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

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

This quick reference guide compiles key formulas, definitions and theorems required for the Cambridge International AS Level Economics exam. A solid grasp of these quantitative and theoretical tools will strengthen your analysis and evaluation skills. Refer back to this handbook as you practise past papers and master each topic.

本速查手册汇编了剑桥国际AS经济考试所需的关键公式、定义和定理。扎实掌握这些定量与理论工具将提升你的分析与评价能力。备考练习时，随时翻阅本手册，助你吃透每个主题。

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

PED measures the responsiveness of quantity demanded to a change in price. It is a key indicator for firms when setting prices and predicting revenue changes. The basic formula uses percentage changes.

PED 衡量需求量对价格变动的反应程度，是企业定价和预测收入变化的关键指标。基础公式使用变化百分比。

PED = (%ΔQd) / (%ΔP)

To accurately calculate PED between two points on a demand curve, the midpoint (arc) method is preferred. It uses average quantity and average price to avoid the asymmetry problem.

为精确计算需求曲线上两点间的弹性，通常采用中点法（弧弹性）。该方法使用平均量和平均价，避免基数不对称问题。

PED = ( (Q₂ – Q₁) / ((Q₁+Q₂)/2) ) ÷ ( (P₂ – P₁) / ((P₁+P₂)/2) )

The absolute value of PED determines the type of elasticity. The following table classifies the results and their revenue implications.

PED 的绝对值决定了弹性类型。下表对结果及其收入效应进行了归类。

Value of \|PED\|	Classification	Effect on Total Revenue
\|PED\| > 1	Price elastic	Price rise decreases TR; price fall increases TR
\|PED\| < 1	Price inelastic	Price rise increases TR; price fall decreases TR
\|PED\| = 1	Unit elastic	TR remains unchanged when price changes
\|PED\| = 0	Perfectly inelastic	TR changes in direct proportion to price
\|PED\| = ∞	Perfectly elastic	Any price rise drops quantity demanded to zero

\|PED\| 数值	分类	对总收入 (TR) 的影响
\|PED\| > 1	富有弹性	涨价使 TR 减少；降价使 TR 增加
\|PED\| < 1	缺乏弹性	涨价使 TR 增加；降价使 TR 减少
\|PED\| = 1	单位弹性	价格变动时 TR 保持不变
\|PED\| = 0	完全无弹性	TR 与价格同比例变动
\|PED\| = ∞	完全弹性	任何涨价都会使需求量降至零

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

PES measures the responsiveness of quantity supplied to a change in price. It is shaped largely by the time period and the flexibility of production. The formula follows the same logic as PED.

PES 衡量供给量对价格变动的反应程度，主要由时间长短和生产的灵活程度决定。其公式逻辑与 PED 相同。

PES = (%ΔQs) / (%ΔP)

Use the midpoint formula for accuracy between two supply points:

在供给曲线上两点间计算时，同样采用中点公式以确保准确：

PES = ( (Q₂ – Q₁) / ((Q₁+Q₂)/2) ) ÷ ( (P₂ – P₁) / ((P₁+P₂)/2) )

PES > 1: elastic supply – producers can adjust output quickly.
PES < 1: inelastic supply – output responds slowly to price changes.
PES = 0: perfectly inelastic supply (e.g., theatre seats on a given night).
PES = ∞: perfectly elastic supply (rare, constant cost conditions).

PES > 1：供给富有弹性 – 生产者能迅速调整产量。
PES < 1：供给缺乏弹性 – 产量对价格变动反应缓慢。
PES = 0：完全无弹性供给（如特定场次的剧院座位）。
PES = ∞：完全弹性供给（罕见，恒成本条件）。

3. Cross-Price Elasticity of Demand (XED) | 需求的交叉价格弹性 (XED)

XED measures how the demand for one good responds to a price change in another good. It reveals the relationship between goods.

XED 衡量一种商品的需求对另一种商品价格变动的反应，揭示了商品之间的相互关系。

XED = (%ΔQd of good A) / (%ΔP of good B)

XED > 0: the goods are substitutes (e.g., tea and coffee).
XED < 0: the goods are complements (e.g., printers and ink cartridges).
XED = 0: the goods are unrelated.
The larger the absolute value, the stronger the relationship.

XED > 0：替代品（如茶与咖啡）。
XED < 0：互补品（如打印机与墨盒）。
XED = 0：无关商品。
绝对值越大，关系越强。

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

YED captures how quantity demanded changes as consumer income changes. It helps classify normal and inferior goods, and also distinguishes luxury from necessity goods.

