IB CCEA Economics Formula Handbook | IB CCEA 经济：公式汇总手册

📚 IB CCEA Economics Formula Handbook | IB CCEA 经济：公式汇总手册

This handbook brings together the essential formulas required for the IB CCEA Economics course. From microeconomic elasticities to macroeconomic aggregates, each section presents the key relationships in a clear, bilingual format. Understanding these formulas is not about memorisation alone; it is about seeing how one variable responds to another and interpreting the real-world implications of those responses.

本手册汇总了 IB CCEA 经济学课程所需的核心公式。从微观弹性到宏观总量，每一节都以清晰的双语形式呈现关键关系。理解这些公式不仅是为了记忆，更是为了看清一个变量如何对另一个变量做出反应，并解读这些反应在现实世界中的含义。

1. Price Elasticity of Demand (PED) | 需求价格弹性

Price elasticity of demand measures the responsiveness of quantity demanded to a change in price. It is a vital tool for businesses when setting prices and for governments when imposing indirect taxes.

需求价格弹性衡量需求量对价格变化的反应程度。它是企业定价和政府征收间接税时的重要工具。

PED = %ΔQD / %ΔP

where %ΔQD is the percentage change in quantity demanded and %ΔP is the percentage change in price. Use the midpoint (arc) method for greater accuracy when data points are discrete:

其中 %ΔQD 是需求量的百分比变化，%ΔP 是价格的百分比变化。当数据点为离散值时，使用中点（弧）法可获得更高精度：

PED = (ΔQ / Qave) ÷ (ΔP / Pave)

If |PED| > 1, demand is elastic – a price cut raises total revenue.

如果 |PED| > 1，需求富有弹性——降价能增加总收益。
If |PED| < 1, demand is inelastic – a price rise raises total revenue.

如果 |PED| < 1，需求缺乏弹性——提价能增加总收益。
If |PED| = 1, demand is unit elastic – total revenue is maximised.

如果 |PED| = 1，需求单位弹性——总收益达到最大。

2. Cross-Price Elasticity of Demand (XED) | 需求交叉价格弹性

Cross-price elasticity shows how the demand for one good changes when the price of another good changes. The sign of XED reveals the relationship between the two goods.

交叉价格弹性表明一种商品的需求如何随另一种商品价格的变化而变化。XED 的符号揭示两种商品之间的关系。

XED = %ΔQD of Good A / %ΔP of Good B

If XED > 0, the goods are substitutes (e.g., tea and coffee).

如果 XED > 0，两种商品互为替代品（如茶和咖啡）。
If XED < 0, the goods are complements (e.g., printers and ink cartridges).

如果 XED < 0，两种商品互为互补品（如打印机和墨盒）。
If XED = 0, the goods are unrelated.

如果 XED = 0，两种商品不相关。

The larger the absolute value, the stronger the relationship. Firms use XED to anticipate the impact of competitors’ pricing or bundling strategies.

绝对值越大，关系越强。企业利用 XED 来预测竞争对手的定价或捆绑销售策略的影响。

3. Income Elasticity of Demand (YED) | 需求收入弹性

Income elasticity measures the sensitivity of demand to changes in consumer income. It helps classify goods and predict shifts in demand as economies grow.

收入弹性衡量需求对消费者收入变化的敏感度。它有助于对商品进行分类，并预测经济增长过程中需求的变动。

YED = %ΔQD / %ΔY

where Y stands for income.

其中 Y 代表收入。

If YED > 0, the good is normal. For YED > 1, it is a luxury; for 0 < YED ≤ 1, it is a necessity.

如果 YED > 0，该商品为正常品。YED > 1 为奢侈品；0 < YED ≤ 1 为必需品。
If YED < 0, the good is inferior – demand falls as income rises (e.g., own-label products).

如果 YED < 0，该商品为低档品——需求随收入上升而下降（如自有品牌产品）。

Firms use YED to forecast sales during different stages of the economic cycle.

企业利用 YED 来预测经济周期不同阶段的销售情况。

4. Price Elasticity of Supply (PES) | 供给价格弹性

Price elasticity of supply captures how quickly producers can change output when market price changes. It depends on factors like spare capacity, stock levels, and the time period considered.

供给价格弹性反映市场价格变化时生产者改变产量的速度。它取决于闲置产能、库存水平以及考虑的时间周期等因素。

PES = %ΔQS / %ΔP

PES > 1: supply is elastic – producers can respond easily to price changes.

PES > 1：供给富有弹性——生产者能轻松对价格变化做出反应。
PES < 1: supply is inelastic – output is difficult to adjust quickly.

PES < 1：供给缺乏弹性——产量难以快速调整。
PES = 0: perfectly inelastic supply (e.g., a concert venue with fixed seats in the short run).

