📚 Year 10 CAIE Economics Formula & Theorem Quick Reference Handbook | 10年级CAIE经济：公式定理速查手册
This bilingual handbook collects every essential formula, definition and economic theorem you will meet in the Year 10 CAIE Economics course. Use it for last‑minute revision, quick checks during homework, or as a portable reference whenever you need to calculate elasticities, costs or macroeconomic indicators. Each section pairs an English explanation with a matching Chinese paragraph so you master the concepts in both languages.
这本双语手册汇集了所有你在10年级CAIE经济课程中会遇到的关键公式、定义和经济定理。你可以用它进行考前冲刺复习、做作业时快速查阅，或者当作一本便携式参考手册，随时计算弹性、成本或宏观经济指标。每个部分都采用英中对照的形式，帮助你同时掌握两种语言下的经济学概念。
1. Opportunity Cost & Production Possibility Curve (PPC) | 机会成本与生产可能性曲线
The economic problem arises from unlimited wants but scarce resources, forcing choices to be made. Opportunity cost is the value of the next best alternative foregone when a choice is made – it is the central concept linking scarcity, choice and resource allocation.
经济问题的根源在于无限欲望与稀缺资源之间的矛盾，迫使人们做出选择。机会成本是做出一种选择时所放弃的次优替代品的价值——它是连接稀缺性、选择和资源配置的核心概念。
On a Production Possibility Curve (PPC), opportunity cost is reflected by the downward slope: to produce more of Good X, a country must sacrifice some production of Good Y. The shape of the PPC illustrates increasing opportunity cost when resources are not equally efficient in all uses.
在生产可能性曲线上，机会成本体现为曲线的向下倾斜：要生产更多X商品，国家必须牺牲部分Y商品的生产。当资源在不同用途上的效率不相等时，PPC呈外凸形状，反映了机会成本递增。
Opportunity Cost = Sacrificed quantity of Good Y ÷ Gained quantity of Good X
机会成本 = 放弃的Y商品数量 ÷ 获得的X商品数量
2. The Law of Demand & Demand Curve Shifts | 需求定律与需求曲线移动
The law of demand states that, ceteris paribus, as the price of a good rises, the quantity demanded falls, and vice versa. This inverse relationship is shown by a downward‑sloping demand curve.
需求定律指出，在其他条件不变的前提下，商品价格上升时，需求量下降；价格下降时，需求量上升。这种反向关系通过一条向下倾斜的需求曲线来表现。
A change in price causes a movement along the demand curve (contraction or extension). A change in any non‑price determinant – such as income, tastes, price of substitutes or complements – shifts the entire demand curve to the right (increase) or left (decrease).
价格变化导致需求量沿需求曲线移动（收缩或扩张）。任何非价格决定因素的变化——例如收入、偏好、替代品或互补品价格——都会使整条需求曲线向右移动（增加）或向左移动（减少）。
| Shifter | 移动因素 | Effect on Demand | 对需求的影响 |
|---|---|
| Income (normal good) | 收入（正常品） | Increase → right shift | 增加→右移 |
| Price of substitute rises | 替代品价格上升 | Demand for the good rises → right shift | 该商品需求增加→右移 |
| Price of complement rises | 互补品价格上升 | Demand for the good falls → left shift | 该商品需求减少→左移 |
3. The Law of Supply & Supply Curve Shifts | 供给定律与供给曲线移动
The law of supply states that, ceteris paribus, a higher price leads to a higher quantity supplied, and a lower price reduces the quantity supplied. The supply curve therefore slopes upward.
供给定律指出，在其他条件不变时，价格越高，供给量越大；价格越低，供给量越小。因此供给曲线向右上方倾斜。
Non‑price determinants such as production costs, technology, taxes, subsidies and the number of sellers shift the supply curve. A fall in production costs or an improvement in technology shifts the supply curve to the right (increase). A rise in input prices shifts it to the left (decrease).
