📚 AP Microeconomics: Key Concepts, Formulas & Worked Examples | AP 微观经济：知识点梳理、公式与例题解析
This guide provides a structured review of AP Microeconomics, covering essential concepts, key formulas, and worked examples to help you master the exam. Each section is designed to clarify the theory and show how to apply it in multiple-choice and free-response questions.
本指南系统地梳理了 AP 微观经济学的重要概念、核心公式和例题解析，帮助你掌握考试要点。每一节都旨在阐明理论，并展示如何在选择题和自由作答题中应用这些知识。
1. Scarcity, Opportunity Cost, and the Production Possibilities Curve | 稀缺性、机会成本与生产可能性曲线
Scarcity is the fundamental economic problem: limited resources versus unlimited wants. Every choice involves an opportunity cost, which is the value of the next best alternative foregone. The production possibilities curve (PPC) illustrates these trade-offs between two goods given fixed resources and technology.
稀缺性是最基本的经济问题：有限的资源与无限的欲望。每做一个选择都会产生机会成本，即所放弃的次优选择的价值。生产可能性曲线(PPC)展示了在资源和技术既定的条件下两种商品之间的权衡取舍。
A straight-line PPC indicates constant opportunity cost, while a bowed-out (concave) PPC reflects increasing opportunity cost. Points inside the curve are inefficient, points on the curve are efficient, and points outside are unattainable with current resources.
直线型 PPC 表示机会成本不变，而向外凸的（凹向原点的）PPC 反映了机会成本递增。曲线内部的点效率低下，曲线上的点是有效率的，曲线外的点在当前资源下无法实现。
Opportunity Cost of Good X = (Units of Y given up) / (Units of X gained)
Worked Example: Suppose a farm can produce 100 bushels of wheat or 50 bales of cotton. Moving from 0 to 10 bales of cotton requires sacrificing 20 bushels of wheat. The opportunity cost of one bale of cotton is 20 / 10 = 2 bushels of wheat. This cost can change as production shifts along a curved PPC.
例题： 假设一个农场能生产 100 单位小麦或 50 单位棉花。从生产 0 单位棉花到 10 单位，需要牺牲 20 单位小麦。一单位棉花的机会成本为 20/10 = 2 单位小麦。沿着弯曲的 PPC 移动时，该成本会发生变化。
2. Supply and Demand: Market Equilibrium | 供给与需求：市场均衡
The law of demand states that, ceteris paribus, as price rises, quantity demanded falls. The law of supply asserts that quantity supplied increases with price. Market equilibrium occurs where quantity supplied equals quantity demanded, determining the equilibrium price and quantity.
需求定律指出，在其他条件不变时，价格上升会导致需求量下降。供给定律则表明，价格上升时供给量增加。市场均衡出现在供给量等于需求量的地方，从而决定均衡价格和数量。
Shifts in demand (caused by changes in income, tastes, prices of related goods, expectations, number of buyers) or shifts in supply (input costs, technology, taxes/subsidies, expectations, number of sellers) move the equilibrium. A rightward demand shift increases both price and quantity; a rightward supply shift lowers price and raises quantity.
需求的变化（由收入、偏好、相关商品价格、预期、买者数量引起）或供给的变化（投入成本、技术、税收/补贴、预期、卖者数量）会使均衡移动。需求曲线右移会提高价格和数量；供给曲线右移会降低价格并增加数量。
Worked Example: The market for coffee is in equilibrium at P = $5, Q = 200. A frost destroys coffee plants. Supply shifts left, increasing equilibrium price to $7 and reducing quantity to 150. The new equilibrium reflects the decreased availability.
例题： 咖啡市场的均衡在 P = 5 美元，Q = 200。一场霜冻摧毁了咖啡树，供给曲线左移，均衡价格升至 7 美元，数量降至 150。新的均衡反映了供应减少。
3. Price Elasticity of Demand and Supply | 需求与供给的价格弹性
Price elasticity of demand (PED) measures the responsiveness of quantity demanded to a change in price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. The midpoint (arc) formula is preferred to avoid inconsistency when moving along the curve.
需求的价格弹性 (PED) 衡量需求量对价格变化的反应程度。计算方法为需求量变动的百分比除以价格变动的百分比。推荐使用中点（弧）公式，以避免沿曲线移动时出现不一致。
PED = [(Q₂ − Q₁) / ((Q₁ + Q₂) / 2)] ÷ [(P₂ − P₁) / ((P₁ + P₂) / 2)]
If |PED| > 1, demand is elastic; if |PED| < 1, demand is inelastic; unit elastic when |PED| = 1. Determinants include availability of substitutes, necessity vs. luxury, time horizon, and proportion of income spent. Price elasticity of supply (PES) follows a similar logic.
如果 |PED| > 1，需求富有弹性；|PED| < 1，需求缺乏弹性；|PED| = 1 为单位弹性。影响因素包括替代品的可获得性、必需品与奢侈品、时间长短以及支出占收入的比例。供给的价格弹性(PES)遵循相似的逻辑。
Worked Example: The price of a movie ticket rises from $10 (P₁) to $12 (P₂), and tickets sold fall from 300 (Q₁) to 250 (Q₂). Using midpoint: %ΔQd = (250−300) / ((300+250)/2) = −50/275 ≈ −0.1818; %ΔP = (12−10) / ((10+12)/2) = 2/11 ≈ 0.1818. PED = −0.1818 / 0.1818 = −1.0, so unit elastic in absolute value.
