JL · AP MICROECONOMICS

Unit 3（上）· Production and Costs

生产与成本 — 生产函数、短期成本、长期成本 · 对应 CED 3.1–3.3 · Unit 3 选择题占比约 22–25%（上下册合计）
上下册分工 上册（本册）：企业内部——投入多少、产出多少、花多少钱（3.1–3.3）。
下册：企业怎样用这些成本做决定——利润类型、利润最大化、停产与进出、完全竞争（3.4–3.7）。下册的每一张企业图都建立在本册的成本曲线上，建议先学完本册。
本册学习目标 LEARNING OBJECTIVES
  • 区分短期与长期、固定投入与可变投入 · Distinguish the short run from the long run
  • 计算 TP、MP、AP，解释分工和边际报酬递减 · Calculate product measures and explain diminishing marginal returns
  • 计算并画出 FC、VC、TC、AFC、AVC、ATC、MC，记住它们之间的关系 · Calculate and graph short-run costs
  • 解释 MC 与 MP、AVC 与 AP 的“镜像”关系 · Connect cost curves to the production function
  • 判断成本曲线在不同冲击下怎样移动 · Explain how cost curves shift
  • 理解 LRATC 是怎样由短期 ATC 得到的，区分规模经济、规模报酬不变和规模不经济 · Explain LRATC and returns to scale
  • 用最小有效规模（MES）解释一个市场能容纳多少企业 · Relate MES to market structure
Term 术语Meaning 含义中文
Fixed / Variable InputCannot / can be changed in the short run固定 / 可变投入
Short Run / Long RunAt least one input fixed / all inputs variable短期 / 长期
Total / Marginal / Average ProductTP; MP = ΔTP/ΔL; AP = TP/L总 / 边际 / 平均产量
SpecializationDividing tasks so each worker becomes more productive专业化分工
Diminishing Marginal ReturnsAdding more of one input, others fixed, eventually lowers MP边际报酬递减
Fixed / Variable / Total CostFC (paid even at q = 0); VC; TC = FC + VC固定 / 可变 / 总成本
AFC / AVC / ATCFC/q; VC/q; TC/q = AFC + AVC平均固定 / 可变 / 总成本
Marginal Cost (MC)ΔTC/Δq — cost of one more unit边际成本
Lump-sum / Per-unit TaxSame amount at any output (fixed cost) / paid on each unit (variable cost)定额税 / 从量税
Long-Run ATC (LRATC)Lowest average cost for each output when all inputs can vary长期平均总成本
Economies / Diseconomies of ScaleLRATC falls / rises as output increases规模经济 / 规模不经济
Increasing / Constant / Decreasing Returns to ScaleInputs ×2 → output more than / exactly / less than ×2规模报酬递增 / 不变 / 递减
Minimum Efficient Scale (MES)Smallest output at which LRATC reaches its minimum最小有效规模
考试怎么考 选择题：成本表计算（补全 MC、AVC、ATC、AFC）、读成本曲线图、判断哪些曲线移动、MP/AP 与 MC/AVC 的关系、规模经济的定义。FRQ：常以“产量表 + 工资”的短题出现（算 MP、AFC、MC，判断边际报酬递减和规模经济），也会出现在下册完全竞争长题的企业图里。

3.1The Production Function 生产函数

Unit 2 的供给曲线为什么向上倾斜？答案藏在企业内部：生产更多需要更多投入，而投入的“效率”会随着数量改变。上册从一家奶茶店的后厨开始，讲清楚“产量”和“成本”；下册再用这些成本去回答“生产多少、要不要停产、行业长期会怎样”。

定义 DEFINITION The production function shows the relationship between the quantity of inputs a firm uses and the quantity of output it produces（CED PRD-1.A.1）.
  • Fixed input 固定投入：短期内无法改变数量的投入，例如店面、厂房、大型机器。
  • Variable input 可变投入：随时可以增减的投入，例如员工工时、原材料、电力。
  • Short run 短期：至少有一种投入是固定的；Long run 长期：所有投入都可以调整。
易错 TRAP 短期和长期不是按日历时间划分的：开一家奶茶店，换一个新店面可能一个月就够（长期很短）；建一座芯片厂要好几年（短期很长）。判断标准只有一个：是否还有投入是固定的。
WORKED EXAMPLE 1哪些是固定投入？ 原创

For each firm, classify the input as fixed or variable in the short run.

  1. 奶茶店：店面租约（签了一年）
  2. 奶茶店：牛奶和茶叶
  3. 外卖平台：按单结算的骑手
  4. 芯片厂：光刻机
  5. 网课机构：按课时付费的兼职老师
  6. 航空公司：已经买下的飞机
固定投入：1 店面租约、4 光刻机、6 飞机——短期内无法增减（合同、采购和建设都需要很长时间）。
可变投入：2 原料、3 按单结算的骑手、5 按课时付费的老师——产量变了马上就能调整用量。
规律：大型设备、厂房、长期合同通常是固定投入；原材料、按小时或按件付费的劳动通常是可变投入。

TP, MP, AP 总产量、边际产量、平均产量

公式 FORMULA MP = ΔTPΔL　　AP = TPL MP：多雇 1 个员工增加的产量；AP：平均每个员工的产量。

一家奶茶店只有一个吧台、一台封口机，每小时的产量随员工人数变化：

Workers (L)012345678
Total product TP（杯/小时）01025456070757572
Marginal product MP—101520151050-3
Average product AP—1012.515151412.510.79
TP（杯/小时）20406080① 递增② 递减③ 负TPWorkers (L)MP / AP0123456785101520101520151050−3AP红柱 = 第 L 个员工的 MPAP 最高（15）
上下两张图横轴对齐。① 第 1–3 人：分工使 MP 越来越大，TP 越涨越快；② 第 4–7 人：MP 变小，TP 涨得越来越慢；③ 第 8 人：MP 为负，TP 下降。绿线 AP：MP 柱子高于 AP 时 AP 上升，低于 AP 时 AP 下降，所以 AP 在 L = 3 和 L = 4 时达到最高值 15（第 4 人的 MP 正好等于 15）。
Diminishing Marginal Returns 边际报酬递减（CED PRD-1.A.3） 在其他投入（吧台、封口机）不变时，不断增加一种投入（员工），迟早每多一单位投入带来的产量会越来越少。
  • 递增阶段（第 1–3 人）：一个人又摇茶又收银，手忙脚乱；三个人分工——一人点单、一人做茶、一人封口——每人都更熟练。这就是 specialization 专业化分工。
  • 递减阶段（第 4–7 人）：吧台就那么大，人多了开始排队等封口机，新增的人贡献越来越小。
  • MP 为负（第 8 人）：挤得互相碍事，总产量反而下降。理性的老板不会雇到这一步。
MP 与 AP 的关系——用 GPA 来理解 你的平均分（AP）是 85。下一门课考了 95（边际 MP > 平均），平均分会被拉高；下一门只考 70（MP < 平均），平均分就被拉低。所以：MP > AP 时 AP 上升，MP < AP 时 AP 下降，两者相等时 AP 正好在最高点。另外两个要点：TP 最大时 MP = 0；MP 最高的地方是 TP 曲线由“越涨越快”变成“越涨越慢”的拐点。这条“边际与平均”的规律在 3.2 的成本曲线里还会再用一次。
WORKED EXAMPLE 2披萨店的员工表 原创

A pizza shop with one oven hires workers. Total output per hour is 0, 8, 20, 30, 36, 40, 42 pizzas for 0 to 6 workers. (a) What is the marginal product of the 3rd worker? (b) After which worker do diminishing marginal returns begin? (c) At what number of workers is average product at its maximum? (d) Explain why the shop's MP eventually falls even though every worker is equally skilled.

