AP Microeconomics: Key Formulas Summary | AP 微观经济重要公式汇总

📚 AP Microeconomics: Key Formulas Summary | AP 微观经济重要公式汇总

Mastering the essential formulas is crucial for success in AP Microeconomics. From elasticity to cost curves, these equations underpin graphical analysis and real-world decision-making. This guide compiles the key formulas you need to memorize, with concise explanations and examples.

掌握核心公式对 AP 微观经济学至关重要。从弹性到成本曲线，这些方程式是图形分析和现实决策的基础。本指南汇总了你需要记忆的关键公式，并附有简明解释和示例。

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

The price elasticity of demand measures the responsiveness of quantity demanded to a change in price. The basic formula uses percentage changes.

需求价格弹性衡量需求量对价格变化的反应程度。基本公式使用百分比变化。

PED = %ΔQ_d / %ΔP = (ΔQ_d / Q_d) / (ΔP / P)

For more accuracy, AP often uses the midpoint (arc elasticity) method, which avoids dependence on the choice of starting point.

为了更精确，AP 考试常使用中点法（弧弹性），避免了对起始点选择的依赖。

PED = (ΔQ / ((Q₁+Q₂)/2)) / (ΔP / ((P₁+P₂)/2)) = (ΔQ/ΔP) × ((P₁+P₂)/(Q₁+Q₂))

Elastic (|PED| > 1): %ΔQ_d > %ΔP. Lowering price increases total revenue (TR = P × Q).

富有弹性 (|PED| > 1): %ΔQ_d > %ΔP，降价会使总收入增加。
Inelastic (|PED| < 1): %ΔQ_d < %ΔP. Raising price increases total revenue.

缺乏弹性 (|PED| < 1): %ΔQ_d < %ΔP，提价会使总收入增加。
Unit elastic (|PED| = 1): total revenue remains constant at maximum.

单位弹性 (|PED| = 1): 总收入达到最大且保持不变。

2. Other Elasticities: PES, YED, XED | 其他弹性：供给、收入、交叉弹性

Price elasticity of supply, income elasticity of demand, and cross-price elasticity describe how quantity supplied or demanded responds to determinants other than own price.

供给价格弹性、需求收入弹性以及交叉价格弹性描述供给量或需求量对价格以外决定因素的反应程度。

PES = %ΔQ_s / %ΔP

PES is usually positive. It reflects how easily producers can adjust output.

PES 通常为正，反映生产者调整产出的难易程度。

YED = %ΔQ_d / %ΔIncome

Normal goods have YED > 0; inferior goods have YED < 0. Luxury goods have YED > 1.

正常品 YED > 0；低档品 YED < 0。奢侈品 YED > 1。

XED = (%ΔQ_d of Good A) / (%ΔP of Good B)

Substitutes have XED > 0; complements have XED < 0.

替代品 XED > 0；互补品 XED < 0。

3. Utility Maximization | 效用最大化

Consumers allocate their budget to maximize total utility. The condition for optimal consumption involves equating marginal utility per dollar across goods.

消费者配置预算以最大化总效用。最优消费的条件是使各商品的每元边际效用相等。

MU_x / P_x = MU_y / P_y

Equivalently, the marginal rate of substitution (MRS) equals the price ratio.

等价地，边际替代率等于价格之比。

MRS = MU_x / MU_y = P_x / P_y

If the ratios are not equal, the consumer can reallocate spending to increase total utility.

如果边际效用与价格之比不等，消费者可以通过重新分配支出来增加总效用。

4. Budget Constraint | 预算约束线

The budget constraint shows all affordable combinations of two goods given income and prices. Its equation and slope are essential for understanding consumer choice.

预算约束线表示在给定收入和价格时，两种商品所有可负担的组合。其方程和斜率对理解消费者选择至关重要。

I = P_x·Q_x + P_y·Q_y

Solving for Q_y gives the slope-intercept form, with slope = –P_x/P_y.

解出 Q_y 可得截距形式，斜率为 –P_x/P_y。

A change in income shifts the budget line parallelly.

收入变动使预算线平行移动。
A change in the price of one good rotates the budget line around the intercept of the other good.

一种商品价格变动会使预算线绕另一商品截距点旋转。

5. Costs of Production | 生产成本

Firms use cost relationships to decide output levels. Total, average, and marginal costs are fundamental.

企业利用成本关系决定产量。总成本、平均成本和边际成本是基础。

TC = TFC + TVC

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

MC = ΔTC / ΔQ = ΔTVC / ΔQ

MC cuts ATC and AVC at their minimum points. The relationship between marginal and average is key: when MC < ATC, ATC falls; when MC > ATC, ATC rises.

MC 穿过 ATC 和 AVC 的最低点。边际与平均的关系很关键：MC < ATC 时 ATC 下降；MC > ATC 时 ATC 上升。

Production also involves marginal product (MP) and average product (AP). Costs and product are inversely related.

生产还涉及边际产量 MP 和平均产量 AP。成本与产量呈反向关系。

MP = ΔTotal Product / ΔLabor

When MP is rising, MC is falling, and vice versa. The law of diminishing marginal returns sets in when MP starts to decline.

MP 上升时 MC 下降，反之亦然。边际报酬递减规律始于 MP 开始下降时。

6. Revenues and Profit | 收益与利润

Understanding revenue streams and profit concepts helps firms evaluate performance. Economic profit differs from accounting profit by including opportunity costs.

理解收益流和利润概念有助于企业评估绩效。经济利润包含了机会成本，与会计利润不同。

Total Revenue (TR) = P × Q

Average Revenue (AR) = TR / Q = P

Marginal Revenue (MR) = ΔTR / ΔQ

Accounting Profit = TR – Explicit Costs. Economic Profit = TR – (Explicit Costs + Implicit Costs) = TR – Economic Cost.

