Formula and Theorem Quick Revision Guide for Pre-U CCEA Economics | Pre-U CCEA 经济：公式定理速查手册

📚 Formula and Theorem Quick Revision Guide for Pre-U CCEA Economics | Pre-U CCEA 经济：公式定理速查手册

This quick revision guide collates the essential formulae and theorems required for the Pre-U CCEA Economics syllabus. Mastery of these quantitative and conceptual tools is vital for analysing markets, evaluating policy, and constructing high-scoring essays. Keep this handbook close for regular review and practice.

本速查手册汇集了 Pre-U CCEA 经济课程所必备的核心公式与定理。掌握这些定量与概念工具对于分析市场、评估政策以及构建高分论述题至关重要。请随时参考本手册，定期复习与练习。

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

Price Elasticity of Demand measures the responsiveness of quantity demanded to a change in price. The standard formula is: PED = (% change in quantity demanded) ÷ (% change in price). The absolute value determines the type: |PED| > 1 is elastic, |PED| < 1 is inelastic, |PED| = 1 is unit elastic. The midpoint formula is often used to ensure consistency: PED = [(Q₂ − Q₁) ÷ ((Q₂ + Q₁) ÷ 2)] ÷ [(P₂ − P₁) ÷ ((P₂ + P₁) ÷ 2)]. Remember that PED is usually negative, but we interpret the absolute value. Revenue implications arise: for elastic demand, a price rise reduces total revenue; for inelastic demand, a price rise increases total revenue.

需求价格弹性衡量需求量对价格变化的反应程度。标准公式为：PED = (需求量变动%) ÷ (价格变动%)。通过绝对值判定类型：|PED| > 1 为富有弹性，|PED| < 1 为缺乏弹性，|PED| = 1 为单位弹性。为保证一致性常采用中点公式：PED = [(Q₂ − Q₁) ÷ ((Q₂ + Q₁) ÷ 2)] ÷ [(P₂ − P₁) ÷ ((P₂ + P₁) ÷ 2)]。注意 PED 通常为负值，但我们关注其绝对值。对收入的影响：富有弹性时，提价会使总收入减少；缺乏弹性时，提价会使总收入增加。

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

Income Elasticity of Demand shows how quantity demanded changes as consumer income changes. YED = (% change in quantity demanded) ÷ (% change in income). A positive YED indicates a normal good; a negative YED indicates an inferior good. Among normal goods, YED > 1 marks luxury goods, while 0 < YED < 1 marks necessities. This formula helps predict shifts in demand patterns as an economy grows or contracts.

需求收入弹性反映需求量如何随消费者收入变化而改变。YED = (需求量变动%) ÷ (收入变动%)。YED 为正表示正常品；YED 为负表示低档品。在正常品中，YED > 1 为奢侈品，0 < YED < 1 为必需品。该公式有助于预测经济扩张或收缩时需求模式的变化。

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

Cross Elasticity of Demand measures the responsiveness of demand for one good to a change in the price of another. XED = (% change in quantity demanded of Good A) ÷ (% change in price of Good B). A positive XED means the goods are substitutes; a negative XED means they are complements. The size of the coefficient indicates the strength of that relationship. Firms use XED to anticipate the impact of competitors’ pricing strategies.

需求交叉弹性衡量一种商品的需求量对另一种商品价格变化的反应程度。XED = (A 商品需求量变动%) ÷ (B 商品价格变动%)。XED 为正代表替代品关系；为负代表互补品关系。系数大小反映关系的强弱。企业可利用 XED 预测竞争对手定价策略的影响。

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

Price Elasticity of Supply captures how responsive quantity supplied is to a price change. PES = (% change in quantity supplied) ÷ (% change in price). A value greater than 1 is elastic supply, less than 1 is inelastic, and equal to 1 is unit elastic. Key determinants include production time, availability of spare capacity, and perishability of goods. The formula is central to understanding how quickly markets can adjust to demand shifts.

