Year 10 CIE Economics: Formula & Theorem Quick Reference Guide | 公式定理速查手册

📚 Year 10 CIE Economics: Formula & Theorem Quick Reference Guide | 公式定理速查手册

This quick reference handbook compiles essential formulas, theorems, and key relationships for Year 10 CIE Economics. Use it to revise core concepts quickly and confidently.

本速查手册汇总了 CIE Year 10 经济学的核心公式、定理与关键关系，帮助你快速且自信地复习核心概念。

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1. The Law of Demand & Demand Curve | 需求定律与需求曲线

The law of demand states that, ceteris paribus, as the price of a good rises, the quantity demanded contracts, and as price falls, the quantity demanded extends. This gives the demand curve its downward slope.

需求定律表明，在其他条件不变的情况下，商品价格上升时需求量缩减，价格下降时需求量增加。这使得需求曲线向右下方倾斜。

A linear demand function is expressed as:

线性需求函数表示为：

Q_d = a − bP

where a is the intercept (quantity demanded when P=0) and b is the slope (ΔQ_d/ΔP), showing the inverse relationship between price and quantity demanded.

其中 a 为截距（价格等于零时的需求量），b 为斜率（ΔQ_d/ΔP），反映价格与需求量之间的反向关系。

A movement along the demand curve occurs when only the good's own price changes. A shift of the entire curve occurs when a non-price determinant changes, such as income, tastes, prices of related goods, or expectations.

若仅商品自身价格变动，需求量沿需求曲线移动；若收入、偏好、相关商品价格或预期等非价格因素变动，整条需求曲线发生平移。

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2. The Law of Supply & Supply Curve | 供给定律与供给曲线

The law of supply states that, ceteris paribus, as the price of a good rises, the quantity supplied extends, and as price falls, the quantity supplied contracts. The supply curve therefore slopes upward.

供给定律表明，在其他条件不变的情况下，价格上升时供给量增加，价格下降时供给量减少。因此供给曲线向右上方倾斜。

The linear supply function is typically written as:

线性供给函数通常表示为：

Q_s = c + dP

where c represents the minimum quantity supplied when price is zero (often negative if there is a minimum price required to produce), and d is the slope (ΔQ_s/ΔP), positive in sign.

其中 c 表示价格为零时愿意供给的最小量（若存在最低生产价格，则通常为负值），d 为斜率（ΔQ_s/ΔP），符号为正。

A movement along the supply curve is caused by a change in the good's own price. Shifts occur when factors such as costs of production, technology, taxes, subsidies, or weather conditions change.

商品自身价格变动使供给量沿曲线移动；生产成本、技术、税收、补贴或气候等因素变动则使整条供给曲线平移。

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3. Market Equilibrium | 市场均衡

Market equilibrium occurs where quantity demanded equals quantity supplied at a given price. There is no tendency for change. The equilibrium condition is:

市场均衡出现在某一价格下需求量等于供给量时，不存在自发变动趋势。均衡条件为：

Q_d = Q_s

When the market price is above equilibrium, excess supply (a surplus) pushes the price down. When it is below equilibrium, excess demand (a shortage) pushes the price up. This is the price mechanism's invisible hand.

当市场价格高于均衡价格时，超额供给（盈余）促使价格下降；低于均衡价格时，超额需求（短缺）促使价格上升。这就是价格机制的“看不见的手”。

Algebraically, equilibrium price and quantity are found by solving Q_d = a - bP and Q_s = c + dP simultaneously.

代数上，通过联立 Q_d = a - bP 与 Q_s = c + dP 求解可得均衡价格与数量。

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

PED measures the responsiveness of quantity demanded to a change in the good's own price. The formula is:

PED 衡量需求量对商品自身价格变化的反应程度。计算公式为：

PED = (%ΔQ_d) ÷ (%ΔP)

Alternatively, using the point-slope method:

或使用点斜率法：

PED = (ΔQ_d / ΔP) × (P / Q_d)

PED is always negative due to the law of demand, but economists often ignore the sign and express it in absolute terms.