L123456
TP82030364042
MP81210642
AP81010987
(a) MP3 = 30 − 20 = 10。
(b) MP 在第 2 人达到最高（12），从第 3 个员工开始下降（10 → 6 → 4 → 2），边际报酬递减从这里开始。
(c) AP 在 L = 2 和 L = 3 时都是最大值 10（第 3 人的 MP = 10 正好等于 AP）。
(d) 原因不是后来的人更笨，而是烤箱（固定投入）只有一台：每个员工能用的烤箱越来越少。这就是“其他投入不变”这个前提的作用。
LAB 1一个一个加员工 · Add Workers

奶茶店只有一个吧台和一台封口机（固定投入）。拖动滑块增加员工，看总产量、边际产量和平均产量的变化。

员工人数 L = 3

练习 Practice 3.1

以下为历年 AP 真题（带图的题按原题重绘），点选项即时判分并显示解析。

3.1-12005 AP Micro Q54
When marginal product exceeds average product, which of the following must be true?
  • Average product is increasing.
  • Average product is decreasing.
  • Marginal product is increasing.
  • Total product is decreasing.
  • Total product is at its maximum.
MP > AP 时，新增的这一单位把平均值拉高 → AP 上升（GPA 的道理）。MP 本身可能在上升也可能在下降，不能确定。
3.1-22010 AP Micro Q19
In microeconomics, the short run is defined as which of the following?
  • A period that is less than one year
  • A period that is between one year and four years
  • A period that is too short for a firm to be able to change its level of output
  • A period during which some inputs in a firm's production process cannot be changed
  • A period during which a firm's fixed costs exceed its variable costs
短期 = 至少有一种投入无法改变的时期，不按日历时间划分。
3.1-32012 AP Micro Q6
Suppose that a firm begins to hire workers for a newly completed plant with a fixed amount of machinery. As the firm hires additional workers, one would expect the marginal product to
  • fall initially, but eventually rise
  • rise initially, but eventually fall
  • rise consistently due to diminishing return
  • rise consistently due to the advantages of specialization
  • rise consistently due to economies of scale
新厂房、机器固定：最初几名工人可以分工，MP 上升；人越来越多，每人分到的机器越来越少，MP 最终下降（边际报酬递减）。
3.1-42014 AP Micro 练习卷 Q51
When total physical product is at its maximum, marginal physical product must be
  • greater than one
  • equal to one
  • equal to zero
  • less than zero
  • constant
TP 达到最大时，再多一单位投入不再增加产量，MP = 0（之后 MP 为负，TP 开始下降）。
3.1-52015 AP Micro 练习卷 Q53
Assume that a firm uses only one variable input. If a firm is experiencing diminishing returns, which of the following is true as more of the variable input is used?
  • Marginal cost will decrease at a constant rate.
  • Marginal cost will decrease at a diminishing rate.
  • Marginal cost will increase.
  • Marginal product will increase at a constant rate.
  • Marginal product will increase at a diminishing rate.
边际报酬递减 → MP 下降 → 每多生产一单位需要更多投入 → MC 上升（MC = 工资 ÷ MP）。
3.1-62021 AP Micro 国际卷 Q19
With capital held constant, when Zane employs one additional worker, the marginal product of labor decreases by 5 units. Which economic concept best characterizes Zane’s production process?
  • Diminishing marginal returns
  • Increasing marginal returns
  • Constant returns to scale
  • Economies of scale
  • Diseconomies of scale
资本不变、多雇一个人后 MP 下降 → 边际报酬递减（短期概念）。(C)(D)(E) 都是长期的规模概念。
3.1-72022 AP Micro 国际卷 Q26
If the marginal product of an input is positive and increasing, total product is
  • decreasing at an increasing rate
  • increasing at an increasing rate
  • increasing at a decreasing rate
  • decreasing at a decreasing rate
  • increasing at a constant rate
MP 是 TP 曲线的斜率：MP 为正 → TP 增加；MP 还在变大 → TP 增加得越来越快。
3.1-82025 AP Micro 国际卷 Q3
Which of the following is the best example of a fixed input for a firm producing leather boots in the short run?
  • Industrial sewing machines
  • Leather used to make the boots
  • Thread used to stitch the leather together
  • Unskilled labor working in the factory
  • Electricity used to power the factory
工业缝纫机短期内无法增减，是固定投入；皮革、线、工人、电力都随产量变化，是可变投入。
3.1-92019 AP Micro 练习卷 Q20
Number of workersQuantity of output
00
110
225
335
440
542
Given the production schedule above, what is the maximum number of workers the firm can hire before the effects of diminishing marginal returns set in?
  • 1
  • 2
  • 3
  • 4
  • 5
MP 依次为 10、15、10、5、2：第 2 个工人的 MP 最高，从第 3 个工人开始递减，所以在递减出现之前最多雇 2 人。
3.1-102000 AP Micro Q22
UNITS OF LABORQUANTITY OF OUTPUT0Total OutputAB
按原题重绘
The relationship in the graph above best illustrates the economic concept of
  • opportunity cost
  • diminishing marginal utility in consumption
  • diminishing marginal returns in production
  • production possibilities
  • comparative advantage
TP 先越涨越快（到 A），之后越涨越慢（A 到 B），B 之后开始下降——每多一单位劳动增加的产量越来越少，这就是边际报酬递减。
3.1-112023 AP Micro 国际卷 Q30
Marginal Product of LaborMarginal ProductL₁L₂L₃0Quantity of Labor
按原题重绘（横轴画在 MP = 0 处，往下是负的 MP）
Which of the following will happen if the firm continues to hire additional units of labor beyond L2 in the short run?
  • The firm’s marginal cost will decrease.
  • The firm will begin experiencing diminishing marginal returns.
  • The firm’s fixed cost will increase.
  • The average product of labor will be equal to zero.
  • The total product of labor will decrease.
L₂ 之后 MP 为负：每多雇一单位劳动，总产量反而减少。(B) 边际报酬递减在 MP 最高点 L₁ 之后就已经开始；(D) AP 仍然为正。
3.1-122025 AP Micro 国际卷 Q47
Quantity of LaborQuantity of Output0Marginal ProductAverage ProductL₁L₂L₃
按原题重绘
The graph shows the marginal product and average product curves for a firm.

Which of the following is true about the production function as labor usage increases from L1 to L3 when all other inputs are held constant?
  • There are increasing marginal returns.
  • There are diminishing marginal returns.
  • There are decreasing returns to scale.
  • Total product is maximized when the firm hires L1 units of labor.
  • Total product is maximized when the firm hires L2 units of labor.
L₁ 到 L₃ 之间 MP 一直在下降 → 边际报酬递减。TP 在 MP = 0 的 L₃ 处最大，不是 L₁ 或 L₂。(C) 规模报酬是长期概念，这里其他投入不变。
3.1-132024 AP Micro Q12
Quantity of LaborQuantity of Output0Marginal Product of LaborAverage Product of LaborL₁L₂L₃L₄
按原题重绘
Labor is the only variable input for a firm whose production function is depicted in the graph provided. How many units of labor would maximize total product?
  • L1
  • L2
  • L3
  • L4
  • Cannot be determined from the graph
TP 在 MP = 0 时达到最大：L₄。L₂ 是 MP 最大处，L₃ 是 AP 最大处。

3.2Short-Run Production Costs 短期生产成本

把生产函数换成钱，就得到成本。老板关心的不是“多雇一个人多做几杯”，而是“多做一杯要多花多少钱”。

三种总成本 TOTAL COSTS（CED PRD-1.A.4–5）
  • Fixed cost (FC) 固定成本：不随产量变化，产量为 0 时也要付。例：房租、设备贷款、保险、营业执照。
  • Variable cost (VC) 可变成本：随产量变化。例：原料、按小时付的工资、电费。产量为 0 时 VC = 0。
  • Total cost (TC) = FC + VC。
Quantity (q)Cost ($)0TCVCFC64TC − VC = FC = 64
TC = FC + VC。VC 从 0 开始，FC 是一条水平线（产量为 0 时也要付），TC 就是把 VC 整体往上抬高 FC。
平均成本与边际成本 PER-UNIT COSTS
名称公式含义
AFC average fixed costFC ÷ q每单位分摊的固定成本，产量越大越小
AVC average variable costVC ÷ q每单位的可变成本
ATC average total costTC ÷ q = AFC + AVC每单位的总成本（“单位成本”）
MC marginal costΔTC ÷ Δq = ΔVC ÷ Δq多生产 1 单位增加的成本（FC 不变，所以只看 VC 的变化）
WORKED EXAMPLE 3补全成本表（AP 经典题型） 原创

