JL · AP MICROECONOMICS

Unit 5 · Factor Markets

要素市场 — 生产要素与要素价格、边际收益产品 MRP 与边际要素成本 MRC、劳动需求与供给的移动、完全竞争劳动市场、最低成本组合、买方垄断 · 对应 CED 5.1–5.4 · 选择题占比约 10–13%

换一个角度看企业 Unit 3、Unit 4 里企业是卖方：在产品市场卖东西，决定生产多少。Unit 5 里企业变成买方：在要素市场雇工人、租机器、租土地，决定雇多少。道理完全一样——多雇一个人带来的收益（MRP）和多花的成本（MRC）比一比，MRP = MRC 时利润最大。
上一单元：→ 打开 Unit 4（下）Monopolistic Competition and Oligopoly（与本文件放在同一文件夹）

从前面带过来的工具

边际产量 MP 与边际收益递减（Unit 3 上册 3.1）：多雇一个工人，多出来的产量越来越少——这就是劳动需求向下倾斜的原因。复习：Unit 3（下）及其上册。
MR：完全竞争企业 MR = P；有市场势力的企业 MR < P（Unit 4 上册 4.2）。
边际分析：边际收益 ≥ 边际成本就做，直到两者相等（Unit 1 的 MB = MC、Unit 3 的 MR = MC）。
供求图的移动（Unit 2）：劳动市场也是一个供求市场，价格叫工资，数量叫就业量。

本单元学习目标 LEARNING OBJECTIVES

说出生产要素与要素价格，解释“引致需求” · Describe factors of production, factor prices, and derived demand
从表格计算 MP、MRP、MRC，并决定雇多少工人 · Calculate MRP and MRC and find the profit-maximizing number of workers
解释劳动需求为什么向下倾斜、劳动供给为什么向上倾斜 · Explain the slopes of labor demand and labor supply
分析劳动需求和劳动供给的移动对工资和就业的影响 · Analyze shifts in labor demand and supply
画出完全竞争劳动市场与企业的并排图，说明企业是工资接受者 · Graph a perfectly competitive labor market and a wage-taking firm
用 MP/P 相等找出最低成本的要素组合 · Apply the least-cost rule MP_L/W = MP_K/r
画出买方垄断劳动市场，解释为什么 MFC > 工资，比较买方垄断与完全竞争的工资和就业 · Graph and explain monopsony
分析最低工资在完全竞争和买方垄断劳动市场中的不同效果 · Analyze a minimum wage in both labor markets

Term 术语	Meaning 含义	中文
Factor Market	Market where firms buy (hire) factors of production	要素市场
Factors of Production / Factor Prices	Labor, land, capital (and entrepreneurship) / wage, rent, interest (and profit)	生产要素 / 要素价格
Derived Demand	Demand for a factor comes from demand for the good it produces	引致需求（派生需求）
Marginal Product of Labor (MP_L)	Extra output from one more worker	劳动的边际产量
Marginal Revenue Product (MRP)	Extra revenue from one more unit of a factor = MP × MR	边际收益产品
Value of the Marginal Product (VMP)	MP × P; equals MRP when the output market is perfectly competitive	边际产品价值
Marginal Resource (Factor) Cost (MRC / MFC)	Extra cost of hiring one more unit of a factor	边际要素成本
Wage Taker	A firm that can hire as many workers as it wants at the market wage	工资接受者
Least-Cost Rule	MP_L/W = MP_K/r: the last dollar spent on each input yields the same extra output	最低成本法则
Monopsony	A market with a single buyer of a factor (e.g., the only employer in a town)	买方垄断

考试怎么考 CED 特别指出：要素市场是学生在 AP 考试中最容易失分的部分之一。选择题：从表格算 MRP、雇几个人；哪些因素让劳动需求或供给移动；企业是工资接受者；最低成本组合；买方垄断的 MFC 为什么高于工资、工资和就业比完全竞争低。 FRQ：几乎每年都有一道（或一问）劳动市场：MRP 表格题、并排图、劳动供给移动后企业雇多少、MP_L/W = MP_K/r 的计算，以及买方垄断图。

5.1Introduction to Factor Markets 要素市场入门

一家草莓采摘园要决定的不只是“卖多少草莓”，还有“雇几个采摘工、租几亩地、买几台冷藏车”。前者发生在产品市场，后者发生在要素市场——企业在这里是买方。

同一家企业同时身处两个市场：在产品市场卖草莓、卖奶茶（它是卖方），在要素市场雇工人、租地、租机器（它是买方）。家庭正好反过来：在要素市场卖自己的劳动，拿到工资后到产品市场买东西。

Factors and Factor Prices 生产要素与要素价格

定义 DEFINITION（CED PRD-4.A.1） Factor market 要素市场：企业购买（雇用、租用）生产要素的市场，最重要的是劳动市场。每种要素都有自己的价格，要素的所有者对价格作出反应：工资高的地方工人多，租金高的地方地主愿意出租更多土地。

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劳动 labor → 价格是工资 wage。采摘工、厨师、程序员的工作时间。

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土地 land（自然资源）→ 价格是租金 rent。种草莓的地、店铺所在的位置。

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资本 capital（机器、厂房、设备）→ 价格是利息 interest（或租用设备的租金）。冷藏车、咖啡机、服务器。

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企业家才能 entrepreneurship → 回报是利润 profit。决定种什么、怎么种、承担风险的人。

引致需求 DERIVED DEMAND 企业雇人不是因为喜欢工人，而是因为工人能生产可以卖钱的东西。所以对要素的需求是由对产品的需求引出来的：人们多买草莓，采摘园才多雇采摘工。企业决定雇不雇，看三样东西（CED PRD-4.A.1）：要素的生产率（MP）、产品的价格（P 或 MR）、要素的成本（工资）。

WORKED EXAMPLE 1外卖骑手的需求从哪里来？原创

Explain how each event affects a delivery platform's demand for riders, and identify the factor price that each event concerns. (a) A cold, rainy week makes millions of people order food delivery instead of eating out. (b) The platform's riders get better route-planning software, so each rider completes more deliveries per hour. (c) A restaurant chain leases a bigger kitchen and pays more each month for it.

(a) 外卖订单（产品）需求增加 → 每一单能赚的钱不变但单子多了，平台需要更多骑手。骑手的需求来自外卖的需求——这就是引致需求（derived demand）。对应的要素价格是骑手的工资。

(b) 每个骑手的边际产量提高 → MRP = MP × MR 提高 → 劳动需求增加（CED PRD-4.A.1：雇不雇取决于要素的生产率、产品价格和要素成本）。

(c) 厨房是“土地/建筑”这一类要素，对应的要素价格是租金（rent）。租金越贵，企业对厨房面积的需求量越少（沿着需求曲线移动）。

MRP and MRC 边际收益产品与边际要素成本

两个新的“边际” MRP = ΔTR / ΔL = MP_L × MR Marginal revenue product (MRP) 边际收益产品：多雇一个工人带来的总收益增加。产品市场完全竞争时 MR = P，MRP = MP × P，也叫边际产品价值（VMP）。 MRC（MFC）= ΔTC / ΔL Marginal resource cost (MRC)，也叫 marginal factor cost (MFC)，边际要素成本：多雇一个工人带来的总成本增加。劳动市场完全竞争时，企业按市场工资想雇多少雇多少，MRC = 工资。

雇人的规则（与 MR = MC 同一个道理）只要 MRP > MRC，多雇一个人就能增加利润；一直雇到 MRP = MRC 为止。MRP < MRC 的那个人不雇。

	产品市场（Unit 3–4）	要素市场（Unit 5）
企业的角色	卖方	买方
多一单位带来的收益	MR	MRP = MP × MR
多一单位带来的成本	MC	MRC（MFC）
利润最大化	MR = MC	MRP = MRC
完全竞争时	P = MR（价格接受者）	W = MRC（工资接受者）

WORKED EXAMPLE 2草莓采摘园该雇几个采摘工？原创

A strawberry farm sells strawberries in a perfectly competitive market at $5 per box and hires pickers in a perfectly competitive labor market at a wage of $45 per day. The table shows the total number of boxes picked per day.

Number of pickers	0	1	2	3	4	5	6	7
Total boxes per day	0	20	38	53	65	75	83	88

(a) Calculate the marginal product and the marginal revenue product of the 3rd picker. (b) What is the marginal resource cost of a picker? (c) How many pickers will the farm hire? Explain using marginal analysis. (d) If the wage rose to $75, how many would it hire? (e) Why does the farm's MRP fall as it hires more pickers?

工人数 L	总产量 TP（箱/天）	MP_L	P	MRP = MP × P	MRC = 工资
0	0	—	—	—	—
1	20	20	$5	$100	$45
2	38	18	$5	$90	$45
3	53	15	$5	$75	$45
4	65	12	$5	$60	$45
5	75	10	$5	$50	$45
6	83	8	$5	$40	$45
7	88	5	$5	$25	$45

(a) MP₃ = 53 − 38 = 15 箱；MRP₃ = 15 × $5 = $75（也可以用 ΔTR：$265 − $190 = $75）。

(b) 劳动市场完全竞争，每多雇一人都按市场工资付钱：MRC = 工资 = $45。

(c) 只要 MRP ≥ MRC 就雇：第 5 人 MRP $50 > $45，雇；第 6 人 MRP $40 < $45，不雇 → 5 人。

(d) 第 3 人 MRP $75 = $75，第 4 人 $60 < $75 → 3 人。工资越高，雇得越少。

(e) 地块、篮子等其他投入是固定的，人越多越挤——边际产量递减（Unit 3 上册 3.1）；价格不变，所以 MRP = MP × P 也递减。

每多雇一个采摘工带来的收入（MRP，柱子）越来越少——因为边际产量递减。工资 $45（红线）就是多雇一人多花的钱。绿色柱 MRP ≥ $45，值得雇；第 6 人 MRP 只有 $40，不值得 → 雇 5 人。

把每个工人的 MRP 连起来就是企业的劳动需求曲线：给定一个工资，企业一直雇到 MRP 降到工资为止。工资越高，雇的人越少——劳动需求向下倾斜（CED PRD-4.A.2）。

易错 TRAP

MRP 是收入的增加（钱），MP 是产量的增加（箱）。表格题常常只给产量，要先算 MP 再乘以价格。
“第几个工人的 MRP”看的是这一个工人带来的增加，不是平均每人带来多少（平均产量 × 价格不是 MRP）。
工人越多 MRP 越低，是因为边际产量递减，不是因为后雇的人更懒。

LAB 1草莓园雇几个人？ · MRP vs. Wage

采摘量和上面的例题一样（MP = 20、18、15、12、10、8、5 箱）。拖动草莓价格和市场工资，看每个工人的 MRP 柱子和工资线，草莓园该雇几个人。

草莓价格 P = $5 / 箱

市场工资 W = $45 / 天

Labor Supply and the Labor Market 劳动供给与劳动市场

劳动的卖方是工人。工资越高，愿意工作的人越多（CED PRD-4.A.2）：有人从学校、家里走进劳动市场，有人从别的行业转过来，已经在工作的人也愿意加班。

劳动供给向上倾斜：工资从 W₁ 涨到 W₂，愿意工作的人更多、每人愿意工作的时间也更长——闲暇的机会成本变高了，其他行业的人也会转过来。

延伸：工作还是闲暇（了解即可）每多工作一小时，就少一小时闲暇。工资提高时，闲暇变“贵”了（替代效应，让人多工作）；但收入也变高了，人们可能想多休息（收入效应）。对整个劳动市场来说，AP 考试一律按向上倾斜的劳动供给作答。

劳动市场的均衡：劳动需求（来自企业）与劳动供给（来自工人）的交点决定市场工资 W* 和就业量 L*。和 Unit 2 的供求图一模一样，只是价格叫“工资”，数量叫“劳动”。

练习 Practice 5.1 · 要素市场、MRP 与 MRC

以下为历年 AP 真题（带图和表格的题按原题重绘），点选项即时判分并显示解析。

5.1-12005 AP Micro Q58

Marginal revenue product is defined as the

change in income that occurs when an individual works additional hours
change in total revenue that occurs when one additional unit of the good is produced
change in total revenue that occurs when one additional unit of an input is employed
total revenue divided by the quantity of labor employed
change in total cost that occurs when one additional unit of an input is employed

MRP = 多用一单位投入带来的总收益变化。(B) 多卖一单位产品带来的是 MR；(E) 是 MRC（MFC）。

5.1-22013 AP Micro Q11

The marginal revenue product of labor is the

product price times the wage rate
additional revenue a firm earns when it employs an additional unit of labor
increase in the average product of labor when the firm employs an additional unit of labor
increase in the price of labor when the firm employs an additional unit of labor
marginal revenue plus product price

MRP = 多雇一单位劳动带来的收益增加。(A) 是 P × W，没有意义；(C) 说的是平均产量。

5.1-32013 AP Micro Q28

Marginal resource (factor) cost can be defined as

the change in total resource cost caused by the production of one more unit of output
the change in total revenue caused by the addition of one more unit of a resource
the change in total resource cost caused by the addition of one more unit of a resource
the total resource cost divided by the number of inputs used
total resource cost divided by output

MRC（MFC）= 多用一单位要素带来的总要素成本增加。(A) 是多生产一单位产品的成本（MC）；(B) 是 MRP。

5.1-42000 AP Micro Q58

The concept of derived demand is described by which of the following?

A decrease in the demand for theater tickets will decrease the demand for actresses and actors.
If the salaries of basketball players increase, the quantity of basketball players demanded will decrease.
An increase in the income of consumers will increase the demand for opera tickets.
An increase in the demand for movie tickets will decrease the demand for video rentals.
A decrease in the price of movie tickets will increase the demand for movie tickets.

引致需求：要素（演员）的需求来自产品（戏票）的需求。戏票需求减少 → 演员需求减少 → (A)。

5.1-52018 AP Micro 练习卷 Q28

When the demand for new homes decreases, the demand for construction workers who build homes decreases. This relationship illustrates the concept of

derived demand
diminishing marginal productivity of labor
substitution in production
supply shock
property rights

新房需求减少 → 建筑工人的需求减少：劳动需求来自产品需求，即引致需求。

5.1-62022 AP Micro 国际卷 Q23

Which of the following statements most accurately describes the relationship between corn, an output, and machines, an input, that are used to gather corn?

The price of machines used to gather corn increases when the demand for corn increases.
The price of machines used to gather corn decreases when the demand for corn increases.
The price of machines used to gather corn increases when the demand for corn decreases.
The price of machines used to gather corn increases when the price of wheat, a producer substitute for corn, increases.
The price of machines used to gather corn is unrelated to the demand for corn.

