📚 Year 12 CIE Economics: Formula & Theorem Quick Reference Handbook | Year 12 CIE 经济：公式定理速查手册
This handbook compiles all the essential formulas and theorems you need for the CIE AS Level Economics course. It covers both microeconomics and macroeconomics, from elasticity and cost curves to national income and the multiplier. Each section presents the key equations with concise explanations, ensuring you have a reliable quick-reference tool for revision and exam preparation.
本手册汇编了 CIE AS Level 经济学课程所需的所有核心公式与定理。内容涵盖微观与宏观两大领域，从弹性、成本曲线到国民收入与乘数效应。每个小节都给出了关键方程并配有简明解释，为你提供一份可靠的便捷速查工具，助力复习与应试。
1. Demand, Supply and Elasticity | 需求、供给与弹性
Price elasticity of demand (PED) measures the responsiveness of quantity demanded to a change in the good’s own price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. The sign of PED is typically negative due to the law of demand, but we often refer to its absolute value.
需求价格弹性（PED）衡量需求量对商品自身价格变化的反应程度。计算公式为需求量变动的百分比除以价格变动的百分比。由于需求定律，PED 通常为负值，但我们往往只看其绝对值。
PED = %ΔQd / %ΔP
When |PED| > 1, demand is price elastic: a given percentage change in price leads to a larger percentage change in quantity demanded, so total revenue moves in the opposite direction to price. When |PED| < 1, demand is price inelastic, and total revenue moves in the same direction as price. Unit elastic demand (|PED| = 1) leaves total revenue unchanged when price changes.
当 |PED| > 1 时，需求富有价格弹性：价格给定百分比的变动会引起需求量更大百分比的变动，因此总收益与价格反向变动。当 |PED| < 1 时，需求缺乏价格弹性，总收益与价格同向变动。单位弹性（|PED| = 1）时，价格变动不会改变总收益。
Price elasticity of supply (PES) measures the responsiveness of quantity supplied to a change in price. Its formula is the percentage change in quantity supplied divided by the percentage change in price. PES is normally positive because higher prices encourage more production.
供给价格弹性（PES）衡量供给量对价格变动的反应程度。公式为供给量变动的百分比除以价格变动的百分比。PES 通常为正，因为更高的价格会激励更多生产。
PES = %ΔQs / %ΔP
Income elasticity of demand (YED) shows how demand changes as consumer income changes. It is the percentage change in demand divided by the percentage change in income. A positive YED indicates a normal good; a negative YED indicates an inferior good. For normal goods, YED > 1 suggests a luxury, while 0 < YED < 1 suggests a necessity.
需求收入弹性（YED）反映的是需求如何随消费者收入变化而变化。它是需求量变动的百分比除以收入变动的百分比。YED 为正表示正常品；YED 为负表示低档品。对于正常品，YED > 1 视为奢侈品，而 0 < YED < 1 则为必需品。
YED = %ΔQd / %ΔY
Cross elasticity of demand (XED) measures the responsiveness of demand for good A when the price of good B changes. Complementary goods have a negative XED, while substitutes have a positive XED.
需求交叉弹性（XED）衡量的是 A 商品需求对 B 商品价格变动的反应程度。互补品的 XED 为负，替代品的 XED 为正。
XED = %ΔQd(A) / %ΔP(B)
2. Consumer and Producer Surplus | 消费者与生产者剩余
Consumer surplus is the difference between what consumers are willing to pay for a good and what they actually pay. On a demand-supply diagram, it is represented by the area below the demand curve and above the equilibrium price, up to the quantity traded.
消费者剩余是指消费者为一种商品愿意支付的最高价格与实际支付价格之间的差额。在供需图中，它表现为需求曲线以下、均衡价格以上、直至交易量的区域。
Producer surplus is the difference between the price producers actually receive and the minimum price they would be willing to accept. Graphically, it is the area above the supply curve and below the equilibrium price.
生产者剩余是生产者实际收到的价格与其愿意接受的最低价格之间的差额。图形上，它是供给曲线以上、均衡价格以下的区域。
Both surpluses are maximised at the competitive market equilibrium. Total surplus = consumer surplus + producer surplus. It is often calculated using the formula for the area of a triangle: ½ × base × height, where the base is the equilibrium quantity and the height is the intercept difference.
