📚 Year 12 SQA Economics Formula & Theorem Quick Reference Handbook | Year 12 SQA 经济公式定理速查手册
Mastering the core formulas and economic theorems is essential for success in the SQA Higher Economics course. This quick reference handbook has been carefully compiled to bring together every key equation, relationship, and analytical theorem that you are expected to know, understand, and apply under examination conditions. Whether you are revising for the question paper or checking your understanding of pivotal models such as elasticity, cost theory, the multiplier process, and international trade, this guide will serve as your reliable companion. Each entry is presented with precise definitions, standard formulas, and worked-style explanations that clarify both the mathematical logic and the economic intuition behind the numbers.
掌握核心公式与经济定理是 SQA 高等经济课程取得理想成绩的关键。这本速查手册精心汇集了你在考试中必须知晓、理解并能够灵活运用的每一项关键等式、数量关系和分析定理。无论你是在为笔试刷题复习，还是在检查自己对弹性理论、成本分析、乘数过程和国际贸易等重要模型的理解，这本手册都将是你可靠的伙伴。每个条目都包含精确定义、标准公式，并配有解释性说明，既阐明了数学逻辑，也解析了数字背后的经济学直觉。
1. Price Elasticity of Demand (PED) | 需求的价格弹性
Price elasticity of demand measures the responsiveness of quantity demanded to a change in the price of the good itself. The standard formula is: PED = (% change in quantity demanded) / (% change in price). It is almost always a negative number due to the law of demand, but we typically use the absolute value to describe elasticity. When |PED| > 1, demand is elastic and total revenue moves in the opposite direction to price; when |PED| < 1, demand is inelastic and total revenue moves in the same direction as price; unit elasticity occurs when |PED| = 1, meaning total revenue remains constant as price changes.
需求的价格弹性衡量需求量对商品自身价格变化的反应程度。标准公式为：PED =（需求量变动的百分比）÷（价格变动的百分比）。由于需求定律，该数值几乎总是负数，但我们通常用绝对值来描述弹性程度。当|PED| > 1 时，需求富有弹性，总收益与价格反向变动；当|PED|<1 时，需求缺乏弹性，总收益与价格同向变动；当|PED|=1 时为单位弹性，此时总收益不随价格变化而改变。
To calculate percentage changes accurately, always use the midpoint (arc) method unless the question instructs otherwise: % change = (new value – original value) / midpoint × 100, where midpoint = (original + new) / 2. The factors affecting PED include the availability of substitutes, the degree of necessity, the proportion of income spent, and the time period considered. Examiners frequently ask you to interpret PED values and link them to real-world pricing strategies.
要准确计算百分比变化，除非题目另有说明，一般应采用中点（弧弹性）法：变动百分比 =（新值–原值）÷ 中点值 × 100，中点值 =（原值 + 新值）÷ 2。影响 PED 的因素包括替代品的可得性、必需程度、支出占收入的比例以及所考虑的时间长度。考官经常要求你解读 PED 值并将其与实际的定价策略联系起来。
2. Income Elasticity of Demand (YED) | 需求的收入弹性
Income elasticity of demand measures how quantity demanded responds to changes in consumers’ income. Formula: YED = (% change in quantity demanded) / (% change in income). The sign of YED is crucial for classifying goods: a positive YED indicates a normal good, while a negative YED indicates an inferior good. Among normal goods, a YED greater than 1 identifies a luxury good, and a YED between 0 and 1 identifies a necessity. This classification helps businesses forecast demand over the business cycle and informs government policy on indirect taxation.
需求的收入弹性衡量需求量对消费者收入变化的反应程度。公式为：YED =（需求量变动的百分比）÷（收入变动的百分比）。YED 的符号对商品分类至关重要：正 YED 表示正常品，负 YED 表示低档品。在正常品中，YED 大于 1 的为奢侈品，介于 0 到 1 之间的为必需品。这种分类有助于企业根据经济周期预测需求，也为政府制定间接税政策提供依据。
When calculating YED, the same midpoint formula applies to ensure consistency. Remember that for inferior goods, an increase in income leads to a decrease in demand, shifting the demand curve to the left. Long-term changes in a country’s living standards can shift the pattern of YED across different sectors, making this concept highly relevant for structural change analysis.