玉米需求增加 → 玉米价格上升 → 收割机的 MRP 上升 → 对收割机的需求增加，价格上升（引致需求）→ (A)。

5.1-72005 AP Micro Q43

A firm's demand curve for labor is equal to a segment of its

average variable cost curve
total revenue curve
marginal cost curve
marginal revenue product curve
average product curve

企业雇到 MRP = 工资，所以企业的劳动需求曲线就是（向下倾斜的那段）MRP 曲线。

5.1-82000 AP Micro Q13

An individual's labor supply curve is derived from that person's preferences about the trade-off between income and

work
wealth
nominal wages
productivity
leisure

每多工作一小时就少一小时闲暇：个人劳动供给来自对收入与闲暇的取舍。

5.1-92014 AP Micro 练习卷 Q31

As a factor of production, capital refers to the

money available to start a business
stocks and bonds issued by businesses to raise funds
financial investment of businesses
currency in circulation and deposits in financial institutions
tools and machinery used to produce goods and services

作为生产要素的资本是实物资本：用来生产的工具和机器。钱、股票、债券是金融资产，不是生产要素意义上的资本。

5.1-102016 AP Micro 练习卷 Q59

Number of Workers	Total Product
1	15
2	20
3	24
4	27
5	29

The table above shows the short-run output for a perfectly competitive firm. If the price of the product is $10, what is the marginal revenue product of the third worker hired?

$24
$27
$40
$240
$300

MP₃ = 24 − 20 = 4，MRP = 4 × $10 = $40。(A) 是总产量，(D) 是 TP × P。

5.1-112019 AP Micro 练习卷 Q27

Hours of Labor	Marginal Product
0	0
1	10
2	12
3	9
4	7
5	4

The table above shows how a firm’s hourly level of output changes as more of the labor input is employed. The firm sells its output and hires labor in perfectly competitive markets. The wage paid to labor is $10 per hour, and the price of the firm’s output is $2 per unit. Based on the data in the table, the marginal revenue product of the fourth hour of labor is equal to

第 4 小时 MP = 7，产品价格 $2（题干给出）→ MRP = 7 × $2 = $14。$70 = 7 × 工资，是陷阱。

5.1-122023 AP Micro 国际卷 Q59

ZBA is a typical profit-maximizing firm in a perfectly competitive market that produces and sells widgets at $5 each. ZBA hires labor in a perfectly competitive labor market. The table shows ZBA’s production function for widgets.

Number of Workers	Total Output/Hour
1	3
2	7
3	12
4	14
5	15

What is the marginal revenue product of the third worker?

MP₃ = 12 − 7 = 5，MRP = 5 × $5 = $25。

5.1-132017 AP Micro 练习卷 Q15

Questions 15-16 are based on the chart below for a firm that is perfectly competitive in both the labor and product markets, showing how much daily output a firm can produce using different numbers of workers.

Number of Workers	Output
1	3
2	9
3	16
4	21
5	23
6	24

If output sells for $20 per unit, what is the marginal revenue product of the fifth worker?

$2
$40
$100
$115
$460

MP₅ = 23 − 21 = 2，MRP = 2 × $20 = $40。$460 是 5 人的总收入。

5.2Changes in Factor Demand and Factor Supply 要素需求与供给的变化

劳动市场就是一张供求图：价格是工资，数量是就业量。工资本身变化只是沿着曲线移动；其他因素变化才让曲线整条移动。点按钮看四种移动：

需求增加：奶茶卖得更贵、更好卖 → 店员的 MRP 提高 → 劳动需求右移：工资上升、就业增加。

需求减少：自助点餐机变便宜，店里用机器代替收银员 → 收银员的劳动需求左移：工资下降、就业减少。

供给增加：大批新移民来到这个城市找工作 → 劳动供给右移：工资下降、就业增加。

供给减少：这个职业新增了一项很难的执照考试 → 合格的人变少，劳动供给左移：工资上升、就业减少。

变化	曲线	工资 W	就业量 L
劳动需求增加	D 右移	↑	↑
劳动需求减少	D 左移	↓	↓
劳动供给增加	S 右移	↓	↑
劳动供给减少	S 左移	↑	↓

Shifts in Labor Demand 劳动需求的移动（CED PRD-4.B.1）

劳动需求 = MRP = MP × MR，所以凡是改变 MP 或 MR 的都会移动它

产品的价格（产品的需求）：产品更贵、更好卖 → MRP 上升 → 劳动需求增加（引致需求）。
工人的生产率：培训、更好的工具、更多与劳动互补的资本 → MP 上升 → 劳动需求增加。
其他投入的价格：替代要素（如自助机器）变便宜 → 企业用机器代替人 → 劳动需求减少；互补要素（如电脑之于程序员）变便宜 → 用得更多，工人也更能干 → 劳动需求增加。
雇用这种劳动的企业数量：行业里企业变多 → 市场劳动需求增加。

易错 TRAP

“工资上涨导致企业少雇人”是沿着需求曲线移动，不是需求减少。
产品市场的变化先影响产品价格，再通过 MRP 影响劳动需求——答题时把这条链写出来：需求 ↑ → P ↑ → MRP ↑ → 劳动需求 ↑。

Shifts in Labor Supply 劳动供给的移动（CED PRD-4.B.2）

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移民与人口：移民增加、适龄人口增加 → 供给右移；人口老龄化、大批人退休 → 供给左移。

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教育、培训与执照要求：开设新专业、培训变便宜 → 合格的人变多，供给右移；执照考试变难 → 供给左移。

⛑️

工作条件：工作更安全、更舒服 → 愿意干的人更多；又危险又辛苦 → 供给减少。

🔁

其他选择：别的职业工资上涨，有人转行 → 这一行的供给左移。

🏖️

对闲暇的偏好、财富：更看重休息、更富有 → 愿意工作的时间变少，供给左移。

👩‍💼

社会和文化观念：例如越来越多女性进入职场 → 整体劳动供给右移。

WORKED EXAMPLE 3谁在移动？五个劳动市场原创

For each event, identify the labor market affected, state whether labor demand or labor supply shifts and in which direction, and give the effect on the equilibrium wage and employment.

Electric cars become very popular. (market for battery engineers)
Hospitals buy new diagnostic software that lets each radiologist read twice as many scans per hour. (market for radiologists)
A country lowers the retirement age, and many older drivers leave the workforce. (market for bus drivers)
Self-driving delivery robots become cheap and replace many couriers. (market for couriers)
Wages for software testers rise sharply, so many video editors retrain as testers. (market for video editors)

	移动	原因	W	L
1	需求右移	电动车需求增加 → 电池工程师是引致需求，MRP 上升	↑	↑
2	需求右移	软件提高放射科医生的边际产量（与劳动互补的资本）	↑	↑
3	供给左移	年龄结构变化，能工作的司机变少	↑	↓
4	需求左移	机器人是快递员的替代要素，变便宜后企业少雇人	↓	↓
5	供给左移	其他职业的工资（其他选择）变高，剪辑师转行	↑	↓

判断口诀：影响“企业多想雇人”的（产品价格、生产率、其他投入的价格、企业数量）→ 需求；影响“工人多想干这行”的（人口、移民、教育培训、执照、工作条件、其他职业的工资、对闲暇的偏好、社会观念）→ 供给。

注意第 2、4 题：新技术如果让工人更能干（互补），劳动需求增加；如果代替工人（替代），劳动需求减少。

WORKED EXAMPLE 4电池工程师：需求和供给一起增加原创

At the same time, (i) sales of electric cars boom and (ii) many universities open new battery-engineering programs, so more graduates enter the field. What happens to the equilibrium wage and the number of battery engineers employed? What extra information would you need to determine the change in the wage?

(i) 引致需求增加 → 需求右移：W ↑、L ↑。(ii) 合格的人变多 → 供给右移：W ↓、L ↑。

合起来：就业量一定增加；工资不确定——要知道需求和供给各移动了多少（需求移得多，工资上升；供给移得多，工资下降）。

需求和供给同时增加：就业量一定增加（L₁ → L₂）；工资取决于哪边移得多——这张图里两边移得一样多，工资不变，但只要题目没给幅度，工资就是不确定（indeterminate）。

LAB 2谁在移动？ · Labor Demand or Labor Supply?

对每个事件，判断括号里那个劳动市场的劳动需求或劳动供给怎样移动。（得分：0 / ）

练习 Practice 5.2 · 劳动需求与供给的移动

以下为历年 AP 真题（带图和表格的题按原题重绘），点选项即时判分并显示解析。

5.2-12000 AP Micro Q28

If the price for a product produced in a competitive market increases, which of the following is most likely to occur in the labor market for workers who produce that product?

The demand for labor and the number of workers hired both increase.
The supply of labor and the number of workers hired both increase.
The demand for labor and the number of workers hired both decrease.
The supply of labor and the number of workers hired both decrease.
There is a movement along the demand for labor curve, and firms hire more workers.

产品价格上升 → MRP = MP × P 上升 → 劳动需求右移，雇的人增加。这是曲线的移动，不是沿曲线移动（E 错）。

5.2-22014 AP Micro 练习卷 Q57

Assume that firms sell their output in a perfectly competitive product market and hire labor in a perfectly competitive labor market. If all other factors remain constant, an increase in the demand for the firms’ product will result in which of the following changes in the labor market?

Firms will move down along the demand curve for labor and hire more workers.
The supply curve for labor will shift to the right.
The demand curve for labor will shift to the right.
The supply curve for labor will shift to the left.
The demand curve for labor will shift to the left.

产品需求增加 → 产品价格上升 → MRP 上升 → 劳动需求曲线右移。

5.2-32013 AP Micro Q12

For a competitive labor market, an increase in which of the following will lead to an increase in the demand for labor?

The supply of labor
The minimum wage
The cost of medical benefits provided to the labor hired by firms
Labor union dues
The demand for the good that labor produces

劳动需求是引致需求：产品的需求增加时劳动需求增加。(A) 移动的是供给；(B) 是沿着需求曲线；(C)(D) 提高用工成本。

5.2-42021 AP Micro 国际卷 Q8

Suppose the market for health-care workers is perfectly competitive. Which of the following will happen in the market for health-care workers in the short run if the demand for health care increases?

The supply curve of health-care workers will shift to the right.
The supply curve of health-care workers will shift to the left
The demand curve for health-care workers will shift to the right.
The demand curve for health-care workers will shift to the left.
Neither the demand curve nor the supply curve of health-care workers will shift.

医疗服务需求增加 → 医护人员的 MRP 上升 → 医护人员的需求曲线右移。

5.2-52025 AP Micro 国际卷 Q57

Donatello operates a firm that sells frozen treats in a perfectly competitive market. Which of the following would explain why Donatello is hiring more workers this year than last year?

Other firms have opened more stores selling frozen treats.
The government imposed a per-unit tax on consumers of frozen treats.
The government removed a quota on imported frozen treats.
There was an increase in demand for frozen treats.
There was a decrease in the price of frozen treats.

冷饮需求增加 → 冷饮价格上升 → MRP 上升 → Donatello 多雇人。(A)(B)(C)(E) 都会让他收到的价格下降。

5.2-62022 AP Micro 国际卷 Q20

Heggood, Inc., a perfectly competitive firm, produces hats using capital and labor purchased in competitive factor markets. If the demand for hats increases, Heggood, Inc. will

decrease the price of hats
decrease its demand for labor
decrease the quantity of labor demanded
increase its demand for capital
increase the rental price of capital

帽子需求增加 → 帽子价格上升 → 所有投入的 MRP 上升 → 企业对资本（和劳动）的需求增加。价格接受者不能自己定帽子价格或资本租金。

5.2-72022 AP Micro 国际卷 Q54

Kailas Cars produces cars that are made of both steel and aluminum. Steel and aluminum are substitutes in production. Kailas Cars’ demand for steel will increase if which of the following occurs?

The supply of aluminum increases.
The demand for cars increases.
The supply of gasoline, a complement to cars, decreases.
The wages of workers in the car industry increase.
The amount of time that people keep their cars increases.

钢材需求来自汽车需求：汽车需求增加 → 钢材的 MRP 上升 → (B)。(A) 替代品铝变便宜 → 钢材需求减少；(C)(E) 都让新车需求减少。

5.2-82010 AP Micro Q27

Motivated by lower import prices, United States manufacturers increase their imports of steel from other steel-producing countries. Which of the following best describes the impact of the increased steel imports on the labor market for steelworkers in the United States?

Jobs in the United States steel industry will become less attractive, so wages will have to increase in this market to attract more workers to the United States steel industry.
Domestic steel prices will fall, leading to an increase in sales of domestically produced steel, which increases demand and employment of steelworkers.
The supply of steelworkers will increase, lowering the steelworker wage in the United States.
The supply of steelworkers will decrease, increasing the steelworker wage in the United States.
The demand for United States steelworkers will decline, putting downward pressure on steelworker wages.

进口钢材增加 → 国内钢铁产量减少 → 美国钢铁工人的需求下降，工资承受下行压力（引致需求）。

5.2-92017 AP Micro 练习卷 Q51

As the population of a country ages, the demand for health care is projected to increase. As a result, the health care industry is likely to experience all of the following EXCEPT

an increase in demand for health care workers
an increase in demand for medicine
an increase in the quantity of health care workers supplied
an increase in the wages of health care workers
a decrease in the prices of medicine

医疗需求增加 → 医护人员和药品的需求都增加 → 药品价格上升，不会下降 → 例外是 (E)。

5.2-102019 AP Micro 练习卷 Q58

Assume that firms providing health-care services to older people operate in a perfectly competitive market. What must happen in the market for health-care workers if there is an increase in the number of older people in a country?

The demand for health-care workers will increase.
The marginal factor cost in the health-care industry will decrease.
The number of health-care workers will decrease.
The quality of health-care services will increase.
The wages of health-care workers will decrease.

老年人增多 → 医疗服务需求增加 → 医护人员的需求增加（工资和人数都上升）。

5.2-112017 AP Micro 练习卷 Q25

Which of the following is most likely to cause the demand curve for nurses to shift to the right?

An increase in the number of nurses graduating from nursing schools
An increase in nursing schools’ tuition
An increase in the number of hospitals that employ nurses
A decrease in the marginal productivity of nurses
An improvement in the health of older people

雇护士的医院变多 → 市场对护士的需求右移。(A)(B) 影响的是供给；(D)(E) 让需求减少。

5.2-122018 AP Micro 练习卷 Q14

Which of the following would cause the wage for computer programmers to increase?

A decrease in the amount of physical capital per computer programmer
An improvement in the education of computer programmers
An increase in the social prestige associated with being a computer programmer
A decrease in the value that computer programmers place on leisure
A minimum wage set below the equilibrium wage in the market for computer programmers

教育提高程序员的生产率（MP）→ MRP 上升 → 需求右移 → 工资上升。(C)(D) 让供给增加，工资反而下降；(E) 低于均衡的最低工资不起作用。

5.2-132023 AP Micro 国际卷 Q58

Which of the following reasons could explain why a firm might hire fewer workers?

A decrease in the wage rate
A decrease in labor productivity
An increase in the price of a substitute input
An increase in the price of the firm’s product
An increase in demand for the firm’s product

劳动生产率下降 → MP 下降 → MRP 下降 → 少雇人。(A) 工资下降会多雇人；(C)(D)(E) 都让劳动需求增加。

5.2-142018 AP Micro 练习卷 Q56

Assume that barber shops operate in perfectly competitive product and factor markets. Which of the following will happen to working barbers if the price of haircuts decreases?