A firm's fixed cost is $100. Its total cost at each output level is given below. Complete the table.

qFCVCTCMCAFCAVCATC
01000100————
1??150????
2??180????
3??200????
4??230????
5??280????
6??360????
qFCVCTCMCAFCAVCATC
01000100————
1100501505010050150
21008018030504090
31001002002033.333.366.7
4100130230302532.557.5
510018028050203656
61002603608016.743.360
方法：FC 每一行都是 100；VC = TC − FC；MC = 这一行 TC − 上一行 TC；三个平均值都除以 q。
检查规律：MC 从 50 降到 20 再升到 80；AVC 最低在 q = 4（32.5），ATC 最低在 q = 5（56）；AFC 一直下降。MC 小于平均值时平均值下降，MC 大于平均值时平均值上升。
WORKED EXAMPLE 4从产量推出成本：AVC = w ÷ AP，MC = w ÷ MP 原创 · AP 经典考法

Labor is a firm's only variable input, and the wage is $60 per worker per day. When the firm hires 4 workers, average product is 15 units and marginal product of the 4th worker is 12 units. Calculate (a) AVC at this output and (b) the MC of the last units produced.

(a) 产量 = 4 × 15 = 60，VC = 4 × 60 = $240，AVC = 240 ÷ 60 = $4。等价于 AVC = 工资 ÷ AP = 60 ÷ 15。
(b) 第 4 个工人花 $60，多生产 12 单位 → MC = 60 ÷ 12 = $5。
规律：AP 越高 AVC 越低，MP 越高 MC 越低——所以 AVC 的最低点对应 AP 的最高点，MC 的最低点对应 MP 的最高点。真题 2000 Q51、Q53 就是这种考法。

The Cost Curves 成本曲线：分三步画

四条曲线一次画出来很容易乱。按下面三步，一条一条加：

Quantity (q)Cost per unit ($)0AFCAFC = 32AFC = 16AFC = 8
第 1 步 · AFC = 64 ÷ q：产量翻倍，每单位分摊的固定成本就减半（q = 2 时 32，q = 4 时 16，q = 8 时 8）。AFC 一直下降，但永远不会碰到横轴。
Quantity (q)Cost per unit ($)0ATCAVCAFC = 21.3AFC = 8.0
第 2 步 · ATC = AVC + AFC：ATC 永远在 AVC 上方，两条线之间的竖直距离就是 AFC。q = 3 时差距 21.3，q = 8 时只剩 8——两条线越来越近，但不会相交。
Quantity (q)Cost per unit ($)0MCATCAVCAFCmin AVCmin ATCmin MC$66$158
第 3 步 · 加上 MC：MC 先降后升；MC 从下方穿过 AVC 和 ATC 的最低点；AFC 一直下降；ATC 与 AVC 之间的竖直距离就是 AFC，越来越窄。
必背 KEY RELATIONSHIPS
  1. MC 穿过 AVC 和 ATC 的最低点（又是“边际拉动平均”：MC 在下方时平均值下降，在上方时平均值上升）。
  2. AFC 一直下降（固定成本分摊到越来越多的产量上），但永远不会到 0。
  3. ATC − AVC = AFC，所以两条曲线越来越靠近，但不会相交。
  4. ATC 的最低点在 AVC 最低点的右边，并且更高。
FRQ 画图标准 纵轴 Cost（或 Price/Cost）、横轴 Quantity；ATC、AVC 画成 U 形，ATC 在上；MC 先略降再上升，从下往上穿过 AVC 和 ATC 的最低点（阅卷最常扣分的地方）；题目没要求就不必画 AFC。
WORKED EXAMPLE 5从成本曲线上读出 AFC 和 TFC 原创 · AP 读图考法
Quantity (q)Cost per unit ($)0MCATCAVC$234$7$158ABCD
读图：q = 4 时 ATC = $23（A 点）、AVC = $7（B 点）；q = 8 时 ATC = $15（C 点）、AVC = $7（D 点）。

Using the graph, (a) what does the vertical distance AB represent, and what is its value? (b) Calculate total fixed cost. (c) Calculate total variable cost and total cost when the firm produces 8 units. (d) Explain why distance CD is shorter than distance AB.

(a) AB = ATC − AVC = AFC，q = 4 时等于 23 − 7 = $16。
(b) TFC = AFC × q = 16 × 4 = $64。用 q = 8 验算：(15 − 7) × 8 = 64，一样——TFC 不随产量变化。
(c) TVC = AVC × q = 7 × 8 = $56；TC = ATC × q = 15 × 8 = $120（= 56 + 64）。
(d) CD 也是 AFC。产量从 4 增加到 8，同样的 $64 固定成本被分摊到更多单位上，AFC 从 16 降到 8。
真题对应：2000 Q6（CF 距离代表什么）、2023 FRQ Set 1 Q3（用 ATC − AVC 求 TFC，见下册）。

Why MC Is U-Shaped 为什么 MC 先降后升（CED PRD-1.A.6–7）

成本曲线其实是生产函数的“镜像”。如果每个员工每小时工资 $50，那么多做一杯奶茶的成本 = 50 ÷ MP：

MP（杯）10152015105MP 最高WorkerMC = $50 ÷ MP0$5$3.33$2.5$3.33$5$10MC 最低123456
工资每人每小时 $50。MP 越高，多做一杯花的钱越少：MP 上升时 MC 下降，MP 最高（第 3 人）时 MC 最低，MP 下降（边际报酬递减）时 MC 上升。MC 曲线就是 MP 曲线“倒过来”。
一句话 分工让 MP 上升 → MC 下降；边际报酬递减让 MP 下降 → MC 上升。同理，AP 最高的地方 AVC 最低（AVC = 工资 ÷ AP）。

Cost Shifters 成本曲线的移动（CED PRD-1.A.8）

Quantity (q)Cost per unit ($)0MCAVCATC₁ATC₂
固定成本增加（房租上涨、一次性的 lump-sum 税、营业执照费）：只有 AFC 和 ATC 上移；MC 和 AVC 不变，所以利润最大化的产量也不变。
Quantity (q)Cost per unit ($)0MC₁AVC₁ATC₁MC₂AVC₂ATC₂
可变成本增加（工资上涨、原料涨价、每单位征税 $4）：AVC、ATC、MC 都上移（per-unit tax 使三条曲线都上移 $4）。
WORKED EXAMPLE 6四个事件，成本曲线怎么移动？ 原创

For each event, which of a bubble tea shop's cost curves (AFC, AVC, ATC, MC) shift, and in which direction?

  1. Rent rises from $3,000 to $4,000 per month.
  2. The minimum wage rises.
  3. The government imposes a $0.50 per-cup tax.
  4. A new automatic sealing machine raises each worker's productivity.
1. 房东把月租从 $3,000 涨到 $4,000
固定成本 ↑ → 只有 AFC、ATC 上移（蓝线）；MC、AVC 不变。
2. 最低工资上调，店员时薪提高
可变成本 ↑ → AVC、ATC、MC 都上移（红线）。
3. 政府对每杯征收 $0.5 的税
per-unit tax 是可变成本 → AVC、ATC、MC 都上移 $0.5。
4. 新的自动封口机让每个员工效率提高
生产率 ↑ → MP ↑ → AVC、ATC、MC 都下移（绿线）。
判断口诀：先问“这项成本随产量变化吗？”不变 → 固定成本 → 只动 AFC、ATC；变 → 可变成本 → AVC、ATC、MC 一起动。
易错 TRAP · 两种税 Lump-sum tax（一次性定额税）不管生产多少都交一样多 → 是固定成本 → 只移动 AFC 和 ATC，不影响 MC，短期产量不变。
Per-unit tax（从量税）每生产一单位交一次 → 是可变成本 → AVC、ATC、MC 都上移，产量下降。这是 FRQ 的高频考点。
反过来，技术进步、员工更熟练（生产率提高）会让成本曲线下移。
LAB 2成本曲线实验室 · Cost Curve Lab

