Pre-U Edexcel Economics: Formula & Theorem Quick Reference Guide | Pre-U Edexcel 经济：公式定理速查手册

📚 Pre-U Edexcel Economics: Formula & Theorem Quick Reference Guide | Pre-U Edexcel 经济：公式定理速查手册

This guide compiles the core formulas, identities, and theorems that students must master for the Pre-U Edexcel Economics examination. Each entry is presented with clear notation, followed by a concise explanation in both English and Chinese to support bilingual learning and rapid revision.

本手册汇集了 Pre-U Edexcel 经济学考试必须掌握的核心公式、恒等式和定理。每个条目都配有清晰的符号表达，并在其后用中英双语简明解释，以支持双语学习和快速复习。

1. Price, Income, Cross-Price, and Supply Elasticities | 需求价格弹性、需求收入弹性、交叉弹性和供给弹性

Price Elasticity of Demand (PED) measures the responsiveness of quantity demanded to a change in price.

需求价格弹性 (PED) 衡量需求量对价格变化的反应程度。

PED = %ΔQd / %ΔP = (ΔQd / Qd₀) / (ΔP / P₀)

If |PED| > 1, demand is price elastic; if |PED| < 1, demand is price inelastic; and if |PED| = 1, demand is unit elastic. The sign is typically negative, but absolute value is used for interpretation.

若 |PED| > 1，需求富有价格弹性；若 |PED| < 1，需求缺乏价格弹性；若 |PED| = 1，需求为单位弹性。符号通常为负，但解释时使用绝对值。

Income Elasticity of Demand (YED) shows the relationship between a change in income and the quantity demanded.

需求收入弹性 (YED) 表明收入变化与需求量之间的关系。

YED = %ΔQd / %ΔY

A positive YED indicates a normal good; a negative YED indicates an inferior good. When YED > 1, the good is a luxury.

YED 为正表示正常品；YED 为负表示劣等品。当 YED > 1 时，该商品为奢侈品。

Cross-Price Elasticity of Demand (XED) measures the responsiveness of demand for good A to a change in the price of good B.

需求交叉弹性 (XED) 衡量商品 A 的需求量对商品 B 价格变化的反应程度。

XED = %ΔQd(A) / %ΔP(B)

If XED > 0, the goods are substitutes; if XED < 0, they are complements; if XED = 0, they are independent.

若 XED > 0，两商品互为替代品；若 XED < 0，两商品为互补品；若 XED = 0，两商品互不相关。

Price Elasticity of Supply (PES) captures how responsive quantity supplied is to a change in price.

供给价格弹性 (PES) 反映供给量对价格变化的反应程度。

PES = %ΔQs / %ΔP = (ΔQs / Qs₀) / (ΔP / P₀)

PES is usually positive. A value greater than 1 indicates elastic supply; less than 1 inelastic; zero perfectly inelastic; and infinite perfectly elastic.

PES 通常为正。大于 1 表示供给富有弹性；小于 1 缺乏弹性；零为完全无弹性；无穷大为完全弹性。

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2. Cost, Revenue, and Profit Maximisation | 成本、收益与利润最大化

Total Cost (TC) is the sum of total fixed costs (TFC) and total variable costs (TVC).

总成本 (TC) 是总固定成本 (TFC) 与总可变成本 (TVC) 之和。

TC = TFC + TVC

Average Cost (AC) is total cost divided by output (Q).

平均成本 (AC) 是总成本除以产量 (Q)。

AC = TC / Q or AFC + AVC

where AFC = TFC / Q and AVC = TVC / Q.

其中 AFC = TFC / Q，AVC = TVC / Q。

Marginal Cost (MC) is the addition to total cost from producing one extra unit of output.

边际成本 (MC) 是多生产一单位产量所带来的总成本增加量。

MC = ΔTC / ΔQ

Total Revenue (TR) equals price times quantity sold.

总收益 (TR) 等于价格乘以销售量。

TR = P × Q

Marginal Revenue (MR) is the additional revenue from selling one more unit.

边际收益 (MR) 是多销售一单位产品所带来的额外收益。

MR = ΔTR / ΔQ

Profit maximisation occurs where marginal cost equals marginal revenue, provided that MC cuts MR from below and price covers average variable cost in the short run.

利润最大化 的条件是边际成本等于边际收益，且边际成本从下方穿过边际收益曲线，同时在短期内价格必须覆盖平均可变成本。

Profit max: MR = MC

Economic profit = TR − economic costs (including opportunity cost). Normal profit is zero economic profit, where P = AC.

经济利润 = 总收益 − 经济成本（含机会成本）。正常利润指经济利润为零，此时价格等于平均成本。

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3. Macroeconomic Aggregates and Identities | 宏观经济总量与恒等式

The basic national income identity for an open economy with government is:

开放经济下含政府部门的国民收入基本恒等式为：

Y ≡ C + I + G + (X − M)

where Y is national income/GDP, C is consumption, I is investment, G is government spending, X is exports, and M is imports.