生产成本、技术、税收、补贴以及卖方数量等非价格因素会移动供给曲线。生产成本下降或技术进步使供给曲线向右移动（增加）；投入品价格上涨使供给曲线向左移动（减少）。
Supply function: Qs = c + dP (d > 0)
供给函数：Qs = c + dP (d > 0)
4. Market Equilibrium & Price Mechanism | 市场均衡与价格机制
ls quantity supplied, i.e. Qd = Qs. At this point there is no tendency for price to change – the market clears.
市场均衡发生在需求量等于供给量时，即 Qd = Qs。在这个点上，价格没有变动的趋势，市场出清。
Excess demand (shortage) occurs when the market price is below equilibrium, pushing price up. Excess supply (surplus) occurs when price is above equilibrium, forcing price down. This automatic adjustment is the price mechanism.
当市场价格低于均衡价格时，出现超额需求（短缺），推动价格上涨。当价格高于均衡价格时，出现超额供给（过剩），迫使价格下降。这种自动调节就是价格机制。
Government price controls – maximum price (ceiling) and minimum price (floor) – disrupt this mechanism, creating persistent shortages or surpluses unless accompanied by other measures.
政府实施的价格管制——最高限价和最低限价——会打乱这一机制，除非配合其他措施，否则会导致持续的短缺或过剩。
5. Price Elasticity of Demand (PED) | 需求的价格弹性
PED measures the responsiveness of quantity demanded to a change in price. It is always negative because of the law of demand, but economists usually treat it as an absolute value.
PED衡量需求量对价格变化的反应程度。由于需求定律，它总是负值，但经济学家通常将其表示为绝对值。
PED = (% Change in Quantity Demanded) ÷ (% Change in Price)
PED = （需求量变动的百分比）÷（价格变动的百分比）
) ÷ (ΔP ÷ P₀), where Qd₀ and P₀ are the original quantity and price. The sign is ignored for interpretation.
用初始值计算：PED = (ΔQd ÷ Qd₀) ÷ (ΔP ÷ P₀)，其中 Qd₀ 和 P₀ 为初始数量和价格。解释时忽略负号。
| |PED| Value | 数值 | Elasticity Classification | 弹性分类 |
|---|---|
| > 1 | Price elastic | 富有弹性 |
| = 1 | Unit elastic | 单位弹性 |
| < 1 | Price inelastic | 缺乏弹性 |
| = 0 | Perfectly inelastic | 完全无弹性 |
| = ∞ | Perfectly elastic | 完全弹性 |
6. PED and Total Revenue | PED与总收益
ntity sold. The effect of a price change on TR depends critically on the price elasticity of demand.
总收益是企业从销售中获得的总收入：TR = 价格 × 销售数量。价格变动对总收益的影响关键取决于需求的价格弹性。
If demand is price elastic (|PED| > 1), a price fall raises TR because the proportionate increase in quantity demanded is larger than the proportionate fall in price. A price rise reduces TR.
如果需求富有弹性（|PED| > 1），降价会使总收益增加，因为需求量增加的比例大于价格下降的比例；提价则会减少总收益。
If demand is price inelastic (|PED| < 1), a price rise raises TR (quantity fall proportionately smaller) and a price fall lowers TR. When demand is unit elastic, TR remains constant as price changes.
如果需求缺乏弹性（|PED| < 1），提价会使总收益增加（需求量减少的比例较小），降价则减少总收益。当需求为单位弹性时，价格变化时总收益保持不变。
TR = P × Q ΔTR direction ⇔ |PED|
TR = P × Q TR变动方向取决于|PED|
7. Income Elasticity of Demand (YED) & Cross Elasticity of Demand (XED) | 需求的收入弹性与交叉弹性
YED measures how quantity demanded responds to a change in consumer income. It helps classify goods as normal (YED > 0) or inferior (YED < 0). Luxury goods have YED > 1; necessities have 0 < YED < 1.
YED衡量需求量对消费者收入变化的反应程度。据此可将商品分为正常品（YED > 0）和低档品（YED < 0）。奢侈品 YED > 1，必需品 0 < YED < 1。
YED = (% Change in Quantity Demanded) ÷ (% Change in Income)
YED = （需求量变动的百分比）÷（收入变动的百分比）
XED measures the responsiveness of demand for Good A when the price of Good B changes. A positive XED indicates substitute goods; a negative XED indicates complementary goods. XED close to zero suggests independent goods.