基准：FC = $64，最低 AVC = $6（q = 6），最低 ATC = $15（q = 8）。改变固定成本或每单位成本，虚线是原来的曲线。

固定成本变化（房租、执照费、lump-sum 税）：$0
每单位成本变化（工资、原料、per-unit 税）：$0

练习 Practice 3.2

以下为历年 AP 真题（带图的题按原题重绘），点选项即时判分并显示解析。

3.2-12000 AP Micro Q53
If labor is the only variable input and it costs $15 per hour and if the marginal product of labor is 3 units per hour, the short-run marginal cost of 1 unit of output is approximately
  • $ 0.20
  • $ 3.00
  • $ 5.00
  • $15.00
  • $45.00
MC = 工资 ÷ MP = 15 ÷ 3 = $5：一小时 $15 换来 3 单位，每单位 $5。
3.2-22005 AP Micro Q8
Which of the following best describes the relationship between the average total cost curve and the marginal cost curve in the short run?
  • If the average total cost curve is rising, the marginal cost curve is above the average total cost curve.
  • If the average total cost curve is rising, the marginal cost curve is below the average total cost curve.
  • If the average total cost curve is above the marginal cost curve, the marginal cost curve is rising.
  • If the average total cost curve is below the marginal cost curve, the marginal cost curve is falling.
  • If the average and marginal cost curves intersect, the marginal cost curve is at a minimum.
MC 在 ATC 上方时把平均值往上拉 → ATC 上升。(C) 反了：ATC 在 MC 上方说明 ATC 在下降，并不说明 MC 在上升；(E) 相交时是 ATC 的最低点，不是 MC 的最低点。
3.2-32005 AP Micro Q51
Which of the following best explains why the short-run average total cost curve is U-shaped?
  • Spreading total fixed costs over a larger output, and constant returns
  • Spreading total fixed costs over a larger output, and eventually diminishing returns
  • Increasing total fixed costs and increasing returns
  • Increasing average variable costs and decreasing returns
  • Decreasing average variable costs and increasing returns
ATC = AFC + AVC：前半段固定成本被摊薄（AFC 下降）使 ATC 下降；后半段边际报酬递减使 AVC 和 MC 上升，ATC 转而上升 → U 形。
3.2-42012 AP Micro Q25
If the average variable cost of producing 5 units of a good is $100 and the average variable cost of producing 6 units is $150, then the marginal cost of increasing output from 5 to 6 units is
  • $50
  • $250
  • $300
  • $400
  • $500
VC₅ = 5 × 100 = 500，VC₆ = 6 × 150 = 900，MC = 900 − 500 = $400。注意不能用 150 − 100。
3.2-52012 AP Micro Q36
If labor is the only variable input in the production process, the short-run marginal cost curve is upward sloping because which of the following occurs as more and more labor is added?
  • Output decreases, and thus marginal cost increases.
  • Output increases, and thus marginal cost increases.
  • Output increases at an increasing rate, and thus the cost of producing each additional unit of output increases.
  • Output increases at a decreasing rate, and thus the cost of producing each additional unit of output increases.
  • Output increases at a decreasing rate, and thus the cost of producing each additional unit of output decreases.
边际报酬递减：多加的劳动带来的产量越来越少（产量以递减的速度增加），所以每多生产一单位的成本越来越高。
3.2-62013 AP Micro Q8
If the marginal cost of producing the first unit of some good is $20 and the marginal cost of producing the second unit is $30, the average variable cost of producing 2 units is
  • $5
  • $10
  • $20
  • $25
  • $50
VC₂ = 20 + 30 = 50，AVC = 50 ÷ 2 = $25。（VC 等于各单位 MC 之和。）
3.2-72014 AP Micro 练习卷 Q21
If a new tax on capital increases a firm’s fixed cost of production, which of the following will occur in the short run?
  • Marginal cost will increase.
  • Average variable cost will increase.
  • Average total cost will increase.
  • The profit-maximizing level of output will increase.
  • The profit-maximizing level of output will decrease.
固定成本增加 → AFC 和 ATC 上升；MC、AVC 不变，所以利润最大化产量也不变。
3.2-82014 AP Micro 练习卷 Q23
At 100 units of output, a firm’s total cost is $10,000. If the firm’s total fixed cost is $4,000, its average variable cost is equal to
  • $140
  • $100
  • $60
  • $40
  • $0
VC = 10,000 − 4,000 = 6,000，AVC = 6,000 ÷ 100 = $60。
3.2-92014 AP Micro 练习卷 Q53
As output of a firm increases, the difference between the firm’s average total cost and its average variable cost gets smaller because the firm’s
  • total cost is increasing
  • marginal cost is increasing
  • average fixed cost is decreasing
  • marginal product of labor is decreasing
  • long-run average total cost is decreasing
ATC − AVC = AFC，产量越大，固定成本被分摊得越薄，AFC 越小，两条曲线越靠近。
3.2-102016 AP Micro 练习卷 Q51
A firm is producing 100 units of output at a total cost of $400. The firm’s average variable cost is $3 per unit. What is the firm’s total fixed cost?
  • $1
  • $50
  • $100
  • $300
  • $400
VC = 3 × 100 = 300，FC = 400 − 300 = $100。
3.2-112015 AP Micro 练习卷 Q36
Quantity (units)Total cost
0$30
140
247
351
459
The table above shows a firm’s total cost of producing various units of output. What is the average variable cost of producing three units?
  • $4
  • $7
  • $10
  • $17
  • Cannot be determined from the given information
q = 0 时的总成本就是 FC = $30。VC₃ = 51 − 30 = 21，AVC = 21 ÷ 3 = $7。
3.2-122000 AP Micro Q6
Questions 6-7 refer to the graph below, which shows the cost curves for a profit-maximizing, perfectly competitive firm.
QUANTITYPRICE/COSTS0Marginal CostAverage Total CostAverage Variable CostP₁Q₁P₂Q₂CFD
按原题重绘
The vertical distance CF represents the
  • total cost of producing Q1 units of output
  • average total cost of producing Q1 units of output
  • average fixed cost of producing Q1 units of output
  • average variable cost of producing Q1 units of output
  • amount of the firm's loss resulting from producing Q1 units of output
C 在 ATC 上、F 在 AVC 上，同一产量 Q₁ 下两者的竖直距离 = ATC − AVC = AFC。
3.2-132016 AP Micro 练习卷 Q7
QUANTITY OF LABORMP, AP0MPAPL₁L₂L₃L₄L₅
按原题重绘
The graph above shows the marginal product (MP) and the average product (AP) of labor for a firm that uses labor as the only variable input and hires its labor in a perfectly competitive market. At which quantity of labor does marginal cost change from decreasing to increasing?
  • L1
  • L2
  • L3
  • L4
  • L5
MC = 工资 ÷ MP，工资不变时 MP 最大的地方 MC 最小 → MC 在 L₂ 处由降转升。L₃ 是 AP 最大处，对应的是 AVC 最低点。

3.3Long-Run Production Costs 长期生产成本

短期里奶茶店只能在一个吧台上加人；长期里老板可以换更大的店、加第二台封口机，甚至开一个中央厨房。长期所有投入都可变，所有成本都是可变成本（CED PRD-1.A.9），企业要回答的问题变成了：“开多大规模最划算？”

From SRATC to LRATC 从短期 ATC 到长期 ATC

WORKED EXAMPLE 7预计每天卖多少杯？选小店、中店还是大店 原创

A bubble tea company is choosing among three shop sizes. Each size has its own short-run average total cost. The table shows the cost per cup at different daily outputs. Which size should the company choose for each expected output, and what is its long-run average total cost?