在竞争性市场均衡中，两种剩余均达到最大。总剩余 = 消费者剩余 + 生产者剩余。常用三角形面积公式计算：½ × 底 × 高，其中底为均衡数量，高为纵轴截距之差。
Total Surplus = ½ × Qe × (Max Willingness to Pay – Min Willingness to Accept)
Any price control, indirect tax or subsidy that moves the market away from equilibrium creates a deadweight loss, which is the reduction in total surplus not transferred to anyone.
任何限价、间接税或补贴使市场偏离均衡时，都会产生无谓损失，即总剩余中未被任何人获得的损失部分。
3. Costs, Revenue 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 cost (AC or ATC) is total cost divided by output. Marginal cost (MC) is the change in total cost from producing one more unit.
总成本（TC）是总固定成本（TFC）与总可变成本（TVC）之和。平均成本（AC 或 ATC）为总成本除以产量。边际成本（MC）是增加一单位产量所带来的总成本变动。
TC = TFC + TVC
AC = TC / Q
MC = ΔTC / ΔQ
Total revenue (TR) is price times quantity sold. Average revenue (AR) equals TR/Q, which is simply the price. Marginal revenue (MR) is the additional revenue from selling one more unit. For a perfectly competitive firm, AR = MR = P; for a monopolist, MR lies below AR.
总收益（TR）等于价格乘以销售量。平均收益（AR）等于 TR/Q，也就是价格。边际收益（MR）是增加一单位销售所带来的额外收益。对完全竞争企业，AR = MR = P；对垄断企业，MR 曲线位于 AR 曲线下方。
TR = P × Q
AR = TR/Q = P
MR = ΔTR / ΔQ
The profit-maximising rule for any firm is to produce the output where marginal cost equals marginal revenue (MC = MR). Normal profit occurs when AR = AC (zero economic profit). Supernormal profit arises when AR > AC.
任何企业实现利润最大化的法则是：在边际成本等于边际收益的产量水平上生产（MC = MR）。当 AR = AC 时，企业获得正常利润（经济利润为零）。当 AR > AC 时，出现超常利润。
4. Market Structures: Perfect Competition and Monopoly | 市场结构：完全竞争与垄断
In perfect competition, many firms sell identical products and are price-takers. The demand curve facing the firm is perfectly elastic (horizontal) at the market price. In the short run, the firm can make supernormal profits, but free entry in the long run drives price down to the minimum of AC, yielding only normal profit. Allocative efficiency is achieved because P = MC, and productive efficiency occurs as the firm produces at the minimum point of its AC curve.
在完全竞争中，众多企业销售同质产品，都是价格接受者。企业面临的需求曲线在市场价格水平上完全弹性（水平）。短期内企业可获得超常利润，但长期中自由进入会使价格降至平均成本的最低点，仅留存正常利润。由于 P = MC，实现了配置效率；同时企业在 AC 曲线最低点生产，实现了生产效率。
Monopoly exists when a single firm dominates the market. The monopolist is a price-maker and faces a downward-sloping demand curve. Profit maximisation still follows MR = MC, but price is set above marginal cost (P > MC), resulting in allocative inefficiency and a deadweight welfare loss. Monopolies may also suffer from x-inefficiency and may not produce at minimum AC.
垄断存在于单一企业主导市场的情形。垄断者是价格制定者，面临向下倾斜的需求曲线。利润最大化依然遵循 MR = MC，但价格制定在边际成本之上（P > MC），导致配置无效率和福利的无谓损失。垄断企业还可能存在 X-无效率，且未必在最低平均成本处生产。
In contestable market theory, even a monopoly may behave like a competitive firm if there is no barriers to entry or exit. The threat of potential competition ensures prices remain close to average cost.
