📚 Pre-U CIE Economics: Quick Reference Handbook of Formulas and Theorems | Pre-U CIE 经济：公式定理速查手册
This quick reference handbook brings together the core formulas and theorems you need to master for Pre-U CIE Economics. Use it to revise elasticities, cost structures, multiplier theory, exchange‑rate mechanics and more — each entry is paired with straightforward explanations to solidify your understanding.
本速查手册汇总了 Pre‑U CIE 经济学所需的核心公式与定理。你可以用它复习弹性、成本结构、乘数理论、汇率机制等内容，每个条目都配有清晰的中英文解释，帮助巩固理解。
1. Elasticities | 弹性
Price elasticity of demand (PED) measures the responsiveness of quantity demanded to a change in 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）衡量需求量对价格变化的反应程度，计算方法为需求量变动的百分比除以价格变动的百分比。
PED = %ΔQd / %ΔP
When using the midpoint (arc) method, PED = [(Q2 – Q1) / ((Q1+Q2)/2)] / [(P2 – P1) / ((P1+P2)/2)]. If |PED| > 1 demand is elastic; if |PED| < 1 demand is inelastic; unit elastic when |PED| = 1. Total revenue rises with a price cut when demand is elastic.
使用中点（弧弹性）法时，PED = [(Q2 – Q1) / ((Q1+Q2)/2)] / [(P2 – P1) / ((P1+P2)/2)]。若 |PED| > 1，需求富有弹性；若 |PED| < 1，需求缺乏弹性；|PED| = 1 即单位弹性。当需求富有弹性时降价会使总收入增加。
Income elasticity of demand (YED) = %ΔQd / %ΔY. Normal goods have positive YED (luxuries: YED > 1; necessities: 0 < YED < 1); inferior goods have negative YED.
需求的收入弹性（YED）= %ΔQd / %ΔY。正常品的 YED 为正（奢侈品 YED > 1，必需品 0 < YED < 1）；低档品的 YED 为负。
Cross‑price elasticity of demand (XED) = %ΔQd of good A / %ΔP of good B. XED > 0 for substitutes, XED < 0 for complements.
需求的交叉价格弹性（XED）= A 商品需求量变动的百分比 / B 商品价格变动的百分比。XED > 0 为替代品，XED < 0 为互补品。
Price elasticity of supply (PES) = %ΔQs / %ΔP. Its value depends on time horizon, spare capacity, and the ability to store output.
供给的价格弹性（PES）= %ΔQs / %ΔP。其数值取决于时间长短、闲置产能以及储存产出的能力。
2. Costs, Revenues and Profit | 成本、收益与利润
Total cost (TC) is the sum of total fixed cost (TFC) and total variable cost (TVC). Average total cost (ATC) = TC / Q, which also equals AFC + AVC.
总成本（TC）等于总固定成本（TFC）与总可变成本（TVC）之和。平均总成本（ATC）= TC / Q，也等于 AFC + AVC。
TC = TFC + TVC
Marginal cost (MC) is the addition to total cost from producing one more unit of output.
边际成本（MC）是多生产一单位产出所增加的总成本。
MC = ΔTC / ΔQ
Total revenue (TR) = Price × Quantity. Average revenue (AR) = TR / Q, which is always equal to price. Marginal revenue (MR) is the extra revenue from selling one more unit.
总收入（TR）= 价格 × 数量。平均收入（AR）= TR / Q，始终等于价格。边际收入（MR）是多销售一单位所带来的额外收入。
TR = P × Q AR = P MR = ΔTR / ΔQ
A firm maximises profit where marginal cost equals marginal revenue (MC = MR). If price exceeds average total cost at this output, the firm earns supernormal profit.
企业在边际成本等于边际收入（MC = MR）时实现利润最大化。若此产出水平下的价格高于平均总成本，企业便获得超额利润。
The break‑even point occurs where TR = TC or, equivalently, AR = ATC. The shutdown point for a firm in the short run is where price falls below average variable cost (AVC).
盈亏平衡点在 TR = TC 或者说 AR = ATC 时出现。短期中企业的停业点出现在价格低于平均可变成本（AVC）时。
3. Market Structures and Efficiency | 市场结构与效率
Under perfect competition, the firm is a price taker so P = AR = MR = demand. Long‑run equilibrium occurs where P = MC = minimum ATC, achieving both allocative efficiency (P = MC) and productive efficiency (P = min ATC).
在完全竞争下，企业是价格接受者，因此 P = AR = MR = 需求线。长期均衡时 P = MC = 最低 ATC，同时实现了配置效率（P = MC）与生产效率（P = 最低 ATC）。
A monopolist faces a downward‑sloping demand curve. Marginal revenue is always below average revenue, and the relationship is given by MR = P(1 – 1/|PED|). The monopolist maximises profit at MC = MR and then charges the price on the demand curve.
垄断者面临向下倾斜的需求曲线，边际收入始终低于平均收入，两者的关系为 MR = P(1 – 1/|PED|)。垄断者在 MC = MR 处实现利润最大化，并按需求曲线定价。
Allocative efficiency requires P = MC; productive efficiency requires production at the lowest point on the ATC curve; dynamic efficiency refers to innovation and investment over time, often associated with supernormal profit in imperfectly competitive markets.