其中 Y 为国民收入/GDP，C 为消费，I 为投资，G 为政府支出，X 为出口，M 为进口。

Disposable income (Yd) is national income plus transfers minus taxes:

可支配收入 (Yd) 等于国民收入加转移支付减税收：

Yd = Y + TR − T

The GDP deflator measures the level of prices of all new, domestically produced, final goods and services in an economy.

GDP 平减指数衡量经济中所有新生产的、国内最终产品和服务的价格水平。

GDP Deflator = (Nominal GDP / Real GDP) × 100

Real GDP = Nominal GDP / (Price Index / 100).

实际 GDP = 名义 GDP / (价格指数 / 100)。

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4. Multipliers and the Circular Flow | 乘数与循环流转

The simple spending multiplier (k) occurs when an initial injection of spending leads to a larger final increase in national income.

简单支出乘数 (k) 表示一笔初始注入支出会引致国民收入的更大最终增加。

k = 1 / (1 − MPC) = 1 / MPS

MPC is the marginal propensity to consume, and MPS is the marginal propensity to save, with MPC + MPS = 1.

MPC 为边际消费倾向，MPS 为边际储蓄倾向，且 MPC + MPS = 1。

The tax multiplier is negative and smaller in absolute value than the spending multiplier:

税收乘数为负值，其绝对值小于政府支出乘数：

Tax multiplier = −MPC / MPS or −MPC / (1 − MPC)

Open-economy multiplier includes the marginal propensity to import (MPM):

开放经济乘数包含边际进口倾向 (MPM)：

k_open = 1 / (MPS + MPM) or 1 / (1 − MPC + MPM)

A higher MPM reduces the size of the multiplier.

更高的 MPM 会减小乘数的大小。

The money multiplier in banking shows how an initial deposit can expand the money supply:

银行体系中的货币乘数表明一笔初始存款如何扩大货币供给：

Money multiplier = 1 / Reserve Requirement Ratio (RRR)

Note: the actual money multiplier may be smaller if banks hold excess reserves or the public holds cash.

注意：如果银行持有超额准备金或公众持有现金，实际货币乘数可能会更小。

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5. Inflation Measure and the Quantity Theory of Money | 通货膨胀衡量与货币数量论

The inflation rate is the percentage change in a general price index, typically the Consumer Price Index (CPI) or GDP deflator.

通货膨胀率是一般价格指数（通常为消费者价格指数 CPI 或 GDP 平减指数）的百分比变化。

Inflation rate = (Price Index in Year t − Price Index in Year t−1) / Price Index in Year t−1 × 100%

A simple CPI is calculated as:

简单的 CPI 计算公式为：

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

The Quantity Theory of Money is summed up by the equation of exchange:

货币数量论由交易方程式概括：

MV = PT or MV = PY

where M is the money supply, V is the velocity of circulation, P is the price level, T is the volume of transactions, and Y is real output. Assuming V and Y are constant in the short run, a change in M leads to a proportional change in the price level.

其中 M 为货币供给，V 为货币流通速度，P 为价格水平，T 为交易量，Y 为实际产出。假设短期内 V 和 Y 不变，M 的变化将引起价格水平同比例变化。

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6. Unemployment and Okun’s Law | 失业与奥肯定律

The unemployment rate measures the percentage of the labour force that is jobless and actively seeking work.

失业率衡量的是劳动力中没有工作但正在积极寻找工作的人所占的百分比。

Unemployment rate = (Number of unemployed / Labour force) × 100

The labour force is the sum of employed and unemployed individuals who are of working age and available for work.

劳动力是就业者与失业者之和，他们属于劳动年龄且具有工作能力。

Okun’s Law describes an empirical relationship between the output gap and cyclical unemployment.

奥肯定律描述了产出缺口与周期性失业之间的经验关系。

Okun’s Law: %Output gap ≈ −k × (Actual unemployment rate − Natural rate of unemployment)

where k is typically around 2 to 3 for developed economies. A 1 percentage point increase in cyclical unemployment is associated with approximately a 2% to 3% fall in real GDP relative to potential GDP.

其中 k 在发达经济体中通常约为 2 到 3。周期性失业每增加 1 个百分点，实际 GDP 相对于潜在 GDP 大约下降 2% 到 3%。

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7. Balance of Payments and Exchange Rates | 国际收支与汇率

The Balance of Payments (BoP) is divided into the current account, capital account, and financial account. A key identity is:

国际收支 (BoP) 分为经常账户、资本账户和金融账户。一个关键恒等式为：

Current Account Balance + Capital Account Balance + Financial Account Balance ≡ 0

The current account includes trade in goods and services, primary income, and secondary income.