The marginal product of the last barber hired will not change.
The marginal product of the last barber hired will decrease.
The marginal revenue product curve will shift to the right.
The marginal revenue product curve will shift to the left.
There will be a movement upward along the marginal revenue curve.

理发价格下降 → MRP = MP × P 下降 → MRP 曲线左移。理发师的 MP 本身不因价格而变。

5.2-152005 AP Micro Q13

A profit-maximizing firm that sells its output in a perfectly competitive market hires two additional workers, calculating that the contribution to total revenue of the last worker hired just equals the extra cost of hiring that worker. Six months later, the firm finds that the last worker's contribution to total revenue is less than the extra cost of hiring that worker. Which of the following may have occurred in the interim to explain this change?

The firm laid off some workers.
The market supply for the firm's product decreased.
The market demand for the firm's product decreased.
A technological advance increased the productivity of the firm's workforce.
The firm negotiated new contracts with workers, lowering wages.

最后一个工人的 MRP 下降到低于工资 → MP × P 下降。产品需求减少 → 价格下降 → MRP 下降 → (C)。其他选项都让 MRP 上升或 MRC 下降。

5.2-162021 AP Micro 国际卷 Q7

Which of the following will shift the demand curve for a factor of production to the left?

A decrease in the price of the factor of production
A decrease in the price of a substitute factor of production
An increase in the price of the product produced by the factor
An increase in the marginal product of the factor
An improvement in technology used by the factor of production

替代要素变便宜 → 企业改用替代要素 → 对这种要素的需求左移。(A) 是沿曲线移动；(C)(D)(E) 让需求右移。

5.2-172025 AP Micro 国际卷 Q42

Which of the following would cause a decrease in both the market wage and the equilibrium quantity of labor?

A decrease in the supply of labor
A decrease in the price of labor
A decrease in the price of capital, a substitute for labor
An increase in the minimum wage
An increase in the productivity of labor

资本是劳动的替代品，资本变便宜 → 企业用机器代替人 → 劳动需求左移 → 工资和就业量都下降。

5.2-182025 AP Micro 国际卷 Q53

Shrimp and chicken are substitute inputs in the production of frozen meals. Both shrimp and chicken are sold in perfectly competitive markets. If the government imposes a per-unit tax on shrimp, how will the demand for chicken and the equilibrium price of frozen meals be affected in the short run?

Demand for Chicken: Increase；Equilibrium Price of Frozen Meals: Increase
Demand for Chicken: Increase；Equilibrium Price of Frozen Meals: Decrease
Demand for Chicken: Increase；Equilibrium Price of Frozen Meals: No change
Demand for Chicken: Decrease；Equilibrium Price of Frozen Meals: Increase
Demand for Chicken: Decrease；Equilibrium Price of Frozen Meals: Decrease

虾被征税变贵 → 改用鸡肉（替代投入）→ 鸡肉需求增加；两种投入都更贵了，冷冻餐的供给减少 → 冷冻餐价格上升。

5.2-192012 AP Micro Q13

Businesses employ workers from city neighborhoods and rural areas. These workers are perfect substitutes and cannot relocate in the short run. The government offers businesses a wage subsidy if they hire workers from city neighborhoods. What is the effect of the subsidy on the wage rate of rural workers and on the total hours they work?

Wage Rate of Rural Workers: Increase；Total Hours Worked by Rural Workers: Decrease
Wage Rate of Rural Workers: No change；Total Hours Worked by Rural Workers: Increase
Wage Rate of Rural Workers: No change；Total Hours Worked by Rural Workers: Decrease
Wage Rate of Rural Workers: Decrease；Total Hours Worked by Rural Workers: Decrease
Wage Rate of Rural Workers: Decrease；Total Hours Worked by Rural Workers: No change

只补贴雇城市工人 → 城市工人对企业来说更便宜，而两者完全可替代 → 对农村工人的需求左移；农村工人短期不能搬走（供给不变）→ 农村工资和工作时间都下降。

5.2-202005 AP Micro Q14

Suppose that a large number of unskilled workers enter a nation's labor market. If the labor market is competitive, the number of unskilled workers hired and the wage rate will most likely change in which of the following ways?

Number of Unskilled Workers Hired: Increase；Wage Rate: Increase
Number of Unskilled Workers Hired: Increase；Wage Rate: Decrease
Number of Unskilled Workers Hired: Increase；Wage Rate: Not change
Number of Unskilled Workers Hired: Decrease；Wage Rate: Increase
Number of Unskilled Workers Hired: Decrease；Wage Rate: Decrease

大量非技术工人进入 → 劳动供给右移 → 就业增加、工资下降。

5.2-212010 AP Micro Q28

When labor supply in a competitive labor market increases, the equilibrium wage rate and employment will change in which of the following ways?

Wage Rate: Increase；Employment: Increase
Wage Rate: Increase；Employment: Decrease
Wage Rate: Decrease；Employment: Increase
Wage Rate: Decrease；Employment: Decrease
Wage Rate: Decrease；Employment: No change

劳动供给增加 → 沿着向下倾斜的劳动需求曲线 → 工资下降、就业增加。

5.2-222016 AP Micro 练习卷 Q27

If a large number of unskilled workers enter the labor market, which of the following is most likely to occur in the labor market for unskilled workers?

The supply curve will shift to the right and the wage rate will decrease.
The supply curve will shift to the left and the wage rate will increase.
The demand curve will shift to the right and the wage rate will increase.
The demand curve will shift to the left and the wage rate will decrease.
There will be a movement up along the demand curve and the wage rate will increase.

非技术工人增多 → 劳动供给右移 → 工资下降。

5.2-232015 AP Micro 练习卷 Q43

Suppose that people who work in the paint industry face a great risk of developing an incurable disease. A medical breakthrough that eliminates the risk will most likely cause which of the following shifts in the supply and demand curves for workers in the paint industry?

Supply Curve: Shift right；Demand Curve: No shift
Supply Curve: Shift left；Demand Curve: No shift
Supply Curve: Shift left；Demand Curve: Shift left
Supply Curve: Shift left；Demand Curve: Shift right
Supply Curve: No shift；Demand Curve: Shift left

消除了致病风险，这份工作更有吸引力 → 每个工资下愿意干的人更多 → 劳动供给右移；工人的 MRP 没变，需求不动。

5.2-242018 AP Micro 练习卷 Q29

Which of the following is likely to shift an industry’s labor supply curve to the left?

A decrease in immigration restrictions
A decrease in the cost of child care
An increase in the number of remote-working jobs
An increase in preference for leisure
An increase in wages

更看重闲暇 → 每个工资下愿意工作的时间减少 → 劳动供给左移。(A)(B)(C) 让供给增加；(E) 是沿着供给曲线移动。

5.2-252024 AP Micro Q49

The labor market for medical assistants is perfectly competitive. Which of the following would cause the supply curve of medical assistants to shift to the right?

An increase in the number of retired medical assistants
A decrease in the number of hours worked by medical assistants
A decrease in the expected future wages paid to medical assistants
A decrease in the requirements for medical assistant certification
A decrease in the number of students enrolled in medical assistant programs

降低资格证书的要求 → 进入这个职业更容易 → 劳动供给右移。其他选项都让供给减少。

5.2-262000 AP Micro Q43

In a perfectly competitive labor market for nurses, all of the following statements are true EXCEPT:

The imposition of an effective minimum wage will result in unemployment.
An increase in the marginal product of nurses will increase the demand for nurses and increase wages.
An increase in the supply of nurses will create unemployment and leave wages unchanged.
An increase in the demand for health care will increase the demand for nurses and increase wages.
Revoking work permits for foreign nurses will increase wages of domestic nurses.

竞争性劳动市场里护士供给增加 → 工资下降、就业增加，不会出现“工资不变而失业”→ 错误的是 (C)。

5.2-272005 AP Micro Q30

Which of the following tends to increase the gap in earnings between skilled and unskilled workers over time?

An increase in the demand for unskilled workers relative to skilled workers
An increase in the supply of skilled workers relative to unskilled workers
A decrease in the demand for unskilled workers relative to skilled workers
A decrease in both the demand for and the supply of skilled workers
An increase in both the demand for and supply of unskilled workers

对非技术工人的需求相对技术工人减少 → 非技术工人的工资相对下降 → 收入差距扩大。(A)(B) 缩小差距；(D)(E) 方向不确定。

5.2-282022 AP Micro 国际卷 Q25

Consider two groups of workers in competitive labor markets. Workers in group X have a skill set unique to producing computers, and workers in group Y have a skill set that can be used to produce either computers or smartphones. When the price of smartphones decreases, the wages paid to workers producing smartphones decrease. Which of the following could happen to the wages of workers in group X?

There would be no change in wages because workers in group X do not have the skills to produce smartphones.
There would be no change in wages because the supply of and demand for workers producing computers would both shift to the left.
Wages would decrease because the supply of workers producing computers would increase, with more workers from group Y seeking jobs with firms producing computers.
Wages would decrease because the supply of workers producing computers would decrease, with more workers from group X seeking training to qualify for jobs with firms producing smartphones.
Wages would increase because workers in group X have specialized skills.

Y 组工人能做电脑也能做手机。手机行业工资下降 → Y 组转去做电脑 → 电脑工人的供给增加 → X 组的工资也下降。

5.3Profit-Maximizing Behavior in Perfectly Competitive Factor Markets 完全竞争要素市场

Hire Until MRP = Wage 雇到 MRP 等于工资

完全竞争劳动市场 PERFECTLY COMPETITIVE LABOR MARKET（CED PRD-4.C.1–C.2）

雇这种劳动的企业很多，工人也很多、技能相同；任何一家企业都影响不了工资。
工资由市场的劳动供求决定，每家企业是工资接受者（wage taker）：它面对的劳动供给是一条水平线，多雇一个人的成本就是工资，MRC = W。
企业只要 MRP > W 就继续雇，一直雇到 MRP = W（= MRC）。
企业在劳动市场是工资接受者，不代表它在产品市场也是价格接受者：一家垄断企业也可能在完全竞争的劳动市场里招人。

对照完全竞争的产品市场产品市场：市场定价格 → 企业面对水平的 D = MR = P → 生产到 MR = MC。
劳动市场：市场定工资 → 企业面对水平的 S = MRC = W → 雇到 MRP = MRC。

Side-by-Side Graphs 市场与企业并排图

FRQ 最常见的画法：左边画整个劳动市场（向上倾斜的 S、向下倾斜的 D），右边画一家企业（水平的 W = MRC、向下倾斜的 MRP = D），两张图的工资对齐。点按钮看劳动供给减少时两张图怎么变：

① 开始：市场的劳动供求决定工资 $45。单个草莓园太小，影响不了市场工资——它是工资接受者，面对的劳动供给是 $45 处的水平线，也就是它的 MRC。它雇到 MRP = $45：5 人。

② 市场供给减少：很多采摘工去了工厂上班，市场劳动供给左移（S₁ → S₂），市场工资涨到 $55。每个草莓园面对的水平线也跟着上移到 $55。

③ 企业少雇人：草莓园的 MRP 没变，但 MRC 变成 $55，第 5 个人的 MRP 不到 $55 → 只雇到 MRP = $55 的 4 人。市场就业量从 4,500 人降到 3,500 人。

WORKED EXAMPLE 5采摘工去了工厂：工资涨了，草莓园雇几个？原创

The strawberry farm from 5.1 (MRP of pickers 1–7: $100, $90, $75, $60, $50, $40, $25) hires in a perfectly competitive labor market. A new factory opens nearby and many pickers leave to work there. (a) Draw side-by-side graphs of the labor market for pickers and the farm, and show the effect. (b) The market wage rises from $45 to $55. How many pickers does the farm hire now? (c) What happens to the farm's daily wage bill? (d) Did the farm's demand for labor change?

(a) 劳动市场：供给左移，工资上升、市场就业减少。企业：水平的 W = MRC 线上移，企业沿着自己的 MRP 曲线往左，少雇人。（见上面的三步并排图。）

(b) 第 4 人 MRP $60 ≥ $55，雇；第 5 人 MRP $50 < $55，不雇 → 4 人。

(c) 原来 5 × $45 = $225；现在 4 × $55 = $220。

(d) 没有。企业的劳动需求是 MRP 曲线，草莓的价格和工人的 MP 都没变，所以需求曲线不动；变的是 MRC（工资），企业是沿着需求曲线少雇人。

易错 TRAP

企业图里的劳动供给是水平线（工资接受者），市场图里的才向上倾斜。
市场工资变化 → 企业的 MRC 线移动，企业沿着 MRP 曲线调整；企业的 MRP 曲线只在产品价格或生产率变化时移动。
MRP 是企业的劳动需求，不是供给。

练习 Practice 5.3（一）· 雇到 MRP = 工资

以下为历年 AP 真题（带图和表格的题按原题重绘），点选项即时判分并显示解析。

5.3-12012 AP Micro Q58

A profit-maximizing firm should hire an input up to the point at which

marginal physical product equals marginal revenue product
marginal revenue equals marginal factor cost
marginal revenue product equals marginal revenue
marginal revenue product equals marginal factor cost
marginal physical product equals marginal factor cost

任何投入都雇到 MRP = MFC（MRC）为止。(B) 混淆了 MR 与 MFC；(E) 比较的是产量和成本，单位不同。

5.3-22025 AP Micro 国际卷 Q13

A profit-maximizing firm hiring workers from a perfectly competitive labor market will continue to hire workers until the wage rate is equal to

average variable cost
average revenue
marginal revenue
(marginal cost) × (marginal product of labor)
(marginal revenue) × (marginal product of labor)

竞争劳动市场 MFC = 工资，所以雇到 工资 = MRP = MR × MP_L。

5.3-32000 AP Micro Q14

A profit-maximizing firm will hire

labor until its wage rate equals its average revenue product
labor until its wage rate equals its marginal revenue product
labor until its wage rate equals the interest rate
capital until the interest rate equals the wage rate
capital until the interest rate exceeds the wage rate

利润最大的企业雇劳动到 工资 = MRP。(A) 平均收益产品不是边际量。

5.3-42010 AP Micro Q58

A perfectly competitive profit-maximizing firm will continue to hire additional units of an input as long as the

marginal product of the input is maximized
marginal cost of employing the input is maximized
value of the marginal product of the input exceeds the price of the input
revenue associated with the employment of the last unit of the input is maximized
price of the product is greater than the marginal cost of the input

完全竞争企业只要投入的 VMP（= MP × P = MRP）大于投入价格就继续用，直到相等。

5.3-52019 AP Micro 练习卷 Q43

Which of the following indicates that a perfectly competitive firm has hired the profit-maximizing amount of labor?

The total product of labor exceeds the total real wage payments to workers.
The average product of labor exceeds the real wage paid to workers.
The marginal revenue product of labor is below the wage paid to workers.
The marginal revenue product of labor is above the wage paid to workers.
The marginal revenue product of labor equals the wage paid to workers.

