📚 Year 12 WJEC Economics: Formula & Theorem Quick Reference Handbook | Year 12 WJEC 经济：公式定理速查手册
This handbook compiles the essential formulas and theorems you need to master for the Year 12 WJEC Economics course. Each section provides a formula, a brief explanation, and paired English-Chinese descriptions to reinforce your understanding and aid bilingual revision. Use it alongside past papers and your class notes for the most effective preparation.
本手册汇编了 Year 12 WJEC 经济课程所需掌握的关键公式与定理。每个部分都提供公式、简要解释以及英中对照说明，以强化理解并辅助双语复习。请结合历年真题和课堂笔记一起使用，以获得最佳备考效果。
1. Price Elasticity of Demand (PED) | 需求价格弹性
Price elasticity of demand (PED) measures the responsiveness of quantity demanded to a change in price. It is defined as the percentage change in quantity demanded divided by the percentage change in price.
需求价格弹性（PED）衡量需求量对价格变动的反应程度。它的定义是需求量的百分比变化除以价格的百分比变化。
PED = %ΔQd ÷ %ΔP
The value of PED is normally negative because of the law of demand, but we usually take the absolute value. If |PED| > 1, demand is price elastic; if |PED| < 1, demand is price inelastic; if |PED| = 1, demand is unit elastic.
由于需求定律，PED 值通常为负，但我们一般取其绝对值。如果 |PED| > 1，需求富有弹性；如果 |PED| < 1，需求缺乏弹性；如果 |PED| = 1，需求具有单位弹性。
Key determinants of PED include the availability of substitutes, the proportion of income spent on the good, whether the good is a necessity or luxury, and the time period considered.
影响 PED 的关键因素包括替代品的可用性、该商品占收入的比例、商品是必需品还是奢侈品，以及所考虑的时间周期。
2. Income Elasticity of Demand (YED) | 需求收入弹性
Income elasticity of demand (YED) measures how quantity demanded responds to a change in consumers’ income. It is calculated as the percentage change in quantity demanded divided by the percentage change in income.
需求收入弹性（YED）衡量需求量对消费者收入变化的反应。它的计算方法是需求量的百分比变化除以收入的百分比变化。
YED = %ΔQd ÷ %ΔY
For normal goods, YED is positive; for inferior goods, YED is negative. If YED > 1, the good is a luxury; if 0 < YED < 1, the good is a necessity.
对于正常商品，YED 为正；对于劣质商品，YED 为负。如果 YED > 1，该商品是奢侈品；如果 0 < YED < 1，该商品是必需品。
3. Cross Elasticity of Demand (XED) | 需求交叉弹性
Cross elasticity of demand (XED) indicates the responsiveness of the quantity demanded of one good (A) to a change in the price of another good (B). It is the percentage change in quantity demanded of good A divided by the percentage change in price of good B.
需求交叉弹性（XED）表示一种商品 (A) 的需求量对另一种商品 (B) 价格变动的反应程度。它是商品 A 需求量的百分比变化除以商品 B 价格的百分比变化。
XED = %ΔQA ÷ %ΔPB
If XED > 0, the goods are substitutes; if XED < 0, they are complements; if XED ≈ 0, they are unrelated.
如果 XED > 0，两种商品互为替代品；如果 XED < 0，它们互为互补品；如果 XED 接近 0，则它们互不相关。
4. Price Elasticity of Supply (PES) | 供给价格弹性
Price elasticity of supply (PES) measures how much the quantity supplied of a good changes in response to a change in its price. It is the percentage change in quantity supplied divided by the percentage change in price.
供给价格弹性（PES）衡量商品供给量对其价格变动的反应程度。它是供给量的百分比变化除以价格的百分比变化。
PES = %ΔQs ÷ %ΔP
PES is generally positive. If PES > 1, supply is price elastic; if PES < 1, supply is price inelastic; if PES = 1, supply is unit elastic. The main determinant of PES is the time period and the ability of producers to alter output.