在可竞争市场理论中，若无进入或退出壁垒，即便垄断企业也可能表现得如同竞争性企业一样。潜在竞争的威胁使价格保持在接近平均成本的水平。
5. Market Failure and Government Intervention | 市场失灵与政府干预
Market failure occurs when the free market fails to allocate resources efficiently. Externalities cause a divergence between private and social costs or benefits. The formulas below capture the relationship:
市场失灵是指自由市场无法有效配置资源。外部性导致私人成本或收益与社会成本或收益之间出现背离。以下公式反映了这种关系：
Social Marginal Cost (SMC) = Private Marginal Cost + External Marginal Cost
Social Marginal Benefit (SMB) = Private Marginal Benefit + External Marginal Benefit
A negative production externality means SMC > PMC, leading to overproduction. A positive consumption externality means SMB > PMB, leading to underconsumption. Government can impose a Pigouvian tax equal to the external cost to internalise the externality and achieve the socially optimal output where SMC = SMB.
负生产外部性意味着 SMC > PMC，导致过度生产。正消费外部性意味着 SMB > PMB，导致消费不足。政府可征收等于外部成本的庇古税，将外部性内部化，使产量回到 SMC = SMB 的社会最优水平。
The Coase theorem suggests that if property rights are well defined and transaction costs are low, private bargaining can solve externalities without government intervention. Public goods are non-rivalrous and non-excludable, leading to the free-rider problem and underprovision by the market.
科斯定理指出，若产权界定清晰且交易成本较低，私人协商便可解决外部性而无须政府干预。公共品具有非竞争性和非排他性，这会导致搭便车问题和市场供给不足。
6. Macroeconomic Indicators | 宏观经济指标
Gross Domestic Product (GDP) measures the total value of final goods and services produced within a country in a given period. The expenditure approach sums consumption (C), investment (I), government spending (G) and net exports (X – M).
国内生产总值（GDP）衡量一国在一定时期内生产的最终产品与服务的总价值。支出法将消费（C）、投资（I）、政府支出（G）和净出口（X – M）加总。
GDP = C + I + G + (X – M)
Nominal GDP is measured at current prices, while real GDP is adjusted for inflation. The GDP deflator is a broader price index used to convert nominal GDP into real GDP.
名义 GDP 按现价计算，而实际 GDP 则剔除了通货膨胀的影响。GDP 平减指数是一个更广泛的价格指数，用来将名义 GDP 转化为实际 GDP。
Real GDP = (Nominal GDP / GDP Deflator) × 100
GDP Deflator = (Nominal GDP / Real GDP) × 100
The Consumer Price Index (CPI) tracks the cost of a fixed basket of goods and services over time. The inflation rate is the percentage change in the CPI from one period to the next.
消费者价格指数（CPI）追踪一篮子固定商品和服务随时间变化的成本。通货膨胀率是 CPI 从一个时期到下一时期的百分比变化。
CPI = (Cost of basket in current year / Cost of basket in base year) × 100
Inflation Rate = [(CPIt – CPIt-1) / CPIt-1] × 100%
The unemployment rate is the percentage of the labour force that is actively seeking work but cannot find employment. The labour force includes those employed and the unemployed.
失业率是指劳动力中积极寻找工作但未能就业的人口所占的百分比。劳动力包括已就业者和失业者。
Unemployment Rate = (Number of Unemployed / Labour Force) × 100%
7. Aggregate Demand and Aggregate Supply | 总需求与总供给
Aggregate demand (AD) is the total planned expenditure on domestic goods and services at each price level. It is composed of consumption, investment, government spending and net exports. The AD curve slopes downward due to the wealth effect, interest rate effect and international trade effect.
总需求（AD）是各个价格水平上对国内商品和服务的计划支出总量，由消费、投资、政府支出和净出口构成。AD 曲线因财富效应、利率效应和国际贸易效应而向下倾斜。
AD = C + I + G + (X – M)
Aggregate supply (AS) reflects the total output firms are willing to produce at different price levels. The short-run AS curve is upward sloping because input prices like wages may be sticky. The long-run AS (LRAS) is vertical at the full-employment level of output, indicating that in the long run, the economy’s capacity is determined by factor endowments and technology, not the price level.
总供给（AS）反映企业各个价格水平愿意生产的总产出。短期 AS 曲线向上倾斜，因为工资等投入价格具有粘性。长期总供给（LRAS）在充分就业产出水平上垂直，表明长期中经济产能由要素禀赋和技术决定，与价格水平无关。
Macroeconomic equilibrium occurs where AD intersects AS. Demand-side and supply-side shocks can shift these curves, altering real GDP and the price level.
