📚 Year 13 AQA Economics: Formula & Theorem Quick Reference Handbook | Year 13 AQA 经济：公式定理速查手册
This quick reference handbook compiles the essential formulae, theorems and quantitative relationships required by the Year 13 AQA Economics specification. It is designed as a last-minute revision tool: every equation is paired with its economic meaning, the assumption behind it, and the way examiners expect you to use it in calculation and analysis questions. From short-run cost curves and profit maximisation to the multiplier, the Phillips curve, exchange-rate arithmetic and the Gini coefficient, each formula below is examinable and each interpretation is worth marks.
本速查手册汇集了 Year 13 AQA 经济课程所需的核心公式、定理与关键数量关系，专为考前快速复习设计：每一个公式都配以经济含义、成立前提，以及考官的评分期待——如何在计算题与分析题中正确运用。从短期成本曲线、利润最大化，到乘数效应、菲利普斯曲线、汇率计算与基尼系数，以下每个公式都在考纲范围内，每一句解读都能转化为分数。
1. Costs and Production | 成本与生产
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）与总变动成本（TVC）之和。
TC = TFC + TVC
Average fixed cost (AFC) equals TFC divided by output Q, while average variable cost (AVC) equals TVC divided by Q.
平均固定成本（AFC）等于 TFC 除以产量 Q，平均变动成本（AVC）等于 TVC 除以 Q。
AFC = TFC ÷ Q AVC = TVC ÷ Q
Average total cost (ATC) can be expressed as TC ÷ Q, or as the sum of AFC and AVC.
平均总成本（ATC）可以表示为 TC ÷ Q，或 AFC 与 AVC 之和。
ATC = TC ÷ Q = AFC + AVC
Marginal cost (MC) is the addition to total cost from producing one more unit of output.
边际成本（MC）是多生产一单位产出所带来的总成本增量。
MC = ΔTC ÷ ΔQ
The law of diminishing marginal returns states that as more units of a variable factor are added to a fixed factor, the marginal product of the variable factor eventually falls, so MC eventually rises.
边际收益递减规律表明：当可变要素不断增加并投入到固定要素之上时，可变要素的边际产量最终下降，因此 MC 最终上升。
When MC is below ATC, ATC is falling; when MC is above ATC, ATC is rising.
当 MC 低于 ATC 时，ATC 下降；当 MC 高于 ATC 时，ATC 上升。
The MC curve intersects both the ATC and AVC curves at their minimum points.
MC 曲线在 ATC 与 AVC 的最低点与之相交。
AFC falls continuously as Q rises, because a fixed numerator is divided by a growing denominator.
随着 Q 上升，AFC 持续下降，因为固定的分子被越来越大的分母所除。
| Item | Formula | Meaning |
| ATC | TC ÷ Q | Cost per unit at any output level |
| MC | ΔTC ÷ ΔQ | Cost of the last unit produced |
| Minimum ATC | MC = ATC | Productive efficiency point |
2. Revenue, Profit and Market Efficiency | 收益、利润与市场效率
Total revenue (TR) equals price multiplied by quantity sold. Average revenue (AR) equals TR divided by Q and is identical to the demand curve faced by the firm; marginal revenue (MR) is the change in TR from selling one extra unit.
总收益（TR）等于价格乘以销售量。平均收益（AR）等于 TR 除以 Q，它与企业面对的需求曲线重合；边际收益（MR）是多销售一单位所带来的 TR 变化量。
TR = P × Q AR = TR ÷ Q = P MR = ΔTR ÷ ΔQ
Profit is total revenue minus total cost, and the profit-maximising rule is to produce where marginal revenue equals marginal cost.
利润等于总收益减去总成本，利润最大化的法则是：在边际收益等于边际成本处生产。
Profit = TR − TC Profit max: MR = MC
At the profit-maximising output, MC must be rising and must cut MR from below; if MR exceeds MC, expanding output adds profit, and if MC exceeds MR, cutting output adds profit.
