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

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

This quick reference handbook compiles the essential formulae, definitions, and theoretical relationships required for the Cambridge International AS Level Economics syllabus. It is designed as a revision tool to help you recall key quantitative concepts and apply them accurately in examination contexts.

本速查手册汇编了剑桥国际AS水平经济学教学大纲所要求的基本公式、定义和理论关系。它旨在作为复习工具，帮助您回忆关键的定量概念并在考试中准确应用。

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

Price elasticity of demand (PED) measures the responsiveness of the quantity demanded of a good to a change in its own price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.

需求的价格弹性（PED）衡量一种商品的需求量对其自身价格变动的反应程度。它由需求量变动的百分比除以价格变动的百分比计算得出。

PED = %ΔQd ÷ %ΔP

The standard formula uses percentage changes so that the value is independent of the units in which price and quantity are measured.

标准公式使用百分比变化，目的是让数值摆脱价格与数量计量单位的影响。

When moving along a demand curve between two points, it is often preferable to use the midpoint (arc) elasticity to obtain an average elasticity over the range:

当沿着需求曲线在两个点之间变动时，通常最好使用中点（弧）弹性法以得到该区间的平均弹性：

PED = [(Q₂ − Q₁) ÷ ((Q₁ + Q₂) ÷ 2)] ÷ [(P₂ − P₁) ÷ ((P₁ + P₂) ÷ 2)]

The value of PED can be interpreted as follows:

PED 的数值可作如下解读：

If PED > 1, demand is price elastic. A given percentage change in price leads to a larger percentage change in quantity demanded.

若 PED > 1，需求富有价格弹性。价格给定的百分比变动会导致需求量发生更大比例的变动。

If PED < 1, demand is price inelastic. The percentage change in quantity demanded is smaller than the percentage change in price.

若 PED < 1，需求缺乏价格弹性。需求量变动的百分比小于价格变动的百分比。

If PED = 1, demand has unitary elasticity. Quantity demanded changes by exactly the same percentage as price.

若 PED = 1，需求具有单位弹性。需求量变动的百分比与价格变动的百分比完全相等。

If PED = 0, demand is perfectly inelastic. Quantity demanded does not respond to price changes at all.

若 PED = 0，需求完全无弹性。需求量对价格变动完全没有反应。

If PED = ∞, demand is perfectly elastic. Consumers are prepared to buy any quantity at one fixed price but zero at any higher price.

若 PED = ∞，需求完全弹性。在一个固定价格上消费者愿意购买任何数量，但价格稍高则需求降为零。

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

Income elasticity of demand measures the responsiveness of demand for a good to a change in consumers’ income.

需求的收入弹性衡量一种商品的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. If YED > 1, the good is a luxury (demand rises more than proportionately with income). If 0 < YED < 1, the good is a necessity.

正的 YED 表示该商品为正常品。若 YED > 1，该商品为奢侈品（需求增长幅度大于收入增长幅度）；若 0 < YED < 1，该商品为必需品。

A negative YED indicates an inferior good. As income rises, demand for inferior goods falls.

负的 YED 表示该商品为劣质品。随着收入上升，对劣质品的需求会下降。

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）的需求对另一种商品（B）价格变动的反应程度。

XED = %ΔQd of A ÷ %ΔPrice of B

If XED > 0, the two goods are substitutes. A rise in the price of B leads to an increase in the demand for A.

若 XED > 0，两种商品互为替代品。B 的价格上升会导致对 A 的需求增加。

If XED < 0, the two goods are complements. A rise in the price of B reduces the demand for A.

若 XED < 0，两种商品互为互补品。B 的价格上升会减少对 A 的需求。

If XED equals 0 or is close to zero, the goods are unrelated.

若 XED 等于零或接近于零，则两种商品相互独立。

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

Price elasticity of supply measures the responsiveness of the quantity supplied of a good to a change in its own price.

供给的价格弹性衡量一种商品的供给量对其自身价格变动的反应程度。

PES = %ΔQs ÷ %ΔP

The midpoint formula can also be applied for arc supply elasticity to obtain an average value between two points.

弧供给弹性也可应用中点公式以获得两点之间的平均值。

A PES greater than 1 indicates elastic supply; less than 1 indicates inelastic supply; equal to 1 indicates unitary elastic supply. A PES of zero means perfectly inelastic supply (fixed quantity), while infinite PES represents perfectly elastic supply.

