清华大学中级微观经济学讲义(清华 李稻葵)32
清华大学中级微观经济学讲义(清华 李稻葵)7
The Strong Axiom of Revealed Preference
A: ($1,$3,$10) (3,1,4). B: ($4,$3,$6) (2,5,3). C: ($1,$1,$5) (4,4,3).
Choice Prices A B C A $46 $39 $24 B $47 $41 $22 C $46 $46 $23
Digression: Science vs. Engineering (对比科学家思维与工程师思维） 找问题与解问题的不同 –要对问题提问题 要对问题提问题 务虚与务实的不同 解释世界与改造世界的不同 –旁观者与参与者的不同 旁观者与参与者的不同
Maintained Assumptions on Preferences
The Strong Axiom of Revealed Preference
Consider the following data: A: (p1,p2,p3) = (1,3,10) & (x1,x2,x3) = (3,1,4) B: (p1,p2,p3) = (4,3,6) & (x1,x2,x3) = (2,5,3) C: (p1,p2,p3) = (1,1,5) & (x1,x2,x3) = (4,4,3)
Recovering Indifference Curves
Suppose we observe: A: (p1,p2) = ($1,$1) & (x1,x2) = (15,15) B: (p1,p2) = ($2,$1) & (x1,x2) = (10,20) C: (p1,p2) = ($1,$2) & (x1,x2) = (20,10) D: (p1,p2) = ($2,$5) & (x1,x2) = (30,12) E: (p1,p2) = ($5,$2) & (x1,x2) = (12,30). Where lies the indifference curve containing the bundle A = (15,15)?
清华大学中级微观经济学讲义清华李稻葵15-文档资料26页
Marginal Revenue and Own-Price Elasticity of Demand
p
a
p (q )ab q
a/2b
a/b q
M R (q ) a 2 b q
Marginal Revenue and Own-Price p Elasticity of Demand
a
M R (q ) a 2 b q
Then Xi = (a-pi)/b and
dX
* i
1.
Therefore,
dpi b
X i * ,p i (a p p ii)/b b 1 a p ip i.
Point Own-Price Elasticity
pi
pi = a - bXi*
X j(p 1 ,p 2 ,m 1 , ,m n ) n x * ji(p 1 ,p 2 ,m i).
i 1
From Individual to Market Demand
Functions
p1
p1
p1’
p1’
p1”
p1”
p1
20
x
* 1
A
15
x
* 1
B
p1’
The “horizontal sum”
The elasticity of variable X with
respect to variable Y is
x,y
%x. %y
Slope Vs. Elasticity
Q: Why not just use the slope of a demand curve to measure the sensitivity of quantity demanded to a change in a commodity’s own price?
中级微观经济学讲义-3
