Pre-U AQA Economics: Formula & Theorem Quick Reference Handbook | Pre-U AQA 经济：公式定理速查手册

📚 Pre-U AQA Economics: Formula & Theorem Quick Reference Handbook | Pre-U AQA 经济：公式定理速查手册

This quick reference handbook compiles the essential formulas, theorems and key relationships required for the AQA Pre-U Economics examination. It is designed to help you revise efficiently, linking each tool to the relevant theoretical context. Use it alongside past papers and case studies to deepen your ability to apply economic reasoning under timed conditions.

本速查手册汇集了 AQA Pre-U 经济学考试所需的核心公式、定理和关键关系，旨在帮助你高效复习，并将每个工具与相应的理论背景联系起来。请结合历年真题和案例分析一起使用，以加深在限时条件下运用经济推理的能力。

1. Demand, Supply and Elasticity | 需求、供给与弹性

Price Elasticity of Demand (PED) measures responsiveness of quantity demanded to a change in price. Using the midpoint method: PED = (ΔQd / average Qd) ÷ (ΔP / average P). The value is always negative, but we refer to its absolute size.

需求价格弹性 (PED) 衡量需求量对价格变化的反应程度。采用中点法时：PED = (ΔQd / 平均 Qd) ÷ (ΔP / 平均 P)。数值本身为负，但我们通常关注其绝对值。

Income Elasticity of Demand (YED) is YED = %ΔQd / %ΔY. A positive YED indicates a normal good; a negative YED an inferior good. Luxuries have YED > 1, necessities have 0 < YED < 1.

需求收入弹性 (YED) 为 YED = %ΔQd / %ΔY。YED 为正表明该商品是正常品；为负表明是低档品。奢侈品的 YED > 1，必需品的 YED 介于 0 和 1 之间。

Cross Elasticity of Demand (XED) = %ΔQd of good A / %ΔP of good B. Substitutes have XED > 0; complements have XED < 0; unrelated goods have XED close to zero.

需求交叉弹性 (XED) = 商品 A 需求量变动% / 商品 B 价格变动%。替代品的 XED > 0；互补品的 XED < 0；无关商品的 XED 接近零。

Price Elasticity of Supply (PES) = %ΔQs / %ΔP. The main determinants are time period, spare capacity, stock levels and the ease of factor substitution.

供给价格弹性 (PES) = %ΔQs / %ΔP。主要决定因素包括时间长短、闲置产能、库存水平以及要素替代的难易程度。

Theorem – Elasticity and total revenue: When demand is elastic (|PED| > 1), a price cut raises total revenue. When demand is inelastic (|PED| < 1), a price rise raises total revenue. Total revenue is maximised where |PED| = 1.

定理 – 弹性与总收入关系：当需求富有弹性 (|PED| > 1) 时，降价会增加总收入。当需求缺乏弹性 (|PED| < 1) 时，提价会增加总收入。总收入在 |PED| = 1 处达到最大。

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2. Consumer Choice and Utility | 消费者选择与效用

Total Utility (TU) is the satisfaction from consuming a given quantity. Marginal Utility (MU) = ΔTU / ΔQ. The Law of Diminishing Marginal Utility states that as consumption increases, MU eventually declines.

总效用 (TU) 是消费一定数量商品所带来的满足感。边际效用 (MU) = ΔTU / ΔQ。边际效用递减定律指出，随着消费量增加，边际效用最终会下降。

Consumer equilibrium (cardinal approach): A rational consumer allocates spending so that MUx / Px = MUy / Py. This ensures the last pound spent on each good yields the same marginal utility.

消费者均衡（基数法）：理性消费者会如此分配支出：MUx / Px = MUy / Py。这确保花在每种商品上的最后一英镑带来的边际效用相等。

Indifference curve analysis: The consumer’s optimum is where the marginal rate of substitution (MRS) equals the price ratio, i.e. MRS = Px / Py, at the tangency between the budget line and the highest attainable indifference curve.

无差异曲线分析：消费者的最优选择发生在边际替代率 (MRS) 等于价格比率之处，即 MRS = Px / Py，这是预算线与可达到的最高无差异曲线相切的点。

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3. Production, Costs and Revenue | 生产、成本与收益

Law of Diminishing Returns (short run): As more of a variable factor is added to a fixed factor, the marginal product eventually falls. Marginal Product (MP) = ΔTP / ΔL.