在利润最大化产量处，MC 必须上升并自下向上穿过 MR；若 MR 大于 MC，增产可增加利润；若 MC 大于 MR，减产可增加利润。
un equilibrium P = MC = minimum ATC, delivering both allocative and productive efficiency.
在完全竞争中，企业是价格接受者，故 P = AR = MR；长期均衡时 P = MC = 最低 ATC，同时实现配置效率与生产效率。
e efficiency requires P = MC, so price reflects the marginal social cost of the last unit.
配置效率要求 P = MC，即价格反映最后一单位产品的边际社会成本。
Productive efficiency requires production at the minimum point of the ATC curve.
生产效率要求在 ATC 曲线最低点生产。
X-inefficiency exists when a firm produces above its ATC curve because of weak competitive pressure.
当企业因竞争压力不足而在 ATC 曲线之上生产时，就存在 X 低效率。
Consumer surplus is the area below the demand curve and above price; producer surplus is the area above the supply curve and below price. Deadweight loss appears when output deviates from the allocatively efficient level.
消费者剩余是需求曲线以下、价格以上的面积；生产者剩余是供给曲线以上、价格以下的面积。当产量偏离配置效率产量时，就出现无谓损失。
3. Market Structure and Concentration Measures | 市场结构与集中度衡量
The n-firm concentration ratio adds the market shares of the largest n firms and expresses them as a percentage of total market sales.
n 企业集中度把最大的 n 家企业的市场份额相加，并以占市场总销售额的百分比表示。
CRₙ = (Σ market shares of largest n firms) × 100%
The Herfindahl-Hirschman Index squares each firm's percentage market share and sums the results, so it gives extra weight to very large firms.
赫芬达尔—赫希曼指数（HHI）把每家企业的百分比市场份额平方后加总，因此对超大企业给予更大权重。
HHI = Σ (market shareᵢ)²
A market with five equal firms each holding 20% gives HHI = 20² + 20² + 20² + 20² + 20² = 2000, whereas a market with one firm at 90% and ten firms at 1% gives HHI = 8100 + 10 = 8110, indicating far greater concentration.
若市场由五家各占 20% 的企业构成，HHI = 20² + 20² + 20² + 20² + 20² = 2000；若一家占 90%、十家各占 1%，则 HHI = 8100 + 10 = 8110，说明集中度远高于前者。
The Lerner Index measures monopoly power as the extent to which price exceeds marginal cost, and it can be rewritten in terms of price elasticity of demand.
勒纳指数以价格超过边际成本的程度衡量垄断力量，并可用需求价格弹性改写。
Lerner Index = (P − MC) ÷ P = 1 ÷ |PED|
off the demand curve, so price exceeds marginal cost and the markup depends on the elasticity of demand.
不完全竞争企业在 MR = MC 处决定产量，再从需求曲线上读取价格，因此价格高于边际成本，加成幅度取决于需求弹性。
Elastic demand (|PED| large) means a small markup and price close to marginal cost.
需求富有弹性（|PED| 大）意味着加成小，价格接近边际成本。
Inelastic demand (|PED| small) means a large markup and greater monopoly power.
需求缺乏弹性（|PED| 小）意味着加成大，垄断力量更强。
Contestability depends on sunk costs and barriers to entry and exit, not on the number of firms alone.
可竞争性取决于沉没成本与进出壁垒，而不只取决于企业数量。
4. Elasticity Formulae | 弹性公式
Price elasticity of demand measures the responsiveness of quantity demanded to a change in price.
需求价格弹性衡量需求量对价格变化的反应程度。
PED = %ΔQd ÷ %ΔP
Income elasticity of demand measures the responsiveness of demand to a change in income, and cross elasticity of demand measures the responsiveness of demand for good A to a change in the price of good B.