计算 YED 时同样使用中点公式以确保一致性。要记住，对于低档品，收入增加会导致需求下降，需求曲线向左移动。一国生活水平的长期变化会改变不同行业的 YED 模式，使得该概念与结构变迁分析密切相关。
3. Cross Elasticity of Demand (XED) | 需求的交叉弹性
Cross elasticity of demand measures the responsiveness of demand for one good (Good A) to a change in the price of another good (Good B). Formula: XED = (% change in quantity demanded of A) / (% change in price of B). The sign and magnitude of XED reveal the relationship between the two goods: a positive XED signals substitutes, a negative XED signals complements, and a value close to zero suggests the goods are independent. The closer the absolute value is to zero, the weaker the relationship.
需求的交叉弹性衡量一种商品（A）的需求量对另一种商品（B）价格变化的反应程度。公式为：XED =（A 需求量变动的百分比）÷（B 价格变动的百分比）。XED 的符号和数值揭示了两种商品之间的关系：正 XED 表示替代品，负 XED 表示互补品，数值接近零则表明两种商品相互独立。绝对值越接近零，关系越弱。
Firms use XED to map out their competitive landscape and to anticipate the impact of rivals’ pricing decisions. For example, a high positive XED between two brands of coffee suggests that a price cut by one will significantly reduce demand for the other. Similarly, a strong negative XED between printers and ink cartridges implies that a rise in printer prices will reduce the demand for cartridges as well.
企业利用 XED 来勾勒竞争格局并预判对手定价决策的影响。例如，两种咖啡品牌之间较高的正 XED 意味着其中一方降价会显著减少另一方的需求。同样，打印机和墨盒之间强烈的负 XED 意味着打印机价格上涨也会降低墨盒的需求。
4. Price Elasticity of Supply (PES) | 供给的价格弹性
Price elasticity of supply measures the responsiveness of quantity supplied to a change in price. Formula: PES = (% change in quantity supplied) / (% change in price). Unlike PED, PES is usually positive because the law of supply states that quantity supplied moves in the same direction as price. PES can range from perfectly inelastic (0) to perfectly elastic (∞). The key determinants of PES are the time period, the mobility of factors of production, the level of spare capacity, and the ease of storing inventory.
供给的价格弹性衡量供给量对价格变化的反应程度。公式为：PES =（供给量变动的百分比）÷（价格变动的百分比）。与 PED 不同，PES 通常为正，因为供给定律表明供给量与价格同向变动。PES 的范围可以从完全无弹性（0）到完全弹性（∞）。决定 PES 的关键因素包括时间周期、生产要素的流动性、闲置产能水平以及库存存储的难易程度。
In the short run, supply tends to be relatively inelastic because firms face fixed capacity constraints. Over time, as firms can invest in new capital and new entrants can join the market, supply becomes more price elastic. A solid understanding of PES enables you to explain why agricultural prices are often volatile while manufactured goods’ prices are comparatively stable.
短期来看，由于企业面临固定的产能约束，供给往往相对缺乏弹性。随着时间的推移，企业可以进行新的资本投资且新厂商可以进入市场，供给变得更有弹性。扎实理解 PES 能让你解释为什么农产品价格常剧烈波动而工业品价格相对稳定。
5. Total Revenue and the Elasticity Link | 总收益与弹性关联
Total revenue (TR) is the income a firm receives from selling its product, calculated as TR = Price × Quantity. The relationship between price changes and total revenue depends entirely on the price elasticity of demand. If demand is elastic, a price decrease raises total revenue because the proportionate increase in quantity demanded exceeds the proportionate fall in price. If demand is inelastic, a price decrease reduces total revenue, and a price increase raises total revenue.