边际报酬递减律（短期）：在固定要素基础上持续增加可变要素，边际产量最终会下降。边际产量 (MP) = ΔTP / ΔL。

Cost formulas: Total Cost (TC) = Total Fixed Cost (TFC) + Total Variable Cost (TVC). Average Total Cost (ATC) = TC ÷ Q, Average Variable Cost (AVC) = TVC ÷ Q, Average Fixed Cost (AFC) = TFC ÷ Q. Marginal Cost (MC) = ΔTC / ΔQ.

成本公式：总成本 (TC) = 总固定成本 (TFC) + 总变动成本 (TVC)。平均总成本 (ATC) = TC ÷ Q，平均变动成本 (AVC) = TVC ÷ Q，平均固定成本 (AFC) = TFC ÷ Q。边际成本 (MC) = ΔTC / ΔQ。

Theorem – MC cuts ATC and AVC at their minimum: When MC is below ATC, ATC falls; when MC is above ATC, ATC rises; therefore MC intersects ATC (and AVC) at their lowest points.

定理 – MC 与 ATC、AVC 的最低点相交：当 MC 低于 ATC 时，ATC 下降；当 MC 高于 ATC 时，ATC 上升；因此 MC 穿过 ATC（和 AVC）的最低点。

Revenue: Total Revenue (TR) = P × Q. Average Revenue (AR) = TR ÷ Q = P. Marginal Revenue (MR) = ΔTR / ΔQ. In perfectly competitive markets, AR = MR = P.

收益：总收益 (TR) = P × Q。平均收益 (AR) = TR ÷ Q = P。边际收益 (MR) = ΔTR / ΔQ。在完全竞争市场中，AR = MR = P。

Profit maximisation: Firms produce where MR = MC. At this level of output, any further unit would add more to cost than to revenue. In the short run, a firm should shut down if P < AVC.

利润最大化：企业在 MR = MC 处生产。在这一产量下，任何额外单位带来的成本增加都将超过收益增加。短期中，若 P < AVC，企业应停止生产。

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4. Market Structures and Pricing | 市场结构与定价

Perfect Competition: In long-run equilibrium, P = MR = MC = AR = min ATC. Firms earn normal profit. Productive and allocative efficiency are achieved.

完全竞争：在长期均衡下，P = MR = MC = AR = ATC 最低点。企业仅获得正常利润。实现了生产效率和配置效率。

Monopoly power: A monopolist faces a downward-sloping demand curve, so MR < P. The relationship is MR = P (1 + 1/PED). The Lerner Index measures market power: L = (P – MC) / P = -1/PED. Profit maximisation still occurs at MR = MC.

垄断势力：垄断者面临向下倾斜的需求曲线，因此 MR < P。其关系为 MR = P (1 + 1/PED)。勒纳指数用于衡量市场势力：L = (P – MC) / P = -1/PED。利润最大化仍然在 MR = MC 处。

Oligopoly concentration measures: The n-firm concentration ratio sums the market shares of the largest n firms. Herfindahl-Hirschman Index (HHI) = Σ(s_i)², where s_i is the market share of firm i. A higher HHI indicates a more concentrated market.

寡头集中度指标：n 企业集中度为前 n 家最大企业的市场份额之和。赫芬达尔-赫希曼指数 (HHI) = Σ(s_i)²，其中 s_i 为企业 i 的市场份额。HHI 值越高，市场越集中。

Monopolistic Competition: Long-run equilibrium delivers only normal profit because of free entry. The firm’s demand curve is tangent to the ATC curve, so P = ATC, but P > MC, meaning allocative inefficiency persists.

垄断竞争：由于自由进入，长期均衡下企业仅获得正常利润。企业需求曲线与 ATC 曲线相切，因此 P = ATC，但 P > MC，意味着仍然存在配置无效率。

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5. Factor Markets | 要素市场

Marginal Physical Product (MPP) is the extra output from one more unit of labour. Marginal Revenue Product (MRP) = MPP × MR. In a perfectly competitive product market, MR = P, so MRP = MPP × P, which is the Value of Marginal Product (VMP).

