清华大学中级微观经济学讲义
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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-1
二理论的构成二理论的构成公理假设断言公理假设断言aa一经济学的理论要素一经济学的理论要素第一讲第一讲经济学方法简略经济学方法简略局部条件验证解释局部条件验证解释cc事件行为结果事件行为结果ee三理论的逻辑关系三理论的逻辑关系aaaacccceeee一经济学的理论要素一经济学的理论要素第一讲第一讲经济学方法简略经济学方法简略猜想猜想推测推测解释解释二科学认知的检验二科学认知的检验第一讲第一讲经济学方法简略经济学方法简略二科学认知的检验二科学认知的检验二验证
第一讲 经济学方法简略
四、最优化的数学基础
（三）等式约束极值问题－续（4） 等式约束极值问题－
max = f ( x, a ) x 最优化问题： 最优化问题： s.t . g( x, a ) = 0 拉格朗日函数 L( x, a; λ ) = f ( x, a ) − λg( x, a ) 值函数： V(a ) = max{f ( x, a ) : g( x, a ) = 0} = f ( x(a ), a ) 值函数：
引入环境参数 a： 1. 最优选择和环境参数的 关系： 关系： max f ( x, a )问题的一阶条件为 f x ( x, a ) = 0，假设满足隐函数定理 ，
x
则存在显函数 x* = x(a )。代入一阶条件得恒等 式f x ( x(a ), a ) ≡ 0。两边 dx * f xa 对a求导可以得到 =− 。 da f xx 2. 最大值和环境参数的关 系： 代入目标函数， 把x* = x(a )代入目标函数，得值函 数y * = f ( x(a ), a )。两边对 a求导 dy * dx* dy * 称为包络定理。 可以得到 = fx + fa，则成立关系 = f a ( x(a ), a ), 称为包络定理。 da da da
第一讲 经济学方法简略
四、最优化的数学基础
（三）等式约束极值问题－续（4） 等式约束极值问题－
max = f ( x, a ) x 最优化问题： 最优化问题： s.t . g( x, a ) = 0 拉格朗日函数 L( x, a; λ ) = f ( x, a ) − λg( x, a ) 值函数： V(a ) = max{f ( x, a ) : g( x, a ) = 0} = f ( x(a ), a ) 值函数：
引入环境参数 a： 1. 最优选择和环境参数的 关系： 关系： max f ( x, a )问题的一阶条件为 f x ( x, a ) = 0，假设满足隐函数定理 ，
x
则存在显函数 x* = x(a )。代入一阶条件得恒等 式f x ( x(a ), a ) ≡ 0。两边 dx * f xa 对a求导可以得到 =− 。 da f xx 2. 最大值和环境参数的关 系： 代入目标函数， 把x* = x(a )代入目标函数，得值函 数y * = f ( x(a ), a )。两边对 a求导 dy * dx* dy * 称为包络定理。 可以得到 = fx + fa，则成立关系 = f a ( x(a ), a ), 称为包络定理。 da da da
微观经济学--清华讲义
y1
y
短期供给曲线
完全竞争厂商的长期均衡 p LMC LAC
成本不变行业中的长期均衡
p
LMC
p
LAC
S1
p'1
E'1
S2
p1
E
LS
E1
E2
D2
D1
O
y1
O
y
成本递增行业中的长期均衡
p
p
p'1
LAC2
p2
LAC1
E"
p1 E'
S1 E'1
S2 LS
E2 E1
D2
D1
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y
成本递减行业中的长期均衡
p
p
S1
p'1
LAC1
p2
LAC2 E'
p1 E"
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p
垄断厂商的短期均衡：
p
y : MR MC; p : p p( y) p'
垄断厂商的长期均衡： y : MR LMC; p : p p( y) O
p
分割市场与价格歧视：
MR1( y1) MR2 ( y2 )
如何影响供给的？
3. 运用供求分析说明： （1）“谷贱伤农”的道理何在？ （2）为什么20世纪70年代石油输出国组织要限制石
油产量？
三、计算与证明
某厂商面对的市场需求曲线为Q=20-3P，求价格P=2 时需求的点弹性值。该厂商如何调整价格才能使 总收益增加？
历年考题
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 =
清华大学李稻葵中级微观经济学讲义
Chapter One
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:
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清华李稻葵13共54页文档
What do we do in this Chapter?