雇到利润最大时 MRP = 工资。(C) MRP < 工资说明雇多了；(D) MRP > 工资说明雇少了。

5.3-62024 AP Micro Q53

A firm hiring labor from a perfectly competitive labor market will have hired more than the profit-maximizing quantity of labor when the

marginal revenue product of labor is greater than its marginal factor cost
marginal revenue product of labor is less than its marginal factor cost
marginal revenue product of labor is equal to its marginal factor cost
total revenue is greater than the total cost
total revenue is equal to the total cost

雇得比利润最大的数量多 → 最后一个工人带来的收入 < 成本 → MRP < MFC。（2024 年非官方打字答案键给 (A)，有误：MRP > MFC 表示雇少了。）

5.3-72013 AP Micro Q54

If a competitive firm pays its workers the value of the marginal product of the last worker hired, which of the following is true?

The firm will not earn any economic profits.
Workers will look for employment elsewhere.
The wage will be less than the marginal product.
The firm will not maximize profits.
The contribution of the last worker hired to the firm’s profit will be zero.

竞争企业 VMP = MRP；工资 = 最后一个工人的 VMP → 最后一个工人对利润的贡献 = MRP − W = 0（正是利润最大的雇用量）。

5.3-82014 AP Micro 练习卷 Q58

A profit-maximizing firm will continue to hire workers until the

marginal factor cost of labor is equal to the marginal revenue product of labor
marginal factor cost of labor is equal to the price of the good produced using labor
marginal product of labor is equal to the marginal revenue product of labor
marginal product of labor is equal to the marginal factor cost of labor
marginal product of labor is equal to the price of labor

雇到 MFC = MRP。竞争劳动市场里 MFC 就是工资。

5.3-92015 AP Micro 练习卷 Q28

A profit-maximizing firm will continue to hire workers until the marginal revenue product of labor is equal to the

marginal product of labor
marginal revenue product of capital
demand for labor
price of the good that labor is producing
marginal factor cost

雇到 MRP = MFC。

5.3-102022 AP Micro 国际卷 Q27

For a firm operating in perfectly competitive product and factor markets, the marginal revenue product of labor is equal to the

marginal product of labor
price of labor multiplied by the marginal product of labor
price of labor multiplied by the price of the output
price of the output divided by the price of labor
price of the output multiplied by the marginal product of labor

产品市场完全竞争 MR = P → MRP = MR × MP = P × MP_L。

5.3-112012 AP Micro Q56

Firm XYZ produces and sells corn in a perfectly competitive market and hires its workers in a perfectly competitive labor market. Which of the following best describes the demand curve for XYZ’s corn and XYZ’s demand curve for labor?

Demand for XYZ’s Corn: Horizontal；XYZ’s Labor Demand: Horizontal
Demand for XYZ’s Corn: Horizontal；XYZ’s Labor Demand: Downward sloping
Demand for XYZ’s Corn: Horizontal；XYZ’s Labor Demand: Vertical
Demand for XYZ’s Corn: Downward sloping；XYZ’s Labor Demand: Downward sloping
Demand for XYZ’s Corn: Downward sloping；XYZ’s Labor Demand: Horizontal

玉米市场完全竞争 → 企业面对的玉米需求水平；企业的劳动需求 = MRP 曲线，因为边际产量递减而向下倾斜。水平的是企业面对的劳动供给。

5.3-122015 AP Micro 练习卷 Q13

Assume a perfectly competitive labor market. Which of the following correctly describes the individual firm’s demand curve for labor and the market demand curve for labor?

Firm’s Demand Curve for Labor: Downward sloping；Market Demand Curve for Labor: Downward sloping
Firm’s Demand Curve for Labor: Downward sloping；Market Demand Curve for Labor: Horizontal
Firm’s Demand Curve for Labor: Horizontal；Market Demand Curve for Labor: Downward sloping
Firm’s Demand Curve for Labor: Horizontal；Market Demand Curve for Labor: Horizontal
Firm’s Demand Curve for Labor: Horizontal；Market Demand Curve for Labor: Upward sloping

企业的劳动需求 = MRP，向下倾斜；市场劳动需求是各企业 MRP 的加总，也向下倾斜 → (A)。水平的是单个企业面对的劳动供给（工资）。

5.3-132012 AP Micro Q55

In a perfectly competitive free market economy, a wage gap between two workers can be explained by differences in all of the following EXCEPT their

years of schooling
occupations
marginal products
marginal revenue products
tastes for luxury goods

竞争市场里工资 = MRP = MP × P：受教育年限、职业、MP、MRP 不同都能解释工资差别；工人自己爱不爱买奢侈品不影响他的 MRP → (E)。

5.3-142015 AP Micro 练习卷 Q12

A perfectly competitive firm hires three workers in a perfectly competitive labor market. The marginal products of the three workers are shown in the table below.

Worker	Marginal Product
1	50
2	30
3	20

Which of the following will be true?

Each worker will receive a wage based on the marginal product of the last worker hired.
Each worker will receive a wage based on the marginal product of the first worker hired.
Each worker will receive a wage based on the average of the marginal products of the workers.
Worker 1 will receive the highest wage.
Worker 3 will receive the highest wage.

竞争劳动市场里所有工人拿同样的市场工资，企业雇到最后一个工人的 MRP = 工资 → 工资取决于最后一个工人的边际产量（不是第一个，也不是平均）。

5.3-152000 AP Micro Q55

ABC Limited, Inc., sells its product in a perfectly competitive market for a price of $15 per unit and hires workers at a daily wage of $75. Labor is the only factor cost, and the firm is currently earning profits. If ABC hires one more worker and output increases by 5 units per day, the firm's profits will

decrease by $5
decrease by $75
increase by $75
increase by $15
remain unchanged

多雇的工人 MRP = 5 × $15 = $75，正好等于工资 $75 → 多出的收入等于多出的成本 → 利润不变。

5.3-162016 AP Micro 练习卷 Q28

Assume that a profit-maximizing, perfectly competitive firm hires labor in a perfectly competitive labor market. If the market wage is $12 per hour and the price of the product is $3 per unit, the firm will

hire more workers if each worker can produce 3 units per hour
hire another worker if the output per hour of the additional worker exceeds 4 units
hire fewer workers, since the hourly wage exceeds the cost of producing one unit of output
not hire any workers, since the cost of labor is greater than the price of the output
continue to operate in the short run but not in the long run

再雇一人的条件：MRP = MP × $3 > $12 → MP > 4 → (B)。(A) MP = 3 时 MRP 只有 $9。

5.3-172016 AP Micro 练习卷 Q57

The last worker currently employed by a firm has a marginal product of 3 units per hour and is paid $20 per hour. Assuming that both the labor market and product market are perfectly competitive and that the product’s price is $5 per unit, the firm should do which of the following?

Decrease wages
Increase wages
Employ more workers
Employ fewer workers
Increase the product’s price

最后一个工人 MRP = 3 × $5 = $15 < 工资 $20 → 雇多了，应减少工人（减少后 MP 上升，直到 MRP = $20）。

5.3-182012 AP Micro Q26

Questions 26-27 are based on the following table, which shows the relationship between the number of workers and coal output (in tons per day).

Number of Workers	Total Output of Coal
0	0
1	25
2	44
3	60
4	70
5	75

How many workers would the coal company want to hire if the price of coal were competitively priced at $5 per ton and the wage rate were $40 per day?

MP = 25、19、16、10、5，MRP = MP × $5 = 125、95、80、50、25。工资 $40：第 4 人 $50 > $40，第 5 人 $25 < $40 → 4 人。

5.3-192014 AP Micro 练习卷 Q29

Number of Workers	Parts per Week
0	0
1	100
2	190
3	270
4	340
5	400
6	450
7	480

The table above describes the production function of an auto parts manufacturer. Assume that the firm can hire as many workers as it wants at the market wage rate of $600 per week per worker and sell as many auto parts as it wants at the price of $10 per part. To maximize profits, the firm should hire

0 workers
1 worker
3 workers
5 workers
7 workers

MP = 100、90、80、70、60、50、30，MRP = MP × $10 = 1,000、900、800、700、600、500、300。工资 $600：第 5 人 MRP = $600 = 工资，第 6 人 $500 < $600 → 5 人。

5.3-202016 AP Micro 练习卷 Q42

Quantity of Labor	Marginal Product	Marginal Revenue Product
0	---	---
1	20	$40
2	14	28
3	12	24
4	8	16
5	6	12
6	4	8

Based on the table for a perfectly competitive firm above, if the wage rate for labor is $15, how many units of labor should the firm hire?

表中已给 MRP：第 4 单位 $16 > $15，第 5 单位 $12 < $15 → 4 单位。

5.3-212023 AP Micro 国际卷 Q55

The table provided shows the daily output for a profit-maximizing T-shirt firm that is operating in a perfectly competitive product market and hires labor from a perfectly competitive labor market. If each T-shirt sells for $10 and the equilibrium daily wage is $100, how many workers will the firm hire to maximize profit?

Number of Workers	Quantity of T-Shirts
0	0
1	24
2	44
3	60
4	72
5	80

MP = 24、20、16、12、8，MRP = MP × $10 = 240、200、160、120、80。工资 $100：第 4 人 $120 雇，第 5 人 $80 不雇 → 4 人。

5.3-222023 AP Micro 国际卷 Q60

Number of Workers	Total Output/Hour
1	3
2	7
3	12
4	14
5	15

If the hourly wage is $9, how many workers will the firm hire to maximize profit?

MP = 3、4、5、2、1，MRP = MP × $5 = 15、20、25、10、5。工资 $9：第 4 人 $10 > $9 雇，第 5 人 $5 不雇 → 4 人。

5.3-232024 AP Micro Q21

Carnival Funnel Cakes sells its funnel cakes for $4 in a perfectly competitive market and hires workers from a perfectly competitive labor market at a wage of $10. The graph provided shows the total product curve for funnel cakes. Assuming labor is the only variable input, what is the profit-maximizing number of workers that Carnival Funnel Cakes will hire?

按原题重绘

3 workers
4 workers
5 workers
6 workers
7 workers

从总产量图读出 MP：3、4、5、7、6、3、2、−2；MRP = MP × $4 = 12、16、20、28、24、12、8、−8。工资 $10：第 6 人 $12 > $10 雇，第 7 人 $8 不雇 → 6 人。

5.3-242014 AP Micro 练习卷 Q42

按原题重绘

The graph above shows the marginal revenue product (MRP) and the market wage rate for a profit-maximizing firm. Which of the following is true of the firm’s hiring of labor?

It should hire 15 workers.
It should hire between 15 and 40 workers.
It should hire 40 workers.
It should hire between 40 and 90 workers.
It should hire 90 workers.

要在 MRP 下降的那一段与工资相等。15 到 90 人之间每个人的 MRP 都高于 $10，所以一直雇到 MRP 降回 $10 的 90 人。15 人处 MRP 正在上升，那是利润最低的点。

5.3-252019 AP Micro 练习卷 Q26

Questions 25-26 refer to the data in the table below.

A perfectly competitive firm operates with a fixed amount of capital that costs $1,000 per day. Labor is the only variable input. The firm hires labor in a perfectly competitive labor market at $100 per day per worker. The table below shows the firm’s production function.

Number of Workers Hired	Quantity of Output (units)
0	0
1	10
2	30
3	54
4	75
5	85
6	90

The firm will maximize profit in the short run if it

shuts down and the price is $10
produces 30 units and the price is $4
produces 30 units and the price is $10
produces 54 units and the price is $4
produces 85 units and the price is $10

MP = 10、20、24、21、10、5。P = $10 时 MRP = 100、200、240、210、100、50，工资 $100 → 雇 5 人（第 5 人 MRP = 工资，4 人和 5 人利润相同），产量 85；TR $850 > 可变成本 $500，营业 → (E)。P = $4 时每个 MRP 都低于 $100，且 TR < TVC，会停产。

5.3-262025 AP Micro 国际卷 Q30

A firm hires labor and rents machines as variable inputs from perfectly competitive factor markets to produce Good X. The firm also requires land, as a fixed input, for its operation. The firm’s short-run profit-maximizing quantity of output would not be affected by a change in which of the following?

The price of land
The price of Good X
The marginal product of labor
The marginal product of machines
The wage rate

土地是固定投入，它的价格是固定成本，不影响 MR 和 MC → 不改变利润最大的产量。产品价格、MP_L、机器的 MP、工资都会改变 MR 或 MC。

Minimum Wage in a Competitive Labor Market 完全竞争劳动市场的最低工资

完全竞争劳动市场里有效的最低工资（高于均衡工资 $45）：企业只雇 3,000 人（需求），却有 6,000 人想按 $60 工作（供给）——劳动过剩（失业）3,000 人，就业量从 4,500 降到 3,000，出现无谓损失。保住工作的人工资提高了；劳动需求越缺乏弹性，就业减少得越少。

选择题常见问法有效（binding）最低工资 → 劳动供给量增加、需求量减少、就业减少、出现失业（劳动过剩）；保住工作的工人收入增加。劳动需求越缺乏弹性，就业减少得越少。注意：买方垄断市场里的最低工资结论不一样（见 5.4）。

练习 Practice 5.3（二）· 竞争劳动市场的最低工资

以下为历年 AP 真题（带图和表格的题按原题重绘），点选项即时判分并显示解析。

5.3-272014 AP Micro 练习卷 Q13

In a perfectly competitive labor market, an increase in an effective minimum wage will result in

an increase in the supply of workers
a decrease in the supply of workers
a decrease in the demand for workers
more workers being hired
fewer workers being hired

有效最低工资高于均衡工资 → 沿着劳动需求曲线，企业的需求量减少 → 雇的人更少。两条曲线都不移动（A、B、C 错）。

5.3-282021 AP Micro 国际卷 Q4

If a binding minimum wage increases in a perfectly competitive labor market, then which of the following will likely occur in the labor market?

The supply of workers will increase.
The supply of workers will decrease.
The demand for workers will increase.
The demand for workers will decrease.
The quantity of workers supplied will increase.

更高的最低工资 → 沿着供给曲线，劳动供给量增加（需求量减少，过剩扩大）；曲线本身不移动。

5.3-292017 AP Micro 练习卷 Q32

If the government eliminates an effective minimum wage in a competitive labor market, which of the following is true?

Minimum wage workers will experience no change in hourly pay.
Minimum wage workers will experience a decrease in hourly pay.
The number of people employed will decrease because people do not want to work for low wages.
There will be an excess demand for workers.
There will be an increase in the supply of workers.

取消有效最低工资 → 工资降到均衡水平 → 原来拿最低工资的工人时薪下降，就业增加，不会出现劳动短缺。

5.3-302005 AP Micro Q57

按原题重绘

The graph above illustrates the labor market for teenage workers. The current minimum wage for all workers is W₁. If Congress introduces a subminimum wage, W₂ that applies only to teenagers, what is the most likely effect on teenage employment?

