📚 Year 12 OCR Economics: Formula and Theorems Quick Reference | Year 12 OCR 经济：公式定理速查手册
This quick reference guide compiles all the essential formulas and theorems you need for the Year 12 OCR Economics specification. From microeconomic elasticities to macroeconomic multipliers, each formula is presented with a brief explanation to help you master the numerical and conceptual elements of the course.
本速查手册汇编了Year 12 OCR 经济课程所需的所有核心公式和定理。从微观经济弹性到宏观经济乘数，每个公式都附带简要说明，帮助您掌握课程中的计算和概念要点。
1. Price Elasticities of Demand (PED, YED, XED) | 需求价格弹性、收入弹性、交叉弹性
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. The midpoint formula is often used to avoid differing results depending on the direction of change: PED = (ΔQd / average Qd) ÷ (ΔP / average P).
需求价格弹性（PED）衡量需求量对价格变动的反应程度。计算公式为需求量变动百分比除以价格变动百分比。为消除变动方向的影响，常使用中点公式：PED = (ΔQd / 平均Qd) ÷ (ΔP / 平均P)。
PED = %ΔQd / %ΔP
If PED > 1, demand is price elastic; if PED < 1, demand is price inelastic; if PED = 1, demand is unit elastic. For a linear demand curve, elasticity varies along the curve: above the midpoint demand is elastic, below it is inelastic, and at the midpoint it is unit elastic.
若 PED > 1，需求富有价格弹性；PED < 1，需求缺乏价格弹性；PED = 1，需求具有单位弹性。对于线性需求曲线，弹性沿曲线变化：中点以上富有弹性，中点以下缺乏弹性，中点处为单位弹性。
Income elasticity of demand (YED) shows how demand changes with income. YED = %ΔQd / %ΔY. Normal goods have positive YED; inferior goods have negative YED. Luxury goods have YED > 1, while necessities have 0 < YED < 1.
需求收入弹性（YED）显示需求随收入变动的程度。YED = %ΔQd / %ΔY。正常品的YED为正，劣等品的YED为负。奢侈品的YED > 1，必需品则介于0和1之间。
Cross elasticity of demand (XED) measures the responsiveness of demand for good A to a change in the price of good B. XED = %ΔQdA / %ΔPB. Positive XED indicates substitutes; negative XED indicates complements; zero or near-zero suggests no relationship.
需求交叉弹性（XED）衡量商品A的需求对商品B价格变动的反应程度。XED = %ΔQdA / %ΔPB。XED 为正表示替代品，为负表示互补品，为零或接近零表示不相关。
2. Price Elasticity of Supply (PES) | 供给价格弹性
Price elasticity of supply (PES) measures the responsiveness of quantity supplied to a change in price. PES = %ΔQs / %ΔP. The main determinants include the time period, availability of spare capacity, ease of factor substitution, and the level of stocks.
供给价格弹性（PES）衡量供给量对价格变动的反应程度。PES = %ΔQs / %ΔP。主要决定因素包括时间周期、闲置产能的可获得性、要素替代的难易程度以及存货水平。
PES = %ΔQs / %ΔP
If PES > 1, supply is price elastic; if PES < 1, supply is price inelastic; if PES = 1, unit elastic supply. In the momentary period supply is perfectly inelastic (PES = 0); in the short run it is relatively inelastic; in the long run it becomes more elastic.
若 PES > 1，供给富有价格弹性；PES < 1，供给缺乏价格弹性；PES = 1，单位弹性供给。在瞬时时期内，供给完全无弹性（PES = 0）；短期中相对缺乏弹性；长期中变得更富有弹性。
3. Consumer Choice and Utility | 消费者选择与效用
The law of diminishing marginal utility states that as a consumer increases consumption of a good, the additional satisfaction (marginal utility) from each extra unit eventually declines. Total utility is the sum of marginal utilities. The consumer maximises utility where the marginal utility per pound spent is equal across all goods.
边际效用递减规律指出，随着消费者对某种商品的消费量增加，每额外一单位所带来的额外满足感（边际效用）最终会下降。总效用是边际效用的总和。当用于每种商品的最后一英镑所带来的边际效用相等时，消费者实现了效用最大化。
MUₐ / Pₐ = MUₙ / Pₙ
This is the equi-marginal principle. It can also be expressed as the ratio of marginal utilities being equal to the ratio of prices: MUₐ / MUₙ = Pₐ / Pₙ. If this equality is not met, the consumer can reallocate spending to increase total utility.
这就是等边际原理。也可表示为边际效用之比等于价格之比：MUₐ / MUₙ = Pₐ / Pₙ。若不满足这一等式，消费者可通过调整支出组合来增加总效用。
4. Costs of Production | 生产成本
Total cost (TC) is the sum of total fixed costs (TFC) and total variable costs (TVC). Average total cost (ATC) = TC / Q. Average fixed cost (AFC) = TFC / Q, and average variable cost (AVC) = TVC / Q. Marginal cost (MC) is the change in total cost from producing one more unit: MC = ΔTC / ΔQ.
