📚 Year 13 OCR Economics: Formula & Theorem Quick Reference | Year 13 OCR 经济：公式定理速查手册
This quick reference handbook gathers the essential formulas, theorems, and key quantitative relationships you need for Year 13 OCR Economics. Use it to reinforce your understanding of microeconomics and macroeconomics, from elasticity and costs to the multiplier and trade. Each entry provides a clear statement of the formula or concept followed by its application.
本速查手册汇集了Year 13 OCR经济学所需的关键公式、定理和重要数量关系。它帮助你巩固微观经济学和宏观经济学的理解，从弹性、成本到乘数和贸易。每个条目都清晰陈述公式或概念及其应用。
1. Elasticity Formulas | 弹性公式
Price Elasticity of Demand (PED) measures the responsiveness of quantity demanded to a change in price. The formula is: PED = %ΔQd / %ΔP. Always take the absolute value; if |PED| > 1, demand is price elastic; if |PED| < 1, demand is price inelastic; if |PED| = 1, demand is unit elastic.
需求价格弹性(PED)衡量需求量对价格变化的反应程度。公式为：PED = %ΔQd / %ΔP。总是取绝对值；若|PED|>1，需求富有弹性；若|PED|<1，需求缺乏弹性；若|PED|=1，需求为单位弹性。
Income Elasticity of Demand (YED) indicates how demand responds to a change in income: YED = %ΔQd / %ΔY. Normal goods have a positive YED (luxuries > 1, necessities 0-1), while inferior goods have a negative YED.
需求收入弹性(YED)显示需求如何响应收入变化：YED = %ΔQd / %ΔY。正常商品YED为正（奢侈品>1，必需品0-1），而劣质品YED为负。
Cross Elasticity of Demand (XED) captures the relationship between two goods: XED = %ΔQd of good A / %ΔP of good B. Substitutes have a positive XED, complements have a negative XED, and unrelated goods have XED close to zero.
需求交叉弹性(XED)捕捉两种商品间关系：XED = A商品需求量变化百分比 / B商品价格变化百分比。替代品XED为正，互补品为负，不相关商品XED接近零。
Price Elasticity of Supply (PES) measures the responsiveness of quantity supplied: PES = %ΔQs / %ΔP. PES > 1 indicates elastic supply, PES < 1 inelastic supply, and PES = 1 unit elastic supply. The key determinants include production time, spare capacity, and stock levels.
供给价格弹性(PES)衡量供给量的反应程度：PES = %ΔQs / %ΔP。PES>1表示供给富有弹性，PES<1缺乏弹性，PES=1为单位弹性。关键决定因素包括生产时间、闲置产能和库存水平。
2. Costs, Revenue and Profit Maximisation | 成本、收益与利润最大化
Total Cost (TC) is the sum of Total Fixed Cost (TFC) and Total Variable Cost (TVC): TC = TFC + TVC. Average Cost (AC) is the cost per unit: AC = TC / Q. Marginal Cost (MC) is the change in total cost from producing one more unit: MC = ΔTC / ΔQ. The MC curve passes through the minimum point of the AC curve.
总成本(TC)是总固定成本(TFC)与总可变成本(TVC)之和：TC = TFC + TVC。平均成本(AC)是每单位成本：AC = TC / Q。边际成本(MC)是多生产一单位产量带来的总成本变动：MC = ΔTC / ΔQ。MC曲线穿过AC曲线的最低点。
Total Revenue (TR) = Price × Quantity sold, TR = P × Q. Average Revenue (AR) = TR / Q, which equals the price and is the firm’s demand curve. Marginal Revenue (MR) = ΔTR / ΔQ. Under perfect competition AR = MR; under imperfect competition MR lies below AR.
总收益(TR) = 价格 × 销售量，TR = P × Q。平均收益(AR) = TR / Q，等于价格，也就是企业的需求曲线。边际收益(MR) = ΔTR / ΔQ。完全竞争下AR=MR；不完全竞争下MR位于AR下方。
The profit-maximising rule is to produce where MC = MR, provided MC is rising. Normal profit occurs when AC = AR; supernormal profit occurs when AC < AR (AR > AC). The shutdown point in the short run is where P = AVC.
利润最大化条件是在MC = MR处生产，且MC上升。正常利润出现在AC = AR时；超常利润出现在AC < AR（AR > AC）时。短期停业点是P = AVC处。
3. Market Structures | 市场结构
In perfect competition, firms are price takers. The demand curve is perfectly elastic: AR = MR = Price. Profit maximisation occurs at MC = MR, which equals price. In the long run, only normal profits are made because supernormal profits attract new entry, shifting supply until AR = AC.
