📚 Year 13 CCEA Economics: Formula & Theorem Quick-Reference Handbook | Year 13 CCEA 经济：公式定理速查手册
This concise handbook gathers the essential formulas, theorems and definitions required for the Year 13 CCEA Economics specification. It is designed to support daily revision and help you move confidently between microeconomic and macroeconomic analysis. Keep it close when tackling data-response questions and extended essays.
本手册汇集了 Year 13 CCEA 经济学课程中必备的公式、定理与核心定义，旨在辅助日常复习，帮助你自如地在微观与宏观分析之间切换。在应对数据分析题和长篇论述时，随时翻阅可巩固关键思路。
1. Price, Income and Cross Elasticities | 价格、收入与交叉弹性
Price elasticity of demand (PED) measures the responsiveness of quantity demanded to a change in price, always reported as a positive absolute value unless stated otherwise. The coefficient is calculated using the percentage change in quantity demanded relative to the percentage change in price.
PED = (%ΔQd) / (%ΔP)
需求的价格弹性（PED）衡量需求量对价格变动的反应程度，通常以正绝对值表示。其系数由需求量变动的百分比除以价格变动的百分比得出。
If |PED| > 1 demand is elastic; if |PED| < 1 it is inelastic; a coefficient of exactly 1 denotes unit elasticity, while perfectly inelastic (0) and perfectly elastic (∞) are the two extreme cases. Factors such as the availability of substitutes, the proportion of income spent and the time period all influence the value.
若 |PED| > 1，需求富有弹性；|PED| < 1 则缺乏弹性；系数恰好为 1 时为单位弹性；完全无弹性（0）和完全弹性（∞）是两个极端。替代品的可得性、支出占收入的比例以及时间长短等因素都会影响弹性值。
Price elasticity of supply (PES) applies the same logic to the producer side. It reflects how easily firms can expand output in response to a price change, depending largely on spare capacity, stock levels and production time lags.
PES = (%ΔQs) / (%ΔP)
供给的价格弹性（PES）将同样逻辑应用于生产者一方，反映企业面对价格变动时扩大产出的难易程度，主要取决于闲置产能、库存水平和生产时滞。
Income elasticity of demand (YED) captures how quantity demanded shifts when household income changes. A positive YED indicates a normal good; a negative YED identifies an inferior good. The magnitude further distinguishes necessities (0 < YED < 1) from luxury items (YED > 1).
YED = (%ΔQd) / (%ΔY)
需求的收入弹性（YED）反映需求量如何随家庭收入变化而改变。YED 为正表示正常品，为负则为劣等品。系数的大小还可进一步区分必需品（0 < YED < 1）和奢侈品（YED > 1）。
Cross elasticity of demand (XED) measures the impact of the price of one good on the demand for another. Substitute goods have a positive XED; complementary goods have a negative XED. A coefficient close to zero suggests no significant relationship.
XED = (%ΔQd of good A) / (%ΔP of good B)
需求的交叉弹性（XED）衡量一种商品价格变动对另一种商品需求的影响。替代品的 XED 为正，互补品为负；系数接近零则表明两者无明显关联。
2. Costs, Revenue and Profit Maximisation | 成本、收益与利润最大化
Total cost (TC) is the sum of total fixed cost (TFC) and total variable cost (TVC). Average cost (ATC) is total cost divided by output, while marginal cost (MC) is the addition to total cost from producing one extra unit.
TC = TFC + TVC | ATC = TC / Q | MC = ΔTC / ΔQ
总成本（TC）是总固定成本（TFC）与总可变成本（TVC）之和。平均成本（ATC）为总成本除以产量，边际成本（MC）则是多生产一单位产品所带来的总成本增加量。
Total revenue (TR) equals price multiplied by quantity sold. Average revenue (AR) is identical to the demand curve for a price-taking firm. Marginal revenue (MR) is the extra revenue from selling one more unit. The profit-maximising rule in all market structures is MR = MC; if MR exceeds MC, the firm can increase profit by expanding output.
TR = P × Q | AR = TR / Q | MR = ΔTR / ΔQ
总收益（TR）等于价格乘以销售量。平均收益（AR）对价格接受者而言等同于需求曲线。边际收益（MR）是额外销售一单位所带来的收益增加量。所有市场结构中利润最大化的条件均为 MR = MC；若 MR 大于 MC，企业可通过扩大产量增加利润。
Normal profit is the minimum return required to keep resources in their current use; it is included in cost curves, so the firm breaks even when AR = ATC. Supernormal profit occurs when AR > ATC. The shutdown point in the short run is where price falls below average variable cost (P < AVC).
