AP Microeconomics - 究极拖延症患者尝试补救

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本文标题:AP Microeconomics - 究极拖延症患者尝试补救

文章作者:gyro永不抽风

发布时间:2020年03月16日 - 18:03

最后更新:2021年01月14日 - 14:01

原始链接:http://hexo.gyrojeff.moe/2020/03/16/AP-Microeconomics-%E7%A9%B6%E6%9E%81%E6%8B%96%E5%BB%B6%E7%97%87%E6%82%A3%E8%80%85%E5%B0%9D%E8%AF%95%E8%A1%A5%E6%95%91/

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Production Possibility Frontier (PPF) - 生产可能性边界

  • PPF 向外凸起
  • 线上:Efficient,线外:Impossible,线内:Inefficient
不存在Most Efficient
向外凸起的原因:OC不断增加(Law of Increasing Opportunity Cost)

Circular-Flow Diagram - 循环流向图

Leakages - 漏出/流出

可以理解为在整个图当中,**** 少了

  • Savings - 储蓄(人们把一部分钱存起来,市场上钱少了)
  • Taxation - 税收(市场上的钱给了政府,钱少了)
  • Imports - 进口(花钱买别人的东西,钱少了)

Leakages - 漏出/流出

可以理解为在整个图当中,****多了

  • Investment - 投资(投资者的钱进入市场,钱多了)
  • Government Spending - 市政开销(政府花钱,钱流入市场,钱多了)
  • Exports - 出口(东西卖给别人,钱多了)

Absolute Advantage & Comparative Advantage - 绝对优势与比较优势

  • Absolute Advantage - 单位时间内能生产出更多的商品
  • Comparative Advantage - 能以更小的机会成本来生产
机会成本:为了得到某东西而必须放弃的东西,在题目中如果只有两种商品可以用来被生产,那么单位时间内生产一单位某商品的OC就是单位时间内生产另外一种商品的能力除以此商品的产量。
注意:单位是unit,而不是时间(可以通过倒数转换)
在题目中两个商品的情况,不可能生产两个商品都有比较优势

Demand & Supply - 需求和供给

Demand和Quantity of Demand

  • Demand是指整个需求 ——– 整个曲线
  • Quantity of Demand是指需求量 ——– 曲线上的点

Supply和Quantity of Supply

同上

Law of Demand - 需求定律

在其他条件不变的情况下,当某商品的价格上升时,该商品的需求量下降。

$$
P \uparrow ~~~~\longrightarrow ~~~~ Q_D \downarrow
$$

物以稀为贵

Law of Supply - 供给定律

在其他条件不变的情况下,某商平的供给量随着它的价格的上升而增加。

$$
P \uparrow ~~~~ \longrightarrow ~~~~ Q_S \uparrow
$$

商品分类

Normal Good & Inferior Good - 正常商品 / 低档商品

  • Normal Good : 人们有钱以后想买的东西
  • Inferior Good : 人们有钱以后不想买的东西

Substitutes & Complements - 替代品 / 互补品

  • Substitutes : 一个东西卖得好,另外一个东西卖的差
  • Complements : 一个东西卖得好,另外一个东西也随之卖得好

Control on Prices - 价格管制

Price Ceiling - 价格天花板

Price Floor - 价格地板

Taxation - 税收

结论1:税收由缺乏弹性的一方承担得较多
结论2:可以通过税收wedge来计算

Business cycle - 经济周期

Definition: Fluctuations in economic activity, such as employ- ment and production.

螺旋上升
划分:2~10年的扩张和收缩

$$
\bbox[#EFF,15px,border:2px solid green]{\color{black}{\text {Prosperity - 繁荣} \rightarrow \color{red}{\text {Peak}} \color{black}{\rightarrow \text {Recession - 衰退}} \rightarrow \text {Depression - 萧条} \rightarrow \color{red}{\text {Trough}} \color {black}{\rightarrow \text {Recovery - 复苏}}}}
$$

Elasticity - 弹性

弹性描述的是一个量对于另一个量变化的反应程度

$$
\varepsilon_{yx} = \lim _{ \Delta x \rightarrow 0} \frac {\Delta y} y \Big / \frac {\Delta x} x = y’ \cdot \frac x y
$$

记忆方法:一般来说,弹性都是xxx除以一个价格

需求价格弹性

衡量某商品的需求量对其自身价格变动的反应程度

影响因素

  1. 相近商品的可得性 Availability of Cloase Substitues: 具有相近替代品的商品,一般需求弹性较大
    通俗理解:如果有替代品,你涨价,我就去买别人,所以这个对价格的变化需求量就会变化很大,所以弹性较大
  2. 必需品和奢侈品 Necessities versus Luxuries: 必需品(necessities)通常而言缺乏弹性,奢侈品(luxuries)通常富有弹性
    理解方法:刚需的弹性为零。奢侈品在涨价后,既然是奢侈品,那么可买可不买,所以奢侈品对价格的变动其需求量变化较大,弹性较大
  3. 市场的定义 Definition of the Market: 狭义市场比广义市场更有需求弹性
    理解方法:举个例子,如果要买纸巾:单一品牌纸巾的市场,相比于所有纸巾所构成的市场,弹性较大,因为整个市场需求量差不多是固定的,而一个品牌如果涨价,消费者就回去寻找替代品,这个和第一条规则类似
  4. 时间维度 Time Horizon: 某商品的长期需求通常比短期需求更加具有弹性
    理解方法:我加钱可以一点一点的涨,到头来还是要买

