生产、成本与完全竞争模型

AP 微观经济学 · 第 3 主题

训练

讲义词汇表

3.1

生产函数

大纲

Enduring Understanding	Learning Objective	Essential Knowledge
PRD-1 Firms' production and cost constraints over different input and output levels shape optimal decisions in the short run and long run.	PRD-1.A a. Define (using graphs where appropriate) key terms and concepts relating to production and cost. b. Explain (using graphs where appropriate) how production and cost are related in the short run and long run. c. Calculate (using data from a graph or table as appropriate) the various measures of productivity and short-run and long-run costs.	PRD-1.A.1 The production function explains the relationship between inputs and outputs both in the short run and the long run. PRD-1.A.2 Marginal product and average product change as input usage changes, and hence, total product changes. PRD-1.A.3 Diminishing marginal returns occur as the firm employs more of one input, holding other inputs constant, to produce a product (output) in the short run.

来源:美国大学理事会 AP 课程与考试说明

生产函数(production function)把投入连接到产出。在短期(short run)至少一个投入(通常是资本)是固定(fixed)的;在长期(long run)所有投入都变化。

总产量(total product)是总产出。
边际产量(marginal product)(MP)是来自多一单位可变投入(通常是劳动)的额外产出:$MP=\dfrac{\Delta\ \text{output}}{\Delta\ \text{labor}}$。
平均产量(average product)是每个工人的产出。

随着你把工人加到固定的资本,MP 最终下降——边际收益递减法则(law of diminishing marginal returns)。MP 的这个形状是驱动下面成本曲线形状的东西。

词汇表训练

英文	中文	拼音
production function	生产函数	shēng chǎn hán shù
short run	短期	duǎn qī
fixed	固定	gù dìng
long run	长期	cháng qī
Total product	总产量	zǒng chǎn liàng
Marginal product	边际产量	biān jì chǎn liàng
Average product	平均产量	píng jūn chǎn liàng
law of diminishing marginal returns	边际收益递减法则	biān jì shōu yì dì jiǎn fǎ zé

练习卷

3.2

短期生产成本

大纲

Enduring Understanding	Learning Objective	Essential Knowledge
PRD-1 Firms' production and cost constraints over different input and output levels shape optimal decisions in the short run and long run.	PRD-1.A a. Define (using graphs where appropriate) key terms and concepts relating to production and cost. b. Explain (using graphs where appropriate) how production and cost are related in the short run and long run. c. Calculate (using data from a graph or table as appropriate) the various measures of productivity and short-run and long-run costs.	PRD-1.A.4 Fixed costs and variable costs determine the total cost. PRD-1.A.5 Marginal cost, average (fixed, variable, and total) cost, total cost, and total variable cost change as total output changes, but total fixed cost remains constant at all output levels, including zero output. PRD-1.A.6 Production functions with diminishing marginal returns yield an upward-sloping marginal cost curve. PRD-1.A.7 Specialization and the division of labor reduce marginal costs for firms. PRD-1.A.8 Cost curves can shift in response to changes in input costs and productivity.

来源:美国大学理事会 AP 课程与考试说明

短期成本曲线

成本分成固定和可变:

短期边际、平均和平均可变成本曲线

固定成本(fixed cost)(FC)不随产出变化(工厂的租金)。
可变成本(variable cost)(VC)随产出上升(材料、劳动)。
总成本(total cost)$TC=FC+VC$。

每单位成本最重要:

平均固定成本(average fixed cost)$AFC=FC/Q$ 持续下降(分摊固定成本)。
平均可变成本(average variable cost)$AVC=VC/Q$ 和平均总成本(average total cost)$ATC=TC/Q$ 是 U 形的。
边际成本(marginal cost)$MC=\dfrac{\Delta TC}{\Delta Q}$ 是多一单位的成本。

两个关键事实:MC 是 MP 的镜像(当 MP 上升时,MC 下降,反之亦然),而 MC 在它们的最小点切 AVC 和 ATC 两者(当边际低于平均时,平均下降;当高于时,它上升)。

