📚 Year 13 OCR Economics: Formula & Theorem Quick Reference Handbook | Year 13 OCR 经济：公式定理速查手册
This quick-reference handbook brings together the essential formulas, quantitative relationships and key theorems you need for the Year 13 OCR Economics specification. Every entry is presented first in English, then immediately in Chinese, so you can revise bilingually and ensure deep understanding. Use this rapid check-list to secure marks on calculations, data-response questions and essay reasoning.
这本速查手册汇集了 Year 13 OCR 经济课程所需的关键公式、数量关系和重要定理。每个条目先提供英文解释，紧接着给出中文对应，帮助你在双语复习中巩固理解。用这份快速检索清单来稳稳拿下计算题、数据回应题和论述推理中的分数。
1. Price Elasticities | 价格弹性
Price elasticity of demand (PED) measures how responsive quantity demanded is to a change in the good's own price.
需求的价格弹性（PED）衡量需求量对商品自身价格变化的反应程度。
PED = (%ΔQd) / (%ΔP)
Values greater than 1 in magnitude indicate elastic demand; less than 1 indicate inelastic demand. Note that PED is typically negative, but we often quote the absolute value.
数值大小超过 1 表示需求有弹性；小于 1 表示需求缺乏弹性。注意 PED 通常为负数，但我们常引用其绝对值。
Price elasticity of supply (PES) measures the responsiveness of quantity supplied to a change in price.
供给的价格弹性（PES）衡量供给量对价格变化的反应程度。
PES = (%ΔQs) / (%ΔP)
PES is always positive. A value above 1 indicates elastic supply; below 1 indicates inelastic supply.
PES 恒为正数。数值大于 1 表示供给有弹性；小于 1 表示供给缺乏弹性。
Cross elasticity of demand (XED) describes how the demand for good A changes when the price of good B changes.
需求的交叉弹性（XED）描述商品 B 的价格变化如何影响商品 A 的需求量。
XED = (%ΔQd of good A) / (%ΔP of good B)
A positive XED denotes substitutes; a negative XED denotes complements. A value near zero implies unrelated goods.
正 XED 表示替代品；负 XED 表示互补品。数值接近零意味着无关商品。
Income elasticity of demand (YED) captures how quantity demanded shifts when consumers' real income alters.
需求的收入弹性（YED）捕捉消费者实际收入变动时需求量的变化。
YED = (%ΔQd) / (%Δ real income)
Positive YED signals a normal good (luxury if YED > 1, necessity if 0 < YED < 1). Negative YED points to an inferior good.
正 YED 表示正常品（若 YED > 1 为奢侈品，若 0 < YED < 1 为必需品）。负 YED 指向劣等品。
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).
总成本（TC）是总固定成本（TFC）与总可变成本（TVC）之和。
TC = TFC + TVC
Average total cost (ATC or AC) is obtained by dividing total cost by output (Q).
平均总成本（ATC 或 AC）由总成本除以产量（Q）求得。
AC = TC / Q, AVC = TVC / Q, AFC = TFC / Q
Marginal cost (MC) is the addition to total cost from producing one more unit.
边际成本（MC）是增加一单位产量所引起的总成本增量。
MC = ΔTC / ΔQ
Total revenue (TR) equals price multiplied by quantity sold. Average revenue (AR) is revenue per unit, and marginal revenue (MR) is the extra revenue from selling one more unit.
总收益（TR）等于价格乘以销售量。平均收益（AR）是每单位收益，边际收益（MR）是多销售一单位所带来的额外收益。
TR = P × Q, AR = TR / Q = P, MR = ΔTR / ΔQ
al profit occurs when AR > AC; normal profit is included in costs and occurs when AR = AC.
利润（π）等于总收益减总成本。当 AR > AC 时出现超常利润；正常利润已包含在成本内，此时 AR = AC。
π = TR – TC
The profit-maximising condition for any firm is to produce up to the point where marginal revenue equals marginal cost (and MC is rising).
任何企业实现利润最大化的条件是：在边际收益等于边际成本（且 MC 处于上升阶段）的产量处进行生产。
Profit-maximisation rule: MR = MC
In the short run a firm should shut down if price falls below average variable cost (P < AVC).
在短期，若价格跌至平均可变成本以下（P < AVC），企业应当停工。
3. Market Structures: Key Relationships | 市场结构：关键关系
In perfect competition the firm is a price-taker. Its demand curve is perfectly elastic, so price equals average revenue equals marginal revenue.
完全竞争市场中企业是价格接受者。其需求曲线完全弹性，因此价格等于平均收益也等于边际收益。
Perfect competition: P = AR = MR
Under monopoly the firm faces a downward-sloping demand curve. If demand is linear (P = a – bQ), total revenue is TR = aQ – bQ² and marginal revenue has twice the slope.
垄断厂商面对向下倾斜的需求曲线。若需求为线性形式 P = a – bQ，则总收益为 TR = aQ – bQ²，边际收益曲线的斜率为需求曲线的两倍。
Linear demand: P = a – bQ, MR = a – 2bQ
long run, monopolistically competitive firms see AR = AC, eliminating supernormal profit.