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。平均固定成本（AFC）= TFC / Q，平均可变成本（AVC）= TVC / Q。边际成本（MC）是增加一单位产量所带来的总成本变化量：MC = ΔTC / ΔQ。
TC = TFC + TVC
ATC = TC / Q
MC = ΔTC / ΔQ
A firm’s short-run cost curves are typically U-shaped due to first increasing, then diminishing marginal returns. The MC curve intersects both AVC and ATC at their minimum points. The gap between ATC and AVC narrows as output increases because AFC falls continuously.
企业的短期成本曲线通常呈U形，原因在于边际报酬先递增后递减。MC曲线分别在AVC和ATC的最低点与之相交。随着产量增加，由于AFC持续下降，ATC与AVC之间的差距逐渐缩小。
5. Profit Maximisation and Market Structures | 利润最大化与市场结构
A firm maximises profit by producing the quantity where marginal cost equals marginal revenue (MC = MR). In perfect competition, a firm’s MR equals price (P), so the condition becomes MC = P. In imperfectly competitive markets, the firm faces a downward-sloping demand curve, so MR < P, and profit maximisation still occurs at MC = MR.
企业在边际成本等于边际收益（MC = MR）的产量水平实现利润最大化。在完全竞争市场中，企业的MR等于价格（P），因此条件变为 MC = P。在不完全竞争市场中，企业面临向下倾斜的需求曲线，因此 MR < P，利润最大化仍然发生在 MC = MR 处。
Profit maximisation: MC = MR
Economic profit (supernormal profit) exists when P > ATC; normal profit occurs when P = ATC; the firm makes a loss when P < ATC but will continue in the short run if P ≥ AVC. The shutdown point is where P = AVC.
当 P > ATC 时存在经济利润（超额利润）；当 P = ATC 时获得正常利润；当 P < ATC 时企业发生亏损，但只要 P ≥ AVC，在短期仍将继续经营。停业点为 P = AVC。
Shutdown condition: P < AVC
6. Macroeconomic Indicators | 宏观经济指标
Gross Domestic Product (GDP) can be measured by the expenditure approach: GDP = C + I + G + (X – M), where C is consumption, I is investment, G is government spending, X is exports, and M is imports. Nominal GDP is valued at current prices; real GDP is adjusted for inflation.
国内生产总值（GDP）可通过支出法衡量：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。名义GDP以当前价格计算；实际GDP剔除了通胀影响。
GDP = C + I + G + (X – M)
The inflation rate is commonly measured by the Consumer Price Index (CPI). Inflation rate = [(CPI current – CPI previous) / CPI previous] × 100. CPI weightings reflect the average household’s spending pattern. Deflation refers to a sustained fall in the general price level, while disinflation is a slowdown in the rate of inflation.
通胀率常用消费者价格指数（CPI）衡量。通胀率 = [(当前CPI – 前期CPI) / 前期CPI] × 100。CPI权重反映普通家庭的支出模式。通缩指价格总水平的持续下降，而通胀减速则是通胀率上升速度的放缓。
Inflation rate = (ΔCPI / CPIₚᵣₑᵥᵢₒᵤₛ) × 100
The unemployment rate is the percentage of the labour force that is actively seeking work but unable to find employment. Unemployment rate = (Number of unemployed / Labour force) × 100. The labour force consists of all employed and unemployed individuals who are able and willing to work.
失业率是劳动力中正在积极求职但未找到工作的人所占的百分比。失业率 = (失业人数 / 劳动力) × 100。劳动力包括所有有能力且愿意工作的就业者和失业者。
Unemployment rate = (Unemployed / Labour force) × 100
7. Aggregate Demand and the Multiplier | 总需求与乘数
Aggregate demand (AD) is the total planned spending on domestic goods and services at a given price level. AD = C + I + G + (X – M). A shift in any component causes the AD curve to shift. The multiplier effect states that an initial injection of spending leads to a larger final increase in national income.
总需求（AD）是在给定价格水平下对国内商品和服务的计划总支出。AD = C + I + G + (X – M)。任一组分的变化都会导致AD曲线移动。乘数效应指出，初始注入的支出会带来国民收入的更大最终增加。
AD = C + I + G + (X – M)
The simple multiplier (k) is given by k = 1 / (1 – MPC) or k = 1 / MPS, where MPC is the marginal propensity to consume and MPS the marginal propensity to save. When the economy is open and there is taxation, the multiplier must account for all withdrawals: k = 1 / (MPS + MPT + MPM), where MPT is the marginal propensity to tax and MPM the marginal propensity to import.
简单乘数（k）由 k = 1 / (1 – MPC) 或 k = 1 / MPS 给出，MPC为边际消费倾向，MPS为边际储蓄倾向。在开放经济且存在税收的情况下，乘数须考虑所有漏出：k = 1 / (MPS + MPT + MPM)，其中MPT为边际税收倾向，MPM为边际进口倾向。
Simple multiplier: k = 1 / MPS
Full multiplier: k = 1 / (MPS + MPT + MPM)
The change in national income equals the initial injection multiplied by the multiplier: ΔY = k × ΔJ. The multiplier is larger when withdrawals are smaller.