因需求定律，PED 恒为负值，但经济学家通常忽略符号，以绝对值表示。

|PED| > 1	Elastic: quantity demanded responds more than proportionately to a price change.	富有弹性：需求量变动的比例大于价格变动的比例。
|PED| = 1	Unit elastic: quantity demanded changes in exact proportion to price.	单位弹性：需求量与价格同比例变动。
|PED| < 1	Inelastic: quantity demanded responds less than proportionately.	缺乏弹性：需求量变动的比例小于价格变动的比例。
|PED| = 0	Perfectly inelastic: quantity demanded does not change when price changes.	完全无弹性：价格变动时需求量不变。
|PED| = ∞	Perfectly elastic: any price rise reduces quantity demanded to zero.	完全弹性：价格任何上升都会导致需求量降至零。

Key determinants of PED include availability of substitutes, degree of necessity, proportion of income spent, and the time period under consideration.

影响 PED 的主要因素包括替代品的可获得性、必需程度、支出占收入的比例以及考察的时间长短。

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

YED measures the responsiveness of quantity demanded to a change in consumers' income. The formula is:

YED 衡量需求量对消费者收入变动的反应程度。公式为：

YED = (%ΔQ_d) ÷ (%ΔY)

where Y represents income. Unlike PED, the sign of YED is crucial. A positive YED indicates a normal good; a negative YED indicates an inferior good.

其中 Y 代表收入。与 PED 不同，YED 的符号至关重要。YED 为正表示正常品；YED 为负表示低档品。

For normal goods, if 0 < YED < 1, the good is a necessity (income inelastic); if YED > 1, it is a luxury (income elastic).

对于正常品，若 0 < YED < 1，则为必需品（收入缺乏弹性）；若 YED > 1，则为奢侈品（收入富有弹性）。

Firms use YED to forecast sales during economic booms and recessions and to plan the structure of their product portfolio.

企业利用 YED 预测经济繁荣与衰退时的销售量，并规划产品组合的结构。

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6. Cross Elasticity of Demand (XED) | 需求交叉弹性

XED measures the responsiveness of the quantity demanded of one good (A) to a change in the price of another good (B).

XED 衡量一种商品 (A) 的需求量对另一种商品 (B) 价格变动的反应程度。

XED = (%ΔQ_d of good A) ÷ (%ΔP of good B)

A positive XED indicates substitute goods (e.g., Coke and Pepsi). A negative XED indicates complementary goods (e.g., printers and ink cartridges). A value close to zero suggests the goods are unrelated.

XED 为正表示替代品（如可口可乐与百事可乐）；为负表示互补品（如打印机与墨盒）；接近于零则表示商品间无关联。

The magnitude, not just the sign, indicates the strength of the relationship. A highly positive XED means the substitutes are very close.

不仅符号，数值的大小也反映关联的强弱。高度正值的 XED 意味着替代品关系非常紧密。

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

PES measures the responsiveness of quantity supplied to a change in the good's own price.

PES 衡量供给量对商品自身价格变动的反应程度。

PES = (%ΔQ_s) ÷ (%ΔP)

1 is inelastic supply; PES = 0 is perfectly inelastic; PES = ∞ is perfectly elastic.

因供给定律，PES 通常为正值。PES > 1 为富有弹性；PES < 1 为缺乏弹性；PES = 0 为完全无弹性；PES = ∞ 为完全弹性。

Key determinants of PES are the length of the production period, spare capacity, ease of factor substitution, and the number of firms in the market.

影响 PES 的关键因素包括生产周期长短、闲置产能、要素替代的难易程度以及市场中企业的数量。

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8. Total Revenue and Elasticity | 总收益与弹性关系

Total revenue (TR) is the sum of money received by a firm from selling a given quantity of output:

总收益 (TR) 是企业销售一定产量所获得的货币总额：

TR = P × Q

The relationship between price elasticity of demand and total revenue is a vital theorem for pricing decisions:

需求价格弹性与总收益之间的关系是定价决策的重要定理：

• When demand is elastic (|PED| > 1): a price cut raises TR; a price rise lowers TR. 当需求富有弹性：降价增加总收益，提价减少总收益。
• When demand is inelastic (|PED| < 1): a price cut lowers TR; a price rise raises TR. 当需求缺乏弹性：降价减少总收益，提价增加总收益。
• When demand is unit elastic (|PED| = 1): a change in price leaves TR unchanged. 当需求单位弹性：价格变动不影响总收益。

This rule explains why farmers' revenues may not increase after a bumper harvest (inelastic demand for food).

这一规则解释了为何丰收后农民的总收益可能不升反降（食品需求缺乏弹性）。

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9. Costs, Revenue and Profit Formulae | 成本、收益与利润公式

Firms base production decisions on cost and revenue calculations. The fundamental profit equation is:

企业的生产决策基于成本与收益计算。基本利润公式为：

Profit = Total Revenue (TR) − Total Cost (TC)

Total cost (TC) is the sum of total fixed costs (TFC) and total variable costs (TVC). Fixed costs do not vary with output (e.g., rent); variable costs change directly with output (e.g., raw materials).

