📚 SQA Economics Formula & Theorems Quick Reference Handbook | SQA 经济学公式定理速查手册
This comprehensive handbook provides essential formulas and theorems required for the SQA Economics syllabus at Year 11 (National 5/Higher). It covers microeconomic principles, elasticity measures, market structures, macroeconomic indicators, fiscal and monetary policy multipliers, and international trade calculations. Use this resource to master quantitative skills and build confidence for exam success.
本速查手册涵盖了Year 11 SQA经济学课程所必需的核心公式与定理，包括微观经济学原理、弹性测量、市场结构、宏观经济指标、财政与货币政策乘数，以及国际贸易相关计算。通过本手册掌握定量分析技能，提升应试信心，从容应对考试。
1. Demand, Supply, and Equilibrium | 需求、供给与市场均衡
mand equation is Qd = a − bP, where a is the intercept and b is the slope. Supply is often expressed as Qs = c + dP. Market equilibrium occurs when Qd = Qs.
需求函数表示需求量 (Qd) 随价格 (P)、收入 (Y)、偏好及相关商品价格的变化关系。典型的线性需求方程为 Qd = a − bP，其中 a 为截距，b 为斜率。供给通常表达为 Qs = c + dP。市场均衡出现在 Qd = Qs 时。
Equilibrium condition: Qd = Qs
均衡条件：Qd = Qs
Demand function (linear): Qd = a − bP
需求函数（线性）：Qd = a − bP
Supply function (linear): Qs = c + dP
供给函数（线性）：Qs = c + dP
A change in demand shifts the demand curve, while a change in quantity demanded is a movement along the curve caused by a price change. The same distinction applies to supply.
需求的变化导致需求曲线平移，而需求量的变化则是由价格变动引起的沿曲线移动。供给同理。
2. Price Elasticity of Demand (PED) | 需求价格弹性
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. A value greater than 1 indicates elastic demand; less than 1 indicates inelastic demand; equal to 1 is unit elastic.
需求价格弹性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的百分比除以价格变动的百分比。数值大于1表示富有弹性；小于1表示缺乏弹性；等于1为单位弹性。
PED = %ΔQd ÷ %ΔP
需求价格弹性 = 需求量变动百分比 ÷ 价格变动百分比
PED = (ΔQd / Qd) ÷ (ΔP / P)
需求价格弹性 = (ΔQd / Qd) ÷ (ΔP / P)
rage P). This avoids the discrepancy between upward and downward movements on the demand curve.
当使用弧弹性的中点公式时，计算方法为：需求价格弹性 = (ΔQd / 平均Qd) ÷ (ΔP / 平均P)。这样可避免需求曲线上行与下行移动时的数值差异。
PED is closely related to total revenue: if demand is elastic, a price reduction raises total revenue; if inelastic, a price reduction lowers total revenue.
需求价格弹性与总收入密切相关：若需求富有弹性，降价将增加总收入；若缺乏弹性，降价则减少总收入。
3. Income Elasticity of Demand (YED) | 需求收入弹性
YED measures how quantity demanded responds to a change in consumer income. It helps classify goods as normal (YED > 0) or inferior (YED < 0). For normal goods, a YED greater than 1 indicates luxury goods, while between 0 and 1 indicates necessities.
需求收入弹性衡量需求量对消费者收入变动的反应。它用于将商品分为正常品 (YED > 0) 或劣等品 (YED < 0)。对于正常品，YED 大于1为奢侈品，介于0与1之间为必需品。
YED = %ΔQd ÷ %ΔIncome
需求收入弹性 = 需求量变动百分比 ÷ 收入变动百分比
YED = (ΔQd / Qd) ÷ (ΔY / Y)
需求收入弹性 = (ΔQd / Qd) ÷ (ΔY / Y)
Firms use YED to forecast sales growth as the economy expands or contracts, aiding in production and investment planning.
企业利用需求收入弹性预测经济扩张或收缩时的销售增长，从而辅助生产和投资规划。
4. Cross Elasticity of Demand (XED) | 需求交叉弹性
XED measures the sensitivity of demand for one good (X) to a change in the price of another good (Y). Positive XED indicates substitutes; negative XED indicates complements; zero implies no relationship.