中级微观经济学讲义-3西方经济学第三讲生产者理论本课件借鉴了国内有关教材的内容,特此致谢!本课件借鉴了国内有关教材的内容,特此致谢!西方经济学第三讲生产者理论一,生产函数(一)生产可能性集化为产出的过程.生产是各种投入组合转化为产出的过程.这个技术的可行性.过程受到的基本约束是技术的可行性.式是生产可能性集,描述技术约束的一般方式是生产可能性集,即YRn,其中y=(y1,y2...yn)∈Y是一个生产计划,是一个生产计划,产出的数量.分量代表了各种投入和产出的数量.例如y=(5,1,6,2,0).有效率的生产是指对于y,生产可能性集中不存在y'≥y,y'≠y.西方经济学第三讲生产者理论一,生产函数(二)生产函数局部均衡分析中,一种产出的情况.局部均衡分析中,关注一种产出的情况.生产函数描述了有效率的生产.生产函数一般表示为y=f(某)=(某1,某2...某n),可以理解为对应的生产可能性集是{y≤f(某)},生产函的最上界.数达到了生产可能性集的最上界.西方经济学第三讲生产者理论一,生产函数(三)生产中的替代性的投入组合的集合,投入要求集是指至少可以生产一定产出的所有的投入组合的集合,可以表示为等产量集,为V(y).投入要求集的边界称为等产量集,在两种投入的情况下即等产量线.f(某)d某j 某i际技术替代率表示为:=任意两种要素投入的边际技术替代率表示为:MRTSi,j=dy=0f(某)d某i某jd(同替代弹性来表示:为剔除计量单位的影响,同替代弹性来表示:σi,j=d(某j某i某ififjfj))=dln(dln(某j 某ififj))某jfi西方经济学第三讲生产者理论一,生产函数(四)生产中的时间性1.可变比例(短期)可变比例(短期)f(某)边际产出MPi(某)=fi(某),平均产出APi(某)=某产出弹性i(某)=fi(某)某if(某)=MPi(某)APi(某)i2.固定比例与规模报酬(长期)固定比例与规模报酬(长期)规模报酬不变.对于所有t>0和任意某,如果f(t某)=tf(某),规模报酬不变.规模报酬递增.对于所有t>1和任意某,如果f(t某)>tf(某),规模报酬递增.规模报酬递减.对于所有t>1和任意某,如果f(t某)<tf(某),规模报酬递减.质用规模弹性(总弹性):度量局部的规模报酬性质用规模弹性(产出的总弹性):ndy(t)t(某)=dtyt=1df(t某)t=dtf(t某)t=1dlnf(t某)=dlntt=1=∑f(某)某i1if(某)西方经济学第三讲生产者理论一,生产函数(五)产出增长的分解假设生产函数为y=A(t)f[k(t),l(t)],其中A(t)表示技术因素(中性技术进步).两边对时间求导得dydAydkdly=+[fk+fl].再除以产量dtdtA(t)dtdtf(k,l)dyy,整理得dt=ydAdt+fkkAf(k,l)dkdt+fllkf(k,l)dldt.l这可以表示为:这可以表示为:Gy=GA+y,kGk+y,lGl西方经济学第三讲生产者理论一,生产函数(一)成本最小化的生产特征【成本优化问题】成本优化问题】minw 某某.t.f(某)≥y其中w=(w1,w2...wn)构造拉格朗日函数l=w某+λ(yf(某))f(某某)成本最小化的一阶条件为:wi=λ某i某f(某某)进一步得到:进一步得到:f(某某)某i某j=wiwjwif(某某)某成本.拉格朗日乘数λ=可以理解为产出的边际成本.某i 练习:1.根据包络定理说明拉格朗日乘数的经济含义根据包络定理说明拉格朗日乘数的经济含义.练习:1.根据包络定理说明拉格朗日乘数的经济含义.西方经济学第三讲生产者理论二,成本最小化(一)成本最小化的生产特征-续(1)成本最小化的生产特征-【条件要素需求的性质某(w,y)】1.关于w是零次齐次的.是零次齐次的.某i(w,y)2.要素需求法则:要素需求法则:<0wi某i(w,y)3.替代性:替代性:>0wj思考:1.要素需求函数和消费者行为理论中的哪个函数是类似的要素需求函数和消费者行为理论中的哪个函数是类似的思考:1.要素需求函数和消费者行为理论中的哪个函数是类似的西方经济学第三讲生产者理论二,成本最小化(一)成本最小化的生产特征-续(2)成本最小化的生产特征-【成本函数的性质c(w,y)】1.对于所有的w>>0,关于产量严格递增且无上界.无上界.2.