计算方法

$$
\varepsilon = \frac {\Delta Q_D %}{\Delta P %} = \frac {\Delta Q_D}{\Delta P} \frac P {Q_D}
$$

这个弹性通常取绝对值
计算方法:中点法,即$P = \displaystyle\frac {P_1 + P_2} 2$

衡量

  • $\varepsilon > 1$ : Elastic
  • $\varepsilon = 1$ : Unit Elasticity
  • $\varepsilon < 1$ : Inelastic
  • $\varepsilon \rightarrow \infty$ : Perfectly Elastic
  • $\varepsilon = 0$ : Perfectly Inelastic
记忆方法:完全没有弹性,此时$\varepsilon = 0$,这个产品是刚需,就算多贵都得买

线性需求曲线

结论:线性需求曲线的中点弹性为1,越往上弹性越大,越往下弹性越小
Linear Demand Curve Created with Sketch. Linear Demand Curve - 线性需求函数 中点,弹性为1 刚需,弹性为0 弹性为∞ 这一段越往上越大,→∞ 这一段越往下越小,→0 Quantity Price

与Revenue之间的关系

对于Inelastic的商品

$$
P \uparrow~~~~ \longrightarrow~~~~ \text {revenue} \uparrow
$$

对于Elastic的商品

$$
P \uparrow ~~~~ \longrightarrow ~~~~ \text {revenue} \downarrow
$$

需求收入弹性

$$
\varepsilon = \frac {\Delta {Q_D}%} {\Delta \text {Income} %}
$$

  • 正常商品(Normal Goods) : $\varepsilon > 0$ (可理解为需求随工资的增高而增高)
  • 低档商品(Inferior Goods) : $\varepsilon < 0$ (可理解为需求随工资的增高而降低)

需求的交叉价格弹性

$$
\varepsilon = \frac {\Delta Q_{D1} %}{\Delta P_2%}
$$

  • 替代品(Subtitutes) : $\varepsilon > 0$ (可理解为,一个东西需求增高,另一个东西价格也升高,意味着其需求降低,那么两者就位替代品)
  • 互补品(Complements) : $\varepsilon < 0$ (可理解为,一个东西需求增高,另一个东西价格降低,意味着其需求增高,那么两者就位互补品)

供给弹性

衡量供给量对商品价格变动的反应程度

影响的Factors

  1. 卖方变动自己产量的灵活性
    举个例子:买海滨别墅的inelastic,卖书的elastic
  2. 时间维度:长期弹性更大
    和需求价格弹性相同

计算

$$
\varepsilon = \frac {\Delta Q_S %}{\Delta P %} = \frac {\Delta Q_S}{\Delta P} \frac P {Q_S}
$$

这个弹性通常取绝对值
计算方法:中点法,即$P = \displaystyle\frac {P_1 + P_2} 2$
骂人:Next的Note有bug,竟然相同的标题找不到索引,淦

衡量标准

过原点的直线才具有$\varepsilon = 0$(懒得证明了)

注:这里判断弹性的情况和上面的方法相同:越陡峭越缺乏弹性,越躺倒越具有弹性

Welfare Economics - 福利经济学

消费者、生产者和市场的效率

重要概念

  1. Consumer Surplus = Value to buyers – Amount paid by buyers = 需求曲线之下,价格线之下的面积
  2. Producer Surplus = Amount received by sellers – Cost to sellers = 供给曲线之上,价格线之下的面积
  3. Total Surplus = CS + PS = Willingness To Pay - Cost,体现市场效率
  4. 边际买者:价格提高后,第一个离开市场的人
  5. 边际卖者:价格下降后,第一个离开市场的人
背诵:离开市场!!!

图像

征税的代价 - 产生Deadweight Loss

International Trade - 国际贸易

要点

  1. 开放国际贸易,就要接受国际的价格
  2. 如果World Price > Domestic Price,出口
  3. 如果World Price < Domestic Price,进口
  4. Tariff有无谓损失,Quota没有
  5. Tariff政府拿得到钱,有Tax Revenue,Quota没有

国际贸易的图像

国际贸易的好处

  1. 商品多样性增加
  2. 规模经济降低成本(economies of scale)
  3. 竞争程度增加
  4. 科技流动性增加

企业行为

Diminishing Marginal Product - 边际产量递减效应

随着工人的数量增加,边际产量递减

Profit Maximizing - 利润最大化

Profit Maximizing - 发生在 MC = MR

企业都是有minimize cost的incentive的(企业想让ATC变小不一定一定需要靠改变产量)