总收益（TR）是企业销售产品所获得的收入，计算公式为：TR = 价格 × 数量。价格变化与总收益之间的关系完全取决于需求的价格弹性。若需求富有弹性，降价会使总收益增加，因为需求量增加的比例大于价格下降的比例。若需求缺乏弹性，降价反而会使总收益减少，而提价则会增加总收益。
A useful summary table can help you remember these outcomes:
| Elasticity | Price Change | Effect on TR |
|---|---|---|
| Elastic (|PED|>1) | Decrease | TR rises |
| Elastic (|PED|>1) | Increase | TR falls |
| Inelastic (|PED|<1) | Decrease | TR falls |
| Inelastic (|PED|<1) | Increase | TR rises |
A thorough grasp of this linkage is essential for microeconomic analysis and for evaluating pricing strategies of both private firms and state-owned enterprises. In an exam, always state the direction of change and support your conclusion with reference to the elastic or inelastic nature of the product.
透彻理解这一关联对于微观经济分析以及评价私企和国有企业的定价策略都至关重要。在考试中，务必说明变化方向，并引用产品的弹性或缺乏弹性特征来支撑你的结论。
6. Costs of Production | 生产成本
Cost theory underpins the supply decisions of firms. The core cost formulas you must know are: Total Cost (TC) = Total Fixed Cost (TFC) + Total Variable Cost (TVC). Average Total Cost (ATC) = TC / Quantity (Q). Average Fixed Cost (AFC) = TFC / Q. Average Variable Cost (AVC) = TVC / Q. Marginal Cost (MC) is the additional cost of producing one more unit and is calculated as MC = ΔTC / ΔQ. Since fixed costs do not change with output, MC is also equal to ΔTVC / ΔQ.
成本理论是企业供给决策的基础。你必须掌握的核心成本公式包括：总成本（TC）= 总固定成本（TFC）+ 总可变成本（TVC）。平均总成本（ATC）= TC ÷ 产量（Q）。平均固定成本（AFC）= TFC ÷ Q。平均可变成本（AVC）= TVC ÷ Q。边际成本（MC）是每多生产一单位产品所增加的成本，计算为 MC = ΔTC ÷ ΔQ。由于固定成本不随产量变化，MC 也等于 ΔTVC ÷ ΔQ。
The law of diminishing marginal returns explains why the MC curve is typically U-shaped in the short run. As more variable inputs are added to a fixed factor, marginal product initially rises but eventually falls, causing MC to fall and then rise. The point where MC equals ATC marks the minimum efficient scale. Drawing and interpreting these cost curves accurately is a recurring skill tested in the SQA exam.
边际报酬递减规律解释了为什么短期边际成本曲线通常呈 U 形。随着更多的可变投入被追加到固定要素上，边际产量一开始会上升但最终会下降，导致边际成本先降后升。MC 等于 ATC 的那一点标志着最低有效规模。准确绘制并解读这些成本曲线是 SQA 考试中反复考查的技能。
7. Revenue and Profit Maximisation | 收益与利润最大化
Beyond total revenue, you need to work with average revenue (AR) and marginal revenue (MR). AR = TR / Q, which is also the demand curve facing the firm. MR = ΔTR / ΔQ. For a price-taking firm in perfect competition, MR = AR = Price, so the demand curve is perfectly elastic. For a price-making firm with a downward-sloping demand curve, MR lies below AR, and the MR curve is twice as steep as the AR curve when demand is linear.
除了总收益，你还需要掌握平均收益（AR）和边际收益（MR）。AR = TR ÷ Q，这也是企业面对的需求曲线。MR = ΔTR ÷ ΔQ。对于完全竞争中的价格接受者，MR = AR = 价格，因此需求曲线是完全弹性的。对于面临向下倾斜需求曲线的定价者，MR 低于 AR，且当需求为线性时，MR 曲线的斜率是 AR 曲线的两倍。
A firm maximises profit where marginal cost equals marginal revenue (MC = MR), provided that price covers average variable cost in the short run. Profit is calculated as (AR – ATC) × Q. This rule is universal and applies to all market structures. Examiners expect you to identify the profit-maximising output on a diagram and to shade the area of supernormal profit or loss.