正常利润是维持资源当前用途所需的最低回报，已包含在成本曲线内，因此当 AR = ATC 时企业实现盈亏平衡。超常利润出现在 AR > ATC 时。短期停业点则是价格低于平均可变成本（P < AVC）的位置。
3. Market Structures and Efficiency | 市场结构与效率
Economists classify markets by the number of firms, the nature of the product, barriers to entry and the degree of price-setting power. Perfect competition features many small firms, a homogeneous product, no barriers and firms being price takers. Monopoly exists where a single firm dominates, protected by high barriers, while monopolistic competition combines many firms with product differentiation. Oligopoly is characterized by a few interdependent firms whose strategic behaviour can be modelled using game theory.
经济学家依据企业数量、产品性质、进入壁垒以及定价能力对市场分类。完全竞争有众多小企业、同质产品、无壁垒，企业是价格接受者。垄断由单一企业主导并受高壁垒保护；垄断竞争则将众多企业与产品差异化结合；寡头垄断则以少数相互依存的企业为特征，其策略行为可用博弈论加以分析。
Allocative efficiency is achieved when the price of the last unit equals the marginal cost of production (P = MC). Productive efficiency occurs when output is produced at the lowest possible average total cost, where ATC is at its minimum. In perfect competition, long-run equilibrium delivers both efficiencies; a monopoly typically fails on both counts, creating deadweight loss.
当最后一单位产品的价格等于其边际成本（P = MC）时，实现了配置效率。生产效率则出现在产出以尽可能低的平均总成本生产时，即 ATC 处于最低点。完全竞争的长远均衡能同时实现这两种效率；垄断通常两者都无法达到，产生无谓损失。
Concentration ratios measure the combined market share of the largest firms. A three-firm concentration ratio above 70% often signals an oligopolistic market. The Herfindahl-Hirschman Index (HHI) is an alternative measure obtained by summing the squares of individual market shares.
集中度比率衡量最大几家企业的合计市场份额。三家企业的集中度比率超过 70% 往往意味着寡头垄断市场。赫芬达尔-赫希曼指数（HHI）是另一种衡量方式，通过将各企业市场份额的平方加总得到。
4. Aggregate Demand and the Multiplier | 总需求与乘数
Aggregate demand (AD) is the total planned spending on domestic goods and services at a given price level. Its components are consumption (C), investment (I), government spending (G) and net exports (X − M).
AD = C + I + G + (X − M)
总需求（AD）是在既定价格水平下对国内商品与服务的计划支出总量，构成部分为消费（C）、投资（I）、政府支出（G）和净出口（X − M）。
The marginal propensity to consume (MPC) is the fraction of additional income that households spend on consumption. The multiplier (k) captures the magnified impact of an initial injection on national income. Its size depends on the marginal propensity to withdraw (MPW), which sums the marginal propensities to save, tax and import.
k = 1 / (1 − MPC) = 1 / MPS = 1 / MPW
边际消费倾向（MPC）是家庭将额外收入用于消费的比例。乘数（k）反映了初始注入对国民收入的放大效应。其大小取决于边际漏出倾向（MPW），即边际储蓄倾向、边际税率和边际进口倾向之和。
A high MPC leads to a larger multiplier, making fiscal policy more powerful. Conversely, a high marginal propensity to import reduces the multiplier because spending leaks overseas. Understanding the multiplier is essential for evaluating the effectiveness of demand‑side policies.
高 MPC 会使乘数增大，令财政政策更有效力。反之，高边际进口倾向会减小乘数，因为一部分支出流失至海外。理解乘数是评估需求侧政策效果的基础。
5. Aggregate Supply and Macroeconomic Equilibrium | 总供给与宏观经济均衡
Short‑run aggregate supply (SRAS) slopes upward because at least one factor price, typically nominal wages, is sticky. An increase in the price level temporarily raises profit margins, encouraging firms to expand output. The long‑run aggregate supply (LRAS) curve is vertical, representing the economy’s full‑employment output (Yf), determined by the stock of labour, capital and technology.