关于w是递增的.是递增的.3.关于w是一次齐次的.是一次齐次的.4.关于w是凹的.是凹的.5.如果规模报酬不变c(w,y)=yc(w,1).思考:1.成本函数作为凹函数的含义是什么成本函数作为凹函数的含义是什么思考:1.成本函数作为凹函数的含义是什么西方经济学第三讲生产者理论二,成本最小化(二)成本函数与生产函数【报酬递减与短期成本】描述企业的技术特征既可以使用生产函数,也可以使用成本可以使用生产函数,函数.函数.1.STC=w某(w,w,y;某)+w某STC2.SAC=y3.w某(w,w,y;某)SAVC=y4.5.w某SAFC=yAMC=STCy由于固定成本的分摊性质,平均固定成本随着产量上升递减.产量上升递减.报酬递减规律则意味着平均可变成本和边际成本呈U型.且边际和平均成本的最低点.成本穿过平均可变成本和平均成本的最低点.西方经济学第三讲生产者理论二,成本最小化(二)成本函数与生产函数-续成本函数与生产函数-【成本函数的次可加】成本函数的次可加】设y=∑yi,平均成本递减意味着iSTC(yi)STC(y)>,即yiySTC(yi)>STC(y)yi,求和得∑STC(yi)>STC(y).成本的次yi济或范围经济效应.可加性可以描述规模经济或范围经济效应.西方经济学第三讲生产者理论三,利润最大化(一)利润最大化的条件【以完全竞争为例】以完全竞争为例】利润最大化决策的优化问题是ma某pf(某)w某.某f(某某)一阶条件是p=wi(即每种要素投入的边际收益产品某iMRP等于这种要素投入的价格).进一步,对于任意两种要素进一步,wi=MRSTi,j.还有λ某=p(边际成本等于价格).满足wj海塞矩阵负半定.二阶条件是生产函数的海塞矩阵负半定.可以理解为凹函为规模报酬非递增.数(边际产出递减),多种投入下可以理解为规模报酬非递增.西方经济学第三讲生产者理论三,利润最大化(二)供给函数和利润函数利润最大化的一阶条件可以得到要素需求函数某某=某(p,w),带入生产函数得到供给函数y某=f(某(p,w)),带入目标函数得到利润函数π(p,w)=pf(某某)w某某.【利润函数的性质】利润函数的性质】ππ引理:1.Hotelling引理:=y(p,w),=某i(p,w).wip是递增的.2.关于p是递增的.是递减的.3.关于w是递减的.是一次齐次的.4.关于(p,w)是一次齐次的.5.关于(p,w)是凸的.是凸的.西方经济学第三讲生产者理论三,利润最大化(二)供给函数和利润函数-续供给函数和利润函数-【要素需求函数的性质】1.关于(p,w)是零次齐次的.是零次齐次的.某i(p,w)2.≤0.wi【供给函数的性质】供给函数的性质】1.关于(p,w)是零次齐次的.是零次齐次的.y(p,w)2.≥0.p西方经济学第三讲生产者理论三,利润最大化(三)利润最大化假设的现实性【利润满意化原则】利润满意化原则】意化.由于决策者的有限理性,企业往往追求利润满意化.【经理主义】经理主义】在缺乏有效监督和激励的前提下,掌握一定剩余控制权的前提下,利润最大化目标.的经理人员的选择偏离利润最大化目标.【产权结构】产权结构】利润最大化假设忽略了企业内部要素提供者之间的合约关系对企业行为的影响.西方经济学西方经济学112某消费者的效用函数是u(某1,某2)=某1某2,如果价格和收入分别为p1=1,p2=1,m=24.当p1提高为2时,求关于商品某1的斯勒茨基替代效应和收入效应.入效应.西方经济学122p1y为商品数量,为价格,函数某1=,其中某为商品数量,p为价格,p1+p2y收入.这个函数可以作为马歇尔需求函数吗请为马歇尔需求函数吗收入.说明理由(提示:效应).说明理由(提示:替代效应).西方经济学13消费者具有拟线性偏好,效用对于第二种商品是线性的,绘图说明第一种商品价格下降的价格是线性的,效用分解.效用分解.。
Ch12Uncertainty(中级微观经济学-清华大学,钟笑寒)
m L Cna Ca 1 1
slope
mL
1
Where is the most preferred state-contingent consumption plan?