企业在边际成本等于边际收益（MC = MR）处实现利润最大化，条件是在短期内价格能够覆盖平均可变成本。利润的计算公式为：（AR – ATC）× Q。这一规则具有普适性，适用于所有市场结构。考官希望你在图形中识别出利润最大化的产量，并标出超额利润或亏损的区域。
8. The Multiplier Effect | 乘数效应
The multiplier is a cornerstone of Keynesian macroeconomics and a frequent SQA topic. The simple formula is: k = 1 / (1 – MPC) or k = 1 / MPS, where MPC is the marginal propensity to consume and MPS is the marginal propensity to save (MPC + MPS = 1). The multiplier tells us that an initial injection of spending (ΔJ) will lead to a larger final increase in national income (ΔY), such that ΔY = k × ΔJ.
乘数是凯恩斯宏观经济学的基石，也是 SQA 常见考点。简单公式为：k = 1 ÷ (1 – MPC) 或 k = 1 ÷ MPS，其中 MPC 为边际消费倾向，MPS 为边际储蓄倾向（MPC + MPS = 1）。乘数告诉我们，一笔初始注入的支出（ΔJ）会导致国民收入（ΔY）发生更大的最终增加，即 ΔY = k × ΔJ。
When the government sector and foreign trade are introduced, the marginal propensity to withdraw (MPW) becomes MPW = MPS + MPT + MPM, where MPT is the marginal propensity to tax and MPM is the marginal propensity to import. The open-economy multiplier is then k = 1 / MPW. Recognizing that real-world multipliers are smaller than the simplified model suggests is an important evaluative point.
当引入政府部门和对外贸易时，边际漏出倾向（MPW）变为 MPW = MPS + MPT + MPM，其中 MPT 为边际税收倾向，MPM 为边际进口倾向。开放经济条件下的乘数为 k = 1 ÷ MPW。认识到现实中的乘数比简化模型所显示的要小，是一个重要的评析要点。
9. National Income and the Circular Flow | 国民收入与循环流转
National income can be measured using three approaches that should, in theory, yield the same total: the output method, the income method, and the expenditure method. The fundamental identity is: GDP = C + I + G + (X – M), where C is household consumption, I is investment, G is government spending, X is exports, and M is imports. You may also be required to move between Gross Domestic Product (GDP) and Gross National Product (GNP) by adding net property income from abroad.
国民收入有三种核算方法，理论上三者应得出相等的总量：产出法、收入法和支出法。基本恒等式为：GDP = C + I + G + (X – M)，其中 C 为家庭消费，I 为投资，G 为政府支出，X 为出口，M 为进口。你可能还需要在 GDP 和 GNP（国民生产总值）之间进行换算，此时要加上来自国外的净财产收入。
Understanding the circular flow of income and the concepts of injections (investment, government spending, exports) and withdrawals (saving, taxation, imports) is essential for explaining macroeconomic equilibrium. Equilibrium occurs when total injections equal total withdrawals. The circular flow diagram helps visualise how an initial change can ripple through the economy via the multiplier.
理解收入循环流转以及注入项（投资、政府支出、出口）和漏出项（储蓄、税收、进口）的概念对于解释宏观经济均衡是必不可少的。当注入总额等于漏出总额时，经济达到均衡。循环流转图有助于直观展示初始变化如何通过乘数效应波及整个经济。
10. Comparative Advantage and Terms of Trade | 比较优势与贸易条件
Comparative advantage exists when a country can produce a good at a lower opportunity cost than another country. To determine this, set up a table showing the output of two goods, X and Y, that each country can produce with the same resources. Calculate the opportunity cost ratio for each. The country with the lower opportunity cost in good X has a comparative advantage in X and should specialise in it. The gains from trade arise when countries specialise according to comparative advantage and trade at a terms of trade that lies between their respective opportunity cost ratios.