Teenage employment will increase because firms will want to hire more teenagers at W₂ than at W₁.
Teenage employment will increase because more teenagers will want to work at W₂ than at W₁.
Teenage employment will decrease because fewer teenagers will want to work at W₂ than at W₁.
Teenage employment will decrease because firms will want to hire fewer teenagers at W₂ than at W₁.
Teenage employment will stay the same because the market-clearing wage is lower than W₁ and W₂.

W₁、W₂ 都高于均衡工资，就业量由需求量决定。把青少年的最低工资降到 W₂ → 沿需求曲线向下 → 企业想雇更多青少年 → (A)。(B) 就业由需求决定，不是供给。

5.3-312012 AP Micro Q42

An increase in the effective minimum wage will have less of an impact on employment if the demand for labor is

a derived demand
decreasing
relatively elastic
relatively inelastic
unit elastic

最低工资提高时，劳动需求越缺乏弹性，需求量减少得越少，对就业的影响越小。

5.3-322017 AP Micro 练习卷 Q59

An effective minimum wage policy in a competitive market will increase unemployment and increase the total earnings of labor only if the demand for labor is

relatively inelastic
relatively elastic
unit elastic
greater than the supply
positively related to the wage rate

最低工资提高工资、减少就业；总工资收入（W × L）要上升，需求量减少的百分比必须小于工资上升的百分比 → 劳动需求缺乏弹性。

5.3-332005 AP Micro Q27

If a 5 percent wage increase in a particular labor market results in a 10 percent decrease in employment, the demand for labor is

perfectly elastic
relatively elastic
unit elastic
relatively inelastic
perfectly inelastic

劳动需求弹性 = 10% ÷ 5% = 2 > 1 → 富有弹性。

5.3-342023 AP Micro 国际卷 Q32

The government imposition of a minimum wage in a perfectly competitive labor market is a policy that would

be used in a pure market economy
be used in a mixed economy
eliminate deadweight loss
increase the number of workers hired
decrease the supply of labor

政府规定最低工资是对市场的干预 → 属于混合经济（Unit 1 1.2）。同时注意干扰项：有效最低工资会造成 DWL、减少雇用，且不会移动供给曲线。

5.3-352025 AP Micro 国际卷 Q48

Avocado production requires land to grow avocado trees and workers to pick the avocados. Which of the following is most likely to occur if a binding minimum wageprice floor on wages is set in the labor market of avocado-farming workers?

Supply of avocados will decrease.
Demand for avocados will decrease.
There will be a surplus of avocados.
Avocado producers will hire more workers.
The price of land used to grow avocados will increase.

最低工资提高了牛油果的投入成本 → 牛油果供给减少。农场会少雇人（D 错）；消费者需求不变（B 错）；劳动少了，与之互补的土地需求下降（E 错）。

MRP When the Firm Has Market Power 卖方垄断企业的 MRP

MRP = MP × MR（CED PRD-4.C.4）产品市场完全竞争：MR = P，所以 MRP = MP × P，也叫边际产品价值 VMP。
产品市场有市场势力（垄断、垄断竞争、寡头）：多卖要降价，MR < P，所以 MRP < VMP，MRP 曲线更低、更陡，企业雇的人更少。

WORKED EXAMPLE 6小镇唯一的手机壳定制店：MRP ≠ MP × P 原创

The only custom phone-case shop in a small town is a monopolist in its output market, but it hires workers in a perfectly competitive labor market at $25 per day. To sell more cases, it must lower its price. The table shows output and the price at which that output can be sold.

Workers	1	2	3	4	5
Cases per day	10	18	24	28	30
Price ($)	10	9	8	7	6

(a) Calculate the MRP of the 2nd worker. (b) How many workers will the shop hire? (c) Calculate MP × P for the 4th worker, and explain why the shop does not use it as the 4th worker's MRP. (d) Is the shop a wage taker?

工人	产量 Q	MP	能卖的价格 P	TR	MRP = ΔTR	VMP = MP × P
1	10	10	$10	$100	$100	$100
2	18	8	$9	$162	$62	$72
3	24	6	$8	$192	$30	$48
4	28	4	$7	$196	$4	$28
5	30	2	$6	$180	−$16	$12

(a) TR：1 人 $100，2 人 18 × $9 = $162 → MRP₂ = $62。注意不是 MP × P = 8 × $9 = $72：多卖 8 个要把所有手机壳都降价 $1，前 10 个少收了 $10。

(b) 第 3 人 MRP $30 ≥ $25，雇；第 4 人 MRP 只有 $4 < $25 → 3 人。

(c) MP₄ × P = 4 × $7 = $28，但企业多雇第 4 人后，收入只增加 $196 − $192 = $4。有市场势力的企业 MR < P，所以 MRP = MP × MR < MP × P（CED PRD-4.C.4）。

(d) 是。它在产品市场是垄断者，在劳动市场却只是许多雇主之一，只能接受 $25 的市场工资（CED PRD-4.C.1）。

卖方垄断的手机壳店：要多卖就得降价，所以 MR < P，它的 MRP（蓝）低于 MP × P（VMP，绿虚线），而且下降得更快。工资 $25 时，按 MRP 只雇 3 人；如果误用 VMP，会以为第 4 人（VMP $28）也值得雇。

Least-Cost Combination 最低成本组合（CED PRD-4.C.3）

最低成本法则 LEAST-COST RULE MP_L / W = MP_K / r 花在每种投入上的最后一美元带来同样多的产量，生产这个产量的成本就最低。
如果 MP_L/W > MP_K/r：花在劳动上更划算 → 多用劳动、少用资本，直到两边相等（多用劳动会让 MP_L 下降）。利润最大：MRP_L = W 且 MRP_K = r　⇔　MRP_L/W = MRP_K/r = 1 利润最大的组合一定是最低成本组合；但最低成本组合不一定利润最大（它只保证“这个产量”花钱最少，没说产量是不是最好）。

WORKED EXAMPLE 7面包房：多雇一个面包师，还是多租一台烤箱？原创

A bakery hires bakers at a wage of $20 per hour and rents ovens at $10 per hour. The marginal products (loaves per hour) of successive bakers are 10, 8, 6, 4, 2, and of successive ovens are 6, 5, 4, 3, 2. Assume the marginal product of each input does not depend on the amount of the other input, and the bakery sells bread in a perfectly competitive market.

(a) The bakery now uses 2 bakers and 2 ovens. Is it producing its output at the lowest possible cost? If not, which input should it use more of? (b) Find the least-cost combination of inputs for producing 33 loaves per hour. (c) The price of bread is $4. Find the profit-maximizing number of bakers and ovens, and show that the least-cost rule also holds there.

第几个	MP_L（面包师）	MP_L/W	MP_K（烤箱）	MP_K/r
1	10	0.5	6	0.6
2	8	0.4	5	0.5
3	6	0.3	4	0.4
4	4	0.2	3	0.3
5	2	0.1	2	0.2

(a) 最后一个面包师：MP_L/W = 8/20 = 0.4；最后一台烤箱：MP_K/r = 5/10 = 0.5。烤箱每 $1 多做 0.5 个，面包师只有 0.4 个 → 不是最低成本，应该多用烤箱（少用面包师）。

(b) 让两边相等：2 个面包师（0.4）与 3 台烤箱（0.4）。产量 = (10 + 8) + (6 + 5 + 4) = 33 个，成本 = 2 × $20 + 3 × $10 = $70。

(c) 面包师的 MRP = 4 × MP_L = 40、32、24、16、8：雇到第 3 个（$24 > $20，第 4 个 $16 < $20）。烤箱的 MRP = 24、20、16、12、8：租到第 4 台（$12 > $10，第 5 台 $8 < $10）。 → 3 个面包师、4 台烤箱。此时 MP_L/W = 6/20 = 0.3 = MP_K/r = 3/10，最低成本法则也成立；MRP_L/W = MRP_K/r = 1.2（表格是整数，做不到恰好等于 1，最接近的就是这一组）。

每多花 $1 能多做几个面包：先把钱花在柱子更高的那一种投入上。花到最后，两种投入“最后一美元”的产量相等（例如第 2 个面包师和第 3 台烤箱都是 0.4），成本就最低。

FRQ 计算题模板 “The firm uses the cost-minimizing combination. The marginal product of capital is 300 units, the rental price of capital is $60, and the marginal product of labor is 100 units. Calculate the wage.” → 300/60 = 100/W → W = $20。先写出 MP_L/W = MP_K/r，再代数。

LAB 3人和机器怎么配？ · The Least-Cost Rule

还是那家面包房：面包师 $20/小时，烤箱 $10/小时，面包 $4 一个；MP_L = 10、8、6、4、2，MP_K = 6、5、4、3、2。加减面包师和烤箱，看“每一美元的边际产量”、成本和利润。

面包师 L = 2

烤箱 K = 2

练习 Practice 5.3（三）· 卖方垄断企业的 MRP 与最低成本组合

以下为历年 AP 真题（带图和表格的题按原题重绘），点选项即时判分并显示解析。

5.3-362018 AP Micro 练习卷 Q42

Questions 42-43 are based on the following output and total revenue for a monopolist in the product market.

Output Quantity (units)	Total Revenue ($)
0	0
1	11
2	20
3	27
4	32
5	35
6	36
7	35

The marginal product of labor is constant at 1 unit for every additional unit of labor. The monopolist hires labor in a perfectly competitive market at the wage rate of $5 per hour.

What is the marginal revenue product of labor when the firm produces the third unit of output?

第 3 单位产品的 MR = 27 − 20 = $7；每单位劳动的 MP = 1 → MRP = 1 × $7 = $7。垄断企业要用 MR，不能用价格。

5.3-372018 AP Micro 练习卷 Q43

Questions 42-43 are based on the following output and total revenue for a monopolist in the product market.

Output Quantity (units)	Total Revenue ($)
0	0
1	11
2	20
3	27
4	32
5	35
6	36
7	35

The marginal product of labor is constant at 1 unit for every additional unit of labor. The monopolist hires labor in a perfectly competitive market at the wage rate of $5 per hour.

How many units of labor should the firm employ to maximize profits?

MR = 11、9、7、5、3、1、−1；MP = 1，所以每单位劳动的 MRP 依次是 $11、$9、$7、$5……工资 $5：第 4 单位 MRP = $5 = 工资 → 4 单位。

5.3-382005 AP Micro Q42

Assume a firm uses only two inputs, capital (K) and labor (L), to produce its output. Let the marginal product of capital be MP_K, the marginal product of labor be MP_L, the price of capital be P_K, and the price of labor be P_L. The least-cost combination of capital and labor needed to produce a given level of output is given by which of the following?

MP_L/P_L = MP_K/P_K
MP_L/P_L > MP_K/P_K
MP_L/P_K = MP_K/P_L
(MP_L)P_L = (MP_K)P_K
MP_L = MP_K

最低成本：每种投入最后一美元的边际产量相等 → MP_L/P_L = MP_K/P_K。

5.3-392012 AP Micro Q43

If a firm employs only labor and capital in its production process, which of the following best describes the optimal combination of inputs for the firm in the long run?

The marginal product per dollar spent on labor is equal to the marginal product per dollar spent on capital.
The marginal product of labor is equal to the marginal product of capital.
The total product of labor is equal to the total product of capital.
The marginal product of labor and capital are both zero.
All marginal products are equal to all average products.

长期最优组合：花在劳动和资本上的每一美元的边际产量相等。(B) 只比较 MP，没考虑价格。

5.3-402021 AP Micro 国际卷 Q12

Mary manages a manufacturing plant. Two inputs are used to produce the product. To minimize the costs of production, Mary should continue to hire inputs up to the level at which the

price of each input is equal
marginal product of each input is equal
(marginal product × price) of each input is equal
(marginal product ÷ price) of each input is equal
(marginal product − price) of each input is equal

成本最低：每种投入的 MP ÷ 价格 相等。

5.3-412021 AP Micro 国际卷 Q14

At a given quantity of output of a firm, if the marginal product of capital equals the marginal product of labor and the wage rate equals the rental rate of capital, then

the firm is producing that quantity at the lowest cost
the firm should use more capital and less labor to minimize cost
the firm should use less capital and more labor to minimize cost
the firm should use more of both inputs to increase quantity
the firm should use less of both inputs to increase quantity

MP_K = MP_L 且 r = W → MP_K/r = MP_L/W → 已经是最低成本。

5.3-422010 AP Micro Q57

Assume that the last worker a firm hired produces 60 additional units of output per hour and the last machine rented produces 6,000 units of output per hour. A worker's hourly wage rate is $12, and the rental cost of a machine is $1,000 per hour. In order to minimize the cost of its current output, the firm should

do nothing, because the costs of production are minimized
increase the use of labor and decrease the use of capital
increase the use of capital and decrease the use of labor
increase the use of labor and increase the use of capital
decrease the use of labor and decrease the use of capital

MP_L/W = 60/12 = 5，MP_K/r = 6,000/1,000 = 6 → 资本每一美元产出更多 → 多用资本、少用劳动。

5.3-432013 AP Micro Q36

At its current employment level of labor and capital, a firm observes the following.

• Marginal product of labor = 30 units
• Marginal product of capital = 60 units
• Price of labor = $3 per unit
• Price of capital = $15 per unit

Which of the following actions should the firm take in order to achieve the least-cost combination of labor and capital and produce the same level of output?

Labor: Increase；Capital: Increase
Labor: Increase；Capital: Decrease
Labor: Decrease；Capital: Increase
Labor: Decrease；Capital: Decrease
Labor: No change；Capital: No change

MP_L/P_L = 30/3 = 10，MP_K/P_K = 60/15 = 4 → 劳动更划算 → 多用劳动、少用资本（多用劳动使 MP_L 下降，直到两边相等）。

5.3-442014 AP Micro 练习卷 Q22

• The marginal product of labor equals 250 units of output.
• The marginal product of capital equals 750 units of output.
• The price of labor is $50 per person.
• The price of capital is $100 per unit.

Given the information above, which of the following is true for a firm buying its labor and capital inputs in a perfectly competitive market?

The firm is producing its current level of output with the least-cost combination of labor and capital.
The firm is maximizing profits with its current combination of inputs.
The firm’s level of output will remain the same if 1 unit of capital is substituted for 2 units of labor.
The firm’s input costs will decrease if 2 units of labor are substituted for 1 unit of capital.
The firm can reduce the cost of its current level of output by laying off workers and employing more capital.

