📚 IB & OCR Economics: Formula Handbook | IB 与 OCR 经济：公式汇总手册
This comprehensive handbook collects the essential formulas needed for IB and OCR Economics exams. From foundational elasticities to macroeconomic multipliers, every equation is explained in plain English and Chinese, with worked examples where helpful. Use it as a quick reference to secure those calculation marks.
这本全面的手册汇集了 IB 和 OCR 经济考试所需的核心公式。从基础弹性到宏观经济乘数，每个公式都有浅显易懂的英中解释，并附有示例演算。把它当速查手册，稳稳拿下计算分。
1. Price Elasticity of Demand (PED) | 需求价格弹性
ures the responsiveness of quantity demanded to a change in price. The formula is: PED = (% change in quantity demanded) ÷ (% change in price).
需求价格弹性衡量需求量对价格变动的反应程度。公式为：需求价格弹性 = 需求量变动百分比 ÷ 价格变动百分比。
emand is inelastic; if PED = 1, demand is unit elastic. Always use absolute values for PED – ignore the negative sign.
如果 PED > 1，需求富有弹性；PED < 1，需求缺乏弹性；PED = 1，需求单位弹性。PED 总是取绝对值，忽略负号。
- Example: Price rises from $10 to $12 (20% increase); quantity demanded falls from 100 to 80 (20% decrease). PED = 20% / 20% = 1 → unit elastic.
- 示例：价格从 10 美元升至 12 美元（涨幅 20%）；需求量从 100 降至 80（跌幅 20%）。PED = 20% / 20% = 1，单位弹性。
2. Income Elasticity of Demand (YED) | 需求收入弹性
YED gauges how quantity demanded responds to changes in consumer income. Formula: YED = (% change in quantity demanded) ÷ (% change in income).
需求收入弹性表示需求量对消费者收入变动的反应程度。公式：YED = 需求量变动百分比 ÷ 收入变动百分比。
YED > 0 for normal goods; YED < 0 for inferior goods. Among normal goods, YED > 1 suggests luxury goods, while 0 < YED < 1 indicates necessities.
正常品 YED > 0；低档品 YED < 0。在正常品中，YED > 1 为奢侈品，0 < YED < 1 为必需品。
- Example: Income rises by 10%, and demand for organic vegetables rises by 25%. YED = 25% / 10% = 2.5 → luxury good.
- 示例：收入增长 10%，有机蔬菜需求增长 25%。YED = 25% / 10% = 2.5，奢侈品。
3. Cross-Price Elasticity of Demand (XED) | 需求交叉弹性
the responsiveness of demand for Good A when the price of Good B changes. Formula: XED = (% change in quantity demanded of Good A) ÷ (% change in price of Good B).
需求交叉弹性衡量商品 B 价格变动时商品 A 需求量的反应程度。公式：XED = 商品 A 需求量变动百分比 ÷ 商品 B 价格变动百分比。
XED > 0 for substitutes; XED < 0 for complements; XED close to 0 indicates unrelated goods.
替代品 XED > 0；互补品 XED < 0；XED 接近 0 时为无关品。
- Example: If the price of coffee rises by 10% and demand for tea rises by 5%, XED = 5% / 10% = 0.5 → substitutes.
- 示例：咖啡价格上涨 10%，茶叶需求增加 5%。XED = 5% / 10% = 0.5，替代品。
4. Price Elasticity of Supply (PES) | 供给价格弹性
PES shows how responsive quantity supplied is to a price change. Formula: PES = (% change in quantity supplied) ÷ (% change in price).
供给价格弹性表示供给量对价格变动的反应程度。公式：PES = 供给量变动百分比 ÷ 价格变动百分比。
icates unit elastic supply. The value depends on factors like time period and spare capacity.
PES > 1 表示供给富有弹性；PES < 1 表示缺乏弹性；PES = 1 表示单位弹性。数值取决于时间周期和闲置产能等因素。
- Example: Price increases by 15%, quantity supplied increases by 30%. PES = 30% / 15% = 2 → elastic supply.