在完全竞争中，企业是价格接受者。需求曲线完全弹性：AR = MR = 价格。利润最大化在MC = MR处实现，等于价格。长期中只能获得正常利润，因为超常利润吸引新进入者，直至AR = AC。
A pure monopoly faces a downward-sloping demand curve (AR). MR lies below AR and is twice as steep. The monopoly maximises profit where MC = MR, then charges the price from the AR curve at that output. This typically yields supernormal profits, and price exceeds MC, creating allocative inefficiency.
纯垄断面对向下倾斜的需求曲线(AR)。MR位于AR下方且斜率加倍。垄断者在MC = MR处最大化利润，然后在该产量上依据AR曲线定价。通常产生超常利润，价格高于边际成本，造成配置无效率。
Oligopoly features a kinked demand curve: the AR curve has a kink at the prevailing price. The MR curve is discontinuous below the kink. This theory explains price rigidity; firms are reluctant to change prices because a price rise would lead to a large loss of demand (elastic above), while a price cut would be matched by rivals (inelastic below).
寡头垄断的特征是弯折的需求曲线：AR曲线在现行价格处弯折。MR曲线在弯折处下方不连续。该理论解释了价格刚性；企业不愿改变价格，因为提价会导致需求大幅流失（上方弹性），而降价会被对手跟进（下方缺乏弹性）。
Contestable markets are characterised by low barriers to entry and exit, allowing hit-and-run competition. Even a monopoly may be forced to price near average cost if the threat of entry is high, achieving an outcome close to competitive equilibrium.
可竞争市场的特点是进入和退出壁垒低，允许打了就跑的竞争。如果进入威胁大，即使垄断企业也可能被迫将价格定在接近平均成本的位置，实现接近竞争均衡的结果。
4. Labour Market | 劳动力市场
The demand for labour is a derived demand. The Marginal Revenue Product of Labour (MRPL) is the extra revenue generated by employing an additional worker: MRPL = MPL × MR. In perfectly competitive product markets, MR = Price, so MRPL = MPL × P. The firm will hire labour up to the point where MRPL = MCL (Marginal Cost of Labour).
劳动需求是派生需求。劳动的边际收益产品(MRPL)是额外雇用一名工人带来的额外收入：MRPL = MPL × MR。在产品市场完全竞争时，MR=价格，因此MRPL = MPL × P。企业雇用劳动力直到MRPL = MCL（劳动的边际成本）。
In a perfectly competitive labour market, the individual firm is a wage taker, so MCL = wage rate. The firm’s labour demand curve is the MRPL curve. Shifts in MRPL can be caused by changes in labour productivity, the price of the good, or technology.
在完全竞争的劳动力市场中，单个企业是工资接受者，因此MCL=工资率。企业的劳动需求曲线就是MRPL曲线。MRPL的移动可能由劳动生产率、产品价格或技术的变化引起。
Wages are determined by the interaction of labour demand and supply. Elasticity of labour demand and supply influences the impact of shifts. Monopsony power in labour markets can result in wages below MRPL, leading to exploitation of labour.
工资由劳动力供求的相互作用决定。劳动需求的弹性和供给的弹性影响着移动的影响。劳动力市场上的买方垄断力量会导致工资低于MRPL，造成对劳动的剥削。
5. Macroeconomic Indicators and Multiplier | 宏观经济指标与乘数
Gross Domestic Product (GDP) can be measured via expenditure: GDP = C + I + G + (X – M), where C is consumption, I is investment, G is government spending, X is exports, and M is imports. Gross National Income (GNI) adds net income from abroad.
国内生产总值(GDP)可通过支出计量：GDP = C + I + G + (X – M)，其中C为消费，I为投资，G为政府支出，X为出口，M为进口。国民总收入(GNI)在此基础上加上来自国外的净收入。
Average Propensity to Consume (APC) = C / Y; Average Propensity to Save (APS) = S / Y, with APC + APS = 1. Marginal Propensity to Consume (MPC) = ΔC / ΔY; Marginal Propensity to Save (MPS) = ΔS / ΔY, and MPC + MPS = 1. The marginal propensity to withdraw (MPW) includes MPS, marginal rate of tax, and marginal propensity to import.
平均消费倾向(APC)=C/Y；平均储蓄倾向(APS)=S/Y，且APC+APS=1。边际消费倾向(MPC)=ΔC/ΔY；边际储蓄倾向(MPS)=ΔS/ΔY，且MPC+MPS=1。边际漏出倾向(MPW)包含MPS、边际税率和边际进口倾向。
The multiplier effect amplifies an initial injection into the circular flow. The simple multiplier (k) is: k = 1 / (1 – MPC) = 1 / MPW. The larger the MPW, the smaller the multiplier. National income equilibrium in the Keynesian model requires injections = withdrawals: I + G + X = S + T + M.