MP_L/P_L = 250/50 = 5，MP_K/P_K = 750/100 = 7.5 → 资本更划算 → 少用劳动、多用资本可以降低当前产量的成本 → (E)。

5.3-452016 AP Micro 练习卷 Q8

A contractor is employing labor and capital to build an office complex. At the current mix of inputs, the marginal product of labor is 30 square feet per day, and the marginal product of capital is 90 square feet per day. The price of labor is $1,000 per day, and the price of capital is $3,000 per day. To hire inputs in a cost-minimizing way, the firm should

hire more labor and less capital
hire less labor and more capital
hire more labor and more capital
hire less labor and less capital
make no changes to the mix of inputs

MP_L/P_L = 30/1,000 = 0.03，MP_K/P_K = 90/3,000 = 0.03 → 已经相等 → 不用调整。

5.3-462016 AP Micro 练习卷 Q38

Assume that a firm uses labor and capital to produce a product. The firm hires labor at a wage rate of $4 per unit and rents capital at $5 per unit. At its current output level, the marginal physical products of labor and capital are 20 and 30 units, respectively. To minimize its cost of production without changing the level of output, the firm should

make no changes
hire more labor and rent more capital
hire less labor and rent more capital
hire more labor and rent less capital
hire less labor and rent less capital

MP_L/W = 20/4 = 5，MP_K/r = 30/5 = 6 → 资本更划算 → 少雇劳动、多租资本。

5.3-472017 AP Micro 练习卷 Q39

A firm uses capital and labor in its production process. The marginal product for the last unit of labor is 5, the marginal product for the last unit of capital is 10, and the wage is $10. At what cost of hiring each unit of capital would the firm be minimizing the cost of the current output?

5/$10 = 10/r → r = $20。

5.3-482017 AP Micro 练习卷 Q45

Max employs both labor and capital to produce toy trains. Currently the last unit of labor employed has a marginal product of 15 units. The last unit of capital employed has a marginal product of 40 units. The price of labor is $3 per unit, and the price of capital is $10 per unit. Which of the following employment decisions should Max follow to use the least-cost combination of labor and capital to produce the current quantity of toy trains?

Employment of Labor: Increase；Employment of Capital: No change
Employment of Labor: Decrease；Employment of Capital: Increase
Employment of Labor: Decrease；Employment of Capital: Decrease
Employment of Labor: Increase；Employment of Capital: Increase
Employment of Labor: Increase；Employment of Capital: Decrease

MP_L/P_L = 15/3 = 5 > MP_K/P_K = 40/10 = 4 → 增加劳动、减少资本。

5.3-492018 AP Micro 练习卷 Q21

A firm is currently employing a cost-minimizing combination of labor and capital for a given level of output. The firm is employing 20 workers, and the marginal product of the last worker is 40 units of output. The firm is employing 100 units of capital, and the marginal product of the last unit of capital is 10 units of output. If the wage rate is $20 per hour, what is the price of capital?

$2.5 per hour
$5 per hour
$10 per hour
$100 per hour
$200 per hour

40/$20 = 10/r → r = $5。工人数和资本数量是干扰数据。

5.3-502022 AP Micro 国际卷 Q9

Assume that capital and labor are the only two inputs used by a clinic. The table shows the hourly marginal product and the hourly price of capital and labor at the current output level. To minimize costs at the current output level, the clinic should change the hiring of capital and labor in which of the following ways?

	Capital	Labor
Marginal Product	25 units	5 units
Hourly Price	$200	$50

The amount of capital hired should decrease, and the amount of labor hired should increase.
The amount of capital hired should decrease, and the amount of labor hired should decrease.
The amount of capital hired should increase, and the amount of labor hired should decrease.
The amount of capital hired should increase, and the amount of labor hired should increase.
There should be no change to the quantity of capital or labor hired.

资本 25/$200 = 0.125，劳动 5/$50 = 0.10 → 资本每一美元产出更多 → 多用资本、少用劳动。

5.3-512015 AP Micro 练习卷 Q56

A firm sells its output in a perfectly competitive market and hires two inputs, capital and labor, in perfectly competitive factor markets. The product price is $15 per unit, the wage is $75 per day, and the marginal product of capital is 3. If the firm is choosing the least-cost combination of labor and capital, the firm's marginal product of labor and the price of capital must be equal to which of the following?

Marginal Product of Labor: 25；Price of Capital: $5
Marginal Product of Labor: 25；Price of Capital: $45
Marginal Product of Labor: 5；Price of Capital: $15
Marginal Product of Labor: 5；Price of Capital: $25
Marginal Product of Labor: 5；Price of Capital: $45

利润最大且最低成本：P × MP = 要素价格。MP_L = $75 ÷ $15 = 5；资本价格 = $15 × 3 = $45。检验：5/75 = 3/45。

5.3-522000 AP Micro Q44

For a certain firm, the marginal revenue product for the last unit of labor is $60, and the marginal revenue product for the last unit of capital is $100. Which of the following combinations of factor prices would be necessary for the firm to maximize profits?

Price of Labor: $2；Price of Capital: $5
Price of Labor: $3；Price of Capital: $20
Price of Labor: $10；Price of Capital: $10
Price of Labor: $2；Price of Capital: $25
Price of Labor: $60；Price of Capital: $100

利润最大要求每种投入的 MRP = 价格：劳动 $60、资本 $100。其他组合连 MRP/P 相等都做不到。

5.3-532018 AP Micro 练习卷 Q51

Max Company produces electronic gadgets using labor and capital. If Max increases labor and decreases capital to produce the same quantity of gadgets, what will happen to the marginal product (MP) of labor and the MP of capital?

MP of Labor: Decrease；MP of Capital: Increase
MP of Labor: Decrease；MP of Capital: No change
MP of Labor: Increase；MP of Capital: Increase
MP of Labor: Increase；MP of Capital: Decrease
MP of Labor: No change；MP of Capital: Increase

边际产量递减：多用劳动 → MP_L 下降；少用资本 → MP_K 上升。这正是“调整后两边比率会趋于相等”的原因。

5.4Monopsonistic Markets 买方垄断

定义 DEFINITION（CED PRD-4.D） Monopsony 买方垄断：某种要素只有一个买方。最典型的是劳动市场里唯一的雇主。它面对的是整个市场向上倾斜的劳动供给：想多雇人，就得提高工资——它是工资制定者（wage setter），不是工资接受者。

⛏️

偏远矿区唯一的矿业公司：镇上的矿工除了它没有别的雇主可选。

🏥

山区小镇唯一的医院：护士要么在这里工作，要么搬到别的城市。

🏭

“工厂镇”：几家企业合并成一家后，成了当地某种工人的唯一雇主（这正是 2025 年国际卷 Q60 的情境）。

易错 TRAP · 买方垄断 ≠ 卖方垄断 monopoly 是产品市场里唯一的卖家（MR < P）；monopsony 是要素市场里唯一的买家（MFC > W）。一家企业可以只是其中一种，也可以两者都是。

Why MFC > Wage 为什么边际要素成本高于工资

想多雇一个人，就得把工资提高一点；而且每个人都要按新的工资付钱（不能只给新人高工资）。所以多雇一个人的成本 = 新人的工资 + 给原来所有人涨的钱（CED PRD-4.D.1）。

WORKED EXAMPLE 8山区小镇唯一的医院雇几位护士？原创

The only hospital in a remote mountain town is the sole employer of nurses there. To hire more nurses it must raise the wage, and it pays every nurse the same wage. The wage needed to hire 1, 2, 3, 4, 5, 6 nurses is $20, $22, $24, $26, $28, $30 per hour, and the MRP of the 1st through 6th nurse is $60, $50, $40, $30, $22, $14.

(a) Calculate the marginal factor cost of the 4th nurse and explain why it exceeds the wage. (b) How many nurses will the hospital hire, and what wage will it pay? (c) If the market for nurses were perfectly competitive, how many nurses would be hired and at what wage? (d) At the monopsony outcome, compare the MRP of the last nurse with the wage.

护士人数	需要付的工资 W（供给）	总工资 TLC	MFC = ΔTLC	MRP
1	$20	$20	$20	$60
2	$22	$44	$24	$50
3	$24	$72	$28	$40
4	$26	$104	$32	$30
5	$28	$140	$36	$22
6	$30	$180	$40	$14

(a) 雇 3 人总工资 3 × $24 = $72，雇 4 人 4 × $26 = $104 → MFC₄ = $32。比 $26 多出的 $6 是前 3 位护士每人涨的 $2（CED PRD-4.D.2：MFC 大于劳动的供给价格）。

(b) 比较 MRP 与 MFC：第 3 位 $40 ≥ $28，雇；第 4 位 $30 < $32，不雇 → 3 位护士；工资只需付到能招到 3 人的水平：$24（读供给，不是 MFC 的 $28）。

(c) 完全竞争时每家医院是工资接受者，雇到 MRP = 工资（供给）：第 4 位 $30 ≥ $26，第 5 位 $22 < $28 → 4 位，工资 $26。

(d) 第 3 位护士的 MRP $40 > 工资 $24：买方垄断者付给工人的工资低于工人带来的边际收益产品。与竞争市场相比，雇的人更少、工资更低。

小镇医院多雇一位护士，要把工资提高 $2，而且所有护士都要涨（不能只给新人高工资）。所以多雇第 4 位护士的成本 = 她自己的 $26 + 前 3 位每人多 $2（$6）= $32，比工资高。人越多，要涨薪的人越多，MFC 和工资的差距越大。

画图规则 MFC 曲线从供给曲线的起点出发，在供给上方，而且更陡（供给是直线 W = a + bL 时，MFC = a + 2bL：同一个纵截距、斜率加倍——和“MR 在需求下方、斜率加倍”正好是镜像）。

How Many to Hire, What to Pay 雇多少、付多少

两步走雇多少：MRP = MFC　→　付多少：从这个数量往下读供给曲线和垄断企业“产量看 MR = MC，价格读需求”是同一个套路：数量由两条“边际”线的交点决定，价格（工资）从市场曲线上读。

① 定雇多少：MRP 与 MFC 相交：L = 4。在这之前 MRP > MFC，多雇有利；之后 MRP < MFC。

② 定付多少：从 L_m = 4 往下走到供给曲线：只要付 $12 就能招到 4 个人，所以工资 W_m = $12（不是 MFC 的 $20）。

③ 与竞争比较：完全竞争劳动市场会在 S = MRP 处：L_c = 6、W_c = $16。买方垄断雇得少（4 < 6）、工资低（$12 < $16），L = 4 到 6 之间 MRP 高于供给的部分是无谓损失。

	完全竞争劳动市场	买方垄断
雇主	很多，工资接受者	一个，工资制定者
企业面对的劳动供给	水平（W = MRC）	市场供给，向上倾斜
MRC（MFC）与工资	MRC = W	MFC > W（MFC 在供给上方）
雇多少	MRP = W	MRP = MFC
付多少	市场工资	供给曲线上对应的工资
例子中的结果	L = 6，W = $16	L = 4，W = $12
最后一个工人的 MRP 与工资	相等	MRP（$20）> W（$12）

WORKED EXAMPLE 9用字母读买方垄断图（AP 选择题考法）原创

The graph shows the labor market for a monopsonist. Using the labels, identify (a) the number of workers it hires and the wage it pays, (b) the marginal factor cost of the last worker hired, (c) the employment and wage if the labor market were perfectly competitive, and (d) the minimum wage that would make the monopsonist hire the competitive number of workers.

一个买方垄断的劳动市场：a 是 MRP 与 MFC 的交点，b 是 MRP 与供给的交点，c 在供给上，d 在 MFC 上。

(a) MRP = MFC 在 a 点 → 雇 L₁；从 L₁ 往下读供给（c 点）→ 工资 W₁。最常见的错误是选 W₃（那是 MFC 的高度）。

(b) 最后一个工人的 MFC = MRP = W₃（a 点的高度），比他拿到的工资 W₁ 高。

(c) 竞争市场在供给与 MRP 的交点 b：L₂、W₂。W₄ 是 L₂ 处 MFC 的高度，与竞争结果无关。

(d) 最低工资定在 W₂：MFC 在 L₂ 以内变成 W₂ 的水平线，正好与 MRP 交于 b，雇 L₂。

Minimum Wage in a Monopsony 买方垄断市场的最低工资

在完全竞争劳动市场，有效最低工资让就业减少（5.3）。在买方垄断市场，定得合适的最低工资反而能让就业和工资同时增加：

最低工资 = $16（等于竞争工资）：在 6 个人以内，多雇一个人只多花 $16，MFC 变成 $16 的水平线（灰色虚线是原来的 MFC）。MRP = $16 在 L = 6 → 医院雇 6 人、付 $16——就业和工资都增加，无谓损失消失。

最低工资定得太高 = $20：MFC 是 $20 的水平线，MRP = $20 在 L = 4 → 只雇 4 人。再高（比如 $22）就业还会降到 3 人。

最低工资	没有	$14	$16	$18	$20	$22
就业量	4	5	6	5	4	3
工资	$12	$14	$16	$18	$20	$22

结论最低工资在买方垄断工资（$12）和竞争工资（$16）之间时，就业增加；正好等于竞争工资时，就业达到竞争水平、DWL 消失；高于竞争工资后，就业又开始减少。原因：最低工资让 MFC 在一段范围内变成水平线，买方垄断者“多雇一人要给所有人涨薪”的顾虑消失了。

LAB 4买方垄断与最低工资 · Monopsony and a Minimum Wage

劳动供给 W = 4 + 2L，MFC = 4 + 4L，MRP = 28 − 2L。拖动最低工资（拖到最左边表示没有最低工资），看这家唯一的雇主雇多少人、付多少工资。

最低工资 = 没有

练习 Practice 5.4 · 买方垄断

以下为历年 AP 真题（带图和表格的题按原题重绘），点选项即时判分并显示解析。

5.4-12021 AP Micro 国际卷 Q18

A monopsonistic labor market has a

single employer of labor
horizontal labor supply curve
labor force of identically skilled workers
backward bending labor supply curve
demand curve for labor that is perfectly elastic

买方垄断的劳动市场只有一个雇主。它面对向上倾斜的市场劳动供给，不是水平的。

5.4-22024 AP Micro Q25

Which of the following is true of a monopsonist?

A monopsonist controls the product market and pays the same wage rate to all workers.
A monopsonist needs to offer a higher wage to attract additional workers.
A monopsonist produces goods that are sold only in imperfectly competitive product markets.
A monopsonist can charge higher prices for a product it sells without losing all its customers.
If a monopsonist decreases the wage rate paid to its workers, the firm will lose all its workers to competing employers.

买方垄断者面对向上倾斜的劳动供给：想多招人就要提高工资。(A)(C)(D) 说的是产品市场；(E) 描述的是工资接受者。

5.4-32017 AP Micro 练习卷 Q55

The monopsonist’s marginal factor (resource) cost curve for labor is

above the labor supply curve because the product price is found on the demand curve above where marginal cost equals marginal revenue
above the labor supply curve because to hire more workers the firm must raise the wage for all workers
below the labor supply curve because the firm is a wage taker
below the labor supply curve because of diminishing marginal returns to labor
below the labor supply curve because to sell additional units of output the firm must lower its product price

多雇一人必须提高所有工人的工资 → MFC 高于工资 → MFC 曲线在劳动供给曲线上方。

5.4-42022 AP Micro 国际卷 Q34

Which of the following explains why the marginal factor (resource) cost curve lies above the supply curve for labor in a monopsonistic labor market?

The monopsonist must lower its price to sell more output.
Each worker is paid a different wage, based on individual marginal productivity.
The monopsonist has market power and pays whatever wage it desires.
The supply of labor is perfectly elastic.
The monopsonist must increase the wage for all workers to hire more workers.

