需求价格弹性的标准公式衡量需求量对价格变化的反应程度。由于价格与数量之间存在反向关系，该值通常表示为负数，但在解释其大小时负号常被省略。

PED = %Δ Quantity Demanded ÷ %Δ Price

For point elasticity on a linear demand curve, use the following calculation where ΔQ and ΔP represent absolute changes in quantity and price, while P and Q are the original price and quantity coordinates.

对于线性需求曲线上的点弹性，可使用以下计算公式，其中 ΔQ 和 ΔP 代表数量与价格的绝对变化量，P 和 Q 为原始价格与数量坐标。

PED = (ΔQ / ΔP) × (P / Q)

When PED > 1 (in absolute terms), demand is price elastic. A price cut raises total revenue.

当 |PED| > 1 时，需求富有价格弹性。降价会使总收益增加。
When PED < 1 (in absolute terms), demand is price inelastic. A price rise raises total revenue.

当 |PED| < 1 时，需求缺乏价格弹性。涨价会使总收益增加。
When PED = 1, demand is unit elastic. Total revenue is maximised and remains constant with small price changes.

当 |PED| = 1 时，需求具有单位弹性。总收益达到最大，且在微小价格变动下保持不变。

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

YED quantifies how demand shifts in response to changes in consumer income. The sign of YED determines whether a good is classified as normal or inferior; the magnitude distinguishes necessities from luxuries.

需求收入弹性衡量需求如何随消费者收入变化而变动。YED 的正负号决定了一种商品被归类为正常品还是低档品；数值大小则区分必需品与奢侈品。

YED = %Δ Quantity Demanded ÷ %Δ Income

A positive YED indicates a normal good. YED > 1 signals a luxury good, while 0 < YED < 1 signals a necessity.

YED 为正表示正常品。YED > 1 为奢侈品，0 < YED < 1 为必需品。
A negative YED indicates an inferior good, where rising income causes demand to fall.

YED 为负表示低档品，收入上升导致其需求下降。

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

XED measures the responsiveness of demand for Good A following a price change in Good B. This formula is critical for establishing the economic relationship between two products and is frequently tested in multiple-choice and data-response questions.

需求交叉弹性衡量商品 A 的需求对商品 B 价格变化的反应程度。此公式对于确定两种产品之间的经济关系至关重要，在多选题和数据分析题中频繁出现。

XED = %Δ Quantity Demanded of Good A ÷ %Δ Price of Good B

A positive XED reveals substitute goods. If the price of Pepsi rises, the quantity demanded for Coca-Cola increases.

XED 为正表明两种商品互为替代品。如果百事可乐涨价，可口可乐的需求量会上升。
A negative XED reveals complement goods. If the price of printers rises, the quantity demanded for ink cartridges declines.

XED 为负表明两种商品互为互补品。如果打印机涨价，墨盒的需求量会下降。

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

PES captures the sensitivity of quantity supplied to price fluctuations. The defining constraint in PES analysis is the time period: supply grows more elastic as producers gain more time to adjust their productive capacity.

供给价格弹性反映供给量对价格波动的敏感程度。PES 分析中的决定性约束条件是时间周期：生产者获得更多时间来调整其生产能力时，供给会变得更具弹性。

PES = %Δ Quantity Supplied ÷ %Δ Price

Supply is price elastic when PES > 1. This typically applies to manufactured goods in the long run.

当 PES > 1 时，供给富有价格弹性。这通常适用于长期中的制成品。
Supply is price inelastic when PES < 1. Agricultural output and sea-front hotel rooms exhibit this characteristic in the short run.

当 PES < 1 时，供给缺乏价格弹性。农产品产出和海滨酒店房间在短期内表现出这一特征。

5. Consumer & Producer Surplus | 消费者剩余与生产者剩余

Welfare analysis hinges on calculating the area of surplus triangles. Consumer surplus is the difference between what consumers are willing to pay and what they actually pay. Producer surplus is the difference between the market price received and the minimum price at which producers are willing to supply.

福利分析依赖于计算剩余三角形的面积。消费者剩余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。生产者剩余是生产者获得的市场价格与其愿意接受的最低价格之间的差额。

Consumer Surplus = ½ × Base × Height (measured below the demand curve, above equilibrium price)

生产者剩余 = ½ × 底 × 高 (衡量均衡价格以下、供给曲线以上的区域面积)

Total welfare at free-market equilibrium equals the sum of consumer surplus and producer surplus. Any deadweight loss occurs where this total is reduced by market interventions such as indirect taxes, subsidies, or price controls.