XED衡量A商品需求量对B商品价格变化的反应程度。XED为正表示替代品，为负表示互补品，接近于零表示独立品。
XED = (% Change in Qd of Good A) ÷ (% Change in Price of Good B)
XED = （A商品需求量变动的百分比）÷（B商品价格变动的百分比）
8. Price Elasticity of Supply (PES) | 供给的价格弹性
PES measures the responsiveness of quantity supplied to a change in price. Unlike PED, PES is usually positive because higher prices encourage more production.
PES衡量供给量对价格变化的反应程度。与PED不同，PES通常为正值，因为更高的价格会激励厂商生产更多。
PES = (% Change in Quantity Supplied) ÷ (% Change in Price)
PES = （供给量变动的百分比）÷（价格变动的百分比）
Key determinants of PES include the time period (supply is more elastic in the long run), spare production capacity, ease of storing stocks, and the mobility of factors of production. Agricultural goods often have low PES in the short run.
决定PES的主要因素有：时间周期（长期供给弹性更大）、闲置产能、存货储存的便利性以及生产要素的流动性。农产品在短期内往往PES较低。
9. Costs, Revenues & Profit Maximisation | 成本、收益与利润最大化
Firms aim to maximise profit (π), which is the difference between total revenue (TR) and total cost (TC). Profit is maximised when marginal cost (MC) equals marginal revenue (MR), provided MC cuts MR from below.
企业的目标是最大化利润（π），即总收益与总成本之差。当边际成本等于边际收益且MC自下而上穿过MR时，利润达到最大。
Profit = Total Revenue – Total Cost (π = TR – TC)
利润 = 总收益 – 总成本 (π = TR – TC)
(AC) = TC ÷ Quantity. When MC < AC, AC falls; when MC > AC, AC rises. This explains the U‑shape of the average cost curve and the link to economies of scale.
总成本由固定成本和可变成本构成。平均成本 = 总成本 ÷ 产量。当边际成本低于平均成本时，平均成本下降；当边际成本高于平均成本时，平均成本上升。这解释了平均成本曲线的U型特征及其与规模经济的关系。
AC = TC ÷ Q MC = ΔTC ÷ ΔQ
平均成本 = 总成本 ÷ 产量 边际成本 = 总成本变动量 ÷ 产量变动量
10. Macroeconomic Indicators: Unemployment, Inflation & GDP | 宏观经济指标：失业率、通货膨胀与GDP
The unemployment rate measures the proportion of the labour force that is actively seeking work but cannot find employment. It is one of the key indicators of economic health.
失业率衡量了劳动力中积极寻找工作但未能就业的比例，是反映经济健康状况的关键指标之一。
Unemployment Rate = (Number of Unemployed ÷ Labour Force) × 100
失业率 = （失业人数 ÷ 劳动力总数）× 100
Inflation is the sustained rise in the general price level, measured by the Consumer Price Index (CPI). The inflation rate shows how fast prices are rising compared to a base year.
通货膨胀是指总体物价水平的持续上升，通常用消费者价格指数（CPI）来衡量。通胀率反映了与基年相比物价上涨的速度。
Inflation Rate = [(CPI year 2 – CPI year 1) ÷ CPI year 1] × 100
通胀率 = [（第二年的CPI – 第一年的CPI）÷ 第一年的CPI] × 100
Gross Domestic Product (GDP) is the total market value of all final goods and services produced within a country in a year. Real GDP is adjusted for inflation, allowing meaningful comparisons over time.
国内生产总值（GDP）是一个国家在一年内生产的所有最终商品和服务的市场价值总和。实际GDP经通胀调整后，可以进行有意义的跨时期比较。
Real GDP = (Nominal GDP ÷ GDP Deflator) × 100
实际GDP = （名义GDP ÷ GDP平减指数）× 100
These three indicators are central to the government's macroeconomic objectives: low unemployment, low and stable inflation, and steady economic growth.
这三个指标是政府宏观经济目标的核心：低失业率、低且稳定的通胀，以及持续的经济增长。
Published by TutorHao | Economics Revision Series | aleveler.com
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