例题： 电影票价格从 10 美元 (P₁) 涨到 12 美元 (P₂)，售出的票数从 300 张 (Q₁) 降至 250 张 (Q₂)。用中点公式：%ΔQd = (250−300) / ((300+250)/2) = −50/275 ≈ −0.1818；%ΔP = (12−10) / ((10+12)/2) = 2/11 ≈ 0.1818。PED = −0.1818 / 0.1818 = −1.0，绝对值是单位弹性。
4. Consumer Surplus, Producer Surplus, and Efficiency | 消费者剩余、生产者剩余与市场效率
Consumer surplus (CS) is the difference between what consumers are willing to pay and what they actually pay. Producer surplus (PS) is the difference between the market price and the minimum price producers require. Total surplus (CS + PS) is maximized at competitive equilibrium, indicating allocative efficiency.
消费者剩余 (CS) 是消费者愿意支付的最高价格与实际支付价格之间的差额。生产者剩余 (PS) 是市场价格与生产者愿意接受的最低价格之间的差额。总剩余 (CS + PS) 在竞争均衡时达到最大，这意味着配置效率。
Deadweight loss (DWL) represents the loss of total surplus when the market is not at equilibrium—due to price controls, taxes, or market power. On a graph, CS is the area below the demand curve and above the price; PS is above the supply curve and below the price. DWL is the triangle that appears when quantity deviates from the efficient level.
无谓损失 (DWL) 是市场未处于均衡（由于价格管制、税收或市场势力）时总剩余的损失。在图形上，CS 是需求曲线之下、价格线之上的面积；PS 是供给曲线之上、价格线之下的面积。当数量偏离效率水平时，出现的三角形即为无谓损失。
Worked Example: The demand for a good is P = 20 − Q, supply is P = 2 + Q. At equilibrium: 20 − Q = 2 + Q → Q = 9, P = 11. CS = ½ × (20−11) × 9 = 40.5; PS = ½ × (11−2) × 9 = 40.5. Total surplus = 81. A price ceiling at $8 creates a shortage and DWL.
例题： 某商品需求为 P = 20 − Q，供给为 P = 2 + Q。均衡时：20 − Q = 2 + Q → Q = 9, P = 11。CS = ½ × (20−11) × 9 = 40.5；PS = ½ × (11−2) × 9 = 40.5。总剩余 = 81。若设定 8 美元的价格上限，则会产生短缺和无谓损失。
5. Government Interventions: Price Controls, Taxes, and Subsidies | 政府干预：价格管制、税收与补贴
A price ceiling, set below equilibrium (e.g., rent control), causes a persistent shortage. A price floor, set above equilibrium (e.g., minimum wage), creates a surplus. Both generate deadweight loss and reduce total surplus. The incidence of a tax depends on the relative elasticities of demand and supply.
价格上限（低于均衡价，如租金管制）会导致持续的短缺。价格下限（高于均衡价，如最低工资）会造成过剩。两者都会产生无谓损失，减少总剩余。税收负担的分摊取决于需求与供给的相对弹性。
When a per-unit tax is imposed, the supply curve shifts vertically upward by the amount of the tax. Buyers and sellers share the burden, but the more inelastic side bears a greater proportion. A per-unit subsidy shifts the supply curve downward, increasing equilibrium quantity and creating a government cost.
当征收从量税时，供给曲线垂直上移税额的大小。买卖双方共同承担税负，但缺乏弹性的一方承担的比例更大。从量补贴使供给曲线下移，增加均衡数量，同时产生政府成本。
Tax Revenue = Tax per unit × Quantity traded after tax
Worked Example: Original equilibrium: P = $4, Q = 100. A $1 per-unit tax shifts supply upward. New buyer price = $4.60, seller receives $3.60, quantity falls to 90. Tax revenue = $1 × 90 = $90. Consumer tax burden = $0.60 per unit; producer burden = $0.40. DWL = ½ × $1 × (100−90) = $5.
例题： 初始均衡：P = 4 美元，Q = 100。征收 1 美元从量税后供给上移。新的买方价格 = 4.60 美元，卖方实际收入 3.60 美元，数量降至 90。税收收入 = 1 美元 × 90 = 90 美元。消费者税负 = 每单位 0.60 美元；生产者负担 = 0.40 美元。无谓损失 = ½ × 1 美元 × (100−90) = 5 美元。
6. Costs of Production and Profit Maximization | 生产成本与利润最大化
Firms face short-run costs: fixed costs (FC), variable costs (VC), and total cost (TC = FC + VC). Average fixed cost (AFC) declines as output rises. Average total cost (ATC = TC/Q) is U-shaped due to diminishing marginal returns. Marginal cost (MC) is the change in TC from producing one more unit.