所有市场结构都遵循 MR = MC 的利润最大化法则。长期内，垄断竞争厂商将实现 AR = AC，超常利润消失。
4. Labour Market | 劳动力市场
Marginal revenue product (MRP) is the extra revenue generated by employing one additional worker. It represents the demand for labour.
边际收益产品（MRP）是增雇一名工人所带来的额外收益，代表劳动力的需求。
MRP = MPP × MR
the goods market is perfectly competitive, MR equals the product price, so MRP = MPP × P.
此处 MPP（边际实物产品）是额外一单位劳动带来的产出增量。当产品市场为完全竞争时，MR 等于产品价格，因此 MRP = MPP × P。
st of labour (MCL) is simply the wage, and equilibrium employment is set where MRP = wage.
在完全竞争的劳动力市场中，企业面临固定的工资率。劳动的边际成本（MCL）即为工资，均衡就业量在 MRP = 工资处确定。
Perfect labour market: MCL = wage, equilibrium: MRP = wage
A monopsonist, however, faces an upward-sloping labour supply curve, so the marginal cost of labour exceeds the wage rate. Employment is lower and wage lower than in perfect competition.
而在买方垄断情况下，企业面临向上倾斜的劳动力供给曲线，劳动的边际成本超过工资率。此时就业量和工资均低于完全竞争情形。
5. National Income and Living Standards | 国民收入与生活水平
Gross Domestic Product (GDP) measures the total value of output produced within a country's borders in a given period. It can be expressed using the expenditure approach.
国内生产总值（GDP）衡量一国境内在特定时期内生产的全部产出价值，可通过支出法表示。
GDP = C + I + G + (X – M)
Nominal GDP is measured at current prices, while real GDP eliminates the effect of inflation by using constant prices.
名义 GDP 以当前价格计算，而实际 GDP 通过使用不变价格剔除了通胀影响。
Real GDP = (Nominal GDP / GDP deflator) × 100
The GDP deflator is a broad price index that reflects the prices of all goods and services produced domestically.
GDP 平减指数是一个反映国内生产所有商品与服务价格水平的广泛价格指数。
GDP deflator = (Nominal GDP / Real GDP) × 100
Real GDP per capita provides an average measure of living standards, though it omits distribution and non-market activity.
人均实际 GDP 提供了一个平均生活水平的度量，但它忽略了分配问题和非市场活动。
Real GDP per capita = Real GDP / Population
6. The Multiplier and Aggregate Demand | 乘数与总需求
The marginal propensity to consume (MPC) is the fraction of additional income spent on domestic goods. The marginal propensity to withdraw (MPW) is the sum of the tendencies to save, tax and import.
边际消费倾向（MPC）是额外收入中用于国内消费的比例。边际漏出倾向（MPW）为储蓄、税收和进口三方面边际倾向之和。
MPC + MPW = 1, where MPW = MPS + MPT + MPM
The simple Keynesian multiplier (k) measures the final change in national income resulting from an initial injection of spending.
简单的凯恩斯乘数（k）衡量初始支出注入所引起的国民收入最终变动量。
k = 1 / (1 – MPC) = 1 / MPW
Therefore, a change in spending ΔJ leads to a multiplied change in income.
因此，一笔支出变动 ΔJ 会带来数倍于此的收入变动。
ΔY = k × ΔJ
Aggregate demand in the economy is the sum of planned consumption, investment, government spending and net exports.
一个经济体的总需求是计划消费、投资、政府支出和净出口的总和。
AD = C + I + G + (X – M)
7. Inflation and Price Indices | 通货膨胀与价格指数
The consumer price index (CPI) tracks the cost of a fixed basket of goods and services relative to a base year.
消费者价格指数（CPI）追踪一个固定篮子商品和服务相对于基年的成本变化。
CPI = (Cost of basket in current year / Cost of basket in base year) × 100
Inflation is measured as the percentage change in the price index over a period.
通货膨胀通过价格指数在一定时期内的百分比变化来衡量。
Inflation rate = [(CPI_t – CPI_t₋₁) / CPI_t₋₁] × 100
Laspeyres index uses base-period quantities as weights, often overstating inflation because it fails to allow for substitution.
拉氏指数采用基期数量作为权重，由于未考虑替代效应常会高估通胀。
Laspeyres index = (Σ P₁Q₀ / Σ P₀Q₀) × 100
Paasche index weights prices by current-period quantities, which can understate inflation if substitution toward cheaper goods is strong.
帕氏指数以报告期数量作为权重，若消费者大量转向廉价商品可能低估通胀。
Paasche index = (Σ P₁Q₁ / Σ P₀Q₁) × 100
8. International Trade and Comparative Advantage | 国际贸易与比较优势
Comparative advantage exists when a country can produce a good at a lower opportunity cost than another country. The opportunity cost of producing one unit of a good is the quantity of the other good forgone.