不同的Efficiency

Productive Efficiency - 生产最有效率

生产最有效率是 ATC的最低点

此时生产的费用是最低的,所以称Productive Efficiency

Allocative Efficiency - 分配最有效率

分配最有效率是 P = MC = Demand

这里就是需求 = 供给(MC曲线等同于Supply曲线)

经济利润相关

Implicit Cost - 隐性成本

会计利润等于 $\text {Accounting Profit} = \pi + \text {Implicit Cost}$

Economic Profit - 经济利润

经济利润等于 $\pi = (P - ATC) \times Q$

Accounting Profit - 会计利润

只要有会计利润,就是赚钱的(因为经济利润还计算了机会成本OC)

Economies of Scale - 规模经济

  • $\text {Q} \uparrow \rightarrow \text {ATC} \downarrow$ 称为 economies of scale - 规模经济
    长期ATC下降
  • $\text {Q} \uparrow \rightarrow \text {ATC} 不变$ 称为 constant return to scale - 规模报酬不变
    长期ATC不变
  • $\text {Q} \uparrow \rightarrow \text {ATC} \uparrow$ 称为 diseconomies of scale - 规模不经济
    长期ATC上升
这里,自变量是Q,因变量是ATC

returns to scale - 规模报酬

设生产函数为

$$
Y = A(1, \frac K L, \frac H L, \frac N L)
$$

将所有生产要素的投入扩大$\alpha$倍,产出随之扩大$\delta$倍

$$
\delta Y = A(\alpha + \alpha \frac K L, \alpha \frac H L, \alpha \frac N L)
$$

$\delta > \alpha$ 产出扩大的倍数更多,increasing return to scale
$\delta = \alpha$ 产出扩大的倍数和投入相等,constant return to scale
$\delta < \alpha$ 产出扩大的倍数少,decreasing return to scale

短期和长期

短期成本和长期成本

长期会以最低成本进行生产

$\Longrightarrow$所有短期ATC曲线都位于长期ATC曲线之上或上方

长期经营的一个重要事实

All factors of production are variable

对于长期来说,所有的cost都是variable的,所有的生产要素也都是variable的。比方说:可以关停工厂。

Shutdown - 停止营业

如果在** 短期,$P < AVC$ **,就shutdown

Exit - 退出市场

如果在** 长期,$P < ATC$ **,就exit

继续营业

短期,$AVC < P < ATC$,虽然承受损失(sustain a loss),但是仍然继续营业。

Perfectly Competitive Market - 完全竞争市场

完全竞争市场的特征

  1. 无限多的买者和卖者 - Infinite buyers & sells
  2. 所有卖的商品都一样 - All the goods are identical
  3. 可以自由进入或退出 - Firms can freely exit or enter the market

完全竞争市场的特点

企业和消费者都是价格接受者
$AR = MR = P$
长期的经济利润为0(待下去是因为有会计利润)

长期的价格不会改变,过程:

重要:长期由于$\pi = 0$,$ATC$与$P$相切。
在完全竞争市场,短期的supply curve是MC在AVC以上的部分(因为以下的话要shutdown)
重要:市场的供给曲线是一条horizontal line,而firm的供给曲线是MC
重要:Constant Cost Industry如果Demand增加,短期Profit增加。
重要:Increasing Cost Industry如果Demand增加,并不会把价格拉回均衡点,而是直接增加,profit不增加,ATC上移

Monopoly - 完全垄断市场

完全垄断市场特征

A firm that is the sole seller of a product without close substitutes

  1. 唯一的卖者 - Sole seller of a product
  2. 没有替代品 - Without Close Substitute

完全垄断市场的特点(在没有价格歧视的情况下)

完全垄断企业是价格的制定者(Price maker)
$MC=MR$永远是Profit Maximizing的方法(根据边际产量递减效应)
垄断的代价:产生Deadweight Loss
垄断基本上都是Underallocation(不是Allocative Efficient)
存在经济利润,$\pi = (P - ATC) \times Q$
在完全垄断市场当中,一个Firm就是整个市场
完全垄断市场当中:$P > MC = MR$
$MR$和$D$的曲线具有两倍斜率关系
根据线性需求弹性,中点处为Unit Elastic,上面是Elastic且$MR > 0$,下面是$Inelastic$且$MR < 0$。这很好理解(间前面Revenue和Elastic的关系)
如果$\pi = 0$,则应该是$ATC$和$D$的交点

Price Discrimination - 价格歧视

价格歧视就是对不同的人收取不同的费用,当Deadweight Loss完全消除,就是完全价格歧视($P = WTP\text {(Willingness To Pay)} \Rightarrow \text {Perfect Price Discrimination}$)

价格歧视会蚕食掉Consumer Surplus
条件:1. 知道Demand
2. 别人不会转手卖掉(resale)

垄断的公共政策

  1. 反托拉斯法案(Antitrust Law):组织公司间的合并,允许政府拆分公司。增加市场的竞争性
  2. 对垄断行为管制
  3. 将私人垄断企业变成公共事业
  4. 什么也不做(药品专利)