企业面临短期成本：固定成本 (FC)、可变成本 (VC) 以及总成本 (TC = FC + VC)。平均固定成本 (AFC) 随产量上升而下降。由于边际报酬递减，平均总成本 (ATC = TC/Q) 呈 U 形。边际成本 (MC) 是多生产一单位所导致的总成本变化。
MC = ΔTC / ΔQ
Profit = Total Revenue (TR) − Total Cost (TC)
To maximize profit, a firm produces the quantity where marginal revenue (MR) equals marginal cost (MC). If MR > MC, increasing output adds more to revenue than to cost, so profit rises. If MR < MC, reducing output raises profit. This rule applies to all market structures.
为最大化利润，企业应选择边际收益 (MR) 等于边际成本 (MC) 时的产量。若 MR > MC，增产带来的收入增量大于成本增量，利润增加。若 MR < MC，减产会提高利润。这一法则适用于所有市场结构。
Worked Example: A firm sells each unit for $10 (MR = $10). If TC = 100 + 2Q², then MC = 4Q. Set MR = MC: 10 = 4Q → Q = 2.5. At Q=2, profit = 20 − (100+8) = −88; at Q=3, profit = 30 − (100+18) = −88; the best integer is either 2 or 3. This shows the MR=MC rule.
例题： 某企业单价为 10 美元 (MR = 10)。若 TC = 100 + 2Q²，则 MC = 4Q。令 MR = MC：10 = 4Q → Q = 2.5。Q=2 时利润 = 20 − (100+8) = −88；Q=3 时利润 = 30 − (100+18) = −88。最佳整数产量为 2 或 3，体现了 MR=MC 的等边际原理。
7. Perfect Competition | 完全竞争
A perfectly competitive market has many small firms, homogeneous products, no barriers to entry, and perfect information. Firms are price takers, facing a perfectly elastic demand at the market price. Thus, P = MR = AR (average revenue).
完全竞争市场拥有众多小企业、同质产品、无进入壁垒以及完全信息。企业是价格接受者，面临在市场价格处的完全弹性需求。因此，P = MR = AR（平均收益）。
The firm maximizes profit by producing where P = MC. In the short run, firms may earn economic profits or incur losses. Positive economic profits attract new firms in the long run, shifting the market supply right and reducing price until each firm earns zero economic profit (P = minimum ATC).
企业通过生产在 P = MC 的产量实现利润最大化。短期内，企业可能赚取经济利润或遭受亏损。长期中，正的经济利润会吸引新企业进入，使市场供给右移，压低价格，直至每个企业获得零经济利润（P = 最低 ATC）。
Profit = (P − ATC) × Q
Worked Example: Market price = $15, ATC at profit-maximizing output (Q=80) is $12. Profit per unit = $3; total profit = 80 × $3 = $240. Since P > ATC, the firm earns short-run positive profit, encouraging entry until price falls to min ATC.
例题： 市场价格 = 15 美元，利润最大化产量 (Q=80) 下的 ATC 为 12 美元。每单位利润 = 3 美元；总利润 = 80 × 3 美元 = 240 美元。由于 P > ATC，企业在短期内获得正利润，吸引进入，直到价格降至最低 ATC。
8. Monopoly | 垄断
A pure monopoly is a single seller of a unique product with high barriers to entry. The monopolist faces the downward-sloping market demand curve, so price must be lowered to sell more. As a result, marginal revenue is less than price (MR < P) for all but the first unit.
完全垄断是指具有独特产品和高进入壁垒的单一卖家。垄断者面临向下倾斜的市场需求曲线，因此必须降价才能售出更多产品。因此，除了第一单位外，边际收益都小于价格 (MR < P)。
The profit-maximizing rule is still MR = MC, but the price is set on the demand curve above the intersection. This creates a markup over marginal cost and results in a deadweight loss. Monopolies are neither allocatively efficient (P > MC) nor productively efficient (not at min ATC necessarily).
利润最大化法则仍是 MR = MC，但价格是在需求曲线上高于交点处确定。这产生了对边际成本的加价，并导致无谓损失。垄断既没有配置效率（P > MC），也没有生产效率（不一定在最低 ATC 处生产）。
Monopoly Profit = (P − ATC) × Qm
Worked Example: A monopolist has demand P = 50 − Q, thus MR = 50 − 2Q. TC = 10 + Q², MC = 2Q. Set MR = MC: 50 − 2Q = 2Q → Q = 12.5, P = 37.5. Profit = TR − TC = (37.5×12.5) − (10 + 12.5²) = 468.75 − 166.25 = 302.5. The socially efficient Q is where P = MC: 50 − Q = 2Q → Q = 16.67, so DWL exists.
例题： 垄断者面临需求 P = 50 − Q，因此 MR = 50 − 2Q。TC = 10 + Q²，MC = 2Q。令 MR = MC：50 − 2Q = 2Q → Q = 12.5，P = 37.5。利润 = TR − TC = (37.5×12.5) − (10 + 12.5²) = 468.75 − 166.25 = 302.5。社会有效产量由 P = MC 决定：50 − Q = 2Q → Q = 16.67，因此存在无谓损失。
9. Monopolistic Competition and Oligopoly | 垄断竞争与寡
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