当一国以低于另一国的机会成本生产某种商品时，就存在比较优势。生产一单位商品的机会成本是所放弃的另一种商品的数量。
Opportunity cost of good X = (Units of good Y sacrificed) / (Units of good X gained)
By specialising according to comparative advantage and trading, both countries can consume beyond their production possibility frontiers.
根据比较优势进行专业化生产并开展贸易，两国均可实现超出其生产可能性边界的消费。
Terms of trade measure the relative price of a country's exports compared to its imports. An improvement raises the country's gains from trade.
贸易条件衡量一国出口相对于进口的价格状况。改善将提高该国的贸易收益。
Terms of trade index = (Index of export prices / Index of import prices) × 100
9. Exchange Rates and Balance of Payments | 汇率与国际收支
An exchange rate states the price of one currency in terms of another. Appreciation means the domestic currency buys more foreign currency; depreciation means it buys less.
汇率表示一种货币用另一种货币表示的价格。本币升值意味着能兑换更多外币；贬值则兑换得少。
Exchange rate: e.g., £1 = $1.30 (direct quotation from sterling perspective)
The percentage change in an exchange rate can be calculated to assess volatility.
可计算汇率的百分比变化以评估波动性。
% change in exchange rate = [(New rate – Old rate) / Old rate] × 100
Effective exchange rate is a weighted average of a basket of bilateral exchange rates, with weights reflecting trade shares.
有效汇率是一篮子双边汇率的加权平均值，权重反映贸易份额。
EER = Σ (weight × bilateral exchange rate index) / Σ weights
The balance of payments current account summarises trade in goods, services, primary and secondary income. A current account deficit must be matched by a financial account surplus (net capital inflow) and vice versa.
国际收支经常账户概括了货物、服务、初次收入和二次收入的交易。经常账户逆差必须由金融账户顺差（资本净流入）来匹配，反之亦然。
10. Economic Development Indicators | 经济发展指标
The Human Development Index (HDI) combines health, education and income into a single composite measure. It is the geometric mean of three normalised indices.
人类发展指数（HDI）将健康、教育和收入整合为一个复合指标，是三个标准化指数的几何平均数。
HDI = (Health Index × Education Index × Income Index)1/3
Each dimension index is calculated using minimum and maximum values (goalposts):
各维度指数使用最小值和最大值（目标极值）计算：
Index = (Actual value – Minimum) / (Maximum – Minimum)
The income index uses the natural logarithm of GNI per capita to reflect diminishing marginal utility of income.
收入指数使用人均国民总收入的自然对数，以体现收入的边际效用递减。
The Gini coefficient quantifies inequality by comparing the area between the Lorenz curve and the line of absolute equality.
基尼系数通过比较洛伦兹曲线与绝对平等线之间的面积来量化不平等程度。
Gini coefficient = A / (A + B)
Here A is the area between the line of perfect equality and the Lorenz curve, and B is the area under the Lorenz curve. A value nearer to 0 indicates greater equality; nearer to 1 indicates extreme inequality.
此处 A 为完全平等线与洛伦兹曲线之间的面积，B 为洛伦兹曲线下方的面积。系数接近 0 表示较为平等，接近 1 表示极端不平等。
11. Financial Ratios and Quantitative Toolkit | 财务比率与定量工具包
Although not covered in depth by every cohort, several ratios help evaluate firm performance and investment decisions in applied contexts. Return on capital employed (ROCE) shows operating profit as a percentage of capital invested.
虽然并非所有学生都深入学习，但若干比率有助于在应用情境中评估企业绩效和投资决策。已动用资本回报率（ROCE）显示营业利润占投入资本的百分比。
ROCE = (Operating profit / Capital employed) × 100
The current ratio measures a firm's ability to meet short-term obligations using its current assets.
流动比率衡量企业用流动资产偿还短期债务的能力。
Current ratio = Current assets / Current liabilities
Net present value (NPV) and internal rate of return (IRR) appear in cost-benefit analysis. NPV discounts future cash flows to present value; a positive NPV suggests a worthwhile project.
净现值（NPV）和内部收益率（IRR）出现在成本收益分析中。NPV 将未来现金流折现为现值；正值表示项目值得投资。
NPV = Σ (Net cash flow_t / (1 + r)t) – Initial investment
For quick index-number work, remember that percentage changes, ratios and weighted averages are common quantitative tools. Always show your formula, substitute correctly and express answers to an appropriate number of significant figures.
对于快速的指数运算，记住百分比变化、比率和加权平均是常见的定量工具。始终写出公式，正确代入，并用适当的小数位数表达答案。
12. Key Theorems in Context | 关键定理速览
Profit maximisation theorem (MR = MC): In all market structures the last unit produced adds exactly as much to revenue as to cost. If MR > MC, a firm can increase profit by expanding output; if MR < MC, it should cut back.
利润最大化定理（MR = MC）： 在所有市场结构中，最后一单位产量恰好使收益增量等于成本增量。若 MR > MC，企业可扩大产量提高利润；若 MR < MC，则应收缩产量。
Euler's theorem in
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