自然垄断

能够以最低的成本生产,长期ATC下降

Monopolistic Competition - 垄断竞争

垄断竞争的特征

  1. 很多的卖者:很多企业竞争相同的客户群体 - Many Sellers
  2. 产品差异化:每个企业生产的和别人的都略有不同,需求曲线向下倾斜 - Product Differentiation
  3. 自由进出市场 - Free entry and exit

垄断竞争的特点

长期经济利润为零(和完全竞争的调节相类似)
长期:$ATC = P > MC$
有过剩生产能力:Excess Capacity
市场的变动:如果需求变大了,产生了经济利润,那么会有企业进入市场,和已有的几家企业抢生意,导致对于每家公司而言,曲线左移,最后还是会达到均衡。反之亦然。
总结:在垄断竞争当中,总体来说是和完全垄断非常类似,因为每个公司都生产不同的商品,但是他们整体看做一个市场考虑,受到调节,所以长期的经济利润为零,ATC与Demand相切(价格)
Advertise的原因:因为大家的产品比较相似,所以打广告就是为了让别人了解到你的产品,想让消费者选择这个产品,让价格弹性变小。yy:$\varepsilon = 0$时是刚需

Oligopoly - 寡头垄断

就是几家企业搞垄断

有Game Theory(博弈论)、Price Leadership、Collusion、Price Wars

Kinked Demand Curve

产生原因:一家人家降价,会导致一起降价。(两倍斜率在每一段仍然存在)
理解2:别人巴不得你提价流失消费者,降价也争相降价。所以上面more elastic,下面less elastic。
由于中间有断点,所以就算MC降低了,TR、P、Q不一定改变。

Nash Equilibrium - 纳什均衡

在没有条约的约束下,人们很可能会毁约,导致纳什均衡
相互作用的经济参与人在给定其他参与人选定的策略的情况下,每个参与人选择自己最优的策略
判断Nash Equilibrium:没有任何incentive to cheat.
有时,并没有Dominant Strategy,但却有两个Nash Equilibrium(Nash Equilibria)

Prisoners’ Dilemma - 囚徒困境

占优策略:”以不变应万变”

Antitrust Law - 反托拉斯法案

主旨:增加市场的竞争性,拆分公司,阻止合并。

一道恶心题

  • Efficiency : 既可以指Allocation,也可以指Productive
  • 在这里两个公司合并,ATC必然下降(因为享受了economies of scales, AFC减少)

几种市场的总结

生产要素市场 - The Markets for the Factors of Production

Input / Factors of Production - 生产要素

  • Labor - 劳动力
  • Human Capital - 人力资本
  • Natural Resources / Land - 自然资源
  • Capital (Physical Capital) - 实物资本

主要研究Labour($L$),也会研究Capital($K$)

劳动的需求和供给的图像

根据前面提到的循环流向图(Circular Flow Diagram),在生产要素市场当中企业是生产要素的购买者,家庭是生产要素的提供者。图像与之前商品市场中的图像基本相同(包括图像变动),不同之处在于纵轴从价格$P$变为了工资$\text{Wages}(W)$,横轴还是$\text{Quantity}(Q)$(只不过是Labour的数量)

在生产要素市场中Profit Maximizing

重要假设:商品市场和生产要素市场都是竞争性的,也就是说企业在这两个市场当中都是Price Taker

根据边际产量递减性质:$\text {Marginal Product of Labour} (MP_L)$是递减的,而每多雇佣一名工人能给企业带来的利润:$\text {Value of the Marginal Product of Labour}(VMPL)$,又称$\text {Marginal Revenue of Product (of Labour)} (MRP_L)$为:$P \times MP_L$。不难理解,只有当工人带来的收益大于成本才会雇佣,即$MRP_L > \text {Wages}$。

生产要素市场当中的Profit Maximizing就是$MRP_L = \text {Wages}$

例如下表:

由上述论述可得:$\color{red}{}VMPL(MRP_L)就是\text{Demand}曲线$

生产要素市场中的选择

和商品市场当中的消费者选择理论相同,生产要素市场当中的选择理论如下:

$$
\frac {MU_1}{P_1} = \frac {MU_2}{P_2}
$$

曲线的移动

总结:凭感觉,实在背不出来一条一条的

劳动需求曲线的移动

  1. 产出物的价格:$P \uparrow \longrightarrow VMPL \uparrow \longrightarrow D \uparrow$
  2. 技术变革
    • 劳动节约型
    • 历史角度:劳动增加型
  3. 其他生产要素的原因

劳动供给曲线的移动

  1. 爱好改变 e.g. 女性参加工作
  2. 其他工作机会的改变
  3. 移民
注:civilian和army相对

Externality - 外部性

人话:干一件事情对别人(外界)的影响
  • Positive Externality: 做一件事对别人有好处
  • Negative Externality: 做一件事对别人有坏处