PES = 0：完全无弹性供给（例如，短期内座位固定的音乐厅）。

In the market period, PES is close to zero. In the long run, supply becomes increasingly elastic as all factors of production can be varied.

在市场期内，PES 接近于零。长期来看，随着所有生产要素均可变动，供给变得越来越富有弹性。

5. Costs of Production | 生产成本

An understanding of cost structures is essential for the Theory of the Firm. These formulas describe the behaviour of costs as output varies.

理解成本结构对于厂商理论至关重要。以下公式描述了成本随产量变化的行为。

Total Cost (TC) = Total Fixed Cost (TFC) + Total Variable Cost (TVC)

Average costs are derived simply by dividing by the level of output (Q):

平均成本只需除以产量 Q 即可得出：

ATC = TC / Q
AFC = TFC / Q
AVC = TVC / Q

Marginal cost is the extra cost of producing one more unit:

边际成本是额外生产一单位产量所增加的成本：

MC = ΔTC / ΔQ

The MC curve intersects the ATC and AVC curves at their lowest points. When MC < ATC, ATC is falling; when MC > ATC, ATC is rising.

MC 曲线在 ATC 和 AVC 曲线的最低点与其相交。当 MC < ATC 时，ATC 下降；当 MC > ATC 时，ATC 上升。

6. Revenue and Profit | 收益与利润

Revenue concepts link the price of a product to the quantity sold, and profit calculations show the financial health of a firm.

收益概念将产品价格与销售量联系起来，而利润计算则反映企业的财务健康状况。

Total Revenue (TR) = P × Q

Average revenue equals price:

平均收益等于价格：

AR = TR / Q = P

Marginal revenue is the change in total revenue from selling an additional unit:

边际收益是多销售一单位产品带来的总收益变化：

MR = ΔTR / ΔQ

Profit is the difference between total revenue and total cost:

利润是总收益与总成本之间的差额：

Profit = TR – TC

A firm maximises profit where MR = MC, as long as AR ≥ AVC in the short run.

企业利润最大化的条件是 MR = MC，且短期内满足 AR ≥ AVC。

7. Market Concentration Ratios | 市场集中度比率

Concentration ratios measure the extent to which a market is dominated by its largest firms. Higher ratios signal more concentrated, less competitive markets.

集中度比率衡量市场被最大几家企业支配的程度。比率越高，市场越集中，竞争越弱。

CRn = (Combined Sales of n Largest Firms / Total Industry Sales) × 100

Commonly, a five-firm concentration ratio (CR5) or three-firm ratio (CR3) is used. For example, a CR5 above 60% often suggests an oligopolistic market structure.

通常使用五企业集中度（CR5）或三企业集中度（CR3）。例如，CR5 超过 60% 往往表明寡头垄断的市场结构。

The Herfindahl-Hirschman Index (HHI) provides greater precision by summing the squared market shares of all firms:

赫芬达尔-赫希曼指数（HHI）通过加总所有企业市场份额的平方值，提供了更高的精确度：

HHI = Σ (Market Share of each firm)²

An HHI below 1,000 typically indicates an unconcentrated market; above 1,800 indicates high concentration.

HHI 低于 1,000 通常表示市场不集中；高于 1,800 则表示高度集中。

8. National Income Accounting | 国民收入核算

The measurement of economic activity is based on the circular flow of income. The three methods – expenditure, income, and output – should theoretically yield the same Gross Domestic Product (GDP).

经济活动的衡量基于国民收入循环流。支出法、收入法和产出法这三种方法在理论上应得出相同的国内生产总值（GDP）。

GDP (Expenditure) = C + I + G + (X – M)

where C = consumption, I = investment, G = government spending, X = exports, M = imports.

其中 C = 消费，I = 投资，G = 政府支出，X = 出口，M = 进口。

Net Domestic Product (NDP) accounts for capital depreciation:

国内生产净值（NDP）考虑了资本折旧：

NDP = GDP – Depreciation

Gross National Income (GNI) adds net income from abroad:

国民总收入（GNI）则加上来自国外的净收入：

GNI = GDP + Net Income from Abroad

Real GDP strips out the effects of inflation:

实际 GDP 剔除了通货膨胀的影响：

Real GDP = (Nominal GDP / GDP Deflator) × 100

9. The Multiplier and Marginal Propensities | 乘数与边际倾向

The multiplier effect explains how an initial injection into the circular flow can lead to a larger final increase in national income. Its size depends on leakages.

乘数效应解释了最初注入循环流的一笔资金如何导致国民收入最终发生更大的增长。其大小取决于漏出量。

Multiplier (k) = 1 / (1 – MPC) = 1 / MPW

where MPC is the marginal propensity to consume and MPW is the marginal propensity to withdraw (MPS + MPT + MPM). Specifically:

其中 MPC 是边际消费倾向，MPW 是边际漏出倾向（MPS + MPT + MPM）。具体而言：

MPC = ΔC / ΔY : the fraction of additional income spent on consumption.