需求交叉弹性衡量一种商品 (X) 的需求对另一种商品 (Y) 价格变动的敏感度。正值表示替代品；负值表示互补品；零表示无关商品。
XED = %ΔQd of good X ÷ %ΔP of good Y
需求交叉弹性 = 商品X需求量变动百分比 ÷ 商品Y价格变动百分比
XED = (ΔQdₓ / Qdₓ) ÷ (ΔPᵧ / Pᵧ)
需求交叉弹性 = (ΔQdₓ / Qdₓ) ÷ (ΔPᵧ / Pᵧ)
Knowledge of XED assists businesses in pricing strategy and in anticipating competitive responses when rivals alter their prices.
掌握需求交叉弹性有助于企业制定定价策略，并预判竞争对手价格变动时的市场反应。
5. Price Elasticity of Supply (PES) | 供给价格弹性
PES measures the responsiveness of quantity supplied to a price change. Determinants include time period, spare production capacity, and the ease of storing inventory. PES is positive and can range from zero (perfectly inelastic) to infinity (perfectly elastic).
供给价格弹性衡量供给量对价格变动的反应。影响因素包括时间周期、闲置产能和库存储存难易程度。供给价格弹性为正，范围从零（完全无弹性）到无穷大（完全弹性）。
PES = %ΔQs ÷ %ΔP
供给价格弹性 = 供给量变动百分比 ÷ 价格变动百分比
PES = (ΔQs / Qs) ÷ (ΔP / P)
供给价格弹性 = (ΔQs / Qs) ÷ (ΔP / P)
In the immediate market period, supply is often highly inelastic; in the long run, firms can adjust all inputs, making supply more elastic.
在极短期市场，供给通常高度缺乏弹性；而在长期，企业可调整所有投入要素，使供给更具弹性。
6. Consumer and Producer Surplus | 消费者剩余与生产者剩余
Consumer surplus is the difference between the price consumers are willing to pay and the market price they actually pay, summed over all units purchased. Producer surplus is the difference between the market price and the minimum price producers are willing to accept. Total economic welfare is the sum of both surpluses.
消费者剩余是消费者愿意支付的最高价格与实际支付市场价格之间的差额，按购买总数加总。生产者剩余是市场价格与生产者愿意接受的最低价格之间的差额。总经济福利为两者之和。
Consumer Surplus = ∫(Demand curve) − (Price × Quantity)
消费者剩余 = ∫(需求曲线) − (价格 × 数量)
Producer Surplus = (Price × Quantity) − ∫(Supply curve)
生产者剩余 = (价格 × 数量) − ∫(供给曲线)
For linear functions, consumer surplus is the area of the triangle above price and below the demand curve. Similarly, producer surplus is the area below price and above the supply curve.
在线性函数下，消费者剩余是价格线上方、需求曲线下方的三角形面积；生产者剩余是价格线下方、供给曲线上方的三角形面积。
7. Costs, Revenue, and Profit Maximisation | 成本、收益与利润最大化
here marginal cost (MC) equals marginal revenue (MR). For perfect competition, P = MR, so the rule becomes P = MC.
企业以利润最大化为目标，利润 (π) = 总收入 (TR) − 总成本 (TC)。所有市场结构下利润最大化的条件是边际成本 (MC) 等于边际收益 (MR)。在完全竞争市场中，价格等于边际收益，因此规则变为 P = MC。
Profit (π) = TR − TC
利润 = 总收入 − 总成本
Profit maximisation: MC = MR
利润最大化条件：MC = MR
Q. Marginal cost is the change in total cost from producing one more unit: MC = ΔTC ÷ ΔQ.
关键成本概念：平均总成本 (ATC) = 总成本 ÷ 产量；平均可变成本 (AVC) = 总可变成本 ÷ 产量；平均固定成本 (AFC) = 总固定成本 ÷ 产量。边际成本是增加一单位产量所引起的总成本变化：MC = ΔTC ÷ ΔQ。
rginal revenue MR = ΔTR ÷ ΔQ. Under imperfect competition, MR lies below the demand curve.