Negative Externality - 负外部性

负外部性的曲线

理解:因为做一件事对别人有不好的影响,所以供给曲线如果算上社会付出的成本的话,供给曲线需要上移,但是整个需求是没有变化的。

注:注意Social Optima和Market Equilibrium

负外部性的最优实现

外部性内在化(Internalizing the Externality :对生产者进行收税,让生产者考虑自己的行为。

Positive Externality - 正外部性

正外部性的曲线

理解:供给就这么多,没有变,但是因为这些产品有正外部性,对社会有好处,所以社会对这种商品的需求增加了(可以以教育为例)。

正外部性的最优实现

政府补贴:Subsidy

针对外部性的政策

  1. 命令和控制政策(Command-and-Control Policies):直接管制行为
  2. 基于市场的政策(Market-Based Policies):激励私人解决(更有效率)
    • Corrective Taxes(矫正税) / Pigovian Taxes(庇古税)

外部性的私人解决方法

科斯定理(Coase Theorem) :(人话Ver.)如果协商解决不需要成本,那么私人总能解决问题。

交易成本(Transaction Costs):利益相关方在达成和遵守协议的过程中生产的成本。
因为有交易成本,所以私人不一定能解决问题。

物品的性质和种类

物品的性质

  • 排他性(Excludability) :是否能阻止别人用这个东西:你用了别人不能用
  • 竞争性(Rivalry in consumption) :别人用了,就不值钱了

物品的种类

  • 私人物品(Private Goods) :有排他性、有竞争性
    • e.g. 裙子 / 拥挤的收费公路
  • 自然垄断(Natural Monopoly) :有排他性、无竞争性
    • e.g. 消防 / 不拥挤的收费道路
  • 公共资源(Common Resources) :无排他性、有竞争性
    • e.g. 海鱼 / 拥挤的不收费道路
    • 公地悲剧(由负外部性造成):土地是大家的,都放羊,放多了,土地坏掉了,大家都没得放。
  • 公共物品(Public Goods) :无排他性、无竞争性
    • e.g. 国防 / 不拥挤的不收费道路
    • Free Rider Problem,最后有讲。

收入不平等

世界的收入不平等

  • $$衡量标准 = \frac {最富的10%人口的收入}{最穷的10%人口的收入}$$

穷困率 - Poverty Rate

  • 穷困率:家庭收入低于穷困线的人百分比
  • 穷困线:政府制定的标准,低于这个水平就属于生活在贫困之中

洛伦兹曲线和基尼系数 Lorenz Curve & Gini Coefficient

在一个总体(国家、地区)内,以“最贫穷的人口计算起一直到最富有人口”的人口百分比的收入百分比的点组成的曲线。

  • 曲线越靠里,越极端,收入越不平等
  • 曲线越接近 y = x(基准线),收入越平等

零散知识点总结

Free-Rider Problem

烟花的例子

烟花:有人放了就可以看,那么就可以不用买了

具体问题

$$
\text {Free-Rider} \longrightarrow \text{Demand} \downarrow \longrightarrow \text {underproduce}
$$

胜利在望!!最后一章!

消费者选择理论

预算约束 - Budget Constraint

人话:因为只有这么点钱,所以会有限制和约束

无差异曲线 - Indifference Curve

又称Utility Curve。四个性质:

• Property 1: Higher indifference curves are preferred to lower ones. People usually prefer to consume more goods rather than less. This preference for greater quantities is reflected in the indifference curves. As Figure 2 shows, higher indifference curves represent larger quantities of goods than lower indiffer- ence curves. Thus, the consumer prefers being on higher indifference curves.

• Property 2: Indifference curves are downward sloping. The slope of an indiffer- ence curve reflects the rate at which the consumer is willing to substitute one good for the other. In most cases, the consumer likes both goods. Therefore, if the quantity of one good is reduced, the quantity of the other good must increase for the consumer to be equally happy. For this reason, most indiffer- ence curves slope downward.

• Property 3: Indifference curves do not cross. To see why this is true, suppose that two indifference curves did cross, as in Figure 3. Then, because point A is on the same indifference curve as point B, the two points would make the consumer equally happy. In addition, because point B is on the same indif- ference curve as point C, these two points would make the consumer equallyhappy. But these conclusions imply that points A and C would also make the consumer equally happy, even though point C has more of both goods. This contradicts our assumption that the consumer always prefers more of both goods to less. Thus, indifference curves cannot cross.

• Property 4: Indifference curves are bowed inward. The slope of an indifference curve is the marginal rate of substitution—the rate at which the consumer is willing to trade off one good for the other. The marginal rate of substitu- tion (MRS) usually depends on the amount of each good the consumer is currently consuming. In particular, because people are more willing to trade away goods that they have in abundance and less willing to trade away goods of which they have little, the indifference curves are bowed inward. As an example, consider Figure 4. At point A, because the consumer has a lot of Pepsi and only a little pizza, he is very hungry but not very thirsty. To induce the consumer to give up 1 pizza, he has to be given 6 pints of Pepsi: The marginal rate of substitution is 6 pints per pizza. By contrast, at point B, the consumer has little Pepsi and a lot of pizza, so he is very thirsty but not very hungry. At this point, he would be willing to give up 1 pizza to get 1 pint of Pepsi: The marginal rate of substitution is 1 pint per pizza. Thus, the bowed shape of the indifference curve reflects the consumer’s greater willingness to give up a good that he already has in large quantity.