Worked example. 一个企业有固定成本 $FC=\$100$。在 $Q=10$ 它的总成本是 $\$300$,所以可变成本是 $\$200$:那么 $ATC=\tfrac{300}{10}=\$30$、$AVC=\tfrac{200}{10}=\$20$,而 $AFC=\tfrac{100}{10}=\$10$(注意 $AFC+AVC=ATC$)。若把产出提高到 $Q=11$ 把总成本推到 $\$325$,那第 $11$ 单位的边际成本是 $\dfrac{\Delta TC}{\Delta Q}=\dfrac{325-300}{1}=\$25$。

探索

Explore the U-shaped cost curves

As output rises, marginal cost eventually climbs (diminishing returns) and cuts through the U-shaped average cost at its minimum — the most efficient scale.

词汇表训练

英文	中文	拼音
Fixed cost	固定成本	gù dìng chéng běn
Variable cost	可变成本	kě biàn chéng běn
Total cost	总成本	zǒng chéng běn
Marginal cost	边际成本	biān jì chéng běn

练习卷

3.3

长期生产成本

大纲

Enduring Understanding	Learning Objective	Essential Knowledge
PRD-1 Firms' production and cost constraints over different input and output levels shape optimal decisions in the short run and long run.	PRD-1.A a. Define (using graphs where appropriate) key terms and concepts relating to production and cost. b. Explain (using graphs where appropriate) how production and cost are related in the short run and long run. c. Calculate (using data from a graph or table as appropriate) the various measures of productivity and short-run and long-run costs.	PRD-1.A.9 In the long run, firms can adjust all their inputs, and as a result, all costs become variable. PRD-1.A.10 The relationship between inputs and outputs in the long run is described by the scale of production—increasing, decreasing, or constant returns to scale. PRD-1.A.11 The long-run average total cost is characterized by economies of scale, diseconomies of scale, or constant returns to scale (efficient scale). PRD-1.A.12 The minimum efficient scale plays a role in determining the concentration of firms in a market and the market structure.

来源:美国大学理事会 AP 课程与考试说明

在长期所有投入——包括工厂规模——都能变化,所以只有长期平均总成本(LRATC)(long-run average total cost)曲线重要。它的形状显示规模报酬:

长期平均成本曲线上的规模经济和规模不经济

规模经济(economies of scale):LRATC 随着产出增长而下降(批量购买、专业化)。
规模报酬不变(constant returns to scale):LRATC 平坦。
规模不经济(diseconomies of scale):LRATC 上升(一个太大而不能好好管理的企业)。

考试技能: 知道"收益递减"是一个短期思想(一个固定投入)而"规模经济"是一个长期思想(所有投入变化)——考官考查这个区别。

词汇表训练

英文	中文	拼音
Economies of scale	规模经济	guī mó jīng jì
Diseconomies of scale	规模不经济	guī mó bù jīng jì

练习卷

3.4

利润的类型

大纲

Enduring Understanding	Learning Objective	Essential Knowledge
CBA-2 To determine the optimal level at which to pursue an activity whose total benefits exceed total cost, rational economic agents compare marginal benefits and marginal costs.	CBA-2.C a. Define the different types of profit. b. Explain how firms respond to profit opportunities. c. Calculate a firm's profit or loss.	CBA-2.C.1 Firms respond to economic profit (loss) rather than accounting profit. CBA-2.C.2 Accounting profit fails to account for implicit costs (such as cost of financial capital, compensation for risk, or an entrepreneur's time), which, if fully compensated, result in normal profit.

来源:美国大学理事会 AP 课程与考试说明

经济学家计入所有机会成本,包括所有者的:

显性成本(explicit costs)是自掏腰包的支付;隐性成本(implicit costs)是所有者提供资源的机会成本(放弃的薪水、放弃的利息)。
会计利润(accounting profit)$=$ 收入 $-$ 显性成本。
经济利润(economic profit)$=$ 收入 $-$ 显性 $-$ 隐性成本。