宏观经济均衡出现在 AD 与 AS 相交之处。需求侧和供给侧冲击会使这些曲线移动，从而改变实际 GDP 和价格水平。
8. The Multiplier and Fiscal Policy | 乘数与财政政策
The multiplier effect explains how an initial injection into the circular flow of income leads to a larger final increase in national income. The size of the multiplier depends on the marginal propensity to withdraw from the circular flow: saving (MPS), taxation (MPT) and imports (MPM).
乘数效应解释了向收入循环流最初注入的支出如何导致国民收入出现更大的最终增长。乘数的大小取决于从循环流中漏出的边际倾向：边际储蓄倾向（MPS）、边际税率（MPT）和边际进口倾向（MPM）。
k = 1 / (1 – MPC) = 1 / (MPS + MPT + MPM)
Where MPC is the marginal propensity to consume. The change in national income (ΔY) is the multiplier times the initial change in autonomous spending (ΔJ).
其中 MPC 为边际消费倾向。国民收入的变动（ΔY）等于乘数乘以自主支出的初始变动（ΔJ）。
ΔY = k × ΔJ
Fiscal policy uses government spending and taxation to influence AD. An expansionary fiscal policy involves increasing G or reducing taxes, operating through the multiplier to boost output. However, crowding out may occur if increased government borrowing raises interest rates and reduces private investment.
财政政策通过政府支出和税收来影响 AD。扩张性财政政策包括增加 G 或减税，经由乘数作用提振产出。然而，若政府借款增加推高利率并挤出了私人投资，就可能发生挤出效应。
9. Money, Banking and Monetary Policy | 货币、银行与货币政策
The quantity theory of money uses the equation of exchange to link the money supply (M), its velocity of circulation (V), the price level (P) and real output (Y). Assuming V is stable and Y is at full employment, an increase in M leads to a proportionate increase in P, implying inflation is a monetary phenomenon.
货币数量论利用交易方程将货币供给（M）、流通速度（V）、价格水平（P）与实际产出（Y）联系起来。假设 V 稳定且 Y 处于充分就业状态，则 M 的增加会导致 P 的同比例上升，这意味着通货膨胀本质上是一种货币现象。
MV = PY
Monetary policy is conducted by the central bank to control money supply and interest rates. Expansionary monetary policy lowers interest rates to stimulate investment and consumption, shifting AD to the right. Contractionary policy raises rates to dampen inflationary pressures.
货币政策由中央银行执行，以控制货币供给和利率。扩张性货币政策降低利率以刺激投资和消费，使 AD 右移。紧缩性政策则提高利率以抑制通胀压力。
In a fractional reserve banking system, an initial deposit can lead to a multiple expansion of bank credit. The credit multiplier formula is the reciprocal of the reserve requirement ratio. However, the actual money multiplier is smaller due to leakages such as cash holdings by the public.
在部分准备金银行体系中，一笔初始存款可以导致银行信贷的多倍扩张。信用乘数公式为准备金率的倒数。然而，由于公众持有现金等漏出因素，实际货币乘数会更小。
10. International Trade and Exchange Rates | 国际贸易与汇率
The principle of comparative advantage states that countries should specialise in producing goods where they have a lower opportunity cost, and then trade. Total output rises when each country focuses on its comparative advantage.
比较优势原理指出，各国应专业化生产并出口机会成本较低的商品，然后进行贸易。当各国专注于自身比较优势时，总体产出会增加。
The terms of trade measure the rate at which a country’s exports exchange for its imports. An improvement in the terms of trade means a country can buy more imports for a given quantity of exports.
贸易条件衡量一国出口商品换取进口商品的比率。贸易条件改善意味着给定数量的出口可以购买到更多的进口品。
Terms of Trade = (Export Price Index / Import Price Index) × 100
Exchange rates express the price of one currency in terms of another. A floating exchange rate is determined by demand and supply in the foreign exchange market. The real exchange rate adjusts the nominal rate for differences in price levels between countries and is a better indicator of international competitiveness.
汇率表示一种货币用另一种货币表示的价格。浮动汇率由外汇市场上的需求与供给决定。实际汇率对名义汇率进行了各国价格水平差异的调整，
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