注:不同的IC充满了整个平面

极端的IC曲线

消费者的选择

收入的变动 与 Normal Good 和 Inferior Good

价格的变动 与 Substitution Effect 和 Income Effect

吉芬商品 - Giffen Good

价格增加,需求升高的商品

Utility - 效用

  • 可以理解为benefit。
  • 边际效用 - Marginal Utility
  • 重点:** Diminishing Marginal Utility:消费者拥有某商品越多,在额外增加一单位,带来的快乐低。 **

Optimal Consumption Bundle(重要)

$$\frac {MU_X}{P_X} = \frac {MU_Y}{P_Y}$$

其中,$P$为单价。

AP 2020 特辑

考试信息

  1. 考试时间:北京时间5月21日凌晨4点
  2. 两道FRQ
    • Question 1 (55%): 25 minutes + 5 minutes to upload response
    • Question 2
  3. 删减一个单元
    Unit 6 Market Failure and the role of Government (8% - 13%)
  4. Q1 = FRQ2 + FRQ3
  5. Q2 = FRQ1

考点

Units Exam Weighting
Unit 1: Basic Economic Concepts 12-15%
Unit 2: Supply and Demand 20-25%
Unit 3: Production, Cost, and the Perfect Competition model 22-25%
Unit 4: Imperfect Competition 15-22%
Unit 5: Factor Markets 10-13%

考察重点

  • Unit1需要明确 definition
  • Unit2几乎一定会融合在不同市场形式中考察(Unt3+4+5)
    • 从完全竞争(side- by-side graph)/完全垄断/垄断竞争市场的图像中考察需求、供给曲线,弹性等
  • Unit3-4一定会出1道题
    • 市场之间的转化(垄断竞争完全竞争、寡头垄断-完全垄断)
    • 每个市场的图像变化及结论
  • Unit5有可能单独出题,其中一定会包含Unit2的知识点

Unit 1 - FRQ - 1

Nirali is a student at the University of Ainsley. She has 5 hours to study for two exams today. The tables below show Nirali’s expected scores given the amount of time she studies for each exam.

Number of hours Spent Studying Microeconomics Expected Score on Microeconomics exam (100-point scale)
5 100
4 96
3 90
2 82
1 60
0 0
Number of hours Spent Studying History Expected Score on History exam (100-point scale)
0 0
1 40
2 60
3 72
4 77
5 80

(a) Nirali spends 3 hours studying microeconomics and 2 hours studying history. Calculate her gain from the second hour spent studying history.

Solution: $40 \rightarrow 60$, $20$ points on History Exam.

(b) Calculate Nirali’s opportunity cost of the second hour spent studying history.

Solution: $6$ points on Microeconomics Exam.

(c) Assume Nirali increases the time she allocates to studying history. What happens to the opportunity cost of studying history? Explain

Solution: The opportunity cost of studying history will increase.
Explanation:

  • Method 1: Expected score on Microeconmics decreases at an increasing rate for each hour spent on histroy.
  • Method 2: Marginal cost is increasing.

(d) Assume that nirali has a goal of maximizing the sum of her test scores( the score on microeconomics plus the score on history). How many hours should she study for each exam?

Solution: She should study Microeconomics for $2$ hours and study Histroy for $3$ hours, which will enable her to achieve a total score of $154$ points, the maximum total score she can get.

(e) Nirali learns that her tennis practice has been canceled, freeing up an additional hour for studying. Given your answer to part(d), will Nirali allocate the additional hour to studying microeconomics or to studying history to maximize the sum of her test scores? Explain using marginal analysis

Solution: She will allocate the additional hour to studying microeconomics.
Explanation: Because the marginal benefit of learning an additional hour of microeconomics is $90 - 82 = 8$ points and the marginal benefit of learning an additional hour of history is $77 - 72 = 5$. $8 > 5$.

Unit 1 - FRQ - 2

Sasha is a utility-maximizing consumer who spends all of her income on peanuts and bananas, both of which are normal goods

  • (a) Assume that the last unit of peanuts consumed increased Sasha’s total utility from 40 utils to 48 utils and that the last unit of bananas consumed increased her total utility from 52 utils to 56 utils
    • (i) If the price of a unit of peanuts is SI and Sasha is maximizing utility, calculate the price of a unit of bananas
    • Solution:
      $$\frac {MU_1}{P_1} = \frac {MU_2}{P_2}$$
      Thus the price of banana is $(56 - 52) \div (48 - 40) \times 1 = 0.5$ dollars
    • (ii) If the price of a unit of peanuts increases and the price of a unit of bananas remains unchanged from the price you determined in part(a)(i), how will Sasha’s purchase of peanuts change?
    • Solution: She will purchase less peanuts.
  • (b) Assume that the cross-price elasticity of demand between peanuts and bananas is positive. A widespread disease has destroyed the banana crop. What will happen to the equilibrium price and quantity of peanuts in the short run? Explain
  • (c) Assume that the price of bananas increases.
    • (i) Will the substitution effect increase, decrease, or have no effect on the quantity of bananas demanded?
    • (ii) What happens to Sasha’s real income?