总收入 TR = P × Q。平均收益 AR = TR ÷ Q = P。边际收益 MR = ΔTR ÷ ΔQ。在不完全竞争市场，边际收益曲线位于需求曲线下方。
8. Macroeconomic Indicators | 宏观经济指标
e 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.
国内生产总值 (GDP) 衡量一年内一国境内生产的最终商品与服务的总价值。可通过支出法计算：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。
GDP = C + I + G + (X − M)
国内生产总值 = 消费 + 投资 + 政府支出 + (出口 − 进口)
The inflation rate is measured as the annual percentage change in a price index such as the Consumer Price Index (CPI).
失业率指劳动力中没有工作但积极寻找工作的百分比。劳动力 = 就业者 + 失业者。通货膨胀率通过居民消费价格指数 (CPI) 等价格指数的年度百分比变化来测量。
Unemployment Rate = (Unemployed ÷ Labour Force) × 100
失业率 = (失业人口 ÷ 劳动力) × 100
Inflation Rate = (CPIₜ − CPIₜ₋₁) ÷ CPIₜ₋₁ × 100
通货膨胀率 = (本期CPI − 上期CPI) ÷ 上期CPI × 100
al GDP for inflation, using a GDP deflator: Real GDP = Nominal GDP ÷ (GDP Deflator ÷ 100).
实际 GDP 使用 GDP 平减指数剔除通胀影响：实际 GDP = 名义 GDP ÷ (GDP 平减指数 ÷ 100)。
9. Multiplier Effect and Fiscal Policy | 乘数效应与财政政策
The multiplier (k) shows how an initial injection of spending leads to a larger final increase in national income. The simple multiplier is related to the marginal propensity to consume (MPC) or the marginal propensity to withdraw (MPW, which includes saving, taxes, and imports).
乘数 (k) 表明初始支出注入如何导致国民收入更大幅度的最终增长。简单乘数与边际消费倾向 (MPC) 或边际漏出倾向 (MPW，包括储蓄、税收和进口) 相关。
k = 1 ÷ (1 − MPC) = 1 ÷ MPW
乘数 = 1 ÷ (1 − MPC) = 1 ÷ 边际漏出倾向
Change in National Income = k × Initial Injection
国民收入变动 = 乘数 × 初始注入量
Fiscal policy uses government spending (G) and taxation (T) to influence the economy. A balanced budget multiplier can be derived, and the multiplier process helps evaluate the impact of changes in G or T on GDP.
财政政策通过政府支出 (G) 和税收 (T) 影响经济。可推导平衡预算乘数，乘数过程有助于评估政府支出或税收变动对 GDP 的影响。
Automatic stabilisers, such as progressive taxes and unemployment benefits, work without explicit government action to moderate the economic cycle.
自动稳定器（如累进税和失业救济金）无需政府明确行动，即可起到缓和经济周期波动的作用。
10. International Trade and Exchange Rates | 国际贸易与汇率
The terms of trade index compares a country's export prices to its import prices. An improvement means export prices rise relative to import prices, allowing more imports to be purchased per unit of exports.
贸易条件指数比较一国出口价格与进口价格的关系。贸易条件改善意味着出口价格相对进口价格上升，单位出口可购买更多进口品。
Terms of Trade Index = (Index of Export Prices ÷ Index of Import Prices) × 100
贸易条件指数 = (出口价格指数 ÷ 进口价格指数) × 100
Exchange rates can be expressed as the price of one currency in terms of another. A floating exchange rate is determined by supply and demand in foreign exchange markets. The current account of the balance of payments includes the trade balance (X − M), net income from abroad, and net transfers.
汇率表示为一种货币以另一种货币计价的价格。浮动汇率由外汇市场的供求关系决定。国际收支经常账户包括贸易差额 (X − M)、海外净收入和净转移支付。
A depreciation (weakening) of a currency lowers export prices and raises import prices, potentially improving the trade balance if the Marshall-Lerner condition holds: the sum of price elasticities of demand for exports and imports is greater than 1.
货币贬值（走弱）会降低出口价格、提高进口价格，若满足马歇尔-勒纳条件（出口需求弹性与进口需求弹性之和大于1），则可能改善贸易平衡。
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