经常账户包括货物与服务贸易、初次收入和二次收入。

The nominal exchange rate is the price of one currency in terms of another. The real exchange rate adjusts for price level differences:

名义汇率是一种货币以另一种货币表示的价格。实际汇率根据价格水平差异进行了调整：

Real exchange rate = e × (P_domestic / P_foreign)

where e is the nominal exchange rate expressed as foreign currency per unit of domestic currency. A rise in the real exchange rate implies an appreciation in real terms, reducing competitiveness.

其中 e 是以每单位本币折合的外币数量表示的名义汇率。实际汇率上升表示实际升值，竞争力下降。

Purchasing Power Parity (PPP) states that in the long run exchange rates should adjust so that identical goods cost the same in different countries:

购买力平价 (PPP) 指出，长期内汇率应调整到使相同商品在不同国家价格一致的水平：

Spot exchange rate (PPP) = P_domestic / P_foreign

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8. Comparative Advantage and Terms of Trade | 比较优势与贸易条件

Comparative advantage exists when a country can produce a good at a lower opportunity cost than another country.

比较优势指一国能以低于另一国的机会成本生产某种商品。

Opportunity cost of Good X = (units of Good Y sacrificed) / (units of Good X gained).

商品 X 的机会成本 = (牺牲的商品 Y 的数量) / (获得的商品 X 的数量)。

The Terms of Trade (TOT) is an index that measures the relative price of exports to imports:

贸易条件 (TOT) 是衡量出口相对于进口价格的指数：

Terms of Trade = (Index of export prices / Index of import prices) × 100

An improvement in the TOT means export prices rise relative to import prices, enabling a given volume of exports to purchase more imports.

贸易条件改善意味着出口价格相对于进口价格上升，使给定出口量能购买更多的进口品。

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9. Economic Growth and Development Formulae | 经济增长与发展公式

Economic growth is typically measured as the annual percentage increase in real GDP or real GNI per capita.

经济增长通常以实际 GDP 或人均实际 GNI 的年增长率来衡量。

Growth rate of real GDP = [(Real GDP_t − Real GDP_t₋₁) / Real GDP_t₋₁] × 100%

For sustained development, per capita growth = real GDP growth − population growth rate.

对于可持续发展，人均增长 = 实际 GDP 增长率 − 人口增长率。

The Harrod-Domar model suggests a link between savings, capital-output ratio, and growth:

哈罗德-多马模型表明储蓄、资本产出比与增长之间存在联系：

Growth rate (g) = s / v or g = (savings ratio) / (incremental capital-output ratio)

where s is the ratio of saving to national income, and v is the incremental capital-output ratio (ICOR).

其中 s 为储蓄占国民收入的比率，v 为增量资本产出比 (ICOR)。

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10. Important Relationships and Graphs | 重要关系与图形

The Laffer Curve suggests that beyond a certain tax rate, higher tax rates reduce tax revenue.

拉弗曲线表明，当税率超过某一临界点后，更高的税率反而会减少税收收入。

The Phillips Curve historically shows an inverse relationship between inflation and unemployment in the short run. The expectations-augmented Phillips Curve is:

菲利普斯曲线在历史上表明短期内通货膨胀与失业之间存在反向关系。附加预期的菲利普斯曲线为：

π = πᵉ − β(U − Uₙ) + supply shocks

where π is inflation, πᵉ is expected inflation, U is actual unemployment, Uₙ is the natural rate of unemployment, and β is a positive coefficient. In the long run, there is no trade-off; the long-run Phillips Curve is vertical at the natural rate.

其中 π 为通货膨胀率，πᵉ 为预期通货膨胀率，U 为实际失业率，Uₙ 为自然失业率，β 为正值系数。在长期，不存在权衡取舍；长期菲利普斯曲线在自然失业率处垂直。

The Marginal Rate of Substitution (MRS) is the slope of the indifference curve:

边际替代率 (MRS) 是无差异曲线的斜率：

MRS = −ΔY / ΔX = MUₓ / MUᵧ

at the optimal consumption bundle, MRS equals the price ratio: MUₓ / MUᵧ = Pₓ / Pᵧ.

在最优消费组合点，MRS 等于价格比：MUₓ / MUᵧ = Pₓ / Pᵧ。

The Marginal Rate of Transformation (MRT) measures the opportunity cost on the production possibility frontier (PPF):

边际转换率 (MRT) 衡量生产可能性边界 (PPF) 上的机会成本：

MRT = −ΔY / ΔX, slope of PPF

Productive efficiency is achieved when MRT is equal for all goods and economies operate on the PPF. Allocative efficiency occurs when MRS = MRT.

当所有商品的 MRT 相等且经济在 PPF 上运行时，就实现了生产效率。配置效率的实现条件是 MRS = MRT。

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