PES 大于 1 表示供给富有弹性；小于 1 表示供给缺乏弹性；等于 1 表示单位弹性供给。PES 为 0 意味着完全无弹性供给（固定数量），而无穷大的 PES 则表示完全弹性供给。

5. Revenue and Elasticity | 总收入与弹性

Total revenue (TR) is the total amount of money a firm receives from selling its output. It is calculated as:

总收入（TR）是企业因销售其产出而获得的总货币金额。其计算公式为：

TR = Price (P) × Quantity (Q)

The effect of a price change on total revenue depends on the price elasticity of demand.

价格变动对总收入的影响取决于需求的价格弹性。

If demand is elastic (PED > 1), a decrease in price raises total revenue because the percentage increase in quantity demanded exceeds the percentage fall in price. Conversely, a price increase will lower total revenue.

若需求富有弹性（PED > 1），降价会提高总收入，因为需求量增加的百分比大于价格下降的百分比。反之，提价会降低总收入。

If demand is inelastic (PED < 1), a decrease in price reduces total revenue, while a price increase raises total revenue.

若需求缺乏弹性（PED < 1），降价会减少总收入，而提价则会增加总收入。

When demand is unit elastic (PED = 1), total revenue remains constant when the price changes.

当需求具有单位弹性（PED = 1）时，价格变动会使总收入保持不变。

6. Costs of Production | 生产成本公式

Total cost (TC) is the sum of all fixed and variable costs:

总成本（TC）是所有固定成本与可变成本的总和：

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

Average cost (AC, also called average total cost ATC) is total cost per unit of output:

平均成本（AC，也称平均总成本 ATC）是每单位产出的总成本：

AC = TC ÷ Q = AFC + AVC

Average fixed cost (AFC) is total fixed cost per unit of output:

平均固定成本（AFC）是每单位产出的固定成本：

AFC = TFC ÷ Q

Average variable cost (AVC) is total variable cost per unit of output:

平均可变成本（AVC）是每单位产出的可变成本：

AVC = TVC ÷ Q

Marginal cost (MC) is the addition to total cost from producing one more unit of output. Since fixed cost does not change with output, it also equals the change in total variable cost:

边际成本（MC）是多生产一单位产出所导致的总成本的增加量。由于固定成本不随产出变动，它同时也等于总可变成本的变动量：

MC = ΔTC ÷ ΔQ = ΔTVC ÷ ΔQ

7. Profit Maximisation | 利润最大化条件

A firm maximises its total profit by producing at the output level where marginal revenue (MR) equals marginal cost (MC). This is a fundamental equilibrium condition in microeconomics.

企业通过在边际收益（MR）等于边际成本（MC）的产量水平上进行生产来实现利润最大化。这是微观经济学中的一个基本均衡条件。

Profit maximisation: MR = MC

If MR > MC, the firm can increase profit by expanding output. If MR < MC, the firm can increase profit by reducing output.

若 MR > MC，企业可通过扩大产出增加利润；若 MR < MC，企业可通过减少产出增加利润。

In the short run, a firm should shut down if price falls below average variable cost (P < AVC), because it cannot cover even its variable cost of staying open.

在短期内，若价格低于平均可变成本（P < AVC），企业应当暂时关闭，因为持续经营连可变成本都无法弥补。

8. Consumer Equilibrium (Utility) | 消费者均衡(效用)

According to marginal utility theory, a rational consumer maximises total utility by allocating their budget so that the marginal utility per unit of currency spent on each good is equal.

根据边际效用理论，理性消费者通过将预算分配至每种商品上所花费每单位货币的边际效用都相等，从而实现总效用最大化。

MUₐ ÷ Pₐ = MUₓ ÷ Pₓ

This equilibrium condition assumes diminishing marginal utility. As the consumer consumes more of a good, its marginal utility falls, making it rational to switch spending to another good until equality is restored.

该均衡条件以边际效用递减为前提。随着消费者消费更多某种商品，其边际效用下降，因此将支出转向另一种商品直至等式恢复便是理性之举。

If MUₐ ÷ Pₐ > MUₓ ÷ Pₓ, the consumer should buy more of A and less of X to increase total utility.

若 MUₐ ÷ Pₐ > MUₓ ÷ Pₓ，消费者应多买 A 少买 X 以提高总效用。

9. National Income Accounting | 国民收入核算恒等式

National income can be measured by three equivalent methods which must, in principle, give the same total: the output method, the income method, and the expenditure method.