We study a special case of consumer choice under uncertainty; That is, when consumer preference over uncertainty can be reduced to only two parameters: Mean and standard deviation.
Variance measures the r.v.’s variation.
Standard Deviation of a Distribution
The distribution’s standard deviation is the square root of its variance;
s t.d e v [w ]w w 2 S (w sw )2s. s 1 St. deviation also measures the r.v.’s variability.
to be purchased must have rmrf .
Budget Constraints for Risky Assets
rx x r m (1 x )rf. x = 0 rx rf and x = 1 rxrm.
Since stock is risky and risk is a bad, for stock
Random Variable Values
Preferences over Risky Assets
Higher mean return is preferred. Less variation in return is preferred (less risk).
We study a special case of consumer choice under uncertainty; That is, when consumer preference over uncertainty can be reduced to only two parameters: Mean and standard deviation.
Variance measures the r.v.’s variation.
Standard Deviation of a Distribution
The distribution’s standard deviation is the square root of its variance;
s t.d e v [w ]w w 2 S (w sw )2s. s 1 St. deviation also measures the r.v.’s variability.
to be purchased must have rmrf .
Budget Constraints for Risky Assets
rx x r m (1 x )rf. x = 0 rx rf and x = 1 rxrm.
Since stock is risky and risk is a bad, for stock
Random Variable Values
Preferences over Risky Assets
Higher mean return is preferred. Less variation in return is preferred (less risk).
清华大学中级微观经济学讲义
p y w 1 x 1 w 2 x ~ 2 . I.e. yw p 1x1p w 2x ~2.
.
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
.
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
中级微观经济学课件
6
Market Demand versus Individual Demand
▪ The market demand is the sum of all the individual demands
for a particular good or service at each price.
▪ Suppose Joan and Kate are the only two buyers in the
12
P
$6.00 $5.00 $4.00 $3.00 $2.00 $1.00 $0.00
0
No. of Buyers
Suppose the number of buyers increases. Then, at each P, Qd will increase (by 5 in this example).
the price of one good leads to a decrease in the demand for the others. Example: computer and software, Coke and Hamburger
15
Tastes
▪ The most obvious determinant of your demand is your
price of one good leads to an increase in the demand for the other. Example: Coke and Pepsi, KFC and McDonalds.
▪ Complements: two goods for which an increase in
$6.00 $5.00 $4.00 $3.00 $2.00 $1.00
清华大学中级微观经济学讲义清华李稻葵(1)
.c n/
Chapter Fifteen
Market Demand
What Is the Purpose of This Chapter?
• We aggregate individual demand and form a market demand function. • We study a property of the market demand function
From Individual to Market Demand Functions
• Think of an economy containing n consumers, denoted by i = 1, … ,n. • Consumer i’s ordinary demand function for commodity j is
x*1A xB1
An Important Concept: Elasticity
• Elasticity measures the “sensitivity” of one variable with respect to another.
• The elasticity of variable X with respect to variable Y is
dp
dp
X*(p)1
p X*(p)
dX* dp
X*(p)1 .
Revenue and Own-Price Elasticity of Demand
dR dp
X* (p)1
so if 1 then
dR 0 dp
and a change to price does not alter sellers’ revenue.
Chapter Fifteen
Market Demand
What Is the Purpose of This Chapter?
• We aggregate individual demand and form a market demand function. • We study a property of the market demand function
From Individual to Market Demand Functions
• Think of an economy containing n consumers, denoted by i = 1, … ,n. • Consumer i’s ordinary demand function for commodity j is
x*1A xB1
An Important Concept: Elasticity
• Elasticity measures the “sensitivity” of one variable with respect to another.
• The elasticity of variable X with respect to variable Y is
dp
dp
X*(p)1
p X*(p)
dX* dp
X*(p)1 .
Revenue and Own-Price Elasticity of Demand
dR dp
X* (p)1
so if 1 then
dR 0 dp
and a change to price does not alter sellers’ revenue.