Unit 2 - FRQ - 1

The graph below shows the market for widgets. The government is considering intervening in this market.

  • (a) Calculate the total producer surplus at the market equilibrium price and quantity. Show your work.
  • Solution: $20 \times 20 \div 2 = 200$ dollars
  • (b) If the government imposes a price floor at $16, is there a shortage, a surplus, or neither? Explain
  • Solution: Neither, because the price floor is below the equilibrium, thus it is not binding / not effective / ineffective.
  • (c) If instead the government imposes a price ceiling at $12, is there a shortage, a surplus, or neither? Explain
  • Solution: There will be a shortage, because the price ceiling is below the equilibrium and $Q_D > Q_S$ (Quantity Demanded is greater than Quantity Supplied).
  • (d) If instead the government restricts the market output to 10 units, calculate the deadweight loss. Show your work.
  • Solution: $(40 - 10) \times (20 - 10) \div 2 = 150$ dollars.
  • (e) Assume the price decreases from 20 dollars to 12 dollars.
    • (i) Calculate the price elasticity of demand. Show your work.
    • Solution:
      $$ \text {Elasticity of demand} = \Big |\frac {\Delta Q_D\%}{\Delta P\%}\Big | = \Big |\frac {24 - 20} {\frac {24 + 20} 2} \Big / \frac {12 - 20} {\frac {12 + 20} 2}\Big | = 0.36 $$
    • (ii) In this price range, is demand perfectly elastic, relatively elastic, unit elastic, relatively inelastic, or perfectly inelastic?
    • Solution: Since $\varepsilon < 1$, the demand is relatively inelastic in this price range.

Unit 2 - FRQ - 2

The graph above illustrates the market for calculators. S denotes the current supply curve, and D denotes the demand curve.

  • (a) Calculate the producer surplus before the tax
  • Solution: $(5 - 2) \times 90 \div 2 = 135$ dollars.
  • (b) Now assume a per-unit tax of $2 is imposed whose impact is shown in the graph above.
    • (i) Calculate the amount of tax revenue.
    • Solution: $2 \times 60 = 120$ dollars.
    • (ii) What is the after-tax price that the sellers now keep?
    • Solution: $4$ dollars.
    • (iii) Calculate the producer surplus after the tax.
    • Solution: $(4 - 2) \times 60 \div 2 = 60$ dollars.
  • (c) Is the demand price elastic, inelastic, or unit elastic between the prices of 5 dollars and 6 dollars? Explain.
  • Solution:
    • Method 1:
      $$\varepsilon = \Big | \frac {90 - 60} {75} \Big / \frac {5 - 6} {5.5} \Big | = 2.2$$
      Since $\varepsilon > 1$, the demand price is elastic between the prices of 5 dollars and 6 dollars.
    • Method 2: When price change from $5$ dollars to $6$ dollars, the total revenue decreases, thus the price demand is elastic.
  • (d) Assuming no externalities, how does the tax affect allocative efficiency? Explain
  • Solution:
    • Method 1: It produced deadweight loss.
    • Method 2: The Consumer Surplus and Producer Surplus decreased.

Unit 3 - FRQ - 1

Suppose that roses are produced in a perfectly competitive, increasing-cost industry in long-run equilibrium with identical firms.

  • (a) Draw correctly labeled side-by-side graphs for the rose industry and a typical firm and show each of the following
    • (i) Industry equilibrium price and quantity, labeled $P_m$ and $Q_m$, respectively
    • (ii) The firms equilibrium price and quantity, labeled $P_f$ and $Q_f$ respectively
  • (b) Is $P_m$ larger than, smaller than, or equal to $P_f$?
  • Solution: $P_m = P_f$
  • (c) Assume that there is an increase in the demand for roses On your graphs in part(a), show each of the following.
    • (i) The new short-run industry equilibrium price and quantity, labeled $P_{m2}$ and $Q_{m2}$, respectively
    • (ii) The new short-run profit-maximizing price and quantity for the typical firm, labeled $P_{f2}$ and $Q_{f2}$, respectively
  • (d) As the industry adjusts to a new long-run equilibrium,
    • (i) what will happen to the number of firms in the industry? Explain
    • Solution: The number of firms in the industry will increase. Since the profit $\pi = (P - ATC) \times Q > 0$, the existence profit attracts to enter the industry and there is no barrier of entering the market, there will be more firms in the industry.
    • (ii) Will the firm’s average total cost curve shift upward, shift downward, or remain unchanged?
    • Solution: It will shift upward for the reason that it is an Increasing-cost Industry.
  • (e) In the long run, compare the firm’s profit-maximizing price to each of the following
    • (i) $P_f$ in part(a)(ii)
    • Solution: $P > P_f$, Higher
    • (ii) $P_{f2}$ in part(c)(ii)
    • Solution: $P < P_{f2}$, Lower