Expected daily outputSmall shopMedium shopLarge shop
200 杯$5.0$5.6$8.9
400 杯$5.8$4.4$6.5
600 杯$8.2$4.0$4.9
800 杯$12.2$4.4$4.1
预计日销量小店 SRATC₁中店 SRATC₂大店 SRATC₃最便宜LRATC
200 杯$5.0$5.6$8.9小店$5.0
400 杯$5.8$4.4$6.5中店$4.4
600 杯$8.2$4.0$4.9中店$4.0
800 杯$12.2$4.4$4.1大店$4.1
做法：每一行找最小的数字。卖 200 杯选小店（$5.0），卖 400 或 600 杯选中店（$4.4、$4.0），卖 800 杯选大店（$4.1）。
LRATC 就是最后一列：在每个产量下，选最合适的规模后能达到的最低平均成本。这就是“长期平均总成本”的意思。
MES：LRATC 最早降到最低的 $4.0 是在 600 杯，所以 MES = 600 杯（规模再大也不会更便宜）。
每天的产量（杯）每杯平均成本 ($)02004006008001000$2$4$6$8$10LRATC小店中店大店
三条虚线是三种店面规模的短期 ATC。每个产量下取最低的那条，连起来的粗蓝线就是 LRATC。只有三种规模时 LRATC 有“波浪”；如果店面规模可以连续选择，波浪会被抹平，变成一条光滑曲线（见下图）。
QuantityCost per unit ($)0Q₁SRATC₁Q₂SRATC₂Q₃SRATC₃Q₄SRATC₄Q₅SRATC₅LRATC
标准的“包络线”图（AP 真题常见画法）：每条短期 ATC 只在一个点碰到 LRATC（黑点）。LRATC 下降段上，切点在各条 SRATC 最低点的左边；LRATC 最低点（Q₃）处，SRATC₃ 的最低点正好就是 LRATC 的最低点。
易错 TRAP LRATC 不是把各条 SRATC 的最低点连起来！它是每个产量下“最低的那条 SRATC”的高度。在规模经济阶段，企业用一个稍大的工厂、在其 SRATC 最低点左边生产，往往比用小工厂在最低点生产更便宜。
LAB 3选店面规模 · Choose a Plant Size

拖动“预计日销量”，看三种店面在这个产量下每杯成本是多少，哪一种最便宜。粗蓝线 LRATC 就是“每个产量下最便宜的选择”。

预计日销量 = 400 杯

Economies and Diseconomies of Scale 规模经济与规模不经济

Quantity (q)LRATC ($)0LRATCMES① 规模经济LRATC 下降② 报酬不变LRATC 水平③ 规模不经济LRATC 上升
LRATC 的三个阶段。MES（最小有效规模）= LRATC 刚刚降到最低点时的产量。
三个阶段（CED PRD-1.A.10–11）
LRATC 随产量…名称对应的“规模报酬”常见原因
下降Economies of scale 规模经济Increasing returns to scale：投入 ×2，产出 > ×2更细的分工、大批量采购折扣、把研发和广告等大额固定成本分摊到更多产量上、用得起更先进的大型设备
不变Constant returns to scale 规模报酬不变投入 ×2，产出正好 ×2规模扩大的好处和坏处相互抵消（efficient scale 有效规模）
上升Diseconomies of scale 规模不经济Decreasing returns to scale：投入 ×2，产出 < ×2组织太大，沟通协调困难、管理层级过多、员工积极性下降
易错 TRAP · 两种“递减”别混淆 边际报酬递减是短期概念：只增加一种投入，其他投入固定。
规模不经济（规模报酬递减）是长期概念：所有投入同比例增加。
一家企业完全可能在短期面临边际报酬递减，同时在长期仍处于规模经济阶段（真题 2010 Q23 就考这一点，见练习）。
WORKED EXAMPLE 8读懂 LRATC 表 原创

The table shows a firm's long-run average total cost at different output levels.

Output1,0002,0003,0004,0005,0006,000
LRATC ($)1086667.5

(a) Over which range does the firm experience economies of scale, constant returns to scale, and diseconomies of scale? (b) What is the minimum efficient scale? (c) If total market demand at a price of $6 is 6,000 units, what is the largest number of firms that can each produce at minimum efficient scale?

(a) 1,000 → 3,000：LRATC 从 10 降到 6，规模经济；3,000 → 5,000：保持 6，规模报酬不变；5,000 → 6,000：升到 7.5，规模不经济。
(b) MES = LRATC 刚到最低点的产量 = 3,000。
(c) 6,000 ÷ 3,000 = 2 家（下面的 MES 小节会专门讲这个算法）。
WORKED EXAMPLE 9投入翻倍，产出变多少？ 原创

A bakery can vary all its inputs in the long run. The table shows output for different input combinations.

WorkersOvensLoaves per day
11100
22250
44500
88800

Identify the returns to scale for each doubling of inputs, and explain what happens to long-run average total cost if input prices are constant.

1 → 2：投入 ×2，产出 100 → 250（×2.5）→ 规模报酬递增 → LRATC 下降（规模经济）。
2 → 4：投入 ×2，产出 250 → 500（×2）→ 规模报酬不变 → LRATC 不变。
4 → 8：投入 ×2，产出 500 → 800（×1.6）→ 规模报酬递减 → LRATC 上升（规模不经济）。
投入价格不变时，总成本和投入同比例变化，所以“产出增长比投入快”就意味着每单位成本下降。

MES and Market Structure 最小有效规模与市场结构（CED PRD-1.A.12）

为什么奶茶店满街都是，而有些行业全世界只有一两家公司？关键在于：一家企业要做多大才能把成本降到最低，以及市场一共有多大。分两步看：

一家店每天的产量（杯）每杯的长期平均成本 ($)02008001000$2$4$6$8$10LRATCMES$4500规模太小：每杯成本高超过 500 杯，成本不再下降
第一步，只看一家企业：奶茶店每天做到 500 杯时，每杯成本降到最低的 $4。500 杯就是这家店的最小有效规模（MES）。
全城奶茶市场在最低成本价格下一共买 10,000 杯；每家要做到 500 杯 才能达到最低成本10,000 ÷ 500 = 20 → 能容纳约 20 家店 → 很多企业，竞争激烈某种光刻机第1家剩下 40 台，不够第 2 家达到 MES市场在最低成本价格下一共买 100 台；每家要做到 60 台 才能达到最低成本100 ÷ 60 ≈ 1.7 → 只容得下 1 家达到最低成本 → 自然垄断或寡头
第二步，把 MES 放到整个市场里比较：灰色长条是市场总需求量，彩色块是一家企业达到最低成本所需的规模。能放进几块，市场就大致能容纳几家有效率的企业。
结论 能容纳的有效率企业数 ≈ 市场需求量（在最低成本价格下）÷ MES MES 相对于市场越小，能容纳的企业越多，越接近完全竞争；MES 相对于市场越大，能容纳的企业越少，往往形成寡头。如果整个市场的需求量还不到一家企业的 MES（LRATC 在整个需求范围内都在下降），一家企业供应全市场最便宜——这就是 Unit 4 的自然垄断。
WORKED EXAMPLE 10理发店、加油站、地铁：各能容纳几家？ 原创

For each market, the table shows the quantity demanded at the price equal to the lowest possible LRATC, and the minimum efficient scale of one firm.

MarketQuantity demandedMES of one firm
Haircuts in a town 小镇理发3,000 per day60 per day
Gas on a highway 高速路段加油40,000 liters per day10,000 liters per day
Subway rides in a city 城市地铁2 million per dayLRATC still falling at 3 million

(a) About how many efficient firms can each market support? What market structure is likely? (b) Traffic on the highway doubles. What happens to the number of gas stations? (c) A new self-service pump lowers a gas station's MES to 5,000 liters. What happens?

(a) 理发：3,000 ÷ 60 = 50 家 → 企业很多，接近竞争市场。加油：40,000 ÷ 10,000 = 4 家 → 少数几家，寡头。地铁：整个城市的需求（200 万）还没到 LRATC 的最低点，一家公司做全部的量都还在规模经济阶段 → 1 家成本最低，自然垄断。
(b) 需求翻倍：80,000 ÷ 10,000 = 8 家，市场容得下更多企业，竞争更激烈。市场变大和 MES 变小效果相同。
(c) 40,000 ÷ 5,000 = 8 家。技术让 MES 变小，同样的市场可以容纳更多有效率的企业。
记住比较的是比例：看 MES 相对于市场需求有多大，而不是 MES 本身大不大。
LAB 4市场能装下几家？ · How Many Efficient Firms Fit?