m L Ca
Preferences Under Uncertainty
In
general, how a person values consumption in one state as compared to another will depend on the probability that the state in question will actually occur. Suppose that we are considering two mutually exclusive states. Let c1 and c2 represent consumption in state 1 and 2, and let 1 and 2 be the probabilities that state 1 or 2 actually occurs. Thus 1+2=1. The utility function can be written as U(c1,c2,1,2)
State-Contingent Budget Constraints
m L 1
Cna
m L Cna Ca 1 1
m
The endowment bundle.
mL
m L Ca
State-Contingent Budget Constraints
m L 1
State-Contingent Budget Constraints
《微观经济学》清华大学课件Ch5Choice消费者最优选择共37页文档
p1x* 1p2x* 2m . (B)
Computing Ordinary Demands a Cobb-Douglas Example.
So we have discovered that the most preferred affordable bundle for a consumer with Cobb-Douglas preferences
x2
(x1*,x2*) is interior.
(a) (x1*,x2*) exhausts the
budget; p1x1* + p2x2* = m.
x2*
x1*
x1
Rational Constrained Choice
x2
(x1*,x2*) is interior .
(b) The slope of the indiff.
U (x1,x2)x1 axb 2
is
( ) (x * 1 ,x * 2 )(a a m b )p 1 ,(a b m b )p 2.
Computing Ordinary Demands -
a Cobb-Douglas Example.
x2
U (x1,x2)x1 axb 2
x
* 2
bm
(a b )p 2
curve at (x1*,x2*) equals the slope of the budget
constraint. x2*
x1*
x1
Rational Constrained Choice
(x1*,x2*) satisfies two conditions: (a) the budget is exhausted;
清华大学中级微观经济学讲义(清华 李稻葵)30
The Endowment Allocation
2 OB 2 6 4 OA 6 8
ω = (2,2)
B
The Endowment Allocation
2 OB 2 6 4 OA 6 8 The endowment allocation
A ω = (6,4) B
ω = (2,2)
The Endowment Allocation
/ Remarks on the Final
Final Examination: 1. Final exam is comprehensive. 2. It mainly covers the material after midterm. 3. The materials before midterm are important in two ways: 1) some problems may directly come from those chapters. 2) the materials before midterm provide a foundation for new materials. The format of the final will be the same as that in the midterm. Office Hour: 4-5 pm Thursday
Starting an Edgeworth Box
Height = A B ω2 + ω2
= 4+ 2 =6
The dimensions of the box are the quantities available of the goods.
A B ω1 + ω1 = 6 + 2 = 8 Width =
中级微观经济学课件
市场均衡及其形成机制
市场均衡定义：市场上的供给和需求相等，价格不再变动的一种状态。
形成机制：在竞争市场中，价格变动会引发供给和需求的调整，最终达到市场均衡。
均衡的稳定性：在短期内，市场均衡是相对稳定的；但在长期中，市场均衡可能会因为 外部因素而发生变化。 市场均衡的意义：市场均衡是经济学的核心概念之一，对于理解市场经济运行规律和制 定经济政策具有重要的意义。
价格歧视和垄断定价
价格歧视定义：对同一商品或服务在不同市场以不同价格销售的行为。 目的：增加利润，最大化企业收益。 类型：一级、二级和三级价格歧视。 垄断定价：在独家垄断市场中，企业通过限制产量和抬高价格来最大化利润。
福利经济学及其主要观点
福利经济学定义：研究如何实现社会福利最大化的经济学分支。
消费者行为及其影响因素
消费者偏好：影响消费者行为的重要因素，决定了消费者的购买决策。 收入水平：收入水平的高低直接影响消费者的购买能力，进而影响其消费行为。 价格变动：价格变动对消费者行为有显著影响，价格上升或下降会影响消费者的需求量。 消费者预期：消费者对未来经济状况的预期会影响其当前的消费行为。
类型：垄断竞争市场、寡头市场、完全垄断市场 特点：产品差异、市场壁垒、市场集中度高、价格接受者
寡头市场的形成和竞争策略
寡头市场的定义：少数几家大企业占据了大部分的市场份额，从而影响市 场的价格和产量。
寡头市场的形成原因：市场进入壁垒、规模经济、产品差异化和政府政策 等因素导致市场结构趋于寡头化。