YED 反映需求量随消费者收入变动的程度，用于区分正常品与劣等品，以及奢侈品与必需品。

YED = (%ΔQd) / (%ΔY)

where Y stands for income.

其中 Y 代表收入。

YED > 0: normal good. If YED > 1, the good is a luxury; if 0 < YED < 1, it is a necessity.
YED < 0: inferior good – demand falls as income rises.
YED = 0: perfectly income-inelastic – demand stays unchanged regardless of income (staple goods).

YED > 0：正常品。若 YED > 1 则为奢侈品；若 0 < YED < 1 则为必需品。
YED < 0：劣等品 – 收入上升时需求量反而下降。
YED = 0：完全收入无弹性 – 收入变化时需求量不变（基本必需品）。

5. Utility and the Law of Diminishing Marginal Utility | 效用与边际效用递减规律

Utility theory explains consumer behaviour. Total utility (TU) is the overall satisfaction from consuming a given quantity of a good. Marginal utility (MU) is the additional satisfaction from consuming one more unit.

效用理论解释消费者行为。总效用 (TU) 是消费一定量商品所获得的全部满足感。边际效用 (MU) 是额外消费一单位所带来的满足增量。

MU = ΔTU / ΔQ

The law of diminishing marginal utility states that as consumption of a good increases, the MU derived from each additional unit eventually declines. This explains why demand curves slope downwards.

边际效用递减规律指出：随着商品消费量的增加，每额外一单位带来的边际效用最终会下降。这解释了需求曲线向下倾斜的原因。

For a consumer maximising utility with a given income, the optimal consumption bundle satisfies the equi-marginal principle:

在给定收入下实现效用最大化的消费者，其最优消费组合满足等边际原理：

MUₐ / Pₐ = MU_b / P_b = MU_c / P_c …

This means the last pound spent on each good yields the same marginal utility. If one ratio is higher, the consumer should reallocate spending to increase total utility.

这意味着花在每种商品上的最后一英镑所带来的边际效用相等。若某一比率较高，消费者应当重新分配支出以提升总效用。

6. Costs of Production | 生产成本

Firms face fixed and variable costs in the short run. Understanding cost structures is essential for pricing and output decisions. All cost formulas are derived from total cost (TC), total fixed cost (TFC) and total variable cost (TVC).

企业在短期面临固定成本和可变成本。理解成本结构对于定价和产量决策至关重要。所有成本公式均由总成本 (TC)、总固定成本 (TFC) 和总可变成本 (TVC) 导出。

TC = TFC + TVC

AFC = TFC / Q
AVC = TVC / Q
AC (or ATC) = TC / Q = AFC + AVC

The most important dynamic cost measure is marginal cost:

最重要的动态成本指标为边际成本：

MC = ΔTC / ΔQ

In the short run, AFC falls continuously as output expands (spreading overheads). AVC typically falls then rises due to the law of diminishing returns, giving the AC curve its characteristic U-shape. MC intersects both AVC and AC at their minimum points.

在短期，AFC 随产量扩张而持续下降（分摊固定成本）。AVC 因边际收益递减规律一般先降后升，使得 AC 曲线呈典型的 U 形。MC 曲线分别穿过 AVC 与 AC 的最低点。

7. Revenue and Profit | 收益与利润

Revenue concepts connect output decisions to market prices. Total revenue (TR) is the money received from sales. Average revenue (AR) equals price per unit, and marginal revenue (MR) is the change in TR from selling one more unit.

收益概念将产量决策与市场价格联系起来。总收益 (TR) 为销售收入。平均收益 (AR) 等于单位价格，边际收益 (MR) 是额外销售一单位带来的 TR 变化。

TR = P × Q
AR = TR / Q = P
MR = ΔTR / ΔQ

For a price-taking firm in perfect competition, MR = AR = P and the MR curve is horizontal. For a downward-sloping demand curve (imperfect competition), MR lies below AR and may become negative.

对于完全竞争中的价格接受者，MR = AR = P，MR 曲线为水平线。若面临向下倾斜的需求曲线（非完全竞争），MR 位于 AR 下方且可能为负。

Profit is the gap between total revenue and total cost:

利润是总收益与总成本之差：

Profit = TR – TC

Firms can also calculate profit per unit as AR – AC.