自由市场均衡下的总福利等于消费者剩余与生产者剩余之和。当间接税、补贴或价格管制等市场干预导致这一总和减少时，便会产生无谓损失。

6. Maximum Price and Minimum Price Interventions | 最高限价与最低限价干预

A maximum price (price ceiling) is set below the free-market equilibrium to protect consumers. This creates excess demand, and the quantity traded equals the quantity supplied at that ceiling. A minimum price (price floor) is set above the equilibrium, generating excess supply.

最高限价（价格天花板）设定在自由市场均衡价格之下以保护消费者。这会造成超额需求，实际交易量等于限价下的供给量。最低限价（价格地板）设定在均衡价格之上，产生超额供给。

For a maximum price, measure the shortage as Qd – Qs at the ceiling price. The welfare loss appears as an under-production deadweight triangle beside the restricted quantity.

对于最高限价，短缺量按限价下的 Qd – Qs 计算。福利损失表现为受限制产量旁的三角形无谓损失区域。
For a minimum price, measure the surplus as Qs – Qd at the floor price. Government may need to purchase the excess to maintain the floor, incurring a fiscal cost equal to the floor price multiplied by the surplus quantity.

对于最低限价，剩余量按地板价格下的 Qs – Qd 计算。政府可能需要购买超额部分以维持地板价，财政成本等于地板价格乘以剩余数量。

7. Incidence of Taxation and Subsidy | 税收与补贴的归宿

The division of an indirect tax burden between consumers and producers depends on the relative elasticities of demand and supply. The side of the market that is more inelastic bears a greater share of the tax. Similar logic applies to the distribution of subsidy benefits.

间接税负在消费者与生产者之间的分摊取决于需求与供给的相对弹性。市场中弹性较小的一方承担更大份额的税收。同样的逻辑也适用于补贴利益的分配。

Consumer Tax Burden = (P₂ – P₁) × Q₂

消费者税负 = (税后价格 – 税前均衡价格) × 税后交易量

Producer Tax Burden = Total Tax Revenue – Consumer Burden

生产者税负 = 总税收收入 – 消费者税负

Total tax revenue received by the government equals the per-unit tax multiplied by the post-tax quantity traded. The deadweight loss of an indirect tax is the triangle between the original equilibrium quantity and the restricted post-tax quantity where marginal social benefit exceeds marginal social cost.

政府获得的总税收收入等于单位税额乘以税后交易量。间接税的无谓损失是介于原均衡数量与受限税后数量之间的三角形区域，这里边际社会收益超过边际社会成本。

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

Aggregate demand (AD) is the sum of planned expenditure on domestic output at a given price level. The multiplier effect explains how an initial injection into the circular flow generates a magnified final increase in national income through successive rounds of spending.

总需求是在给定价格水平下计划用于国内产出的支出总和。乘数效应解释了循环流中的初始注入如何通过连续支出轮次产生被放大数倍的国民收入最终增长。

AD = C + I + G + (X – M)

总需求 = 消费 + 投资 + 政府支出 + (出口 – 进口)

The multiplier coefficient (k) is determined by the marginal propensity to withdraw from the circular flow. The key withdrawal propensities are the marginal propensity to save (MPS), the marginal propensity to tax (MPT), and the marginal propensity to import (MPM).

乘数系数 (k) 由边际漏出倾向决定。关键漏出倾向包括边际储蓄倾向 (MPS)、边际税率 (MPT) 和边际进口倾向 (MPM)。

k = 1 ÷ (MPS + MPT + MPM)

乘数 = 1 ÷ (边际储蓄倾向 + 边际税率 + 边际进口倾向)

Δ National Income = k × Δ Injection

国民收入变动 = 乘数 × 注入变动

9. Average and Marginal Product (Short-Run Production) | 平均产量与边际产量（短期生产）

In the short run, at least one factor of production is fixed. The law of diminishing marginal returns states that as successive units of a variable factor are added to a fixed factor, the marginal product eventually falls. This relationship underpins the shapes of the short-run cost curves.