国民收入可通过三种等价方法加以衡量，它们在原则上须得出相同的总和：产出法、收入法和支出法。

Output = Income = Expenditure

In the circular flow of income, equilibrium occurs when total injections into the flow equal total withdrawals (leakages):

在收入循环流量中，当注入总额等于漏出（撤出）总额时实现均衡：

Injections (I + G + X) = Withdrawals (S + T + M)

I = Investment expenditure
G = Government spending on goods and services
X = Exports of goods and services
S = Saving
T = Net taxation
M = Imports of goods and services

I = 投资支出
G = 政府商品和服务支出
X = 商品和服务的出口
S = 储蓄
T = 净税收
M = 商品和服务的进口

10. The Multiplier | 乘数效应

The multiplier (k) describes the magnification effect of a change in an injection (such as investment or government spending) on the final equilibrium level of national income.

乘数（k）描述了注入量（如投资或政府支出）的变动对最终均衡国民收入水平的放大效应。

The marginal propensity to consume (MPC) is the proportion of additional income that is spent on consumption:

边际消费倾向（MPC）是额外收入中用于消费的比例：

MPC = ΔC ÷ ΔYd

The marginal propensity to save (MPS) is the proportion of additional income that is saved:

边际储蓄倾向（MPS）是额外收入中被储蓄的比例：

MPS = ΔS ÷ ΔYd

In a simple closed economy without a government sector, MPC + MPS = 1. The multiplier is then:

在一个没有政府部门的简单封闭经济中，MPC + MPS = 1，此时乘数为：

k = 1 ÷ (1 − MPC) = 1 ÷ MPS

When there are also withdrawals in the form of taxation and imports, the marginal propensity to withdraw (MPW) equals the sum of MPS, the marginal rate of taxation, and the marginal propensity to import. The multiplier can be expressed as:

当存在税收与进口这类漏出时，边际撤出倾向（MPW）等于 MPS、边际税率和边际进口倾向之和。乘数则可表示为：

k = 1 ÷ MPW

A change in national income (ΔY) is equal to the initial change in an injection (ΔJ) multiplied by the multiplier: ΔY = k × ΔJ.

国民收入的变动（ΔY）等于初始注入变动量（ΔJ）乘以乘数：ΔY = k × ΔJ。

11. Inflation and Index Numbers | 通货膨胀与指数

A consumer price index (CPI) tracks the weighted average price of a basket of goods and services consumed by a typical household.

消费者价格指数（CPI）追踪的是典型家庭消费的一篮子商品和服务的加权平均价格。

CPI = (Cost of basket in current year ÷ Cost of basket in base year) × 100

The inflation rate is the percentage change in the price level over a period of time, usually a year. It is commonly computed using the CPI:

通货膨胀率是指价格水平在一段时期（通常为一年）内的百分比变动。它通常利用 CPI 来计算：

Inflation rate = [(CPIₜ − CPIₜ₋₁) ÷ CPIₜ₋₁] × 100%

To construct a weighted price index, each item is given a weight that reflects its relative importance in household spending. The index is a weighted average of price relatives.

在构建加权价格指数时，每种商品被赋予一个反映其在家庭支出中相对重要性的权重。该指数是价格比率的一个加权平均值。

12. Exchange Rates | 汇率换算

An exchange rate expresses the price of one currency in terms of another. The way the rate is quoted matters for conversions.

汇率表示用一种货币标价的另一种货币的价格。汇率的标价方式会影响换算过程。

If the exchange rate is quoted as the amount of foreign currency per unit of domestic currency, then:

若汇率被标价为每单位本币兑换的外币数量，则：

Amount in foreign currency = Amount in home currency × Exchange rate

Conversely, if the rate is given as the domestic currency price of one unit of foreign currency, the conversion is:

反过来，若汇率被给出为一单位外币对应的本币价格，则换算为：

Amount in home currency = Amount in foreign currency × Exchange rate (direct quote for foreign currency)

A rise in the exchange rate (under the first definition) means the domestic currency appreciates, making imports cheaper and exports more expensive. A depreciation has the opposite effects.

在第一种定义下，汇率上升意味着本币升值，使得进口更便宜而出口更昂贵。本币贬值则会产生相反效果。

Effective exchange rate is a weighted average of a country’s currency relative to a basket of other major currencies, with weights based on trade shares.

有效汇率是一国货币相对于一篮子其他主要货币的加权平均值，权重基于贸易份额确定。

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