供给价格弹性体现供给量对价格变化的反应灵敏度。PES = (供给量变动%) ÷ (价格变动%)。大于 1 表示供给富有弹性，小于 1 为缺乏弹性，等于 1 为单位弹性。关键决定因素包括生产时长、闲置产能可得性以及商品的易腐性。该公式对于理解市场多快能适应需求变化十分关键。

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5. Utility Maximisation | 效用最大化

The utility maximisation condition states that a consumer allocates spending so that the marginal utility per pound spent is equal across all goods. For goods X and Y: MUₓ ÷ Pₓ = MUᵧ ÷ Pᵧ. If the ratios are unequal, the consumer can increase total utility by reallocating spending towards the good with higher marginal utility per pound. This principle underpins the derivation of demand curves and the law of equi‑marginal returns.

效用最大化条件指出，消费者分配支出时应使各商品每英镑的边际效用相等。对于商品 X 和 Y：MUₓ ÷ Pₓ = MUᵧ ÷ Pᵧ。若比率不等，消费者可通过将支出重新分配到每英镑边际效用更高的商品上来增加总效用。该原理构成需求曲线推导与边际均等法则的基础。

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6. Costs, Revenue and Profit Maximisation | 成本、收入与利润最大化

Firms maximise profit where marginal cost equals marginal revenue: MC = MR. Total Cost (TC) = Fixed Cost (FC) + Variable Cost (VC). Average Cost (AC) = TC ÷ Q. Average Revenue (AR) = TR ÷ Q = Price. Marginal Cost (MC) = ΔTC ÷ ΔQ. For perfect competition, AR = MR = Price. In imperfect markets, MR slopes down twice as steeply as AR. Profit is maximised not where total revenue is highest, but where the last unit adds the same to cost as to revenue. Shutdown occurs when Price < AVC in the short run.

企业利润最大化点位于边际成本等于边际收益处：MC = MR。总成本 (TC) = 固定成本 (FC) + 可变成本 (VC)。平均成本 (AC) = TC ÷ Q。平均收益 (AR) = TR ÷ Q = 价格。边际成本 (MC) = ΔTC ÷ ΔQ。在完全竞争市场中，AR = MR = 价格。在不完全市场中，MR 曲线下降速度是 AR 曲线的两倍。利润最大化并非发生在总收益最高时，而是最后一单位带来的成本与收益相同时。短期停业条件为价格 < 平均可变成本 (AVC)。

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7. Market Structure Indicators | 市场结构指标

Concentration ratios measure the combined market share of the largest n firms. An n‑firm concentration ratio, e.g. CR₄ = (Sales of top 4 firms ÷ Total market sales) × 100, indicates market power. High ratios suggest oligopoly or monopoly. The Herfindahl‑Hirschman Index (HHI) sums the squares of market shares of all firms: HHI = Σ sᵢ², where sᵢ is percentage share. HHI below 1500 indicates a competitive market; above 2500 signals high concentration. Both measures guide competition policy.

集中度比率衡量最大 n 家企业的市场份额之和。n 企业集中度比率，例如 CR₄ = (前四大企业销售额 ÷ 市场总销售额) × 100，反映市场势力。高比率表明寡头或垄断。赫芬达尔‑赫希曼指数 (HHI) 是所有企业市场份额百分比的平方和：HHI = Σ sᵢ²，sᵢ 为百分比份额。HHI 低于 1500 表示竞争性市场，高于 2500 表示高度集中。两项指标均用于指导竞争政策。

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8. Multiplier and National Income | 乘数与国民收入

The Keynesian multiplier shows how an initial injection into the circular flow leads to a larger final increase in national income. Multiplier (k) = 1 ÷ (1 − MPC) = 1 ÷ MPS + MPT + MPM, where MPC is marginal propensity to consume, MPS is marginal propensity to save, MPT is marginal propensity to tax, and MPM is marginal propensity to import. The balanced budget multiplier equals 1. The accelerator theory links investment to changes in national income. For an open economy, the multiplier is smaller due to withdrawals.

