📚 Year 12 SQA Economics: Formulae & Theorems Quick Reference | SQA 经济公式定理速查手册
This handbook provides a concise summary of the essential formulae, metrics, and key theorems covered in Year 12 SQA Economics. It is designed as a quick revision aid, linking definitions and calculations to the core microeconomic and macroeconomic topics of the Higher course. Use it to reinforce understanding, check unit consistency, and practise numerical applications.
本手册为 Year 12 SQA 经济学应知应会的公式、指标与核心定理提供精炼总结，旨在作为快速复习帮手，将定义与计算联系到 Higher 课程中的微观与宏观经济核心主题。可用以巩固理解、核对单位并练习定量应用。
1. Elasticity Formulae | 弹性公式
Elasticities measure the responsiveness of one variable to changes in another. The key demand-side elasticities (PED, YED, XED) and price elasticity of supply (PES) all use percentage changes. They allow firms and governments to predict the magnitude of quantity reactions to price, income, and cross-price changes.
弹性衡量一个变量对另一个变量变化的反应程度。关键的需方弹性（PED, YED, XED）与供给价格弹性（PES）均使用百分比变动。企业和政府可据此预判数量对价格、收入及交叉价格变化的反应幅度。
PED = %ΔQd / %ΔP
Price Elasticity of Demand (PED): if |PED| > 1 demand is price elastic; |PED| < 1 demand is price inelastic; |PED| = 1 unit elastic. A negative value confirms the law of demand.
需求价格弹性 (PED)：|PED| > 1 需求富有弹性，|PED| < 1 缺乏弹性，|PED| = 1 单位弹性。负值确认需求定律。
Arc PED = [(Q₂ − Q₁) / (Q₂ + Q₁)] / [(P₂ − P₁) / (P₂ + P₁)]
Arc (midpoint) PED avoids asymmetry when given discrete pairs. Always take the absolute value classification.
弧弹性（中点法）避免离散数据下的不对称性。分类时永远取绝对值。
YED = %ΔQd / %ΔY
Income Elasticity of Demand (YED): YED > 0 ⇒ normal good; YED < 0 ⇒ inferior good. YED > 1 ⇒ luxury (income elastic).
需求收入弹性 (YED)：YED > 0 正常品，YED < 0 劣等品，YED > 1 奢侈品（富有收入弹性）。
XED = %ΔQdA / %ΔPB
Cross Elasticity of Demand (XED): XED > 0 ⇒ substitutes; XED < 0 ⇒ complements; XED ≈ 0 ⇒ unrelated goods.
需求交叉弹性 (XED)：XED > 0 替代品，XED < 0 互补品，XED ≈ 0 无关品。
PES = %ΔQs / %ΔP
1 unit elastic. Key determinants include time period, spare capacity, and factor mobility.
供给价格弹性 (PES)：PES > 1 供给富有弹性，PES < 1 缺乏弹性，PES = 1 单位弹性。主要决定因素有时间段、闲置产能与要素流动性。
2. Revenue, Cost and Profit Metrics | 收益、成本与利润指标
Firms use revenue and cost measures to find the profit-maximising output. Understanding the shapes of marginal and average curves is essential for analysing market outcomes.
企业使用收益与成本指标寻找利润最大化产量。理解边际与平均曲线的形状对分析市场结果至关重要。
TR = P × Q
uals price times quantity sold. AR = TR / Q, so AR always equals price (P). MR = ΔTR / ΔQ.
总收益等于价格乘销售量。AR = TR / Q，因此 AR 永远等于价格 (P)。边际收益 MR = ΔTR / ΔQ。
TC = TFC + TVC
plus variable cost. AFC = TFC / Q, AVC = TVC / Q, AC = AFC + AVC = TC / Q. MC = ΔTC / ΔQ.
总成本为固定成本加变动成本。AFC = TFC / Q，AVC = TVC / Q，AC = AFC + AVC = TC / Q。边际成本 MC = ΔTC / ΔQ。
Profit = TR − TC
o economic profit). Supernormal profit occurs when TR > TC. Loss occurs when TR < TC.
正常利润发生在 TR = TC（经济利润为零）。超常利润 TR > TC。亏损 TR < TC。
MR = MC (Profit-maximisation rule)
All firms, irrespective of market structure, maximise profit where marginal revenue equals marginal cost, provided MC is rising above AVC.
无论何种市场结构，所有企业均在边际收益等于边际成本处实现利润最大化，且需 MC 在 AVC 上方上升阶段。
3. Market Structure Concentration Measures | 市场结构集中度指标
Concentration ratios and the Herfindahl-Hirschman Index (HHI) quantify the degree of market dominance and help distinguish between monopolistic, oligopolistic, and competitive markets.
集中度比率与赫芬达尔-赫希曼指数 (HHI) 量化市场支配程度，有助于区分垄断、寡头和竞争性市场。
CRn = Sum of market shares of the top n firms (%)
Commonly CR3, CR5, or CR10 are reported. A high CRn suggests concentrated market power; e.g., CR3 > 60% may indicate an oligopoly.
常用 CR₃, CR₅, CR₁₀ 报告。高 CRn 意味市场权力集中；如 CR₃ > 60% 可能表明寡头。
HHI = Σ (market shareᵢ)²
Using whole-number percentage shares, HHI ranges from near 0 (perfect competition) to 10 000 (pure monopoly). Values above 1 500–2 000 often signal highly concentrated markets.
使用百分数整数平方和，HHI 从接近 0（完全竞争）到 10 000（纯垄断）。高于 1 500–2 000 常是高度集中市场。
4. National Income Accounting | 国民收入核算
Gross Domestic Product can be measured via expenditure, income, or output approaches. Real values adjust for inflation, enabling meaningful comparisons over time.