乘数效应放大了对循环流的初始注入。简单乘数(k)为：k = 1 / (1 – MPC) = 1 / MPW。MPW越大，乘数越小。凯恩斯模型中的国民收入均衡要求注入=漏出：I+G+X = S+T+M。
6. Aggregate Demand and Aggregate Supply | 总需求与总供给
Aggregate Demand (AD) is the total planned expenditure on goods and services in an economy: AD = C + I + G + (X – M). A fall in any component shifts the AD curve leftwards. The AD curve slopes downward due to the wealth effect, interest rate effect, and net export effect.
总需求(AD)是经济中计划在商品和服务上的总支出：AD = C + I + G + (X – M)。任一组成部分的下降都会使AD曲线左移。AD曲线向下倾斜源于财富效应、利率效应和净出口效应。
Short-run Aggregate Supply (SRAS) is upward sloping: as the price level rises, firms increase output because nominal wages are sticky. Shifts in SRAS can come from changes in costs of production, taxes, or subsidies. Long-run Aggregate Supply (LRAS) in the classical model is vertical at the full-employment level of output (Yf), reflecting that in the long run all prices and wages are flexible.
短期总供给(SRAS)向上倾斜：随着价格水平上升，由于名义工资黏性，企业增加产出。SRAS的移动可能来自生产成本、税收或补贴的变化。古典模型中的长期总供给(LRAS)在充分就业产出水平(Yf)处垂直，反映长期中所有价格和工资均灵活。
The Keynesian LRAS curve is horizontal at low levels of output (large spare capacity) and becomes vertical at full employment. Equilibrium occurs where AD = AS; an output gap exists when actual GDP differs from Yf, either a negative gap (recessionary) or positive gap (inflationary).
凯恩斯主义LRAS曲线在低产出水平时水平（大量闲置产能），并在充分就业时变为垂直。均衡在AD=AS处实现；当实际GDP与Yf不同时存在产出缺口，可以是负缺口（衰退）或正缺口（通胀）。
7. Inflation and Unemployment | 通胀与失业
The Consumer Price Index (CPI) is calculated as: CPI = (Cost of basket in current year / Cost of basket in base year) × 100. The inflation rate is then: (CPI current – CPI previous) / CPI previous × 100.
消费者价格指数(CPI)计算为：CPI = (当年一篮子商品成本 / 基年一篮子商品成本) × 100。然后通胀率 = (本期CPI – 上期CPI) / 上期CPI × 100.
The Quantity Theory of Money states: MV = PY, where M is the money supply, V is velocity of circulation, P is the price level, and Y is real output. In growth rate form: %ΔM + %ΔV ≈ %ΔP + %ΔY. If velocity is stable, excess money growth leads to inflation.
货币数量论公式：MV = PY，其中M是货币供给，V是流通速度，P是价格水平，Y是实际产出。用增长率表示为：%ΔM + %ΔV ≈ %ΔP + %ΔY。若流通速度稳定，货币增长过快会导致通胀。
The short-run Phillips curve shows an inverse relationship between inflation and unemployment. The long-run Phillips curve is vertical at the natural rate of unemployment (NAIRU), indicating no trade-off in the long run. Supply-side shocks can shift the short-run Phillips curve.
短期菲利普斯曲线显示通货膨胀与失业之间的反向关系。长期菲利普斯曲线在自然失业率(NAIRU)处垂直，表明长期不存在权衡取舍。供给侧冲击可使短期菲利普斯曲线移动。
8. International Trade | 国际贸易
The theory of comparative advantage states that countries should specialise in producing goods for which they have the lowest opportunity cost. The opportunity cost is the quantity of one good sacrificed to produce an additional unit of another good. Mutual gains from trade arise when the terms of trade lie between the two countries’ opportunity cost ratios.
比较优势理论认为各国应专门生产机会成本最低的商品。机会成本是为多生产一单位另一种商品所牺牲的该商品数量。当贸易条件处于两国机会成本比率之间时，双方均可从贸易中获益。
The Terms of Trade (ToT) index is: ToT = (Index of export prices / Index of import prices) × 100. A rise in the ToT indicates an improvement (a given volume of exports buys more imports). Deterioration means export prices have fallen relative to import prices.
贸易条件(ToT)指数：ToT = (出口价格指数 / 进口价格指数) × 100。ToT上升表示改善（给定出口量能购买更多进口品）。恶化意味着出口价格相对于进口价格下降。
Trade creation occurs when a customs union removes barriers and lower-cost producers within the union replace higher-cost domestic production. Trade diversion occurs when a higher-cost producer inside the union replaces a lower-cost outside producer due to common external tariffs. The net welfare effect depends on the balance of these effects.
贸易创造发生在关税同盟取消壁垒，同盟内
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