- 示例：价格上涨 15%，供给量增加 30%。PES = 30% / 15% = 2，供给富有弹性。
5. Total Revenue and Marginal Revenue | 总收益与边际收益
Marginal Revenue (MR) is the additional revenue from selling one more unit: MR = ΔTR / ΔQ.
总收益 (TR) = 价格 × 数量。边际收益 (MR) 是多售出一单位产品带来的额外收益：MR = ΔTR ÷ ΔQ。
For perfect competition, MR equals price. For imperfect competition, MR falls below price because the firm must lower the price on all units to sell an extra one.
完全竞争下，MR 等于价格；不完全竞争下，MR 低于价格，因为厂商必须降低所有单位的售价才能多卖一单位。
- Example: A firm sells 50 units at $20 each, TR = $1,000. To sell 51 units, price must drop to $19.50 on all units. New TR = 51 × $19.50 = $994.50, so MR of the 51st unit = $994.50 − $1,000 = −$5.50.
- 示例：企业以单价 20 美元售出 50 件，TR = 1,000 美元。为卖出第 51 件，价格需降至 19.50 美元，新 TR = 51 × 19.50 = 994.50 美元，第 51 件的边际收益 = 994.50 − 1,000 = −5.50 美元。
6. Costs: Total, Average and Marginal | 成本：总成本、平均成本与边际成本
ost (AFC) = TFC / Q. Average Variable Cost (AVC) = TVC / Q. Marginal Cost (MC) = ΔTC / ΔQ.
总成本 (TC) = 总固定成本 (TFC) + 总可变成本 (TVC)。平均总成本 (ATC) = TC ÷ Q。平均固定成本 (AFC) = TFC ÷ Q。平均可变成本 (AVC) = TVC ÷ Q。边际成本 (MC) = ΔTC ÷ ΔQ。
When MC < ATC, ATC is falling; when MC > ATC, ATC is rising. The MC curve intersects ATC and AVC at their minimum points.
当 MC < ATC 时，ATC 下降；当 MC > ATC 时，ATC 上升。MC 曲线在 ATC 和 AVC 的最低点与之相交。
- Example: Output rises from 10 to 11 units, and TC rises from $200 to $218. MC = ($218 − $200) / (11 − 10) = $18.
- 示例：产量从 10 单位增至 11 单位，TC 从 200 美元升至 218 美元。MC = (218 − 200) / (11 − 10) = 18 美元。
7. Profit Maximisation Condition | 利润最大化条件
st (MC), and MC cuts MR from below. In perfect competition, this is also where Price = MC.
厂商在边际收益 (MR) 等于边际成本 (MC)，且 MC 从下方穿过 MR 时实现利润最大化。完全竞争下，这也是价格 = MC 的点。
Profit = TR − TC. At the profit‑ ween TR and TC is the largest. If price < AVC, the firm should shut down in the short run.
利润 = TR − TC。在利润最大化产量处，TR 与 TC 的差距最大。如果价格低于 AVC，企业短期内应停产。
- Example: When Q = 20, MR = $30 and MC = $30. TR = $600, TC = $450, profit = $150.
- 示例：当 Q = 20 时，MR = 30 美元，MC = 30 美元。TR = 600 美元，TC = 450 美元，利润 = 150 美元。
8. National Income Multipliers | 国民收入乘数
fects national income. Formula: Multiplier = 1 / (1 − MPC) = 1 / MPS, where MPC + MPS = 1.
简单乘数表示自发性支出变动对国民收入的影响。公式：乘数 = 1 ÷ (1 − MPC) = 1 ÷ MPS，其中 MPC + MPS = 1。
For an open economy with taxes and imports, the multiplier becomes 1 / [1 − MPC(1 − t) + MPM], where t is the tax rate and MPM the marginal propensity to import.
在存在税收和进口的开放经济中，乘数变为：1 ÷ [1 − MPC(1 − t) + MPM]，其中 t 为税率，MPM 为边际进口倾向。
- Example: MPC = 0.8, so MPS = 0.2. Multiplier = 1 / 0.2 = 5. A $10 billion rise in investment raises national income by $50 billion.