国内生产总值可通过支出法、收入法和产出法核算。实际值剔除通胀，使跨期比较有意义。
Expenditure approach: Y = C + I + G + (X − M)
Consumption (C) + Investment (I) + Government spending (G) + Net exports (X − M). This is the aggregate demand identity in an open economy.
消费 (C) + 投资 (I) + 政府支出 (G) + 净出口 (X − M)。这是开放经济中的总需求恒等式。
Real GDP = Nominal GDP / (GDP Deflator / 100)
Real GDP) × 100. Inflation rate = (Deflator year₂ − Deflator year₁) / Deflator year₁ × 100%.
GDP 平减指数 = (名义 GDP / 实际 GDP) × 100。通胀率 = (平减指数₂ − 平减指数₁) / 平减指数₁ × 100%。
Economic growth rate = (GDP₂ − GDP₁) / GDP₁ × 100%
Usually calculated using real GDP to measure the change in the economy's productive capacity.
通常用实际 GDP 计算，衡量经济生产能力的变动。
5. The Multiplier and Fiscal Policy | 乘数与财政政策
The multiplier effect explains how an initial injection of spending leads to a larger final increase in national income. It depends on the marginal propensities to consume, save, or withdraw.
乘数效应解释初始支出注入如何导致国民收入出现更大幅度的最终增长。其大小取决于边际消费、储蓄或漏出倾向。
k = 1 / (1 − MPC) = 1 / MPS = 1 / MPW
PS = marginal propensity to save, MPW = marginal propensity to withdraw (MPS + MPT + MPM).
MPC 边际消费倾向，MPS 边际储蓄倾向，MPW 边际漏出倾向 (MPS + MPT + MPM)。
ΔY = k × ΔI (or k × ΔG for government spending changes)
An increase in autonomous investment or government spending raises Y by the multiplier times the injection. A simple tax change multiplier is −MPC/MPS.
自发性投资或政府支出的增加使 Y 增加量为乘数乘以注入额。简单税收乘数为 −MPC/MPS。
Balanced-budget multiplier = 1
exactly the amount of the spending increase, provided other withdrawals remain unchanged.
若 ΔG = ΔT，在漏出不变时国民收入上升额恰好等于支出增加额。
6. Inflation and Unemployment Metrics | 通货膨胀与失业指标
Consumer Price Index (CPI) and unemployment rate are key macroeconomic indicators. Measuring them accurately enables the assessment of economic stability and policy effectiveness.
消费者价格指数 (CPI) 与失业率是关键宏观指标，准确计量有助于评估经济稳定性与政策效果。
CPI = (Cost of basket in current year / Cost in base year) × 100
Inflation rate = [(CPI₂ − CPI₁) / CPI₁] × 100%. CPI is a weighted index; weights reflect household spending patterns.
通胀率 = [(CPI₂ − CPI₁) / CPI₁] × 100%。CPI 是加权指数，权重反映家庭支出模式。
Unemployment rate = (Number unemployed / Labour force) × 100%
d (those actively seeking work). The claimant count and ILO measures are common in the UK.
劳动力 = 就业人数 + 失业人数（积极求职者）。英国常用申领人数与国际劳工组织 (ILO) 衡量标准。
Okun's Law: Output gap ≈ −k × (u − uₙ)
Okun' of unemployment from its natural rate to the output gap. A rough approximation is ΔY/Y ≈ 3% − 2 × Δu.
奥肯定律将失业率偏离自然率与产出缺口联系起来。粗略近似为 ΔY/Y ≈ 3% − 2 × Δu。
7. Phillips Curve and Policy Trade-offs | 菲利普斯曲线与政策取舍
The Phillips curve illustrates the short-run trade-off between inflation and unemployment, while the long-run Phillips curve is vertical at the natural rate of unemployment, shaped by expectations.
菲利普斯曲线展示通胀与失业的短期权衡取舍，而长期菲利普斯曲线因预期在自然失业率处垂直。
Short-run Phillips curve: + supply shocks. In the short run, lower unemployment may coincide with higher inflation.
短期菲利普斯曲线：π = πₑ − β(u − uₙ) + 供给冲击。短期内，较低失业可能伴随较高通胀。
Long-run Phillips curve: uₙ, any inflation rate is consistent with the natural rate; no permanent trade-off exists.
长期菲利普斯曲线：在 u = uₙ 处，任何通胀率与自然率并存；不存在永久权衡。
8. International Trade and Comparative Advantage | 国际贸易与比较优势
Comparative advantage is the foundation of gains from trade. Countries specialise based on lower opportunity cost rather than absolute productivity differences alone.
比较优势是贸易得益的基础。各国依据较低的机会成本而非单凭绝对生产率差异进行专业化。
Opportunity cost of X = Units of Y sacrificed / Units of X obtained
A country has a comparative advantage in a good if its opportunity cost is lower than the trading partner's. Mutually beneficial terms of trade lie between the two opportunity cost ratios.
若一国生产某商品的机会成本低于贸易伙伴，该国即具有比较优势。互利的贸易条件介于两国机会成本比率之间。
Terms of Trade (TOT) = (Index of export prices / Index of import prices) × 100
An improvement (rise) in TOT means a country can buy more imports for a given volume of exports. TOT > 100 signifies an improvement over the base year.
贸易条件 (TOT) 改善（上升）意味该国给定出口量可买更多进口品。TOT > 100 表明较基期改善。
9. Exchange Rates and Balance of Payments | 汇率与国际收支
Exchange rates express the value of one currency in terms of another. The balance of payments records all transactions between residents and the rest of the world, and must sum to zero by accounting convention.
汇率表示一种货币以另一种货币计量的价值。国际收支记录居民与世界其它地区的所有交易，按惯例总和为零。
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