短期总供给（SRAS）向右上方倾斜，因为至少在短期内有一种要素价格（通常是名义工资）具有黏性。价格水平上升会暂时提高利润空间，激励企业扩大产出。长期总供给（LRAS）曲线是垂直的，表示充分就业产出（Yf），由劳动力、资本存量和技术水平决定。
Macroeconomic equilibrium occurs at the intersection of AD and SRAS. If the equilibrium lies to the left of LRAS, a negative output gap (recessionary gap) exists; if to the right, there is a positive output gap (inflationary gap). In the long run, factor price adjustments return the economy to Yf unless there is a supply‑side shock.
宏观经济均衡出现在 AD 与 SRAS 的交点。若均衡位于 LRAS 左侧，则存在负产出缺口（衰退缺口）；若位于右侧，则出现正产出缺口（通胀缺口）。长期中，要素价格调整使经济回归 Yf，除非发生供给侧冲击。
The multiplier and the accelerator together explain how output gaps can widen or narrow. The accelerator theory posits that investment depends on the rate of change of national income, not its level, linking demand volatility to capital spending.
乘数与加速数共同解释了产出缺口如何扩大或缩小。加速数理论认为投资取决于国民收入的变化率而非其水平，从而将需求波动与资本支出联系起来。
6. The Phillips Curve and the Trade‑off | 菲利普斯曲线与权衡取舍
The original Phillips curve documented an inverse relationship between the rate of change of money wages and unemployment. Policymakers initially regarded this as a stable menu of trade‑offs: lower unemployment could be ‘bought’ at the cost of higher wage inflation.
最初的菲利普斯曲线记录了货币工资变动率与失业率之间的反向关系。政策制定者起初将其视为一份稳定的取舍菜单：可以以更高的工资通胀为代价“购买”更低的失业率。
The expectations‑augmented Phillips curve shows that the trade‑off holds only in the short run. Once workers anticipate inflation, they demand higher nominal wages, shifting the short‑run curve upward. In the long run, unemployment reverts to its natural rate (NAIRU), and the curve becomes vertical.
π = πᵉ − β(u − uₙ)
附加预期的菲利普斯曲线表明，这一替代关系仅在短期成立。一旦工人预期到通胀，便会要求更高的名义工资，使短期曲线向上移动。长期中，失业率回到自然率（NAIRU），曲线变为垂直。
The long‑run vertical Phillips curve implies that expansionary demand policies cannot permanently reduce unemployment below its natural rate; they only generate accelerating inflation. This insight underpins the need for supply‑side measures to shift the LRAS and lower the natural rate of unemployment.
长期垂直的菲利普斯曲线意味着，扩张性需求政策无法将失业率永久压低至自然率之下，只会产生加速的通胀。这一洞见凸显了采取供给侧措施来移动 LRAS、降低自然失业率的必要性。
7. Comparative Advantage and Terms of Trade | 比较优势与贸易条件
The law of comparative advantage states that countries should specialise in producing the goods for which they have the lowest opportunity cost, even if one country holds an absolute advantage in all products. Specialisation and trade allow both partners to consume beyond their domestic production possibility frontiers.
比较优势法则指出，各国应专业化生产机会成本最低的商品，即便某国在全部商品上都具有绝对优势。专业化与贸易使得双方都能超越本国生产可能性边界进行消费。
Opportunity cost is calculated as the ratio of output sacrificed to output gained. Numerical examples involving two goods and two countries are assessed to determine the pattern of specialisation and the potential gains from trade, measured by the increase in total output.
机会成本的计算方式为牺牲的产出与获得的产出之比。包含两种商品和两个国家的数值案例被用来判断专业化的格局以及通过总产出的增加来衡量的贸易得益。
The terms of trade index measures the relative price of a country’s exports compared to its imports. An improvement means a country can buy more imports for a given volume of exports; a deterioration implies the opposite. The formula uses index numbers, typically with a base year of 100.
Terms of Trade = (Index of Export Prices / Index of Import Prices) × 100
贸易条件指数衡量一国出口相对于进口的价格水平。改善意味着给定数量的出口能换得更多进口；恶化则相反。该公式采用指数形式，通常以基年 100 为基准。
8. Balance of Payments and Exchange Rates | 国际收支与汇率
The balance of payments records all economic transactions between residents of a country and the rest of the world. The current account includes trade in goods, trade in services, primary income and secondary income. The capital and financial accounts record capital transfers and transactions in financial assets.
国际收支记录了一国居民与世界其他地区之间的所有经济交易。经常账户包括货物贸易、服务贸易、初次收入和二次收入
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