- 示例：MPC = 0.8，MPS = 0.2。乘数 = 1 ÷ 0.2 = 5。投资增加 100 亿美元，国民收入增加 500 亿美元。
9. Money Multiplier | 货币乘数
ate from a given monetary base. Formula: Money multiplier = 1 / reserve requirement ratio.
货币乘数表示银行体系从给定的基础货币能创造的最大货币量。公式：货币乘数 = 1 ÷ 法定准备金率。
If the reserve ratio is 10%, the money multiplier is 10. An initial deposit of $1,000 could theoretically generate $10,000 in new loans and deposits. The actual multiplier is often smaller due to cash leakages.
准备金率为 10% 时，货币乘数为 10。初始存款 1,000 美元理论上可创造 10,000 美元的新贷款和存款。但因现金漏出，实际乘数往往更小。
- Example: Reserve ratio = 0.125 (12.5%). Money multiplier = 1 / 0.125 = 8.
- 示例：准备金率 = 0.125（12.5%）。货币乘数 = 1 ÷ 0.125 = 8。
10. Real Interest Rate | 实际利率
rate for inflation. Formula: Real interest rate ≈ Nominal interest rate − Inflation rate.
实际利率扣除了通货膨胀对名义利率的影响。公式：实际利率 ≈ 名义利率 − 通货膨胀率。
inflation). For exam calculations, the simplified version is acceptable unless stated otherwise.
更精确的费雪方程式为：(1 + 名义利率) = (1 + 实际利率) × (1 + 通胀率)。考试计算时，除非特别要求，否则使用简化公式即可。
- Example: Nominal interest rate = 5%, inflation = 2%. Real interest rate ≈ 5% − 2% = 3%.
- 示例：名义利率 5%，通货膨胀率 2%。实际利率 ≈ 5% − 2% = 3%。
11. Exchange Rate Conversions | 汇率换算
it means 1 USD buys 0.75 GBP. To find how many USD is 1 GBP, divide 1 by 0.75 = 1.333 USD.
汇率换算时，使用给定汇率。若 USD/GBP = 0.75，表示 1 美元买 0.75 英镑。求 1 英镑多少美元，用 1 ÷ 0.75 = 1.333 美元。
An appreciation means a currency becomes stronger (worth more of the other currency); depreciation means it becomes weaker. A higher exchange rate can be either positive or negative depending on the quoting convention.
升值意味着一种货币变得更强（可兑换更多其他货币）；贬值则意味着变弱。汇率数值上升是升值还是贬值，取决于标价方式。
- Example: EUR/CNY = 7.80. A phone priced at ￥3,900 costs 3,900 ÷ 7.80 = €500.
- 示例：欧元/人民币 = 7.80。一部手机标价 3,900 元人民币，成本为 3,900 ÷ 7.80 = 500 欧元。
12. Index Numbers and GDP per Capita | 指数与人均 GDP
current period / Value in base period) × 100. Often used for CPI, RPI, and stock indices.
指数将数据表示为相对于基期的数值。公式：指数 = (当前数值 ÷ 基期数值) × 100。常用于 CPI、RPI 和股票指数。
. This measures average living standards, though it ignores income distribution. Real GDP is Nominal GDP adjusted for inflation using a GDP deflator.
人均 GDP = 实际 GDP ÷ 人口。它衡量平均生活水平，但未考虑收入分配。实际 GDP 是名义 GDP 经 GDP 平减指数调整后的结果。
- Example: Nominal GDP = $2 trillion, GDP deflator = 110, Population = 50 million. Real GDP = $2t / 1.10 = $1.818t; GDP per capita = $1.818t / 50m = $36,360.
- 示例：名义 GDP = 2 万亿美元，GDP 平减指数 = 110，人口 = 5,000 万。实际 GDP = 2 万亿 ÷ 1.10 = 1.818 万亿美元；人均 GDP = 1.818 万亿 ÷ 5,000 万 = 36,360 美元。
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