凯恩斯乘数显示循环流动中的初始注入如何使国民收入最终实现更大增幅。乘数 (k) = 1 ÷ (1 − MPC) = 1 ÷ (MPS + MPT + MPM)，MPC 为边际消费倾向，MPS 为边际储蓄倾向，MPT 为边际税收倾向，MPM 为边际进口倾向。平衡预算乘数为 1。加速原理将投资与国民收入变化相联系。开放经济中因漏出项存在乘数会变小。

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9. Money and Inflation | 货币与通货膨胀

The Quantity Theory of Money is expressed as MV = PQ, where M is money supply, V is velocity of circulation, P is the general price level, and Q is real output. Monetarists assume V and Q are stable in the short run, so increases in M lead directly to higher P. The Fisher equation relates nominal interest (i), real interest (r), and expected inflation (πᵉ): i = r + πᵉ. Inflation rate is calculated as (CPIₜ − CPIₜ₋₁) ÷ CPIₜ₋₁ × 100.

货币数量论表达为 MV = PQ，M 为货币供给，V 为货币流通速度，P 为一般物价水平，Q 为实际产出。货币主义者假设短期内 V 与 Q 稳定，因此 M 增加直接导致 P 上升。费雪方程式联系名义利率 (i)、实际利率 (r) 与预期通胀 (πᵉ)：i = r + πᵉ。通胀率计算公式为 (当期 CPI − 前期 CPI) ÷ 前期 CPI × 100。

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10. Unemployment and Labour Market | 失业与劳动力市场

The unemployment rate = (Number of unemployed ÷ Labour force) × 100. The labour force includes those employed plus those actively seeking work. The Phillips curve illustrates the short‑run trade‑off between inflation and unemployment. The natural rate of unemployment (NAIRU) is the rate consistent with stable inflation. Okun’s law links output gaps to changes in unemployment: Δu = −β(g − gₚ), where g is actual output growth, gₚ is potential growth, and β is Okun’s coefficient.

失业率 = (失业人数 ÷ 劳动力人口) × 100。劳动力人口包括就业者和积极寻找工作的人。菲利普斯曲线表明短期内通胀与失业之间存在权衡取舍。自然失业率 (NAIRU) 是与稳定通胀相一致的失业率。奥肯定律将产出缺口与失业变动相联系：Δu = −β(g − gₚ)，其中 g 为实际产出增长，gₚ 为潜在增长，β 为奥肯系数。

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11. Exchange Rates and Balance of Payments | 汇率与国际收支

A country’s balance of payments must balance. The current account balance = balance on trade in goods + balance on trade in services + net primary income + net secondary income. Exchange rate movements correct imbalances. The real exchange rate = (nominal exchange rate × domestic price level) ÷ foreign price level. The Marshall‑Lerner condition states that a depreciation improves the trade balance if the sum of PED for exports and imports > 1. PPP theory suggests exchange rates adjust to equalise the purchasing power of currencies.

一国国际收支必须平衡。经常账户余额 = 货物贸易差额 + 服务贸易差额 + 初次收入净额 + 二次收入净额。汇率变动可调节失衡。实际汇率 = (名义汇率 × 国内价格水平) ÷ 国外价格水平。马歇尔‑勒纳条件指出，若进出口需求弹性之和大于 1，贬值将改善贸易差额。购买力平价理论认为汇率会调整以使各国货币购买力均等。

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12. Economic Growth and Development | 经济增长与发展

Economic growth is typically measured by the percentage change in real GDP: Growth rate = [(GDPₜ − GDPₜ₋₁) ÷ GDPₜ₋₁] × 100. The Harrod‑Domar model links savings and capital to growth: ΔY/Y = s/k, where s is saving rate and k is capital‑output ratio. Solow’s growth model includes technological progress. The output gap = (actual GDP − potential GDP) ÷ potential GDP × 100. The Human Development Index (HDI) combines life expectancy, education, and income to measure development.

经济增长通常以实际 GDP 的百分比变动衡量：增长率 = [(当年 GDP − 上年 GDP) ÷ 上年 GDP] × 100。哈罗德‑多马模型将储蓄与资本同增长联系起来：ΔY/Y = s/k，s 为储蓄率，k 为资本‑产出比率。索洛增长模型纳入技术进步。产出缺口 = (实际 GDP − 潜在 GDP) ÷ 潜在 GDP × 100。人类发展指数 (HDI) 综合预期寿命、教育和收入以衡量发展水平。

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