在短期中，至少有一种生产要素是固定的。边际收益递减规律指出，当可变要素的连续单位被添加到固定要素上时，边际产量最终会下降。这种关系奠定了短期成本曲线形状的基础。

Average Product (AP) = Total Product ÷ Quantity of Variable Factor

平均产量 = 总产量 ÷ 可变要素数量

Marginal Product (MP) = Δ Total Product ÷ Δ Quantity of Variable Factor

边际产量 = 总产量变动量 ÷ 可变要素变动量

The marginal product curve intersects the average product curve at the maximum point of average product. When MP exceeds AP, AP rises; when MP falls below AP, AP declines.

边际产量曲线在平均产量曲线的最高点与之相交。当 MP > AP 时，AP 上升；当 MP < AP 时，AP 下降。

10. Short-Run Cost Formulas | 短期成本公式

Understanding cost structures is essential for evaluating firm behaviour and market outcomes. Distinguish carefully between fixed costs, which do not vary with output, and variable costs, which change as output expands or contracts.

理解成本结构对于评估企业行为与市场结果至关重要。要仔细区分不随产量变化的固定成本与随产量扩张或收缩而变动的可变成本。

Total Cost (TC) = Total Fixed Cost (TFC) + Total Variable Cost (TVC)

总成本 = 总固定成本 + 总可变成本

Average Total Cost (ATC) = TC ÷ Q = AFC + AVC

平均总成本 = 总成本 ÷ 产量 = 平均固定成本 + 平均可变成本

Marginal Cost (MC) = Δ TC ÷ Δ Q

边际成本 = 总成本变动量 ÷ 产量变动量

The marginal cost curve passes through the minimum points of both the average variable cost curve and the average total cost curve. When MC is below ATC, ATC is falling; when MC is above ATC, ATC is rising.

边际成本曲线穿过平均可变成本曲线与平均总成本曲线的最低点。当 MC 低于 ATC 时，ATC 正在下降；当 MC 高于 ATC 时，ATC 正在上升。

11. Profit Maximisation and Revenue | 利润最大化与收益

Firms in all market structures maximise profit where marginal cost equals marginal revenue (MC = MR). For a perfectly competitive firm, price equals marginal revenue (P = MR). For a monopolist, marginal revenue lies below the demand curve, and the firm must lower price on all units to sell one more.

所有市场结构中的企业都在边际成本等于边际收益 (MC = MR) 处实现利润最大化。对于完全竞争企业，价格等于边际收益 (P = MR)。对于垄断企业，边际收益位于需求曲线下方，企业必须降低所有单位的价格才能多卖出一单位。

Profit Maximisation Condition: MC = MR

利润最大化条件：MC = MR

Total Revenue (TR) = Price × Quantity

总收益 = 价格 × 数量

Average Revenue (AR) = TR ÷ Q = Price

平均收益 = 总收益 ÷ 数量 = 价格

Profit, whether normal or supernormal, is calculated as total revenue minus total cost. Normal profit, where AR = ATC, represents the minimum return necessary to keep resources in their current use and is included within total cost for economists.

利润，无论是正常利润还是超额利润，均按总收益减去总成本计算。正常利润（AR = ATC）代表将资源保留在当前用途所需的最低回报，并在经济学家的核算中已包含在总成本之内。

12. Terms of Trade and Current Account | 贸易条件与国际收支经常账户

The terms of trade index measures the relative movement of export and import prices. An improvement in the terms of trade means a country can buy more imports for a given quantity of exports. However, the volume effect of price changes must also be considered when assessing the balance of trade.

贸易条件指数衡量出口价格与进口价格的相对变动。贸易条件的改善意味着一国用给定数量的出口能购买更多进口。然而，在评估贸易余额时，还必须考虑价格变动带来的数量效应。

Terms of Trade Index = (Export Price Index ÷ Import Price Index) × 100

贸易条件指数 = (出口价格指数 ÷ 进口价格指数) × 100

The current account balance sums the trade in goods, trade in services, primary income flows, and secondary income transfers. A deficit indicates that expenditure on imports, income outflows, and transfers exceeds revenue from exports, income inflows, and inward transfers.

经常账户余额是货物贸易、服务贸易、初次收入流动和二次收入转移的总和。赤字表示进口支出、收入流出和转移支出超过了出口收入、收入流入和向内转移的收入。

Current Account Balance = (X – M) + Net Primary Income + Net Secondary Income

经常账户余额 = (出口 – 进口) + 净初次收入 + 净二次收入

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Year 12 CAIE Economics Formula & Theorem Quick Reference Handbook | CAIE 经济：公式定理速查手册