总成本 (TC) 为总固定成本 (TFC) 与总可变成本 (TVC) 之和。固定成本不随产量变化（如租金），可变成本随产量直接变化（如原材料）。

TC = TFC + TVC

Average cost (ATC) and average revenue (AR) can then be derived:

进而可得出平均成本与平均收益：

ATC = TC ÷ Q

AR = TR ÷ Q

Marginal cost (MC) is the addition to total cost from producing one extra unit:

边际成本 (MC) 是额外生产一单位产品所增加的总成本：

MC = ΔTC ÷ ΔQ

sing output level occurs where MC = MR (marginal revenue), provided MC cuts MR from below.

利润最大化产量出现在边际成本等于边际收益 (MC = MR) 处，且前提是 MC 从下方穿过 MR。

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10. Average and Marginal Revenue | 平均收益与边际收益

Average revenue (AR) is revenue per unit sold. For any firm, AR equals the price at which the product is sold:

平均收益 (AR) 是每单位售出商品带来的收入。对于任何企业，AR 等于产品售价：

AR = P

Marginal revenue (MR) is the extra revenue from selling one more unit. The relationship between MR and AR depends on market structure:

边际收益 (MR) 是额外销售一单位产品所增加的总收入。MR 与 AR 的关系取决于市场结构：

• Under perfect competition: The firm is a price-taker, so AR = MR = P. The demand curve for the firm is horizontal. 在完全竞争下：企业是价格接受者，因此 AR = MR = P，企业面对的需求曲线为水平线。
• Under imperfect competition (monopoly, oligopoly, monopolistic competition): The firm faces a downward-sloping demand curve; to sell an extra unit, it must lower the price on all units, so MR < AR. MR curve lies below the AR (demand) curve. 在不完全竞争下（垄断、寡头、垄断竞争）：企业面临向右下方倾斜的需求曲线；为多售一单位，必须降低所有单位的价格，因此 MR < AR，MR 曲线位于 AR 曲线下方。

revenue in a straight-line demand curve P = a - bQ is MR = a - 2bQ (for the linear case).

若需求曲线为线性 P = a - bQ，则边际收益为 MR = a - 2bQ。

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11. Opportunity Cost Principle | 机会成本定理

Opportunity cost is the fundamental concept of economics. It is defined as the value of the next-best alternative forgone when a choice is made.

机会成本是经济学的基础概念，定义为做出选择时所放弃的次优选项的价值。

There is no single formula, but the theorem is: every choice incurs an opportunity cost, and rational economic agents weigh marginal benefits against marginal opportunity costs when making decisions.

虽然没有单一公式，但其定理为：每一次选择都产生机会成本，理性经济主体在决策时比较边际收益与边际机会成本。

For production, the opportunity cost of producing an additional unit of good X is the amount of good Y that must be sacrificed, represented by the slope of the production possibility curve (PPC):

就生产而言，多生产一单位 X 的机会成本是必须牺牲的 Y 的数量，由生产可能性曲线 (PPC) 的斜率表示：

Opportunity Cost = |ΔY / ΔX|

This reflects the law of increasing opportunity cost as the PPC is usually concave to the origin.

这反映了机会成本递增规律，PPC 通常凹向原点。

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12. Production and Productivity | 生产与生产率

Productivity measures the efficiency of resource use. Labour productivity is a key indicator:

生产率衡量资源使用效率。劳动生产率是一项关键指标：

Labour Productivity = Total Output ÷ Number of Workers

otal Output ÷ Number of Capital Units. Productivity rises when output increases per unit of input, often thanks to technology, training, or specialisation.

类似的，资本生产率 = 总产出 ÷ 资本单位数。单位投入的产出增加时，生产率提高，这通常得益于技术、培训或专业化。

Total factor productivity (TFP) considers all inputs, but at Year 10 level the focus is on single-factor productivity measures. Rising productivity can shift the PPF outward, enabling economic growth.

全要素生产率 (TFP) 考虑所有投入，但在 Year 10 阶段重点关注单一要素生产率。生产率的提升可使生产可能性边界外移，实现经济增长。

The law of diminishing marginal returns states that when additional units of a variable factor are added to a

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