配置效率要求 P = MC；生产效率要求在 ATC 曲线的最低点生产；动态效率指长期中的创新与投资，常与不完全竞争市场中的超额利润相关。
In oligopoly, firms may engage in strategic interaction. A Nash equilibrium occurs when each firm chooses its best strategy given the strategies of others, and no firm has an incentive to deviate unilaterally.
在寡头市场中，企业进行策略互动。纳什均衡是指每个企业在给定其他企业策略的情况下选择了自己的最佳策略，且没有企业有单方面偏离的动机。
4. National Income Accounting | 国民收入核算
Gross Domestic Product (GDP) can be measured using the expenditure approach: sum of consumption (C), investment (I), government spending (G) and net exports (X – M).
国内生产总值（GDP）可用支出法衡量，为消费（C）、投资（I）、政府支出（G）和净出口（X – M）的总和。
GDP = C + I + G + (X – M)
The income approach sums factor incomes: wages, rent, interest and profit. The output approach adds up the value added at each stage of production.
收入法将工资、租金、利息和利润等要素收入加总；产出法则加总各生产阶段的增加值。
Gross National Product (GNP) = GDP + net property income from abroad. Net National Product (NNP) = GNP – depreciation.
国民生产总值（GNP）= GDP + 来自国外的净财产收入。国民生产净值（NNP）= GNP – 折旧。
Real GDP = (Nominal GDP / GDP deflator) × 100. The GDP deflator measures the overall price level and is calculated as (Nominal GDP / Real GDP) × 100.
实际 GDP = （名义 GDP / GDP 平减指数）× 100。GDP 平减指数衡量总体价格水平，计算公式为（名义 GDP / 实际 GDP）× 100。
5. Aggregate Demand and the Multiplier | 总需求与乘数
Aggregate demand (AD) is the total spending on domestic goods and services, written as AD = C + I + G + (X – M). The consumption function is C = a + bYd, where b is the marginal propensity to consume (MPC) and Yd is disposable income.
总需求（AD）是对国内商品和服务的总支出，写作 AD = C + I + G + (X – M)。消费函数为 C = a + bYd，其中 b 是边际消费倾向（MPC），Yd 是可支配收入。
C = a + bYd
The simple multiplier (k) depends on the marginal propensity to save (MPS = 1 – MPC). k = 1 / (1 – MPC) = 1 / MPS.
简单乘数（k）取决于边际储蓄倾向（MPS = 1 – MPC）。k = 1 / (1 – MPC) = 1 / MPS。
k = 1 / MPS
When the government sector is included, the tax multiplier is –MPC / MPS. The balanced‑budget multiplier equals one: an equal increase in government spending and lump‑sum taxes raises GDP by the same amount.
引入政府部门后，税收乘数为 –MPC / MPS。平衡预算乘数等于 1：政府支出和一次性税收等额增加会使 GDP 增加相同的数额。
In an open economy, imports act as a leakage. The multiplier becomes k = 1 / (MPS + MPT + MPM), where MPT is the marginal propensity to tax and MPM the marginal propensity to import.
在开放经济中，进口构成漏出。乘数变为 k = 1 / (MPS + MPT + MPM)，MPT 为边际税收倾向，MPM 为边际进口倾向。
6. Money, Banking and Monetary Policy | 货币、银行与货币政策
The quantity theory of money states that the money supply multiplied by its velocity equals the price level times real output.
货币数量论指出，货币供给量乘以流通速度等于价格水平乘以实际产出。
MV = PY
Under the assumption of stable velocity and full employment, an increase in M leads to a proportional increase in P, implying inflation is always a monetary phenomenon.
在流通速度稳定和充分就业的假设下，M 的增加会导致 P 同比例上升，意味着通货膨胀始终是一种货币现象。
The deposit (credit) multiplier measures how much the money supply can expand from an initial injection of reserves. The simple multiplier is the reciprocal of the reserve ratio.
存款（信贷）乘数衡量初始准备金注入能创造多少货币供给。简单乘数为准备金率的倒数。
Money multiplier = 1 / reserve ratio
Central banks use policy interest rates to influence borrowing, spending and inflation. The transmission mechanism links changes in the official rate to market rates, asset prices, exchange rates and ultimately aggregate demand.
中央银行利用政策利率影响借贷、支出与通胀。传导机制将官方利率的变动与市场利率、资产价格、汇率以及最终的总需求联系起来。
7. Inflation and Unemployment | 通货膨胀与失业
The inflation rate is the percentage change in a price index, typically the Consumer Price Index (CPI).
通货膨胀率是价格指数（通常为消费者价格指数 CPI）的百分比变化。
Inflation rate = [(CPIt – CPIt-1) / CPIt-1] × 100
The unemployment rate is the number of unemployed people actively seeking work divided by the labour force, expressed as a percentage.
失业率是正在积极寻找工作的失业人数除以劳动力总数，以百分比表示。
Unemployment rate = (Unemployed / Labour force) × 100
The Phillips curve suggests a short‑run trade‑off between inflation and unemployment: lower unemployment can be associated with higher wage inflation. In the long run, the expectations‑augmented Phillips curve is vertical at the natural rate of unemployment.