企业也可将单位利润表示为 AR – AC。

8. Profit Maximisation and Efficiency | 利润最大化与效率

The profit-maximising condition is one of the key theorems in microeconomics. A firm maximises profit by producing the output where marginal revenue equals marginal cost.

利润最大化条件是微观经济学的核心定理之一。企业通过生产边际收益等于边际成本的产量来实现利润最大化。

MR = MC

If MR > MC, the additional revenue from one more unit exceeds the additional cost, so output should be expanded. If MR < MC, the firm should reduce output. Only at MR = MC is profit maximised (or losses minimised). This rule applies to all market structures.

若 MR > MC，额外一单位的收益大于其成本，应扩大产量；若 MR < MC，则应减产。唯有在 MR = MC 时实现利润最大化（或损失最小化）。该法则适用于所有市场结构。

Efficiency concepts link to optimal resource allocation:

Allocative efficiency occurs when P = MC. Price reflects the true cost of production and consumer welfare is maximised.
Productive efficiency exists when firms produce at the lowest possible average cost, i.e., at the minimum point of the AC curve.

分配效率（P = MC）：价格反映了生产的真实成本，消费者福利最大化。
生产效率：企业在尽可能低的平均成本处生产，即位于 AC 曲线最低点。

Under perfect competition, both efficiencies are achieved in the long run. Monopolies and other imperfect markets typically fail to meet these conditions.

在完全竞争市场中，长期内两种效率均可实现；垄断及其他非完全竞争市场通常无法同时满足这些条件。

9. Taxation and Subsidies | 税收与补贴

Indirect taxes and subsidies shift the supply curve and affect market outcomes. The burden of a tax is shared between consumers and producers depending on relative elasticities.

间接税与补贴使供给曲线移动，影响市场结果。税收负担根据相对弹性由消费者与生产者分担。

When an ad valorem or specific tax is imposed, the new price (Pc) is higher for consumers, and the net price received by producers (Pp) is lower. The difference equals the tax per unit:

征收从量税或从价税后，消费者支付的新价格 (Pc) 上升，生产者获得的净价 (Pp) 下降。二者之差等于单位税额：

Tax per unit = Pc – Pp

The incidence of a tax falls more heavily on the side of the market that is more inelastic. A useful sharing formula (though not always required) is:

税收归宿更多地落在更缺乏弹性的一方。一个常用的分摊公式（虽非必考）为：

Consumer burden share = PES / (PES + |PED|)

Government tax revenue equals the per-unit tax multiplied by the new quantity traded (Q₂ after tax). Similarly, the total subsidy cost to the government equals subsidy per unit × Q₂ after subsidy.

政府税收收入等于单位税额乘以税后交易量 (Q₂)。同理，补贴总成本等于单位补贴额乘以补贴后交易量。

Tax revenue = tax per unit × Q₂ (post-tax)
Subsidy cost = subsidy per unit × Q₂ (post-subsidy)

Subsidies shift the supply curve downward (to the right), lowering the price for consumers and raising the effective price for producers.

补贴使供给曲线下移（右移），降低消费者价格同时提高生产者实际获得的价格。

10. Aggregate Demand and the Consumption Function | 总需求与消费函数

Macroeconomic equilibrium requires a thorough understanding of aggregate demand (AD). AD comprises consumption (C), investment (I), government spending (G) and net exports (X – M).

宏观经济均衡要求深入理解总需求 (AD)。AD 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)

Consumption is the largest component and is modelled by the consumption function. The simple linear form links consumption to disposable income (Yd).

消费是最大组成部分，可用消费函数建模。简单的线性形式将消费与可支配收入 (Yd) 联系起来。

C = a + bYd

Where ‘a’ is autonomous consumption (spending even when income is zero), and ‘b’ is the marginal propensity to consume (MPC). The corresponding saving function is:

其中 ‘a’ 为自发性消费（即使收入为零也会发生的支出），’b’ 为边际消费倾向 (MPC)。相应的储蓄函数为：

S = -a + (1-b)Yd

The key propensities:

MPC = ΔC / ΔY
MPS = ΔS / ΔY
MPC + MPS = 1

These relationships underpin the output-expenditure model and the multiplier process. In a closed economy without government, the multiplier depends solely on MPC or MPS.

这些关系是产出-支出模型和乘数过程的基础。在一个无政府的封闭经济中，乘数完全取决于 MPC 或 MPS。

11. The Multiplier and Key Macroeconomic Indicators | 乘数与关键宏观经济指标

The multiplier effect explains how

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