因为经济利润减去更多,它更小。零经济利润(一个正常利润(normal profit))仍然意味着所有者赚取恰好他们资源的机会成本——一个完全可接受的结果。

Worked example. 一个店主收入 $\$200{,}000$ 并付 $\$120{,}000$ 显性成本,所以会计利润是 $\$80{,}000$。但她放弃了别处一个 $\$70{,}000$ 的薪水和她投资的储蓄上 $\$5{,}000$ 的利息—— $\$75{,}000$ 的隐性成本。她的经济利润是 $80{,}000-75{,}000=\$5{,}000$:仍然为正,所以留在生意里真正击败她下一个最好的替代。

词汇表训练

英文	中文	拼音
Explicit costs	显性成本	xiǎn xìng chéng běn
implicit costs	隐性成本	yǐn xìng chéng běn
Accounting profit	会计利润	kuài jì lì rùn
Economic profit	经济利润	jīng jì lì rùn
normal profit	正常利润	zhèng cháng lì rùn

练习卷

3.5

利润最大化

大纲

Enduring Understanding	Learning Objective	Essential Knowledge
CBA-2 To determine the optimal level at which to pursue an activity whose total benefits exceed total cost, rational economic agents compare marginal benefits and marginal costs.	CBA-2.D a. Define (using graphs or data as appropriate) the profit-maximizing rule. b. Explain (using a graph or data as appropriate) the profit-maximizing level of production.	CBA-2.D.1 Firms are assumed to produce output to maximize their profits by comparing marginal revenue and marginal cost.

来源:美国大学理事会 AP 课程与考试说明

每个企业,在每个市场结构里,在边际收入等于边际成本的数量最大化利润:

$$MR=MC.$$

生产每个 MR 超过它 MC 的单位;在它们相等时停止。生产更少留下未制造的有利可图的单位;生产更多添加花费比它们赚的更多的单位。

练习卷

3.6

企业的短期生产决策与长期进入或退出市场的决策

大纲

Enduring Understanding	Learning Objective	Essential Knowledge
PRD-2 Firms' short-run decisions to produce output, and long-run decisions to enter or exit a market, are based on profitability.	PRD-2.A Explain (using graphs or data where appropriate) firms' short-run decisions to produce positive output levels, or long-run decisions to enter or exit a market in response to profit-making opportunities.	PRD-2.A.1 In the short run, firms decide to operate (i.e., produce positive output) or shut down (i.e., produce zero output) by comparing total revenue to total variable cost or price to average variable cost (AVC). PRD-2.A.2 In the absence of barriers to entry or exit, in the long run (i.e., once factors that are fixed in the short run become variable), firms enter a market in which there are profit-making opportunities and exit a market when they anticipate economic losses.

来源:美国大学理事会 AP 课程与考试说明

即使在 $MR=MC$,一个企业必须检查是否运营:

短期——停业规则: 只有当价格覆盖平均可变成本($P\geq AVC$)时才继续生产。若 $P,停业并只损失固定成本。所以企业的短期供给曲线是它最小 AVC 之上的 MC 曲线。
利润检查: 在利润最大化数量把 $P$ 与 $ATC$ 比较—— $P>ATC$ 意味着经济利润、$P 意味着一个损失、$P=ATC$ 意味着盈亏平衡。
长期——进入和退出: 经济利润吸引进入(entry);损失造成退出(exit)。这继续直到经济利润是零。