会计利润 = 总收入 – 显性成本。经济利润 = 总收入 – (显性成本 + 隐性成本) = 总收入 – 经济成本。

A normal profit occurs when economic profit equals zero, meaning the firm is covering all opportunity costs and earning just enough to stay in business.

正常利润指经济利润为零，即企业恰好覆盖所有机会成本，刚好能维持经营。

7. Profit Maximization Rule | 利润最大化法则

All market structures use the same logic: produce the quantity where marginal revenue equals marginal cost.

所有市场结构使用相同的逻辑：在边际收益等于边际成本的产量上进行生产。

MR = MC

If MR > MC, the firm can increase profit by raising output. If MR < MC, it should reduce output. This rule holds regardless of whether the firm is in perfect competition or monopoly.

若 MR > MC，企业可通过增产增加利润。若 MR < MC，应减产。无论完全竞争还是垄断，这一法则都成立。

For a perfectly competitive firm, P = MR, so the rule becomes P = MC. For firms with market power, MR < P, and price is then read from the demand curve at the profit-maximizing quantity.

对于完全竞争企业，P = MR，因此规则变为 P = MC。对于有市场势力的企业，MR < P，利润最大化产量确定后，价格从需求曲线上读取。

8. Perfect Competition | 完全竞争

Perfectly competitive firms are price takers. Their demand curve is horizontal at the market price, so P = MR = AR.

完全竞争企业是价格接受者。其需求曲线为市场价格处的水平线，因此 P = MR = AR。

Profit Maximization: P = MC

Short-run shutdown point: P < minimum AVC. If price falls below AVC, the firm minimizes loss by stopping production.

短期停业点：P < 最低 AVC。若价格低于 AVC，停止生产可最小化亏损。
Short-run breakeven point: P = minimum ATC, earning zero economic profit.

短期盈亏平衡点：P = 最低 ATC，经济利润为零。
Long-run equilibrium: P = minimum ATC, and firms earn zero economic profit due to free entry and exit.

长期均衡：P = 最低 ATC，由于自由进出，企业获得零经济利润。

Productive efficiency occurs at minimum ATC; allocative efficiency occurs where P = MC. Both are achieved in long-run perfect competition.

生产效率在最低 ATC 处实现；配置效率在 P = MC 处实现。长期完全竞争中两者均能达成。

9. Monopoly and Imperfect Competition | 垄断与不完全竞争

A monopoly faces the market demand curve and must lower price to sell more, so MR < P. For a linear inverse demand curve, the MR curve has the same intercept and twice the slope.

垄断企业面临市场需求曲线，必须降价才能多卖，因此 MR < P。对于线性反需求曲线，MR 曲线与需求曲线截距相同、斜率两倍。

Demand: P = a − bQ ⟹ MR = a − 2bQ

Monopoly maximizes profit where MR = MC, then charges the price on the demand curve corresponding to that output. This creates a deadweight loss because P > MC.

垄断在 MR = MC 处最大化利润，然后在需求曲线上找到该产量对应的价格。由于 P > MC，会产生无谓损失。

The Lerner Index measures market power:

Lerner Index = (P − MC) / P = 1 / |PED|

In monopolistic competition, firms have some market power but free entry drives long-run economic profit to zero, with P = ATC and excess capacity (output less than minimum ATC). Oligopoly involves strategic interdependence; no single universal formula applies, but key models include Cournot, Bertrand, and kinked demand curve.

垄断竞争中，企业拥有一定市场势力，但自由进出使长期经济利润为零，P = ATC 且存在超额产能（产量低于最低 ATC）。寡头涉及战略相互依赖，没有单一通用公式，但重要模型包括古诺、伯川德和弯折需求曲线。

10. Factor Markets | 要素市场

Firms hire inputs (e.g., labor) up to the point where the additional revenue from the last unit equals its additional cost. Marginal product and marginal revenue product are central.

企业雇用生产要素（如劳动力）直至最后一单位带来的额外收益等于其额外成本。边际产量和边际收益产品至关重要。

Marginal Product of Labor (MP_L) = ΔTotal Product / ΔL

When the product market is perfectly competitive, the firm’s demand for labor is based on the value of the marginal product:

当产品市场完全竞争时，企业劳动需求基于边际产品价值：

VMP_L = MP_L × P

If the firm has product market power, it uses marginal revenue product:

若企业在产品市场拥有势力，则使用边际收益产品：

MRP_L = MP_L × MR

The profit-maximizing hiring rule is MRP = MFC (marginal factor cost). In a competitive labor market, MFC equals the wage rate (W).

利润最大化的雇用规则为 MRP = MFC（边际要素成本）。在竞争性劳动市场中，MFC 等于工资率 W。

MRP_L = W (competitive labor market)

A minimum wage above equilibrium creates a surplus of labor (unemployment) unless the firm is a monopsony.

高于均衡的最低工资会造成劳动力过剩（失业），除非企业是买方垄断。

11. Tax Incidence and Welfare | 税收归宿与福利

When the government imposes a per-unit tax, the burden is shared between consumers and producers depending on elasticities. The loss in total surplus is deadweight loss.

政府征收从量税时，税负由消费者和生产者根据弹性分担。总剩余损失即为无谓损失。

Consumer Burden = (E_s / (E_s + E_d)) × Tax

Producer Burden = (E_d / (E_s + E_d)) × Tax

These formulas apply for small taxes and linear supply and demand. The more inelastic side bears a larger share.

此公式适用于小额税收及线性供求。

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AP Microeconomics: Key Formulas Summary | AP 微观经济重要公式汇总