Unit 4 - FRQ - 1

In the early twentieth century, limited transportation options and the lack of effective substitutes gave Single Cinema monopoly power in a small town. Assume that Single Cinema is a profit-maximizing firm and currently operates at a negative economic profit in the short run

  • (a) Draw a correctly labeled graph for Single Cinema, and show each of the following
    • (i) The profit-maximizing price and quantity of tickets, labeled as $P_m$ and $Q_m$, respectively
    • (ii) The area representing the negative economic profit, shaded completely
  • (b) Explain why Single Cinema continues to operate in the short run despite earning negative economic profit in the short run
  • Solution: $P > AVC$
  • (c)Would Single Cinema’s total revenue increase, decrease, or stay the same if it decides to sell one fewer ticket than $Q_m$? Explain.
  • Solution:
    • Method 1: $MR > 0$, $TR$ will decrease.
    • Method 2: The demand curve is always elastic when $MR > 0$, thus total revenue will decrease when quantity decrease.
  • (d) Single Cinema hires workers in a perfectly competitive labor market with a downward-sloping demand curve. Suppose the number of workers available in the market decreases
    • (i) What will happen to the wage rate? Explain
    • (ii) What will happen to the marginal revenue product of the last worker hired? Explain

Unit 4 - FRQ - 2

Mary Company, operating in a monopolistically competitive industry, produces a cleaning product called BriteKlean. The company currently produces the profit-maximizing quantity of BriteKlean but is operating at a loss.

  • (a) Draw a correctly labeled graph for Mary Company and show each of the following
    • (i) The profit-maximizing output and price, labeled as Q and PM, respectively
    • (ii) The area of loss, shaded completely
  • (b) what must be true in the short run for the company to continue to produce at a loss?
  • (c) Assume now that the demand for cleaning products increases and that the company is now earning short-run economic profits. Relative to this short-run situation, how does each of the following change in the long run?
    • (i) The number of firms
    • (ii) The company’s profit
  • (d) In the long run, if the company continues to produce, will it produce the allocatively efficient level of output? Explain
  • (e)In the long run, will the company be operating in a region where economies of scale exist? Explain.
  • Solution: It will operate in a region where economies of scale exist, because the firm is in a monopolistically competitive industry. In the long run, $P = ATC > \min ATC$, the firm will always produce where the slope of $ATC$ is negative, from which the company is operating in a region where economies of scale exist.

Unit 4 - FRQ - 3

这一题当中,Nash Equilibrium有两个,已经在图片上标注出来了。做法:画圈圈出对手在不同情况下选择做出的Dominant Strategy或者Strategy,如果一个格子里有两个公司的圈就是均衡。

Unit 5 - FRQ - 1

The John Lamb Company, a profit-maximizing firm producing widgets, is in a perfectly competitive widget market. Assume John Lamb employs a fixed number of employees and rents a machine for a variable number of hours from a perfectly competitive market

  • (a) Using correctly labeled side-by-side graphs of the factor market for machines and the John Lamb Company, show each of the following
    • (i) The equilibrium rental price of machines in the factor market, labeled as $P_R$
    • (ii) John Lamb’s equilibrium rental quantity of machines, labeled as $Q_L$
  • (b) Assume that the popularity of widgets declines, decreasing the demand for widgets. What will happen to each of the following?
    • (i) Marginal product curve for machine-hours
    • Solution: It will remain the same. $MP_M$ doesn’t relate with $P$
    • (ii) Marginal revenue product curve for machine-hours. Explain.
    • Solution: It will decrease, since $MR = P \times MP_M$, with $P$ decreasing, $MR$ will decrease too.
  • (c) John Lamb is employing the cost-minimizing combination of inputs. The marginal product of labor is 28 widgets per worker hour and the wage rate is $14 per hour. The marginal product of the machine is 60 widgets per machine-hour. What is the hourly rental price of a machine?

Unit 5 - FRQ - 2 - Monopsony(单一Employer)

Woodland is a small town in which everyone works for TreeMart, the local lumber company. TreeMart is a monopsonist in the labor market and a perfect competitor in the lumber market. In the short run, labor is the only variable input. The labor market for TreeMart is given in the graph above

  • (a) Identify the profit-maximizing quantity of labor for TreeMart
  • Solution: $MC = MR$, 100.
  • (b)Identify the wage rate Tree Mart pays to hire the profit-maximizing quantity of labor
  • Solution: $10
  • (c) Identify the quantity of labor hired in each of the following situations.
    • (i) Tree Mart operates in a competitive labor market
    • Solution: Competitive $\rightarrow S = D$, 200.
    • (ii) The government imposes a minimum wage of $12.5 Explain.
    • Solution: With the minimum wage of $12.5, according to the supply curve of labor, the company will hire 150 units of labor.

重要注意点

  1. 写清楚单位
posted @ 2021-01-14 14:32  gyro永不抽风  阅读(219)  评论(0编辑  收藏  举报