边际物质产品 (MPP) 是增加一单位劳动所带来的额外产量。边际收益产品 (MRP) = MPP × MR。若产品市场为完全竞争，MR = P，因此 MRP = MPP × P，也称边际产品价值 (VMP)。

Profit-maximising employment: A firm hires labour up to the point where MRP = marginal cost of labour (MCL). If the labour market is perfectly competitive, MCL equals the market wage rate, so the rule becomes MRP = Wage.

利润最大化雇工：企业雇用劳动直至 MRP = 劳动的边际成本 (MCL)。若劳动力市场为完全竞争，MCL 等于市场工资率，因此规则为 MRP = 工资。

Economic rent and transfer earnings: Economic rent is any payment above the minimum needed to keep a factor in its current use. Transfer earnings are the minimum payment required. Total factor earnings = transfer earnings + economic rent.

经济租金与转移收入：经济租金是指超过使要素保留在当前用途所需最低限度的任何报酬。转移收入是最低必需报酬。要素总收入 = 转移收入 + 经济租金。

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6. Market Failure and Government Intervention | 市场失灵与政府干预

Externalities: Marginal social cost (MSC) = Marginal private cost (MPC) + Marginal external cost (MEC). Similarly, Marginal social benefit (MSB) = MPB + MEB. At the socially efficient output, MSB = MSC.

外部性：边际社会成本 (MSC) = 边际私人成本 (MPC) + 边际外部成本 (MEC)。同理，边际社会收益 (MSB) = MPB + MEB。在社会有效产出水平下，MSB = MSC。

Pigouvian tax: To correct a negative production externality, a tax equal to the MEC at the efficient output forces the firm to internalise the external cost.

庇古税：为纠正负生产外部性，对每单位产品征收的税款应等于有效产出水平上的 MEC，从而迫使企业将外部成本内部化。

Coase Theorem: If property rights are clearly defined and transaction costs are low, private bargaining can lead to an efficient outcome regardless of the initial allocation of rights.

科斯定理：如果产权界定清晰且交易成本很低，无论初始权利如何分配，私人谈判都能实现有效结果。

Public goods and market failure: Pure public goods are non-rival and non-excludable. The efficient provision condition is Σ(marginal benefits) = marginal cost, not P = MC.

公共品与市场失灵：纯公共品具有非竞争性和非排他性。其有效提供的条件是所有消费者的边际收益之和等于边际成本，而非 P = MC。

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7. Macroeconomic Indicators and Accounting | 宏观经济指标与核算

Gross Domestic Product (expenditure approach): GDP = C + I + G + (X – M), where C = consumption, I = investment, G = government spending, X = exports, M = imports.

国内生产总值（支出法）：GDP = C + I + G + (X – M)，其中 C 是消费，I 是投资，G 是政府支出，X 是出口，M 是进口。

Real GDP: Real GDP = (Nominal GDP / GDP deflator) × 100. This strips out the effect of inflation to isolate changes in physical output.

实际 GDP：实际 GDP = (名义 GDP / GDP 平减指数) × 100。这样可剔除通胀影响，仅仅反映实际产出的变化。

Inflation measurement: The Consumer Price Index (CPI) measures the cost of a representative basket. Inflation rate = (CPI_current – CPI_previous) / CPI_previous × 100.

通胀测量：消费者价格指数 (CPI) 衡量代表性一篮子商品的成本。通胀率 = (CPI 本期 – CPI 上期) / CPI 上期 × 100。

Unemployment rate: Unemployment rate = (Number unemployed / Labour force) × 100, where the labour force is employed + unemployed, and unemployment follows the ILO definition of actively seeking work.

失业率：失业率 = (失业人数 / 劳动力人数) × 100，其中劳动力为就业者与失业者之和，且失业需符合国际劳工组织“积极寻找工作”的定义。

Balance of Payments: The Current Account + Capital Account + Financial Account + Net errors and omissions = 0. Current account balance ≈ trade balance + net income + net current transfers.

国际收支：经常账户 + 资本账户 + 金融账户 + 净误差与遗漏 = 0。经常账户余额 ≈ 贸易差额 + 净收入 + 净经常转移。

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8. National Income Determination and Multipliers | 国民收入决定与乘数

Consumption function: C = a + b Y_d, where a = autonomous consumption, b = marginal propensity to consume (MPC), and Y_d = disposable income. MPS = 1 – MPC, where MPS is the marginal propensity to save.