PES 通常为正。如果 PES > 1，供给富有弹性；如果 PES < 1，供给缺乏弹性；如果 PES = 1，供给具有单位弹性。PES 的主要决定因素是时间周期以及生产者调整产量的能力。
5. Total Revenue and the Relationship with Elasticity | 总收入及其与弹性的关系
Total revenue (TR) is the money a firm receives from selling its output. It is calculated as price multiplied by quantity sold.
总收入 (TR) 是企业通过销售产品所获得的货币总额。它的计算方法是价格乘以销量。
TR = P × Q
Knowledge of PED is crucial for pricing decisions. If demand is price elastic, a reduction in price leads to a more than proportionate increase in quantity demanded, so TR rises. If demand is price inelastic, a price rise increases TR because quantity demanded falls proportionately less.
了解 PED 对定价决策至关重要。如果需求富有弹性，降价将使需求量以更大比例增加，因此总收入上升。如果需求缺乏弹性，提价将增加总收入，因为需求量的下降比例更小。
6. Opportunity Cost and Comparative Advantage | 机会成本与比较优势
Opportunity cost is the value of the next best alternative forgone when a choice is made. Comparative advantage exists when a country can produce a good at a lower opportunity cost than another country.
机会成本是指做出某种选择时所放弃的次优选择的价值。比较优势是指一个国家能够以比另一个国家更低的机会成本生产某种商品。
Opportunity cost of 1 unit of X = (Units of Y sacrificed) ÷ (Units of X gained)
Even if one country has an absolute advantage in producing all goods, both countries can benefit from specialisation and trade if they have different opportunity cost ratios. This theorem underpins free trade policies.
即使一个国家在所有商品的生产上都具有绝对优势，只要两国的机会成本比率不同，双方就都能从专业化分工与贸易中获益。这个定理是自由贸易政策的理论基础。
7. Aggregate Demand (AD) Formula | 总需求公式
Aggregate demand is the total planned spending on goods and services produced within an economy in a given time period. It is composed of consumption (C), investment (I), government spending (G), and net exports (X − M).
总需求是在一定时期内，经济体内对生产的商品和服务的计划支出总额。它由消费 (C)、投资 (I)、政府支出 (G) 和净出口 (X − M) 构成。
AD = C + I + G + (X − M)
Changes in any of these components can shift the AD curve. For example, an increase in consumer confidence raises C and shifts AD to the right, leading to higher real GDP and possibly inflation.
任何组成部分的变化都会导致总需求曲线移动。例如，消费者信心增强会提高 C，使 AD 曲线右移，从而导致实际 GDP 增加，并可能引发通胀。
8. The Multiplier Effect | 乘数效应
The multiplier quantifies the magnified impact of an initial injection into the circular flow of income on the final level of national income. The size of the multiplier depends on the marginal propensity to withdraw (MPW).
乘数衡量的是初始注入资金经过收入循环流后对最终国民收入水平产生的放大效应。乘数的大小取决于边际漏出倾向 (MPW)。
Multiplier (k) = 1 ÷ MPW = 1 ÷ (MPS + MPT + MPM)
Where MPS is the marginal propensity to save, MPT is the marginal propensity to tax, and MPM is the marginal propensity to import. A higher MPW leads to a smaller multiplier effect.
其中 MPS 是边际储蓄倾向，MPT 是边际税收倾向，MPM 是边际进口倾向。MPW 越高，乘数效应越小。
If the multiplier is known, the change in national income (ΔY) from an injection (ΔJ) can be found as: ΔY = k × ΔJ.
如果已知乘数，则注入资金 (ΔJ) 带来的国民收入变化 (ΔY) 可用公式计算：ΔY = k × ΔJ。
9. Quantity Theory of Money (Fisher Equation) | 货币数量论（费雪方程式）
The quantity theory of money links the money supply in an economy to the price level and the volume of transactions. It is expressed by the Fisher equation.
货币数量论将经济中的货币供应量与价格水平和交易量联系起来。它通过费雪方程式来表达。
MV = PT
Where M is the money supply, V is the velocity of circulation (the rate at which money changes hands), P is the average price level, and T is the number of transactions in a period. In many textbooks this is written as MV = PQ, where Q stands for real output.