调整“市场在最低成本价格下的需求量”和“一家企业的 MES”，看市场能容纳几家达到最低成本的企业。

例子：
市场需求量 = 10000
一家企业的 MES = 500

练习 Practice 3.3

以下为历年 AP 真题（带图的题按原题重绘），点选项即时判分并显示解析。

3.3-12005 AP Micro Q21
Economies of scale exist when
  • the doubling of all inputs doubles the output produced
  • short-run average total cost decreases as output increases
  • short-run average total cost remains constant as output increases
  • long-run average total cost increases as output increases
  • long-run average total cost decreases as output increases
规模经济 = LRATC 随产量增加而下降。(A) 是规模报酬不变；(B)(C) 说的是短期 ATC。
3.3-22010 AP Micro Q7
F&D Manufacturing Company increases all its inputs by 50 percent each. If F&D's output increases by 100 percent, then F&D is experiencing
  • increasing returns to scale
  • constant returns to scale
  • diseconomies of scale
  • increasing marginal cost
  • decreasing profits
投入增加 50%，产出增加 100%（多于 50%）→ 规模报酬递增。
3.3-32012 AP Micro Q22
A farmer grows wheat using two inputs: labor and land whose prices are constant. If she doubles her inputs, she finds that the quantity of wheat produced more than doubles. Therefore, it must be true that in this output range her long-run average total cost curve is
  • upward sloping
  • downward sloping
  • horizontal
  • vertical
  • U-shaped
投入翻倍、产出多于翻倍，而投入价格不变 → 每单位成本下降 → LRATC 向下倾斜（规模经济）。
3.3-42012 AP Micro Q50
If a firm’s production process exhibits economies of scale, which of the following will occur when the firm’s output increases?
  • Its short-run average total costs will rise.
  • Its long-run average total costs will rise.
  • Its long-run average total costs will fall.
  • Its short-run total costs will fall.
  • Its long-run total costs will fall.
规模经济 = 产量增加时 LRATC 下降。长期总成本仍然上升，只是上升得比产量慢。
3.3-52016 AP Micro 练习卷 Q6
If the output of a firm doubles when the firm doubles all of its inputs, the firm must be experiencing
  • economies of scale
  • increasing returns to scale
  • constant returns to scale
  • decreasing returns to scale
  • diseconomies of scale
所有投入翻倍、产出正好翻倍 → 规模报酬不变。
3.3-62017 AP Micro 练习卷 Q28
The table below shows the long-run total cost function of a firm.
Quantity of outputTotal cost ($)
00
110
220
330
440
550
The firm’s cost function exhibits
  • diseconomies of scale
  • constant returns to scale
  • economies of scale
  • decreasing marginal cost
  • increasing marginal cost
LRATC = TC ÷ q = 10 对所有产量都相同 → 规模报酬不变。（MC 也恒为 10，所以不是递增或递减的边际成本。）
3.3-72021 AP Micro 国际卷 Q3
What does the minimum efficient scale measure?
  • The smallest output level at which short-run average total cost is minimized.
  • The smallest output level at which short-run total cost is minimized.
  • The smallest output level at which long-run average total cost is minimized.
  • The largest output level at which long-run average total cost is minimized.
  • The largest output level at which long-run total cost is minimized.
最小有效规模 = LRATC 达到最低时的最小产量。
3.3-82022 AP Micro 国际卷 Q15
As a firm expands its output, it initially experiences economies of scale and then diseconomies of scale. The firm’s long-run average cost curve is
  • horizontal and then upward sloping
  • horizontal and then downward sloping
  • downward sloping and then upward sloping
  • continuously upward sloping
  • continuously downward sloping
先规模经济（LRATC 下降）后规模不经济（LRATC 上升）→ 先向下后向上（U 形）。
3.3-92010 AP Micro Q23
Questions 23-24 refer to the graph below, which shows the cost curves of a firm.
QUANTITYPRICE0Short-run Marginal CostShort-run ATCLong-run ATCP₁Q₁
按原题重绘
If the firm produces Q1 units of output with two inputs, the firm will be experiencing which of the following in the short run and in the long run?
  • Short Run: Increasing marginal returns；Long Run: Economies of scale
  • Short Run: Increasing marginal returns；Long Run: Diseconomies of scale
  • Short Run: Diminishing marginal returns；Long Run: Economies of scale
  • Short Run: Diminishing marginal returns；Long Run: Diseconomies of scale
  • Short Run: Constant marginal returns；Long Run: Diseconomies of scale
在 Q₁ 处，短期 MC 正在上升 → 边际报酬递减；LRATC 在 Q₁ 处仍在下降 → 规模经济。短期递减与长期规模经济可以同时存在。
3.3-102023 AP Micro 国际卷 Q29
QuantityCost0Q₁SRATC₁Q₂SRATC₂Q₃SRATC₃Q₄SRATC₄Q₅SRATC₅LRATC
按原题重绘
The graph provided shows five different short-run average total cost (SRATC) curves of a firm and its long-run average total cost (LRATC) curve. Which of the following is true if the firm is operating on its SRATC2 curve and producing quantity Q2?
  • The firm is producing at the minimum efficient scale.
  • The firm must decrease its output to achieve the minimum efficient scale.
  • The firm must increase its output to achieve the minimum efficient scale.
  • The firm is producing at its productively efficient quantity of output.
  • The firm is experiencing diseconomies of scale.
Q₂ 在 LRATC 的下降段（规模经济），MES 在 LRATC 最低点 Q₃ → 企业要增加产量（扩大规模）才能达到 MES。

ΣSummary 本册总结与易错点

3.1 Production Function

短期 = 至少一种投入固定；长期 = 所有投入可变。MP = ΔTP/ΔL，AP = TP/L。分工 → 边际报酬递增；固定投入不够用 → 边际报酬递减（MP 下降，不一定为负）。MP > AP 时 AP 上升，MP 穿过 AP 最高点；MP = 0 时 TP 最大。

3.2 Short-Run Costs · 计算

TC = FC + VC，FC 在 q = 0 时也存在。AFC = FC/q，AVC = VC/q，ATC = TC/q = AFC + AVC。MC = ΔTC/Δq = ΔVC/Δq。只有一种可变投入时 MC = w/MP，AVC = w/AP。

3.2 Short-Run Costs · 图形与移动

MC 先降后升，穿过 AVC、ATC 的最低点；AFC 一直下降；ATC 与 AVC 的距离 = AFC，越来越小。固定成本（房租、定额税）变化只移动 AFC、ATC；每单位成本（工资、原料、从量税）变化移动 MC、AVC、ATC。

3.3 Long-Run Costs

LRATC 是每个产量下最便宜的那条 SRATC 连成的包络线。LRATC 下降 = 规模经济，水平 = 规模报酬不变，上升 = 规模不经济。MES 是 LRATC 刚降到最低的产量；MES 相对市场需求越大，市场容得下的企业越少。

公式速查

要算什么公式常见用法
边际产量 MPΔTP ÷ ΔL判断从哪个工人开始边际报酬递减
平均产量 APTP ÷ LAP 最高处 MP = AP
固定成本 FCq = 0 时的 TC；或 (ATC − AVC) × q表格第一行、图上两条平均成本线的距离
平均成本AFC = FC/q，AVC = VC/q，ATC = TC/qATC = AFC + AVC
边际成本 MCΔTC ÷ Δq = ΔVC ÷ Δq表格题相邻两行相减
由产量算成本MC = w ÷ MP，AVC = w ÷ AP产量表 + 工资的 FRQ
长期平均成本LRATC = LRTC ÷ q比较两个产量的 LRATC 判断规模经济
易错点 TOP 10
  1. 短期/长期按日历时间划分 ✗ → 看是否还有固定投入。
  2. 边际报酬递减 = MP 变成负数 ✗ → MP 开始下降就是递减，此时 TP 仍在增加。
  3. TP 最大处 = AP 最大处 ✗ → TP 在 MP = 0 处最大，AP 在 MP = AP 处最大。
  4. 边际报酬递减 = 规模不经济 ✗ → 前者是短期（只加一种投入），后者是长期（所有投入一起变）。
  5. MC 穿过 AFC 的最低点 ✗ → MC 穿过 AVC 和 ATC 的最低点；AFC 没有最低点。
  6. ATC 与 AVC 之间的距离不变 ✗ → 距离 = AFC，产量越大距离越小。
  7. 房租或定额税上涨让 MC 上升 ✗ → 固定成本只影响 AFC 和 ATC。
  8. 从量税只让 ATC 上移 ✗ → 每单位成本上升，MC、AVC、ATC 都上移。
  9. LRATC 是各条 SRATC 最低点的连线 ✗ → 是每个产量下最低的那条 SRATC 连成的包络线。
  10. MES 越大，市场里企业越多 ✗ → MES 相对市场需求越大，容得下的企业越少。