买方垄断者要多雇人，必须给所有工人涨工资 → MFC = 新人工资 + 给原有工人的涨幅 > 工资。

5.4-52018 AP Micro 练习卷 Q37

In a monopsonistic labor market, a firm will continue to hire workers until the marginal revenue product of labor

equals marginal factor (resource) cost, resulting in more workers being hired at a lower wage compared with a perfectly competitive labor market
equals marginal factor (resource) cost, resulting in fewer workers being hired at a lower wage compared with a perfectly competitive labor market
equals marginal factor (resource) cost, resulting in fewer workers being hired at a higher wage compared with a perfectly competitive labor market
is less than marginal factor (resource) cost, resulting in more workers being hired at a lower wage compared with a perfectly competitive labor market
is less than marginal factor (resource) cost, resulting in fewer workers being hired at a lower wage compared with a perfectly competitive labor market

买方垄断者雇到 MRP = MFC；MFC 在供给上方 → 雇的人比竞争市场少，付的工资（读供给）也更低。

5.4-62005 AP Micro Q28

Number of Workers	Hourly Wage	Marginal Factor Cost	Marginal Revenue Product
10	$5.00
11	5.10	$6.10/hr	$8.70/hr
12	5.20	6.30/hr	7.60/hr
13	5.30	6.50/hr	6.50/hr
14	5.40	6.70/hr	5.40/hr
15	5.50	6.90/hr	4.30/hr

According to the information in the table above, the twelfth worker would increase the hourly profit by

$0.20
$1.10
$1.30
$2.40
$5.20

第 12 个工人：MRP $7.60 − MFC $6.30 = 多赚 $1.30。（企业会一直雇到 MRP = MFC 的第 13 人。）

5.4-72010 AP Micro Q14

按原题重绘

The graph above shows a monopsony labor market. In the absence of any regulations, which of the following represents the number of workers the firm will hire and the wage rate it will offer to those workers?

Number of Workers: 15；Wage Rate: $30
Number of Workers: 20；Wage Rate: $20
Number of Workers: 20；Wage Rate: $40
Number of Workers: 30；Wage Rate: $30
Number of Workers: 40；Wage Rate: $40

MFC = MRP 在 (20, $40) → 雇 20 人；工资读供给：20 人对应 $20。(C) 用了 MFC 的高度；(D) 30 人、$30 是竞争结果。

5.4-82013 AP Micro Q59

按原题重绘

The graph above shows the conditions that a monopsonist faces in a labor market. How many workers would this monopsonist hire and what wage rate would it pay?

Number of Workers: 5；Wage Rate: $37.50
Number of Workers: 10；Wage Rate: 30
Number of Workers: 10；Wage Rate: 20
Number of Workers: 14；Wage Rate: 24
Number of Workers: 14；Wage Rate: 37.50

MFC 与需求（MRP）交于 10 人 → 雇 10 人；读供给曲线：10 人对应 $20。(B) $30 是 MFC 的高度；(D) 14 人、$24 是竞争结果。

5.4-92015 AP Micro 练习卷 Q60

按原题重绘

In the monopsonistic labor market shown in the diagram above, which of the following indicates the number of workers the firm will hire and the wage rate it will pay?

Number of Workers: L1；Wage Rate: W1
Number of Workers: L1；Wage Rate: W2
Number of Workers: L1；Wage Rate: W3
Number of Workers: L2；Wage Rate: W2
Number of Workers: L2；Wage Rate: W4

MRP = MFC 在 L₁ → 雇 L₁；从 L₁ 往下读供给 → W₁。W₃ 是 MFC 的高度；L₂、W₂ 是竞争结果。

5.4-102016 AP Micro 练习卷 Q58

按原题重绘

Hope Hospital is a monopsonistic employer of nurses. The marginal revenue product of nursing services, the marginal factor (resource) cost of nursing services, and the market supply curve of nursing services are depicted in the figure above by MRP, MFC, and S, respectively. What wage-quantity combination does Hope Hospital choose in order to maximize its profits?

W1 and Q₁
W1 and Q₃
W2 and Q₂
W2 and Q₄
W3 and Q₃

MRP = MFC 在 Q₃ → 雇 Q₃；读供给 S 在 Q₃ 的高度 → W₁。(E) W₃ 是 MFC 的高度；(D) W₂、Q₄ 是竞争结果。原考试只有 41% 的人答对。

5.4-112025 AP Micro 国际卷 Q46

The table shows output and cost data for Whit’s Whistles, a firm that produces whistles.

Number of Workers	Total Output	Marginal Factor Cost ($)
1	16	35
2	35	65
3	51	95
4	65	125
5	77	155

Whit’s Whistles is a profit-maximizing firm that hires workers from a monopsonistic labor market. The market for whistles is perfectly competitive, and the equilibrium price of whistles is $10. How many workers will Whit’s Whistles hire to maximize profits?

MP = 16、19、16、14、12，MRP = MP × $10 = 160、190、160、140、120；与 MFC 35、65、95、125、155 比较：第 4 人 $140 > $125 雇，第 5 人 $120 < $155 不雇 → 4 人。

ΣSummary 本单元总结与易错点

5.1 Factor Markets

劳动、土地、资本、企业家才能 → 工资、租金、利息、利润。要素需求是引致需求。MRP = ΔTR/ΔL = MP × MR，MRC = ΔTC/ΔL；雇到 MRP = MRC。MP 递减 → MRP 向下 → 劳动需求向下倾斜；工资越高愿意工作的人越多 → 劳动供给向上倾斜。

5.2 Shifts

劳动需求随产品价格（需求）、生产率、其他投入的价格（替代品变便宜 → 减少；互补品变便宜 → 增加）、企业数量移动。劳动供给随移民和人口、教育培训与执照、工作条件、其他职业工资、闲暇偏好、社会观念移动。工资变化本身只是沿曲线移动。

5.3 Perfectly Competitive Factor Markets

市场定工资，企业是工资接受者（MRC = W 水平线），雇到 MRP = W。并排图：市场 S、D → W；企业 W 水平线与 MRP 的交点 → 雇用量。卖方有市场势力时 MRP = MP × MR < VMP。最低成本：MP_L/W = MP_K/r；利润最大：MRP_L = W 且 MRP_K = r。有效最低工资 → 就业减少、劳动过剩。

5.4 Monopsony

唯一的雇主面对向上倾斜的供给；多雇一人要给所有人涨薪，MFC > W，MFC 在供给上方（斜率是供给的两倍）。雇到 MRP = MFC，工资读供给 → 比竞争市场雇得少、工资低，MRP > W。最低工资在买方垄断工资与竞争工资之间时，就业和工资都上升。

Product Markets vs. Factor Markets 产品市场与要素市场对照

	产品市场（企业是卖方）	要素市场（企业是买方）
多一单位的收益	MR	MRP = MP × MR（产品市场完全竞争时 = MP × P = VMP）
多一单位的成本	MC	MRC（MFC）
利润最大化	MR = MC	MRP = MRC
完全竞争的企业	价格接受者：D = MR = P 水平	工资接受者：S = MRC = W 水平
只有一家企业	垄断：MR 在需求下方；产量看 MR = MC，价格读需求	买方垄断：MFC 在供给上方；雇用量看 MRP = MFC，工资读供给
与完全竞争相比	产量少、价格高	雇用少、工资低
企业的需求曲线来自	消费者	MRP（引致需求）

易错点 TOP 10

MRP 就是 MP ✗ → MRP 是钱：MP × MR（完全竞争时 MP × P）。
竞争劳动市场里企业面对向上倾斜的劳动供给 ✗ → 企业面对的是工资处的水平线，向上倾斜的是市场供给。
工资上涨使劳动需求减少 ✗ → 是劳动需求量减少（沿着需求曲线）。
市场工资上涨使企业的 MRP 曲线左移 ✗ → 移动的是企业的 MRC（工资）线，企业沿 MRP 少雇人。
垄断卖方企业的 MRP = MP × P ✗ → MRP = MP × MR，比 MP × P 小。
替代投入变便宜，劳动需求增加 ✗ → 减少（企业改用替代投入）；互补投入变便宜才增加。
MP_L/W > MP_K/r 时应多用资本 ✗ → 劳动每一美元更划算，应多用劳动。
买方垄断者付的工资等于 MFC ✗ → 从雇用量往下读供给曲线。
买方垄断的 MFC 在供给下方 ✗ → 在上方，因为要给所有工人涨薪。
最低工资一定减少就业 ✗ → 在买方垄断市场，定在买方垄断工资和竞争工资之间的最低工资会增加就业。

✎Unit 5 Test 单元测验

20 道选择题，全部选自历年 AP 真题（与各节练习不重复，带图和表格的题按原题重绘），建议用时 24 分钟。先全部选完，再点底部“交卷”查看得分和解析。

T12022 AP Micro 国际卷 Q36

The following question is based on the table provided, showing hourly production data and total revenue for a perfectly competitive firm.

Number of Workers Hired	Total Revenue ($)	Quantity Produced
0	0	0
1	50	10
2	95	19
3	135	27
4	170	34
5	200	40

What is the marginal revenue product of the fourth worker?

MRP₄ = ΔTR = $170 − $135 = $35（也可以 MP 7 × 价格 $5）。$7 是 MP。

T22014 AP Micro 练习卷 Q28

The demand curve for labor for a monopolist that faces a perfectly competitive factor market is called the

average product curve
marginal product curve
marginal revenue curve
marginal revenue product curve
value of the average product curve

企业的劳动需求曲线 = MRP 曲线；产品市场垄断时 MR < P，所以用 MRP = MP × MR，而不是 MP × P。

T32010 AP Micro Q43

An increase in the demand for automobiles will cause the demand for skilled automobile workers and the wage rate of skilled automobile workers to change in which of the following ways?

Demand For Workers: Decrease；Wage Rate: Increase
Demand For Workers: Decrease；Wage Rate: Not change
Demand For Workers: Increase；Wage Rate: Decrease
Demand For Workers: Increase；Wage Rate: Increase
Demand For Workers: Not Change；Wage Rate: Increase

汽车需求增加 → 汽车工人的 MRP 上升 → 劳动需求增加，工资上升。

T42023 AP Micro 国际卷 Q45

Robots and workers are substitutes in production and are both variable inputs. Both robots and workers are hired in perfectly competitive factor markets. If the daily rental price of robots increases, which of the following will most likely happen to wages paid to workers and the number of workers employed in the short run?

Wages: Decrease；Number of Workers Employed: Decrease
Wages: Decrease；Number of Workers Employed: Increase
Wages: Increase；Number of Workers Employed: Decrease
Wages: Increase；Number of Workers Employed: Increase
Wages: No change；Number of Workers Employed: No change

机器人（替代品）租金上涨 → 企业改用工人 → 劳动需求右移 → 工资和就业都增加。

T52025 AP Micro 国际卷 Q34

Which of the following changes will increase the equilibrium market wage for plumbers?

A decrease in the market price of plumbing services
A decrease in the amount of vacation time taken by plumbers
A decrease in the productivity of plumbers
An increase in the fees for plumber licenses required to practice plumbing
An increase in the quality of working conditions for plumbers

执照费提高 → 进入这一行的人变少 → 水管工供给减少 → 工资上升。(A)(C) 让需求减少；(B)(E) 让供给增加，工资下降。

T62016 AP Micro 练习卷 Q43

Assume labor and capital are substitute inputs. A manufacturer will employ more labor if

the price of labor increases
the marginal product of labor decreases
the price of capital increases
the marginal product of capital increases
the product’s demand decreases

劳动与资本是替代品：资本变贵 → 企业用劳动代替资本 → 多雇劳动。(A) 劳动变贵会少雇；(B)(E) 让 MRP 下降；(D) 让资本更划算。

T72019 AP Micro 练习卷 Q57

Assume accountants and teachers have identical marginal revenue product schedules. Which of the following provides an explanation for why accountants receive higher starting salaries than school teachers?

Accountants have less human capital than school teachers.
Accountants have lower opportunity cost than school teachers.
Accounting firms provide a more pleasant work environment than schools provide.
The supply of accountants is low relative to the supply of teachers.
Fewer teaching majors graduate from college each year than accounting majors.

MRP（劳动需求）相同，工资差别只能来自供给：会计师的供给相对较少 → 均衡工资更高 → (D)。

T82017 AP Micro 练习卷 Q16

Number of Workers	Output
1	3
2	9
3	16
4	21
5	23
6	24

If output sells for $20 per unit and the daily wage is $100 per worker, how many workers should the firm hire to maximize profit?

MP = 3、6、7、5、2、1，MRP = MP × $20 = 60、120、140、100、40、20。工资 $100：第 4 人 MRP = $100 = 工资 → 雇 4 人。

T92014 AP Micro 练习卷 Q41

Which of the following will occur in a perfectly competitive labor market if Firm X’s demand for labor decreases?

Equilibrium Market Wage Rate: Increase；Employment by Firm X: Increase
Equilibrium Market Wage Rate: No change；Employment by Firm X: No change
Equilibrium Market Wage Rate: No change；Employment by Firm X: Decrease
Equilibrium Market Wage Rate: Decrease；Employment by Firm X: Decrease
Equilibrium Market Wage Rate: Decrease；Employment by Firm X: No change

X 只是众多雇主之一，自己的劳动需求减少不会改变市场工资 → 工资不变，X 少雇人。

T102024 AP Micro Q56

Yann's Waffles can hire all the workers it wants at $20 per hour. Yann's Waffles sells its waffles at $10 each. Assuming that labor is the only variable input, Yann's Waffles will maximize its profits when

the marginal product of the last worker hired is 2 waffles per hour
the marginal revenue product of the last worker hired is $200
the marginal factor (resource) cost of the last worker hired is $200
the total product of all workers hired is 200 waffles per hour
the total revenue from all waffles sold is $200

工资接受者：MFC = $20，雇到 MRP = MP × $10 = $20 → 最后一个工人的 MP = 2 个华夫饼。(B)(C) 把 $200 当成了 MRP 或 MFC。

T112019 AP Micro 练习卷 Q14

A profit-maximizing firm hires labor in a perfectly competitive market. Labor is the only variable input, and the marginal product of the last worker hired is 10 units per hour. If the hourly wage is $20, the firm’s marginal revenue

is $2
is $20
increases as more output is produced
increases first and then decreases as more output is produced
decreases first and then increases as more output is produced

利润最大时 MRP = MP × MR = 工资：10 × MR = $20 → MR = $2。原考试只有 22% 的人答对。

T122015 AP Micro 练习卷 Q42

Assume that the government imposes an effective minimum wage in a perfectly competitive labor market. What will happen to employment and total wage payments?

Employment: Decrease；Total Wage Payments: Increase
Employment: Decrease；Total Wage Payments: Decrease
Employment: Decrease；Total Wage Payments: Indeterminate
Employment: Increase；Total Wage Payments: Increase
Employment: Increase；Total Wage Payments: Indeterminate

有效最低工资：工资上升、劳动需求量减少 → 就业减少；总工资 = 更高的工资 × 更少的人，升还是降取决于劳动需求的弹性 → 不确定。

T132021 AP Micro 国际卷 Q13

Pickleco, a pickle-producing firm, hires labor and capital in perfectly competitive factor markets. The firm is minimizing its costs at the current production level. The marginal product of labor is 100 units and the marginal product of capital is 60 units. If the rental price of capital is $12, what is the wage Pickleco is paying its workers?