其中 M 表示货币供应量，V 表示货币流通速度（货币易手的速率），P 表示平均价格水平，T 表示一段时期内交易的数量。在许多教材中，该方程式写作 MV = PQ，其中 Q 代表实际产出。
Monetarists argue that V and T are relatively stable in the short run, so an increase in M leads directly to an increase in P, i.e., inflation.
货币主义者认为 V 和 T 在短期内相对稳定，因此 M 的增加将直接导致 P 的上涨，即通货膨胀。
10. Costs, Revenues and Profit of the Firm | 企业的成本、收益与利润
Understanding a firm’s cost and revenue structures is fundamental to microeconomics. Total cost (TC) is the sum of total fixed costs (TFC) and total variable costs (TVC). Average total cost (ATC) is TC divided by output (Q).
理解企业的成本与收益结构是微观经济学的基础。总成本 (TC) 是总固定成本 (TFC) 与总可变成本 (TVC) 之和。平均总成本 (ATC) 是 TC 除以产量 (Q)。
TC = TFC + TVC
ATC = TC ÷ Q
MC = ΔTC ÷ ΔQ
Marginal cost (MC) is the additional cost of producing one more unit. On the revenue side, average revenue (AR) equals price and is total revenue per unit: AR = TR ÷ Q = P. Marginal revenue (MR) is the extra revenue from selling one more unit: MR = ΔTR ÷ ΔQ.
边际成本 (MC) 是额外生产一单位产品所增加的成本。在收益方面，平均收益 (AR) 等于价格，即单位总收入：AR = TR ÷ Q = P。边际收益 (MR) 是额外销售一单位产品所带来的额外收益：MR = ΔTR ÷ ΔQ。
Profit is maximised where marginal cost equals marginal revenue (MC = MR). Normal profit occurs when TR = TC.
当边际成本等于边际收益 (MC = MR) 时，利润达到最大化。当总收益等于总成本 (TR = TC) 时，企业获得正常利润。
11. Social Optimum and Market Failure | 社会最优与市场失灵
Market failure occurs when the free market fails to allocate resources efficiently. The social optimum is achieved when the marginal social benefit (MSB) of consumption equals the marginal social cost (MSC) of production.
当自由市场无法高效配置资源时，便会出现市场失灵。社会最优状态是在消费的边际社会收益 (MSB) 等于生产的边际社会成本 (MSC) 时达到的。
Social optimum: MSB = MSC
Negative externalities cause overproduction because MSC > MSB at the free market output. Positive externalities lead to underproduction because MSB > MSC. The free market equilibrium occurs where marginal private benefit (MPB) equals marginal private cost (MPC). Therefore, the divergence MSB − MSC or MPB − MPC signals a misallocation of resources.
负外部性会导致过度生产，因为在自由市场产出下 MSC > MSB。正外部性会导致生产不足，因为 MSB > MSC。自由市场均衡出现在边际私人收益 (MPB) 等于边际私人成本 (MPC) 时。因此，MSB 与 MSC 或 MPB 与 MPC 的偏离意味着资源配置不当。
12. Measuring Unemployment and Inflation | 失业与通胀的衡量
The unemployment rate is one of the key macroeconomic indicators. It measures the percentage of the labour force that is willing and able to work but cannot find employment.
失业率是关键宏观经济指标之一。它衡量劳动力中有意愿且有能力工作但无法找到工作的人所占的百分比。
Unemployment rate = (Number of unemployed ÷ Labour force) × 100%
Inflation is a sustained rise in the general price level. The most common measure in the UK is the Consumer Prices Index (CPI). The inflation rate is the annual percentage change in the CPI.
通货膨胀是总体价格水平的持续上涨。英国最常见的衡量指标是消费者物价指数 (CPI)。通胀率是 CPI 的年度百分比变化。
Inflation rate = [(CPIcurrent − CPIprevious) ÷ CPIprevious] × 100%
Both indicators are vital for assessing economic performance and for guiding monetary and fiscal policies. High inflation erodes purchasing power, while high unemployment indicates unused labour resources.
这两个指标对于评估经济表现以及指导货币与财政政策至关重要。高通胀侵蚀购买力，而高失业率则表明劳动力资源未被充分利用。
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