国民收入的变化量等于初始注入量乘以乘数：ΔY = k × ΔJ。当漏出较小时，乘数较大。
8. Aggregate Supply | 总供给
Short-run aggregate supply (SRAS) shows the relationship between the price level and the quantity of real GDP supplied, holding resource prices (especially money wages) constant. SRAS shifts due to changes in costs of production such as wages, raw material prices, or indirect taxes. A simple SRAS equation is not always required, but the concept of the output gap is key: a positive output gap occurs when actual GDP exceeds potential GDP; a negative output gap when actual GDP is below potential.
短期总供给（SRAS）表示在资源价格（尤其是货币工资）不变的情况下价格水平与实际GDP供给量之间的关系。SRAS会因工资、原材料价格或间接税等生产成本的变化而移动。简单的SRAS方程通常不作要求，但产出缺口概念很关键：当实际GDP超过潜在GDP时为正产出缺口，反之为负产出缺口。
Long-run aggregate supply (LRAS) represents the economy’s maximum sustainable output at full employment. In the classical model, LRAS is vertical at the full-employment level of output, implying that in the long run the economy automatically returns to potential GDP. In the Keynesian model, LRAS is horizontal at low levels of output, then slopes upward and finally becomes vertical, reflecting spare capacity, bottlenecks, and full capacity.
长期总供给（LRAS）代表经济在充分就业时的最大可持续产出。在古典模型中，LRAS在充分就业产出水平处呈垂直状，意味着长期中经济会自动回到潜在GDP。在凯恩斯模型中，LRAS在产量较低时呈水平状，然后向上倾斜，最后垂直，反映了闲置产能、瓶颈和充分产能。
9. International Trade and Exchange Rates | 国际贸易与汇率
Comparative advantage exists when a country can produce a good at a lower opportunity cost than another country. To determine comparative advantage, we compare the opportunity cost ratios. The terms of trade index measures the relative movement of export and import prices: Terms of trade index = (Index of export prices / Index of import prices) × 100. An improvement in the terms of trade means a country can buy more imports with a given quantity of exports.
比较优势是指一国能以低于他国的机会成本生产某种商品。我们通过比较机会成本比来确定比较优势。贸易条件指数衡量进出口价格的相对变动：贸易条件指数 = (出口价格指数 / 进口价格指数) × 100。贸易条件改善意味着用一定量的出口可购买更多进口品。
Terms of trade = (Export price index / Import price index) × 100
Exchange rates express the value of one currency in terms of another. The real exchange rate adjusts the nominal exchange rate for differences in price levels: Real exchange rate = (Nominal exchange rate × Domestic price level) / Foreign price level. A depreciation of the domestic currency makes exports cheaper and imports more expensive, improving the trade balance if the Marshall-Lerner condition holds (sum of PED for exports and PED for imports > 1).
汇率表示一种货币用另一种货币计量的价值。实际汇率根据价格水平差异调整名义汇率：实际汇率 = (名义汇率 × 国内价格水平) / 国外价格水平。本币贬值使出口更便宜、进口更昂贵，若满足马歇尔-勒纳条件（出口和进口的需求价格弹性之和大于1），则贸易收支将改善。
Real exchange rate = (E × P) / P*
10. Government Policy Instruments | 政府政策工具
Fiscal policy involves changing government spending and taxation. A budget deficit occurs when G > T (tax revenue), while a budget surplus occurs when T > G. The structural budget position is adjusted for cyclical fluctuations to show the long-term fiscal stance. The formula for the overall budget balance is simply T – G.
财政政策涉及改变政府支出和税收。当 G > T（税收收入）时出现预算赤字，当 T > G 时出现预算盈余。结构性预算状况剔除了周期性波动，以显示长期财政立场。整体预算余额的公式即为 T – G。
Monetary policy typically uses the interest rate or money supply to influence aggregate demand. The central bank’s policy rate influences commercial bank rates, borrowing costs, and eventually consumption and investment. No single formula is prescribed, but the transmission mechanism links changes in the policy rate to changes in AD: lower rates → cheaper borrowing → higher C and I → higher AD.
货币政策通常运用利率或货币供给来影响总需求。央行的政策利率影响商业银行利率、借贷成本，最终影响消费和投资。虽无单一公式，但传导机制将政策利率变化与AD变化联系起来：利率降低→借贷成本降低→C和I增加→AD增加。
Supply-side policies aim to increase the economy’s productive potential. A common measure of productive capacity is the trend in potential GDP, often estimated using a production function. A simple representation: Y = A f(L, K), where Y is output, A is total factor productivity, L is labour and K is capital. Improvements in A, L or K shift LRAS to the right.
供给侧政策旨在提高经济的生产潜力。潜在GDP的趋势常用来衡量生产能力，通常用生产函数估算。简单表示为：Y = A f(L, K)，其中Y为产出，A为全要素生产率，L为劳动，K为资本。A、L或K的改善会使LRAS右移。
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