词汇表训练

英文	中文	拼音
entry	进入	jìn rù
exit	退出	tuì chū

练习卷

3.7

完全竞争

大纲

Enduring Understanding	Learning Objective	Essential Knowledge
PRD-3 Even with a common goal of profit-maximization, market structure constrains and influences prices, output, and efficiency.	PRD-3.A a. Define (using graphs as appropriate) the characteristics of perfectly competitive markets and efficiency. b. Explain (using graphs where appropriate) equilibrium and firm decision making in perfectly competitive markets and how prices in perfectly competitive markets lead to efficient outcomes. c. Calculate (using data from a graph or table as appropriate) economic profit (loss) in perfectly competitive markets.	PRD-3.A.1 A perfectly competitive market is efficient. Firms in perfectly competitive markets face no barriers to entry and have no market power. PRD-3.A.2 In perfectly competitive markets, prices communicate to consumers and producers the magnitude of others' marginal costs of production and marginal benefits of consumption and provide incentives to act on that information (i.e., price equals marginal cost in an efficient market). PRD-3.A.3 In perfectly competitive markets, firms can sell all their outputs at a constant price determined by the market. PRD-3.A.4 At a competitive market equilibrium, firms are price takers and select output to maximize profit by producing the level of output where the marginal cost equals marginal revenue (at the price). PRD-3.A.5 At a competitive market equilibrium, the price of a product equals both the private marginal benefit received by the last unit consumed and the private marginal cost incurred to produce the last unit, thus achieving allocative efficiency. PRD-3.A.6 In a short-run competitive equilibrium, price can either be above or below its long-run competitive level resulting in profits or losses, motivating entry or exit of firms and moving prices and quantities toward long-run equilibrium. PRD-3.A.7 In a long-run perfectly competitive equilibrium, productive efficiency implies all operating firms produce at efficient scale, price equals marginal cost and minimum average total cost, and firms earn zero economic profit. PRD-3.A.8 Firms may be in a constant cost, increasing cost, or decreasing cost industry. Long-run prices depend on the portion of the long-run cost curves on which firms operate. PRD-3.A.9 A perfectly competitive market in long-run equilibrium is allocatively and productively efficient.

来源:美国大学理事会 AP 课程与考试说明

一个完全竞争(perfectly competitive)市场有许多小企业、一个相同(同质)的产品、自由进入和退出,和完美的信息。每个企业是一个价格接受者(price taker)——太小而不能影响价格——所以它在市场价格面对一条水平需求曲线,而价格 = 边际收入 = 平均收入($P=MR=AR$)。

这就是经济学家看重完全竞争的原因。在长期均衡中,它既是配置有效的(allocatively efficient)又是生产有效的(productively efficient)。配置效率成立,是因为企业在 $P = MC$ 处生产:价格(社会从最后一单位获得的边际收益)等于它的边际成本,所以恰好生产了正确的数量。生产效率成立,是因为自由进入把价格压到平均总成本的最低点,所以商品以尽可能低的成本生产。市场价格本身就是一个信号,传达每个人的边际成本和边际收益。

市场设定价格;价格接受的企业在 MC = P 处生产,这里带短期利润

并排的面板是考试想要的图:市场(左)固定价格 $P^{*}$;企业(右)把它作为一条水平线接受并在 $MC=P$ 处生产。当 $P>ATC$ 时有一个短期利润(阴影框);那个利润吸引进入,它使市场供给右移并把价格推低。

一个完全竞争的企业在长期只赚正常利润

短期: 企业能赚利润、盈亏平衡,或承受一个损失,在 $P=MC$ 处生产。
长期: 进入和退出驱动企业到零经济利润,在 $P=MC=ATC$ 处以最小 ATC 生产。这个双重效率——生产效率(productive efficiency)(最低成本产出)和配置效率(allocative efficiency)($P=MC$,所以最后一单位的价值等于它的成本)——是评判每个其他市场结构的基准。

考试技能: 能够画并排的市场和单个企业图、显示一个短期利润或损失,然后显示进入/退出如何在最小 ATC 恢复长期均衡。

探索

A price-taking firm in a competitive market

In perfect competition the market sets the price and each firm is a price-taker. It produces where price equals marginal cost, earning zero economic profit in the long run.

词汇表训练

英文	中文	拼音
perfectly competitive	完全竞争	wán quán jìng zhēng
price taker	价格接受者	jià gé jiē shòu zhě
allocatively efficient	配置效率	pèi zhì xiào lǜ
productively efficient	生产效率	shēng chǎn xiào lǜ

练习卷

3.7

考试技巧

知道成本曲线:AFC 下降、ATC/AVC 是 U 形的,而 MC 在它们的最小点切 ATC 和 AVC。
每个企业在 MR = MC 最大化利润;检查停业规则(短期 $P \ge AVC$)。
把会计利润(收入 − 显性成本)与经济利润(也减隐性/机会成本)区分开;零经济利润是正常的。
"收益递减"是短期(一个固定投入);"规模经济"是长期(所有投入变化)。
在完全竞争 $P=MR=AR$;进入/退出驱动长期经济利润到最小 ATC 处的零。

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