MPC = ΔC / ΔY：额外收入中用于消费的部分。
MPS = ΔS / ΔY : the fraction saved.

MPS = ΔS / ΔY：用于储蓄的部分。
MPT = ΔT / ΔY : the fraction taken as tax.

MPT = ΔT / ΔY：用于纳税的部分。
MPM = ΔM / ΔY : the fraction spent on imports.

MPM = ΔM / ΔY：用于进口的部分。

The sum of MPC and MPW equals 1. A high MPC makes the multiplier larger; high leakages reduce it.

MPC 与 MPW 之和等于 1。MPC 越高，乘数越大；漏出越多，乘数越小。

10. Unemployment and Inflation Rates | 失业率与通货膨胀率

Labour market indicators and price stability measures are central to macroeconomic analysis. These simple ratios form the foundation of policy evaluation.

劳动力市场指标和物价稳定指标是宏观经济分析的核心。这些简单的比率为政策评估奠定了基础。

Unemployment Rate = (Number of Unemployed / Labour Force) × 100

The labour force includes both employed and unemployed individuals who are actively seeking work. The participation rate is a related measure:

劳动力包括就业者以及正在积极寻找工作的失业者。劳动力参与率是相关指标：

Participation Rate = (Labour Force / Working-Age Population) × 100

Inflation is measured through a price index. The Consumer Price Index (CPI) uses a representative basket of goods. The annual inflation rate is the percentage change in that index:

通货膨胀通过价格指数来衡量。消费者价格指数（CPI）使用一篮子代表性商品。年通胀率是该指数的百分比变化：

Inflation Rate = ((CPI_t – CPI_t-1) / CPI_t-1) × 100

Similarly, the GDP deflator provides a broader measure of inflation across all domestically produced goods:

同样，GDP 平减指数更全面地衡量所有国内生产商品的通胀：

GDP Deflator = (Nominal GDP / Real GDP) × 100

11. Exchange Rates and Terms of Trade | 汇率与贸易条件

International economics introduces formulas that evaluate a country’s external position. Terms of trade reflect export prices relative to import prices, while exchange rates determine one currency’s value against another.

国际经济学引入了评估一国对外状况的公式。贸易条件反映出口价格相对于进口价格的比值，而汇率则决定一种货币对另一种货币的价值。

Terms of Trade = (Index of Export Prices / Index of Import Prices) × 100

An increase in the terms of trade means a country can buy more imports for a given quantity of exports. It is influenced by factors such as commodity price movements and exchange rate fluctuations.

贸易条件提高意味着一国用既定数量的出口可买到更多的进口商品。它受大宗商品价格波动和汇率变动等因素的影响。

For exchange rates, a simple bilateral rate is expressed as the amount of foreign currency per unit of domestic currency, or vice versa. When the pound strengthens, fewer pounds are needed to buy a dollar – the exchange rate moves in favour of the domestic currency.

对于汇率，简单的双边汇率用一单位本币兑换多少外币来表示，或者反过来。当英镑走强时，买一美元所需的英镑减少——汇率向有利于本币的方向移动。

Exchange Rate (GBP/USD) = Number of USD per 1 GBP

Effective exchange rates are weighted averages against a basket of currencies, reflecting trade shares.

有效汇率是对一篮子货币按贸易份额加权的平均值。

12. Productivity and Economic Growth | 生产率与经济增长

Growth accounting helps economists decompose the sources of economic expansion. Labour productivity and the output gap are frequently assessed alongside real GDP growth.

增长核算有助于经济学家分解经济扩张的来源。劳动生产率和产出缺口常常与实际 GDP 增长率一并评估。

Labour Productivity = Real GDP / Number of Employed Persons (or Total Hours Worked)

Growth in labour productivity is a key driver of long-run improvements in living standards.

劳动生产率的增长是长期生活水平提高的关键驱动力。

The output gap shows whether an economy is operating above or below its potential:

产出缺口表明经济运行在潜在产出之上还是之下：

Output Gap = (Actual GDP – Potential GDP) / Potential GDP × 100

A negative output gap signals a recessionary gap with unemployed resources; a positive gap may indicate an inflationary boom.

负的产出缺口表明存在衰退缺口，资源闲置；正的产出缺口可能表示通胀性繁荣。

Finally, the simple growth rate of any variable captures its percentage change:

最后，任何变量的简单增长率都反映其百分比变化：

Growth Rate = ((New Value – Old Value) / Old Value) × 100

This same logic underpins calculations of changes in GDP, inflation, productivity, and more.

同样的逻辑支撑着 GDP 变化、通胀变化、生产率变化等各种计算。

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IB CCEA Economics Formula Handbook | IB CCEA 经济：公式汇总手册