菲利普斯曲线表明短期中通胀与失业之间存在取舍：较低的失业可能伴随较高的工资通胀。长期中，附加预期的菲利普斯曲线在自然失业率处垂直。
Okun’s law quantifies the relationship between the output gap and cyclical unemployment: a 2–3% increase in real GDP above trend is associated with roughly a 1 percentage point fall in the unemployment rate.
奥肯定律量化了产出缺口与周期性失业之间的关系：实际 GDP 超出趋势 2–3%，失业率大约下降 1 个百分点。
8. International Economics: Comparative Advantage and Exchange Rates | 国际经济学：比较优势与汇率
Comparative advantage exists when a country can produce a good at a lower opportunity cost than its trading partner. Total gains from trade arise when countries specialise according to comparative advantage.
当一个国家能以比贸易伙伴更低的机会成本生产某种商品时，便拥有比较优势。当各国按比较优势进行专业化分工时，会出现贸易总收益。
The terms of trade index measures the ratio of export prices to import prices.
贸易条件指数衡量出口价格与进口价格之比。
Terms of trade = (Index of export prices / Index of import prices) × 100
The real exchange rate adjusts the nominal exchange rate for differences in national price levels. A rise indicates appreciation in real terms, reducing competitiveness.
实际汇率是根据各国价格水平差异调整后的名义汇率。实际汇率上升表示实际升值，竞争力下降。
Real exchange rate = (Nominal exchange rate × Domestic price level) / Foreign price level
The Marshall–Lerner condition states that a depreciation of the domestic currency will improve the trade balance if the sum of the absolute price elasticities of demand for exports and imports is greater than one.
马歇尔–勒纳条件指出，如果出口需求和进口需求的绝对值价格弹性之和大于 1，本币贬值将改善贸易收支。
The J‑curve effect shows that in the short run a depreciation may initially worsen the trade balance before improving it, because trade volumes adjust more slowly than prices.
J 曲线效应表明，短期内贬值最初可能使贸易收支恶化，随后才出现改善，因为贸易量的调整慢于价格。
9. Development Economics: Harrod‑Domar Model and Indicators | 发展经济学：哈罗德‑多马模型与指标
The Harrod‑Domar model links the growth rate of output to the savings ratio and the incremental capital‑output ratio (ICOR). A higher savings rate or a lower ICOR generates faster growth.
哈罗德‑多马模型将产出增长率与储蓄率和增量资本产出率（ICOR）联系起来。较高的储蓄率或较低的 ICOR 会带来更快的增长。
g = s / k (ΔY / Y = savings ratio / ICOR)
Where s is the ratio of national saving to national income and k is the capital‑output ratio (COR). The ‘financing gap’ is the difference between required investment and domestic saving, often used to justify foreign aid flows.
其中 s 是国内储蓄与国民收入之比，k 是资本产出率（COR）。‘资金缺口’即所需投资与国内储蓄之间的差额，常被用来论证外援的合理性。
The Human Development Index (HDI) is a geometric mean of normalised indices for life expectancy, education and GNI per capita. A value closer to 1 indicates higher human development.
人类发展指数（HDI）是预期寿命、教育和人均国民总收入三个标准化指数的几何平均数。数值越接近 1 表示人类发展水平越高。
The Gini coefficient is derived from the Lorenz curve: Gini = A / (A + B), where A is the area between the line of perfect equality and the Lorenz curve, and B is the area below the Lorenz curve. A coefficient of 0 represents perfect equality; 1 represents perfect inequality.
基尼系数来自洛伦兹曲线：Gini = A / (A + B)，其中 A 是完全均等线与洛伦兹曲线之间的面积，B 是洛伦兹曲线下方的面积。系数 0 代表完全平等，1 代表完全不平等。
10. Market Failure and Government Intervention | 市场失灵与政府干预
Market failure occurs when the free market fails to achieve allocative efficiency. With a negative production externality, social marginal cost (SMC) exceeds private marginal cost (PMC).
当自由市场无法实现配置效率时便出现市场失灵。存在生产负外部性时，社会边际成本（SMC）高于私人边际成本（PMC）。
SMC = PMC + External marginal cost
With a positive consumption externality, social marginal benefit (SMB) is greater than private marginal benefit (PMB). The socially optimal output occurs where SMB = SMC.
存在消费正外部性时，社会边际收益（SMB）大于私人边际收益（PMB）。社会最优产出出现在 SMB = SMC 处。
The Coase theorem states that if property rights are clearly defined and transaction costs are negligible, private bargaining can lead to the efficient outcome regardless of the initial allocation of rights.
科斯定理指出，在产权明确且交易成本可忽略的条件下，私人谈判会达成有效结果，无论初始权利如何分配。
A Pigouvian tax corrects a negative externality by being set equal to the marginal external cost at the socially efficient level of output, thereby internalising the externality.
庇古税按社会有效产出水平下的边际外部成本设定，将负外部性内部化，从而加以纠正。
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