需求收入弹性衡量需求对收入变化的反应程度；需求交叉弹性衡量商品 A 的需求对商品 B 价格变化的反应程度。
YED = %ΔQd ÷ %ΔY XED = %ΔQd(A) ÷ %ΔP(B)
Price elasticity of supply measures the responsiveness of quantity supplied to a change in price.
供给价格弹性衡量供给量对价格变化的反应程度。
PES = %ΔQs ÷ %ΔP
Percentage change is calculated as the difference divided by the original value, multiplied by 100.
百分比变化的算法是：差值除以原始数值，再乘以 100。
%Δ = (New value − Old value) ÷ Old value × 100%
|PED| > 1: elastic, so a price cut raises total revenue.
|PED| > 1：富有弹性，降价会提高总收益。
|PED| < 1: inelastic, so a price rise raises total revenue.
|PED| < 1：缺乏弹性，提价会提高总收益。
|PED| = 1: unit elastic, total revenue is maximised and MR = 0.
|PED| = 1：单位弹性，总收益最大且 MR = 0。
YED > 1 normal luxury; 0 < YED < 1 normal necessity; YED < 0 inferior good.
YED > 1 为正常奢侈品；0 < YED < 1 为正常必需品；YED < 0 为劣等品。
XED > 0 substitutes; XED < 0 complements; XED = 0 unrelated goods.
XED > 0 为替代品；XED < 0 为互补品；XED = 0 为无关商品。
The burden of an indirect tax falls mainly on consumers when demand is inelastic relative to supply, and mainly on producers when demand is elastic relative to supply.
当需求相对供给更缺乏弹性时，间接税的税负主要由消费者承担；当需求相对供给更富弹性时，税负主要由生产者承担。
5. National Income Accounting and Macroeconomic Indicators | 国民收入核算与宏观指标
Gross domestic product by the expenditure method is the sum of consumption, investment, government spending and net exports.
支出法计算的国内生产总值等于消费、投资、政府支出与净出口之和。
GDP = C + I + G + (X − M)
Gross national income adjusts GDP for net factor income from abroad, and net national income subtracts depreciation from GNI.
国民总收入在 GDP 基础上调整国外净要素收入，国民净收入则从 GNI 中扣除折旧。
GNI = GDP + Net factor income from abroad
Real GDP strips out the effect of price changes by using a base-year price index, and the real growth rate compares real GDP across two periods.
实际 GDP 通过基期价格指数剔除价格变动影响，实际增长率比较两个时期的实际 GDP。
Real GDP = Nominal GDP × (Base year index ÷ Current year index)
Growth rate = (Real GDP₂ − Real GDP₁) ÷ Real GDP₁ × 100%
The inflation rate is the percentage change in the consumer price index, and real interest rates adjust nominal rates for inflation.
通胀率是消费者价格指数的百分比变化，实际利率则是名义利率对通胀进行调整后的结果。
Inflation rate = (CPI₂ − CPI₁) ÷ CPI₁ × 100%
Real interest rate ≈ Nominal interest rate − Inflation rate
Unemployment rate = unemployed ÷ labour force × 100%.
失业率 = 失业人数 ÷ 劳动力 × 100%。
Labour force participation rate = labour force ÷ working-age population × 100%.
劳动参与率 = 劳动力 ÷ 劳动年龄人口 × 100%。
opulation, a rough proxy for living standards that ignores distribution and externalities.
人均 GDP = GDP ÷ 人口，是生活水平的粗略代理指标，但忽略分配与环境外部性。
6. The Multiplier, the Accelerator and the Phillips Curve | 乘数、加速数与菲利普斯曲线
The multiplier shows how an initial change in an injection leads to a larger final change in national income. Its size depends on the marginal propensities to save, tax and import.