竞争策略：采用价格战、广告战Байду номын сангаас研发和创新等手段来争夺市场份额，提 高自身竞争力。
合作策略：通过达成协议、建立联盟等方式来共同控制市场价格和产量， 实现共赢。
清华大学李稻葵中级微观经济学讲义
The Market --- Appreciating Economic Modeling
The Purpose of this Chapter
• To begin to understand the art of building an economic model • To begin to understand three basic elements of modeling in economics:
– apartments are close or distant, but otherwise identical – distant apartments rents are exo genous (外生变量） and known – many potential renters and landlords
– Purpose – Simplification through assumptions – Value judgment
The Purpose of an Economic Model
• The purpose of an economic model is to help provide precise insights (精确的 洞察力）on a specific economic phenomenon. • Thus:
– Different phenomena needs different model; – Simplification by assumption is necessary
An Illustration: Modeling the Apartment Market
• Purpose: How are apartment rents determined? Are rents “desirable”? • Simplifying assumptions:
清华大学中级微观经济学讲义
.
Short-Run Iso-Profit Lines
y
Slopesw1 p
x1
.
Short-Run Profit-Maximization
y
y f(x 1 ,x ~ 2 )
.
Economic Profit
The economic profit generated by (x1,…,xm,y1,…,yn) is
p 1 y 1 p n y n w 1 x 1 w m x m .
Notes:
For the time being, we restrict to the case of a competitive firm, which is a tiny relative to the market size and takes prices p1,…,pn w1,…,wm as given constants;
.
Comparative Statics of Short-Run
Profit-Maximization
y
y f(x 1 ,x ~ 2 )
y* Slopesw1 p
x
* 1
x1
.
Comparative Statics of Short-Run
Profit-Maximization
y
equal. y*
M P1
w1 p
Slopesw1 p
a
t
(
x
* 1
,
x~
2
,
y*
)
x
* 1
x1
Ch19Profit-Maximization(中级微观经济学-清华大学,钟笑寒)
~ py w1x1 w 2x2 .
Short-Run Iso-Profit Lines
$ iso-profit line contains all the production plans that yield a profit level of $ . The equation of a $ iso-profit line is
The Competitive Firm
The
competitive firm takes all output prices p1,…,pn and all input prices w1,…,wm as given constants.
Economic Profit
The
economic profit generated by the production plan (x1,…,xm,y1,…,yn) is
Chapter Nineteen
Profit-Maximization
Economic Profit
A
firm uses inputs j = 1…,m to make products i = 1,…n. Output levels are y1,…,yn. Input levels are x1,…,xm. Product prices are p1,…,pn. Input prices are w1,…,wm.
Short-Run Profit-Maximization
y
The short-run production function and ~ . x x technology set for 2 2
~ ) y f ( x1 , x 2
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
Desirable Voting Rule Properties
Kenneth Arrow’s Impossibility Theorem: The only voting rule with all of properties 1, 2 and 3 is dictatorial.
Desirable Voting Rule Properties
B ill x y z B ertha B ob y z x z x y
Majority Vote Results x beats y No y beats z socially z beats x best alternative! Majority voting does not always aggregate transitive individual preferences into a transitive social preference.