✎Unit 3（上）Test 本册测验

15 道选择题，全部选自历年 AP 真题（与各节练习不重复），建议用时 18 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 Q49
Which of the following is true of production in the long run?
  • At least one factor of production is fixed.
  • Only one factor of production is fixed.
  • Some factors of production are fixed while others are variable.
  • All factors of production are variable.
  • All factors of production, except technology, are fixed.
长期 = 所有生产要素都可以调整。
T22019 AP Micro 练习卷 Q50
Which of the following is true for a firm that uses labor as a variable input and capital as a fixed input in the short run?
  • If the marginal product of labor is negative, the average product of labor must also be negative.
  • If the marginal product of labor is rising, the average product of labor must be greater than the marginal product of labor.
  • If the average product of labor is rising, the marginal product of labor must be rising.
  • If the average product of labor is falling, the marginal product of labor must be less than the average product of labor.
  • The average product of labor can never be equal to the marginal product of labor.
AP 下降说明新增的 MP 低于 AP（把平均拉低）。(A) MP 为负时 AP 仍可为正；(B) MP 上升时一般高于 AP；(C) AP 上升时 MP 在 AP 上方，但 MP 本身可能已在下降；(E) MP 穿过 AP 最高点时两者相等。
T32010 AP Micro Q52
Beyond a certain level of output, the short-run marginal cost will rise because
  • there is no fixed input and costs will increase
  • at least one input is fixed and eventually diminishing returns will occur
  • the cost of the variable input increases when marginal product increases
  • the demand for the good decreases when production is limited
  • input prices increase when production increases and consumption is limited
短期至少有一种投入固定，继续增加可变投入终将出现边际报酬递减 → MP 下降 → MC 上升。
T42023 AP Micro 国际卷 Q1
Which of the following statements about short-run costs is always true as a firm increases its production?
  • Average fixed cost decreases.
  • Average variable cost decreases.
  • Average total cost decreases.
  • Marginal cost is lower than the average variable cost.
  • Marginal cost is lower than the average total cost.
无论产量多大，固定成本都被分摊到更多单位上，AFC 一定下降。AVC、ATC 都是先降后升。
T52019 AP Micro 练习卷 Q18
Which of the following must be true if at the tenth unit of output, marginal cost (MC) is $130 and average total cost (ATC) is $150 ?
  • ATC of producing the ninth unit is higher than $150.
  • ATC of producing the ninth unit is less than $150.
  • MC of producing the ninth unit is higher than $130.
  • Average variable cost of producing the tenth unit is higher than $150.
  • Average variable cost of producing the tenth unit is equal to $20.
第 10 单位的 MC（130）低于 ATC（150），说明这一单位把平均值拉低了 → 第 9 单位时的 ATC 高于 $150。
T62010 AP Micro Q8
At 100 units of a firm's output, average total cost is $10, average variable cost is $8, average fixed cost is $2, and marginal cost is $12. How will each of the following change as the firm's output further increases?
  • Average Total Cost: Increase；Average Variable Cost: Increase；Average Fixed Cost: Increase
  • Average Total Cost: Increase；Average Variable Cost: Increase；Average Fixed Cost: Decrease
  • Average Total Cost: Increase；Average Variable Cost: Decrease；Average Fixed Cost: Decrease
  • Average Total Cost: Decrease；Average Variable Cost: Increase；Average Fixed Cost: Increase
  • Average Total Cost: Decrease；Average Variable Cost: Decrease；Average Fixed Cost: Decrease
MC（12）高于 ATC（10）和 AVC（8）→ 继续增产会把两个平均值都拉高；AFC 永远随产量下降。
T72018 AP Micro 练习卷 Q52
The table below shows a competitive firm’s total variable cost (TVC) and total fixed cost (TFC) at various units of output.
OutputTVCTFC
009
139
289
3159
4269
5389
When output is 3 units, which of the following is correct?
  • Average Variable Cost: 5；Marginal Cost: 6
  • Average Variable Cost: 5；Marginal Cost: 7
  • Average Variable Cost: 6；Marginal Cost: 5
  • Average Variable Cost: 7；Marginal Cost: 7
  • Average Variable Cost: 7；Marginal Cost: 6
AVC₃ = TVC ÷ q = 15 ÷ 3 = 5；MC₃ = TVC₃ − TVC₂ = 15 − 8 = 7。
T82018 AP Micro 练习卷 Q7
Questions 7-8 are based on the table below, which shows a firm’s average variable cost and average total cost.
OutputAverage variable costAverage total cost
1$40$160
23595
34080
44575
55074
65575
The average fixed cost of producing four units of output is equal to
  • $120
  • $95
  • $75
  • $50
  • $30
AFC = ATC − AVC = 75 − 45 = $30（TFC = 30 × 4 = 120，每一行都一样）。
T92025 AP Micro 国际卷 Q14
OutputTotal cost ($)
0100
15150
25225
The table shows the total cost schedule for a firm.

The average variable cost of producing 25 units of output is
  • $4.00
  • $5.00
  • $7.50
  • $9.00
  • $10.00
FC = 产量为 0 时的 TC = $100；AVC = (225 − 100) ÷ 25 = $5。
T102023 AP Micro 国际卷 Q24
Number of casesTotal cost ($)
015
125
245
375
4115
5165
The table provided shows the daily total cost data for Hansel’s Hot Sauce. If the average fixed cost was $5 per case, how many cases of hot sauce had Hansel’s Hot Sauce produced?
  • 1
  • 2
  • 3
  • 4
  • 5
FC = 产量为 0 时的总成本 = $15；AFC = 15 ÷ q = 5 → q = 3。
T112010 AP Micro Q37
Units of labor inputUnits of output
18
220
330
The table above shows the amount of labor inputs necessary to produce given levels of output. If the cost of a unit of labor is $20 and total fixed cost is $100, the average total cost of producing 20 units of output is
  • $1
  • $2
  • $7
  • $40
  • $120
20 单位产量需要 2 单位劳动：VC = 2 × 20 = 40，TC = 100 + 40 = 140，ATC = 140 ÷ 20 = $7。
T122017 AP Micro 练习卷 Q44
Questions 43-44 are based on the output and cost data in the table below.
Quantity of output produced (units)Total variable cost ($)Total cost ($)
1100200
2190290
3270370
4340440
5420520
6510610
7610710
If there is only one variable input, diminishing marginal returns first occur with the production of which unit of output?
  • 7th
  • 6th
  • 5th
  • 4th
  • 3rd
TFC = 100，MC 依次为 100、90、80、70、80、90、100：MC 从第 5 单位开始上升，说明生产第 5 单位时开始出现边际报酬递减（MC = 工资 ÷ MP）。
T132013 AP Micro Q20
If a firm is experiencing economies of scale, which of the following will decrease as output increases?
  • Fixed cost
  • Long-run total cost
  • Long-run average total cost
  • Marginal cost
  • Marginal revenue
规模经济就是长期平均总成本随产量增加而下降。
T142021 AP Micro 国际卷 Q22
If a firm experiences economies of scale over the entire range of output, the long-run average cost curve will be
  • U-shaped
  • upward sloping
  • downward sloping
  • horizontal
  • below the marginal cost curve
整个产量范围都有规模经济 → LRATC 一路向下倾斜（这是自然垄断的成本条件，Unit 4）。
T152024 AP Micro Q33
In the long run, if a firm increases all inputs by 5%, the firm's output increases by 8%. The firm is
  • operating in an industry with low barriers to entry
  • experiencing increasing returns to scale
  • producing at the minimum efficient scale
  • experiencing constant returns to scale
  • experiencing diseconomies of scale
所有投入增加 5%，产出增加 8%（多于 5%）→ 规模报酬递增。
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FRQFree-Response Practice 自由问答

前两道是 AP 真题（产量表 + 成本，是本册最常见的 FRQ 形式），最后一道是原创综合题。先在纸上完整作答，再展开对照。

FRQ 1 · 2017 AP Micro FRQ Q2 · 5 分 · 规模报酬、边际产量、平均总成本 真题

The table below shows the output a firm produces using different amounts of capital (K) and labor (L). The markets for capital and labor are perfectly competitive. The rental rate of capital is $75 per unit, and the wage rate is $200 per unit. In the short run, capital is fixed and labor is variable.