乘数说明初始注入的变化如何带来国民收入更大的最终变化，其大小取决于边际储蓄倾向、边际税收倾向与边际进口倾向。
k = 1 ÷ (1 − MPC) = 1 ÷ (MPS + MPT + MPM)
ΔY = k × ΔJ
y with no government, the multiplier is also 1 ÷ MPS. The larger the leakages, the smaller the multiplier and the weaker the final effect on output.
在没有政府、封闭经济的条件下，由于 MPC + MPS = 1，乘数也等于 1 ÷ MPS。漏出越大，乘数越小，对产出的最终影响越弱。
The accelerator theorem links the level of investment to the change in national income, so investment depends on the rate of growth rather than the level of output.
加速数定理把投资水平与国民收入的变化量联系起来，因此投资取决于增长率而非产出水平本身。
I = a × ΔY ΔI = a × Δ(ΔY)
The short-run Phillips curve shows an inverse trade-off between inflation and unemployment, and it shifts when inflationary expectations or supply-side conditions change.
短期菲利普斯曲线显示通胀与失业之间的反向替代关系；当通胀预期或供给侧条件变化时，曲线发生移动。
Movement along the curve: a demand-side expansion lowers unemployment but raises inflation.
沿曲线移动：需求扩张降低失业但提高通胀。
Shift of the curve: a rise in expected inflation shifts the short-run curve upwards, worsening the trade-off.
曲线移动：预期通胀上升使短期曲线上移，替代关系恶化。
The long-run Phillips curve is vertical at the NAIRU, so there is no permanent inflation-unemployment trade-off.
长期菲利普斯曲线在 NAIRU 处垂直，因此不存在永久的通胀—失业替代关系。
7. Fiscal Policy and Public Finances | 财政政策与公共财政
The budget balance is total government revenue minus total government expenditure. A negative figure is a budget deficit; a positive figure is a surplus.
预算差额等于政府总收入减去政府总支出。负数为预算赤字，正数为预算盈余。
Budget balance = Tax revenue − Government spending
The structural balance strips out the effects of the economic cycle, while the cyclical balance captures the automatic movement of revenue and spending over the cycle.
结构性余额剔除经济周期的影响，周期性余额则反映税收与支出随周期自动变动的那一部分。
Cyclical balance = Actual balance − Structural balance
Tax revenue depends on the tax base multiplied by the effective tax rate, which is why the Laffer curve suggests that beyond some point a higher rate can reduce total revenue.
税收收入取决于税基乘以有效税率，这正是拉弗曲线所揭示的：超过某一点后，提高税率反而可能减少总收入。
Tax revenue = Tax base × Effective tax rate
The national debt to GDP ratio measures debt sustainability, and the public sector net cash requirement records the actual cash the government must borrow in a period.
国债占 GDP 的比率衡量债务可持续性，公共部门净现金需求则记录政府在某一时期实际必须借入的现金。
Debt ratio = Total national debt ÷ Nominal GDP × 100%
Automatic stabilisers raise spending and cut tax revenue in a downturn without any deliberate policy change.
自动稳定器在经济下行时自动增加支出、减少税收，无需刻意改变政策。
Crowding out occurs when higher government borrowing raises interest rates and reduces private investment.
当政府借贷增加推高利率并挤压私人投资时，就发生挤出效应。
The fiscal multiplier is smaller in a small open economy with high MPM and high MPT.
在 MPM 与 MPT 较高的小型开放经济中，财政乘数较小。
8. Money, Banking and Monetary Policy | 货币、银行与货币政策
The credit multiplier shows the maximum expansion of bank deposits from an initial deposit, given the reserve ratio held by banks.
信用乘数显示在给定准备金率下，一笔初始存款所能带来的银行存款最大扩张倍数。
Credit multiplier = 1 ÷ Reserve ratio
The quantity theory of money links the money supply and the velocity of circulation to the price level and the volume of transactions.
货币数量论把货币供应量与货币流通速度同物价水平和交易量联系起来。
MV = PT or MV = PY
If velocity and real output are broadly stable, the growth of the money supply sets the inflation
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