$5.00
$8.33
$12.00
$20.00
$40.00

MP_L/W = MP_K/r：100/W = 60/12 = 5 → W = $20。

T142019 AP Micro 练习卷 Q36

A perfectly competitive firm currently produces 1,000 units of output and hires its resources in a perfectly competitive factor market. It uses both labor and capital as inputs. The price of labor is $40; the price of capital is $100. The marginal product of labor is 8 units, and the marginal product of capital is 10 units. Which of the following must be true?

The firm is currently maximizing its profit.
The firm can produce more than 1,000 units without increasing the total cost if it uses more labor and less capital.
The firm can produce more than 1,000 units without increasing the total cost if it uses more capital and less labor.
The firm can reduce the cost of producing 1,000 units by using less capital and employing the same amount of labor.
The firm can reduce the cost of producing 1,000 units by employing less labor and using the same amount of capital.

MP_L/P_L = 8/40 = 0.2 > MP_K/P_K = 10/100 = 0.1 → 把花在资本上的钱挪到劳动上，总成本不变而产量增加 → (B)。现在不是最低成本，所以也不是利润最大（A 错）。

T152015 AP Micro 练习卷 Q27

Assume that labor and capital are the only two inputs a perfectly competitive firm uses to produce wheat. The firm hires its inputs in perfectly competitive input markets. The unit price of labor is $8 and of capital is $20. When the firm employs the profit-maximizing combination of these two inputs, the marginal product of labor is 2 tons of wheat and of capital is 5 tons of wheat. The price of wheat per ton must be

利润最大时每种投入 P × MP = 要素价格：P × 2 = $8 且 P × 5 = $20 → 小麦价格 P = $4。

T162019 AP Micro 练习卷 Q42

Which of the following is true of a monopsony in a labor market?

It faces a labor supply curve that is horizontal at the competitive market equilibrium wage.
Its marginal factor (resource) cost is the same as the market supply curve.
At its optimal level of employment, it pays a wage rate higher than the competitive market wage rate.
The imposition of a minimum wage results in a larger reduction in employment than is true in a competitive market.
Its marginal factor (resource) cost curve lies above the labor supply curve because hiring an extra worker means paying more to existing workers.

买方垄断者面对向上倾斜的供给，多雇一人要给所有人涨薪 → MFC 曲线在劳动供给上方。(D) 合适的最低工资反而能增加买方垄断市场的就业。

T172023 AP Micro 国际卷 Q43

Which of the following is true at the quantity of labor hired by a profit-maximizing monopsonist?

Marginal revenue product is less than marginal factor cost.
Marginal revenue product is greater than marginal factor cost.
Marginal revenue product is less than the market wage.
Marginal revenue product is greater than the market wage.
Marginal revenue product equals the market wage.

买方垄断者雇到 MRP = MFC，而 MFC 在供给上方，工资读的是供给 → 在这个雇用量上 MRP > 工资。

T182025 AP Micro 国际卷 Q60

The small town of Marketville had four firms producing coal. The four firms then merged into one firm, which is now the sole employer of coal miners in Marketville. What effect will this change have on the market for coal miners in Marketville?

Equilibrium wages and the level of employment will both increase.
Equilibrium wages will increase, and the level of employment will decrease.
Equilibrium wages and the level of employment will both decrease.
Equilibrium wages will decrease, and the level of employment will increase.
Equilibrium wages will decrease, and the level of employment will remain the same.

四家合并成唯一雇主 → 买方垄断：在 MRP = MFC 处雇人，工资读供给 → 工资和就业都下降。

T192021 AP Micro 国际卷 Q36

Which of the following is always true for a firm with monopsony power?

The marginal revenue product curve is upward-sloping.
The marginal revenue product curve lies above the input demand curve.
The marginal factor cost curve lies above the input supply curve.
The marginal factor cost curve lies above the input demand curve.
The input demand curve lies above the marginal factor cost curve.

买方垄断者多雇一单位要提高支付给所有单位的价格 → MFC 曲线总在投入供给曲线上方。

T202023 AP Micro 国际卷 Q18

FishNets hires workers from the labor market depicted in the provided graph. The government imposes a binding minimum wage in the labor market. What is the binding minimum wage that would cause FishNets to hire the same number of workers as a perfectly competitive labor market?

按原题重绘

竞争结果在 MRP = S：60 人、$32（买方垄断只雇 40 人、付 $24）。把最低工资定在 $32：60 人以内 MFC 变成 $32 的水平线，MRP = $32 在 60 人 → 雇到竞争数量。

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FRQFree-Response Practice 自由问答

前三道是 AP 真题，评分标准依照 College Board 官方 Scoring Guidelines 整理；第四道是依照 AP 题型原创的并排图题。先在纸上完整作答（包括画图），再展开对照。

FRQ 1 · 2021 AP Micro FRQ Set 1 Q2 · 5 分 · Schmitt Inc. 代客泊车真题

Number of Workers	Number of Parked Cars
0	0
1	8
2	20
3	34
4	45
5	54
6	60
7	63

Assume that Schmitt Inc. provides car parking services in a perfectly competitive output market and hires labor in a perfectly competitive input market. The market price per car parked is $10, the daily market wage per worker is $100, and fixed costs are $50 per day. The table above shows the number of workers required to park different quantities of cars per day.

(a) Calculate the marginal revenue product of the second worker. Show your work.
(b) How many workers will Schmitt Inc. hire to maximize profit? Relative to this number of hired workers, explain why Schmitt Inc. will not hire one additional worker. Your answer must use marginal analysis and numbers from the table.
(c) Calculate the daily profit for Schmitt Inc. at the profit-maximizing quantity identified in part (b). Show your work.
(d) Suppose new legislation requires each worker in the parking industry to purchase an individual insurance policy at the worker's expense in order to legally park cars.
(i) Will the market wage paid by a typical firm in this industry increase, decrease, or stay the same in the long run?
(ii) For a typical firm in the industry, will the number of workers hired in the short run increase, decrease, or stay the same? Explain.

工人	1	2	3	4	5	6	7
MP（辆）	8	12	14	11	9	6	3
MRP = MP × $10	$80	$120	$140	$110	$90	$60	$30

Point	得分要求与解析
(a) 1 pt	MRP₂ = (20 − 8) × $10 = $120（或 TR $200 − $80）。
(b) 1 pt	雇 4 人；不雇第 5 人，因为第 5 人的 MRP = (54 − 45) × $10 = $90 < 工资 $100。（第 1 人 MRP 只有 $80，低于工资，但第 2–4 人的 MRP 都高于工资，雇前 4 人总共是赚的；判断“雇几人”要看 MRP 开始下降之后，第一个低于工资的是第几人。）
(c) 1 pt	利润 = TR − TC = $10 × 45 − ($50 + 4 × $100) = $450 − $450 = $0。
(d)(i) 1 pt	市场工资上升：工人要自己买保险，同样的工资下愿意干的人变少，市场劳动供给左移。
(d)(ii) 1 pt	雇用量减少：市场供给减少 → 工资上升 → 企业的 MFC（MRC）上升，在 MRP = MFC 处雇的人更少。

FRQ 2 · 2023 AP Micro FRQ Set 1 Q1 (d) · 3 分 · RKB 的劳动市场真题

RKB is a profit-maximizing monopoly that produces a new, patented electronic device.

原题 (a)–(c) 是垄断图，已放在 Unit 4（上）讲义的 FRQ 里；这里只做劳动市场的 (d)。

(d) Assume that RKB hires workers in a perfectly competitive labor market.
  (i) Draw a correctly labeled graph for the labor market, showing the equilibrium wage and quantity of labor, labeled W_E and Q_E, respectively.
  (ii) Suppose immigration increases the number of workers in this labor market. On your graph in part (d)(i), show the new equilibrium wage and quantity of labor, labeled W₂ and Q₂, respectively.
  (iii) RKB uses the optimal combination of capital and labor in its production process. The firm rents capital at $500 per unit, and the last unit of capital rented has a marginal product of 2,500 units. If the marginal product of the last unit of labor hired is 1,000 units, calculate the wage rate. Show your work.

Point	得分要求与解析
(d)(i) 1 pt	正确标注的完全竞争劳动市场：向下倾斜的 D、向上倾斜的 S，标出均衡 W_E、Q_E。
(d)(ii) 1 pt	劳动供给右移，新均衡工资 W₂ 更低、就业 Q₂ 更多。
(d)(iii) 1 pt	MP_K/r = MP_L/W：2,500 / $500 = 1,000 / W → W = $200（要写出算式）。

参考图：完全竞争劳动市场，D 向下倾斜、S 向上倾斜，均衡 W_E、Q_E；移民增加 → 供给右移，W₂ < W_E，Q₂ > Q_E。

注意：RKB 在产品市场是垄断者，在劳动市场却是工资接受者——两个市场的结构可以不同（CED PRD-4.C.1）。

FRQ 3 · 2025 AP Micro FRQ Set 2 Q2 · 5 分 · Quartz Excavations 矿工市场真题

Quartz Excavations is a profit-maximizing firm and the only employer of miners of quartz in a small town. The graph provided shows the labor market for miners.

按原题重绘

A. Identify Quartz Excavations' profit-maximizing number of miners to hire.
B. Will Quartz Excavations pay its profit-maximizing number of miners a wage rate that is equal to $15, greater than $15, or less than $15? Explain using numbers.
C. Suppose the government sets a minimum wage (a price floor on wages) at $25. Calculate the total wage bill for Quartz Excavations at the resulting profit-maximizing number of miners. Show your work.
D. Suppose that instead of a minimum wage, there is now an increase in the demand for quartz.
i. Will the marginal revenue product of miners increase, decrease, or remain the same? Explain.
ii. After the demand for quartz increases, Quartz Excavations hires the new profit-maximizing number of miners. Will the marginal factor cost of the last miner hired be greater than, less than, or equal to the marginal factor cost of the last miner hired before the demand for quartz increased?

Point	得分要求与解析
A 1 pt	4 名矿工（MRP = MFC = $20）。
B 1 pt	Less than $15：买方垄断者的工资由雇用量对应的劳动供给决定，雇 4 人时工资只要 $10。（$15 是 S = MRP 的竞争工资。）
C 1 pt	最低工资 $25 时 MFC 在 10 人以内是 $25 的水平线，MRP = $25 在 2 人 → 雇 2 人，工资总额 = $25 × 2 = $50。
D(i) 1 pt	MRP 上升：石英需求增加 → 石英价格和 MR 上升 → MRP = MP × MR 上升。
D(ii) 1 pt	Greater than：MRP 右移后雇的矿工更多，MFC 曲线向上倾斜，最后一名矿工的 MFC 更高。

参考：没有最低工资时 MRP = MFC 在 4 人（$20），工资读供给 = $10。最低工资 $25 高于竞争工资 $15：MFC 在 10 人以内是 $25 的水平线，MRP = $25 在 2 人 → 雇 2 人，工资总额 $50。

对照 5.4：这道题的最低工资（$25）高于竞争工资 $15，所以就业从 4 人降到 2 人；如果最低工资定在 $10 到 $15 之间，就业反而会增加。

FRQ 4 · 原创 · 6 分 · 自行车装配厂 BrightBikes 原创

BrightBikes assembles bicycles and sells them in a perfectly competitive market. It hires assemblers in a perfectly competitive labor market.

(a) Draw correctly labeled side-by-side graphs of the labor market for assemblers and of BrightBikes. On your graphs, show the market wage, labeled W₁, the market quantity of labor, labeled L_M, and the quantity of labor BrightBikes hires, labeled L_F.
(b) A technical college opens a new program that trains bicycle assemblers. On your graphs in part (a), show the new market wage, labeled W₂, and the new quantity of labor BrightBikes hires, labeled L₂.
(c) Instead, suppose the price of bicycles rises. Will BrightBikes' marginal revenue product of labor increase, decrease, or stay the same? Explain.
(d) BrightBikes also rents robotic arms at $300 per day. The wage is $120 per day, the marginal product of the last assembler is 8 bicycles per day, and the marginal product of the last robotic arm is 16 bicycles per day. Is BrightBikes producing its output at the lowest possible cost? If not, should it use more assemblers or more robotic arms? Explain using numbers.
(e) Suppose instead that BrightBikes becomes the only employer of bicycle assemblers in its town. Will the marginal factor cost of the last assembler hired be greater than, less than, or equal to the wage? Explain.

Point	评分要点与解析（原创题，按 AP 评分方式整理）
(a) 1 pt	市场图：向下倾斜的 D、向上倾斜的 S，交点标 W₁、L_M。
(a) 1 pt	企业图：在 W₁ 处画水平的劳动供给（= MRC），向下倾斜的 MRP（= D），两者交点标 L_F；两图的工资高度对齐。
(b) 1 pt	市场供给右移，W₂ < W₁；企业的水平工资线下移到 W₂，L₂ > L_F（MRP 曲线不动）。
(c) 1 pt	增加：MRP = MP × P，自行车价格上升，每个工人带来的收入增加。
(d) 1 pt	不是最低成本：MP_L/W = 8/120 ≈ 0.067 > MP_K/r = 16/300 ≈ 0.053，装配工每一美元产出更多 → 多用装配工、少用机械臂。
(e) 1 pt	Greater than：唯一的雇主面对向上倾斜的劳动供给，多雇一人必须提高所有装配工的工资，MFC = 新人工资 + 给原有工人的涨幅 > 工资。

(a) 参考图：左边市场 S、D 决定 W₁ 和 L_M；右边企业面对 W₁ 处的水平线（= MRC），在 MRP = W₁ 处雇 L_F。

(b) 参考图：受过培训的装配工变多 → 市场供给右移，工资降到 W₂；企业的水平工资线下移，沿 MRP 多雇到 L₂。

FRQ 答题提醒

表格题：先列 MP，再乘 P（或 MR）得 MRP；“explain using marginal analysis”要写出下一个工人的 MRP 与工资的比较。
并排图：市场图用 S、D；企业图用水平的 W = MRC 和向下倾斜的 MRP；工资高度对齐。
买方垄断图：MFC 在供给上方；雇用量看 MRP = MFC，工资读供给。
MP_L/W = MP_K/r 的计算题一定要写出等式再代数字。

接下来上一单元：→ 打开 Unit 4（下）Monopolistic Competition and Oligopoly（与本文件放在同一文件夹）。
下一单元：→ 打开 Unit 6 Market Failure and the Role of Government（市场失灵与政府的作用——外部性、公共物品、政府干预，以及收入不平等）。

JL · AP Microeconomics · Unit 5 Factor Markets · 题目标签：真题历年 AP 考试原题（含 College Board 练习卷、国际卷），答案均对照官方答案键并重新验算（2024 年题目的答案为自行验算） · 原创依照 AP 题型原创