LaborOutput with K = 1Output with K = 2
000
11020
22550
33875

(a) If the firm uses one unit of capital and one unit of labor, will it be operating with constant, increasing, or decreasing returns to scale? Explain using numbers from the table.
(b) Assume now that the firm currently has two units of capital and is using three units of labor.
  (i) Calculate the marginal product for the third unit of labor. Show your work.
  (ii) Did the firm experience diminishing marginal returns with the addition of the third unit of labor? Explain using numbers from the table.
  (iii) Calculate the firm's average total cost for its current level of production. Show your work.
  (iv) If the firm's output is sold in a competitive market, what is the lowest output price at which the third unit of labor would be hired?

Point得分要求与解析（依照 College Board 官方 Scoring Guidelines 整理）
(a) 1 ptIncreasing returns to scale：K、L 都从 1 翻倍到 2，产量从 10 增加到 50（超过翻倍）；或者 ATC 从 (75 + 200) ÷ 10 = $27.50 降到 (150 + 400) ÷ 50 = $11。
(b)(i) 1 ptMP = (75 − 50) ÷ (3 − 2) = 25。
(b)(ii) 1 ptYes：第 3 个工人的 MP（25）小于第 2 个工人的 MP（50 − 20 = 30）。
(b)(iii) 1 ptATC = (2 × 75 + 3 × 200) ÷ 75 = 750 ÷ 75 = $10（或 AFC 2 + AVC 8）。
(b)(iv) 1 pt第 3 个工人多生产 25 单位，这 25 单位的边际成本 = 200 ÷ 25 = $8；价格至少等于 MC 才值得雇 → P = $8（等价地：P × 25 ≥ $200）。
FRQ 2 · 2024 AP Micro FRQ Set 2 Q2 · 5 分 · Lowen Feline 产量表 真题

The table provided shows the short-run production function for Lowen Feline, a profit-maximizing firm that produces cat food. Lowen Feline sells as many bags of cat food as it wants at a market price of $10 per bag and hires as many workers as it wants at a market wage of $18.

Number of Workers0123456789
Total Quantity of Cat Food (bags)051218232730323332

(a) Lowen Feline's fixed cost is $90. Calculate the average fixed cost if Lowen Feline hires 6 workers. Show your work.
(b) Assume labor is the only variable input to Lowen Feline. Calculate the marginal cost if Lowen Feline increases output from 27 to 30 units. Show your work.
(c) With the hiring of which worker do diminishing marginal returns begin? Explain using numbers.
(d) Determine the profit-maximizing number of workers Lowen Feline will hire. Explain using marginal analysis.
(e) In the long run, a rival company, Gato Food, increases its production from 40 to 50 units, and its total cost increases from $600 to $900. Over the output range of 40 to 50 units, is Gato Food experiencing economies of scale, diseconomies of scale, or constant returns to scale? Explain using numbers.

提示(d) 要用到下册 3.5 的“价格 = MR 与 MC 比较”。可以先用本册的 MC = w ÷ MP 算出每个工人对应的 MC，学完下册再回来核对思路。
Workers123456789
MP57654321−1
MC = 18 ÷ MP3.62.5733.64.56918—
Point评分要点与解析（本讲义按官方题目自行整理，非官方评分标准）
(a) 1 pt6 个工人生产 30 袋：AFC = 90 ÷ 30 = $3。
(b) 1 pt从 27 到 30 袋要多雇 1 个工人（第 6 个），多花 $18：MC = 18 ÷ (30 − 27) = $6。
(c) 1 pt第 3 个工人：MP 从第 2 个工人的 7 降到第 3 个工人的 6。
(d) 1 pt7 个工人。第 7 个工人带来的 2 袋的 MC = 18 ÷ 2 = $9 < P = MR = $10，值得雇；第 8 个工人的 MC = 18 ÷ 1 = $18 > $10，不雇。（等价地：第 7 个工人带来收入 10 × 2 = $20 > 工资 $18，第 8 个只带来 $10 < $18。）
(e) 1 ptDiseconomies of scale：LRATC 从 600 ÷ 40 = $15 升到 900 ÷ 50 = $18。
FRQ 3 · 综合练习 · 7 分 · 蛋糕店的成本表 原创

A bakery produces cakes. In the short run, its oven is fixed and the fixed cost is $60 per day. The table shows the bakery's total cost.

Cakes per day0123456
Total cost ($)6090110125145175215

(a) Calculate the marginal cost of the 4th cake. Show your work.
(b) Assume labor is the only variable input. With the production of which cake do diminishing marginal returns begin? Explain using numbers.
(c) Calculate the average variable cost and the average total cost of producing 5 cakes. Show your work.
(d) At what output is average total cost minimized? Explain using the relationship between marginal cost and average total cost.
(e) The city charges the bakery a license fee of $30 per day, no matter how many cakes it bakes. At 5 cakes, will average variable cost, average total cost, and marginal cost increase, decrease, or stay the same?
(f) Instead, the price of flour rises so that every cake costs $2 more to produce. Will marginal cost and average fixed cost increase, decrease, or stay the same?
(g) In the long run, the owner can build a bigger kitchen. With the bigger kitchen, producing 12 cakes per day costs $360 in total. Compared with producing 5 cakes in the current kitchen, is the bakery experiencing economies of scale, diseconomies of scale, or constant returns to scale? Explain using numbers.

q123456
MC302015203040
AVC302521.6721.252325.83
ATC905541.6736.253535.83
Point得分要求与解析
(a) 1 ptMC4 = 145 − 125 = $20。
(b) 1 pt第 4 个蛋糕：MC 依次为 30、20、15、20，第 4 个蛋糕的 MC 开始上升。工资不变时 MC = w ÷ MP，MC 上升说明 MP 下降。
(c) 1 ptAVC = (175 − 60) ÷ 5 = $23；ATC = 175 ÷ 5 = $35（两个都对才得分）。
(d) 1 pt5 个：第 5 个蛋糕的 MC（30）低于此前的 ATC（36.25），把 ATC 拉低到 35；第 6 个的 MC（40）高于 35，把 ATC 拉高到 35.83。MC 在 ATC 最低点穿过它。
(e) 1 ptAVC 不变（$23），ATC 上升（多 30 ÷ 5 = $6，变成 $41），MC 不变。许可费是固定成本。
(f) 1 ptMC 上升（每个蛋糕多 $2），AFC 不变。面粉是可变成本。
(g) 1 ptEconomies of scale：长期平均成本从 175 ÷ 5 = $35 降到 360 ÷ 12 = $30，产量增加、平均成本下降。
FRQ 答题提醒
  • “Show your work” 要写出算式，例如 “AFC = 90 ÷ 30 = $3”，只写结果可能不得分。
  • “Explain using numbers” 要写出比较的两个数，例如 “MP falls from 7 to 6”。
  • 判断边际报酬递减看 MP 是否下降，不是看 MP 是否为负；只有一种可变投入时，也可以看 MC 是否开始上升。
  • 规模经济题要先算出两个产量的 LRATC 再比较，不要只比较总成本。
接下来 · 下册 本册的成本曲线在下册里会变成企业做决定的工具：会计利润与经济利润、MR = MC、停产点与收支相抵点、完全竞争的短期和长期均衡。
→ 打开 Unit 3（下）Profit and Perfect Competition（与本文件放在同一文件夹）

JL · AP Microeconomics · Unit 3（上）Production and Costs · 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 年选择题的答案为自行验算） · 原创 依照 AP 题型原创