当一个国家能以比另一个国家更低的机会成本生产某种产品时，就存在比较优势。要确定比较优势，需要先列出一个表格，显示每个国家用相同资源所能生产的 X 和 Y 两种产品的产量。然后分别计算每个国家生产这两种产品的机会成本比。生产产品 X 机会成本较低的国家就在 X 上具有比较优势，应该专门生产该产品。贸易收益来自于各国按照比较优势进行专业化生产，并以介于各自机会成本比之间的贸易条件进行交换。
The terms of trade index is given by (index of export prices / index of import prices) × 100. An improvement in the terms of trade means a country can buy more imports for a given volume of exports, which raises living standards. However, worsening terms of trade can harm an economy heavily reliant on primary product exports. This theorem is frequently linked to the Prebisch-Singer hypothesis in development economics.
贸易条件指数的计算公式为：（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数量的出口可以换回更多的进口，从而提高生活水平。然而，贸易条件恶化可能会严重损害依赖初级产品出口的经济体。该定理在发展经济学中常与普雷维什-辛格假说联系起来。
11. Unemployment and Inflation Measurement | 失业与通胀的度量
The unemployment rate is calculated as (number of unemployed / labour force) × 100, where the labour force includes all those actively seeking work plus those in employment. The claimant count and the Labour Force Survey (ILO measure) are the two main measures used in the UK. You must know the different types of unemployment: cyclical (demand-deficient), structural, frictional, and seasonal. Each has distinct causes and requires different policy responses.
失业率的计算公式为：（失业人数 ÷ 劳动力）× 100，其中劳动力包括所有正在积极求职者以及就业者。英国的两种主要测量方法是申请失业救济人数和国际劳工组织标准下的劳动力调查。你必须了解失业的不同类型：周期性（需求不足型）、结构性、摩擦性和季节性。每种类型都有不同的成因，需要不同的政策应对。
Inflation is typically measured by the Consumer Price Index (CPI). The annual inflation rate is (% change in CPI) = (CPI current year – CPI previous year) / CPI previous year × 100. You may also encounter the Retail Price Index (RPI) and the GDP deflator. The GDP deflator is calculated as (Nominal GDP / Real GDP) × 100, and it captures the price changes of all domestically produced goods and services, not just those in a consumer basket.
通货膨胀通常用消费者价格指数（CPI）来衡量。年度通胀率计算公式为：（当年 CPI – 上年 CPI）÷ 上年 CPI × 100。你还可能遇到零售价格指数（RPI）和 GDP 平减指数。GDP 平减指数的计算公式为：（名义 GDP ÷ 实际 GDP）× 100，它涵盖了所有国内生产商品和服务的价格变化，而不仅仅是一篮子消费品。
12. Fiscal Policy and the Budget Balance | 财政政策与预算平衡
The government’s budget balance is the difference between its total revenue (primarily taxation, T) and its total spending (G). The formula is Budget balance = T – G. A positive balance is a budget surplus, while a negative balance is a budget deficit. The structural budget position refers to the part of the deficit or surplus that is not attributable to the economic cycle, giving a clearer picture of the underlying fiscal stance.
政府预算平衡是其总收入（主要是税收 T）与总支出（G）之间的差额。公式为：预算平衡 = T – G。正余额为预算盈余，负余额为预算赤字。结构性预算状况是指赤字或盈余中不受经济周期影响的部分，它能更清晰地反映潜在的财政立场。
The overall impact of fiscal policy on aggregate demand can be analysed through the net injection (G – T). Expansionary fiscal policy (increasing G or cutting T) boosts aggregate demand, shifting the AD curve to the right, but it may widen the deficit and lead to crowding out of private investment if financed by borrowing. Contractionary policy does the opposite. A strong numerical grasp of these relationships allows you to critically evaluate government policy statements using demand-side models.
财政政策对总需求的整体影响可通过净注入（G – T）来分析。扩张性财政政策（增加 G 或减少 T）会提振总需求，使 AD 曲线右移，但若通过借贷融资，可能会扩大赤字并挤出私人投资。紧缩性财政政策则相反。熟练掌握这些数量关系，使你能够运用需求侧模型批判性地评估政府的政策声明。
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