消费函数：C = a + b Y_d，其中 a 为自主性消费，b 为边际消费倾向 (MPC)，Y_d 为可支配收入。MPS = 1 – MPC，MPS 为边际储蓄倾向。

The simple multiplier: k = 1 / (1 – MPC) = 1 / MPS. Any initial injection of spending increases national income by k times the initial amount.

简单乘数：k = 1 / (1 – MPC) = 1 / MPS。任何初始支出注入将使国民收入增加初始金额的 k 倍。

Multiplier with government and foreign trade: When taxes are a function of income (t = marginal tax rate) and MPM is the marginal propensity to import, the multiplier becomes k = 1 / (1 – MPC(1 – t) + MPM). This is smaller than the simple multiplier.

含政府和外贸的乘数：当税收是收入的函数（t 为边际税率）且 MPM 为边际进口倾向时，乘数变为 k = 1 / (1 – MPC(1 – t) + MPM)，结果小于简单乘数。

Accelerator effect: Net investment depends on the change in output, not the level of output. A rise in national income can induce a proportionally larger increase in investment, amplifying the cycle.

加速效应：净投资取决于产出的变化而非产出水平。国民收入的上升会引发投资按比例更大幅度的增加，从而放大经济周期。

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9. Money, Inflation and Unemployment | 货币、通胀与失业

Quantity Theory of Money: The equation of exchange is MV = PY, where M = money supply, V = velocity of circulation, P = price level, Y = real output. Assuming V and Y are stable in the short run, changes in M lead to proportional changes in P.

货币数量论：交易方程式为 MV = PY，其中 M 为货币供给，V 为流通速度，P 为价格水平，Y 为实际产出。若短期假定 V 和 Y 稳定，M 的变化将导致 P 同比例变化。

Fisher equation: Nominal interest rate = Real interest rate + Expected inflation. Lenders demand compensation for the erosion of purchasing power.

费雪方程：名义利率 = 实际利率 + 预期通胀率。贷款人要求对购买力侵蚀进行补偿。

Short-run Phillips Curve: Suggests an inverse relationship between inflation and unemployment. The long-run Phillips curve is vertical at the natural rate of unemployment, implying no trade-off in the long run.

短期菲利普斯曲线：表明通胀与失业之间存在反向关系。长期菲利普斯曲线在自然失业率处垂直，意味着长期中不存在权衡取舍。

Okun’s Law: A rule of thumb linking changes in unemployment to changes in GDP. For every 2-3 percentage points increase in real GDP relative to potential, the unemployment rate falls by about 1 percentage point. This varies by country.

奥肯定律：这是一条将失业变化与 GDP 变化联系起来的经验法则。通常，实际 GDP 相对于潜在 GDP 每上升 2-3 个百分点，失业率将下降大约 1 个百分点。具体幅度因国而异。

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10. International Economics | 国际经济学

Comparative advantage: A country has comparative advantage in producing a good if its opportunity cost of producing that good is lower than another country’s. Specialisation and trade can increase total world output.

比较优势：倘若一国生产某种商品的机会成本低于另一国，则该国具有比较优势。专业化分工与贸易能够增加世界总产出。

Terms of Trade: Terms of trade index = (Index of export prices / Index of import prices) × 100. An improvement means a country can buy more imports for a given volume of exports.

贸易条件：贸易条件指数 = (出口价格指数 / 进口价格指数) × 100。指数上升意味着用同样的出口量可以换回更多的进口品。

Real exchange rate: Real exchange rate = Nominal exchange rate × (Domestic price level / Foreign price level). This measures the relative purchasing power of a currency adjusted for inflation differences.

实际汇率：实际汇率 = 名义汇率 × (本国物价水平 / 外国物价水平)。它衡量经通胀差异调整后的货币相对购买力。

Marshall-Lerner condition: A depreciation of the domestic currency will improve the trade balance only if the sum of the absolute price elasticities of demand for exports and imports is greater than one (|PED_ex| + |PED_im| > 1).

马歇尔-勒纳条件：本币贬值要改善贸易收支，必须满足出口需求和进口需求的价格弹性的绝对值之和大于 1 (|PED_ex| + |PED_im| > 1)。

J-curve effect: After depreciation, the trade balance often worsens in the short run before it improves, because contracts are fixed and quantities adjust slowly.

J 曲线效应：本币贬值后，短期内贸易收支常常先恶化后改善，原因在于合同价格锁定且数量调整缓慢。

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