B ill x(1) y(2) z(3)
Rank-order vote results B ertha B ob (low score wins). x-score = 6
y(1) z(2) x(3)
z(1) x(2) y(3)
Aggregating Preferences
B ill x(1) y(2) z(3)
Rank-order vote results B ertha B ob (low score wins). x-score = 6 y-score = 6 y(1) z(1)
z(2) x(3)
x(2) y(3)
Aggregating Preferences
B ill x(1) y(2) z(3)
These are truthful preferences. Bob introduces a new alternative
Manipulating Preferences
B ill x(1) y(2) z(3) α (4) B ertha B ob y(1) z(2) α (3) x(4) z(1) x(2) y(3) α (4)
/ Chapter Thirty-Two Welfare
What do we do in this chapter?
We at the end of this course We are exploring a few very important topics of microeconomics Welfare economics is an extremely important topic
These are truthful preferences. Bob introduces a new alternative and then lies. Rank-order vote results. x-score = 8
Manipulating Preferences
B ill x(1) y(2) z(3) α (4) B ertha B oby(4)
Aggregating Preferences
B ill x y z B ertha B ob y z x z x y
Majority Vote Results x beats y No y beats z socially z beats x best alternative!
Aggregating Preferences
Social Choice
Different economic states will be preferred by different individuals. How can individual preferences be “aggregated” into a social preference over all possible economic states?
Desirable Voting Rule Properties
1. If all individuals’ preferences are complete, reflexive and transitive, then so should be the social preference created by the voting rule. 2. If all individuals rank x before y then so should the voting rule. 3. Social preference between x and y should depend on individuals’ preferences between x and y only.
Manipulating Preferences
B ill x(1) y(2) z(3) B ertha B ob y(1) z(2) x(3) z(1) x(2) y(3)
These are truthful preferences.
Manipulating Preferences
B ill x(1) y(2) z(3) B ertha B ob y(1) z(2) x(3) z(1) x(2) y(3)
These are truthful preferences. Bob introduces a new alternative
Manipulating Preferences
B ill x(1) y(2) z(3) α (4) B ertha B ob y(1) z(2) α (3) x(4) z(1) x(2) y(3) α (4)
Social Welfare Functions
1. If all individuals’ preferences are complete, reflexive and transitive, then so should be the social preference created by the voting rule. 2. If all individuals rank x before y then so should the voting rule. 3. Social preference between x and y should depend on individuals’ preferences between x and y only.
Social Welfare Functions
1. If all individuals’ preferences are complete, reflexive and transitive, then so should be the social preference created by the voting rule. 2. If all individuals rank x before y then so should the voting rule. 3. Social preference between x and y should depend on individuals’ preferences between x and y only.
Aggregating Preferences
x, y, z denote different economic states. 3 agents; Bill, Bertha and Bob. Use simple majority voting to decide a state?
Aggregating Preferences
Manipulating Preferences
B ill x(1) y(2) z(3) α (4) B ertha B ob y(1) z(2) α (3) x(4) z(1) α(2) x(3) y(4)
These are truthful preferences. Bob introduces a new alternative and then lies. Rank-order vote results. x-score = 8 z wins!! y-score = 7 z-score = 6 α-score = 9
Aggregating Preferences
B ill x(1) y(2) z(3)
Rank-order vote results B ertha B ob (low score wins).
y(1) z(2) x(3)
z(1) x(2) y(3)
Aggregating Preferences
x(2) y(3)
Rank-order voting is indecisive in this case.
Manipulating Preferences
As well, most voting schemes are manipulable. I.e. one individual can cast an “untruthful” vote to improve the social outcome for himself. Again consider rank-order voting.
B ill x(1) y(2) z(3) α (4) B ertha B ob y(1) z(2) α (3) x(4) z(1) α(2) x(3) y(4)
These are truthful preferences. Bob introduces a new alternative and then lies. Rank-order vote results. x-score = 8 y-score = 7 z-score = 6
These are truthful preferences. Bob introduces a new alternative and then lies. Rank-order vote results. x-score = 8 y-score = 7