中级微观经济学课件
中级微观经济学课件中级微观经济学课件第一讲显示偏好【教学目的和要求】显示偏好理论（Revealed Preference）是中级微观经济学中有关消费理论的重要内容。
消费需求理论在给定消费者偏好以及预算约束下研究消费者选择以及需求问题；显示偏好理论则是从消费者的选择来辨析其偏好关系，即从其行为的信息揭示偏好的信息。
通过本章的学习，学生需要掌握直接显示偏好和间接显示偏好的概念，重点理解显示偏好弱公理和显示偏好强公理的内容和检验方法，了解显示偏好原理的应用。
【主要内容】1.显示偏好的概念2.从显示偏好到偏好3.恢复偏好4.显示偏好弱公理、检验显示偏好弱公理5.显示偏好强公理、如何检验显示偏好强公理6.指数、价格指数【教学总时数】 3【参考资料】：《微观经济学：现代观点》第七章【作业与思考题】：《微观经济学：现代观点（练习册）》（第八版）7.1,7.3,7.5,7.7,7.9第二讲斯勒茨基方程【教学目的和要求】当某商品价格发生变化时，会对该商品的需求量产生两种影响效应：一种是因为相对价格的变化所引起需求量的改变，称之为替代效应（SubstitutionEffect），如商品价格下降意味该商品相对其他商品更便宜了；一种是因为价格变化引起货币购买力发生变化从而对商品需求量的影响，称之为收入效应（Income Effect），如商品价格下降意味货币实际购买力增加了。
本章通过运用斯勒茨基方程（Slutsky Equation）对这两种效应进行分解说明，进一步揭示需求法则。
通过本章的学习，学生需要了解替代效应和收入效应的的概念，能够辨析总效应的符号和产生原因；掌握计算替代效应和收入效应的方法；理解斯勒茨基替代和希克斯替代的区别于联系；熟练掌握运用替代效应和收入效应分析实际问题的方法。
【主要内容】1.替代效应、收入效应的概念2.替代效应的符号3.需求的总变动4.变动率5.需求法则6.替代效应和收入效应的例子7.希克斯替代效应8.补偿需求曲线【教学总时数】 3【参考资料】：《微观经济学：现代观点》第八章【作业与思考题】：《微观经济学：现代观点（练习册）》（第八版）8.2-8.9第三讲购买和销售【教学目的和要求】斯勒茨基方程阐述给定收入下价格变动所带来的替代效应和收入效应。
中级微观经济学课件
❖ 消费者有如下选择:
• 价格 (p1,p2)=($2,$2) 时，选择 (x1,x2)
= (10,1).
• 价格 (p1,p2)=($2,$1)时，选择 (x1,x2) =
(5,5).
• 价格 (p1,p2)=($1,$2)时，选择 (x1,x2) =
(5,4).
每个商品束按各组价格计算的支出
Choices Prices
❖ 如果观察到的行为是最优化行为，那么 这种行为一定满足显示偏好强公理。
消费者效用最大化行为：消费者总是选择 他能够负担的最佳物品。
其最优选择一定满足显示偏好强公理。 总能找到选择的性状良好的偏好。这就是
最优化行为的偏好。
例题2 检验强显示偏好
❖ 消费者有如下选择:
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)
[案例评析]：
❖ 在初级微观经济学中，消费者偏好必须满足三个基本假设： ❖ 1．消费者能对任意两种物品的不同组合进行比较或排序。对于两个商品组合A和B，消费
者能确定对两个组合的喜欢程度的比较，如对A的偏好大于对B的偏好，对B的偏好大于对 A的偏好，对A、B的偏好相同，及A>B、A<B或者A=B，三者必居其一。 ❖ 2．费者偏好的可传递性，偏好在逻辑上是一致的。对于任何三个商品组合A、B、C，如 果消费者对A的偏好大于对B的偏好，对B的偏好大于对C的偏好，即若A>B、B>C，则必 有A>C。 ❖ 3．“多比少好”的原则或非饱和性。当全部商品都是值得拥有时，则消费者总是偏好数 量较多的商品组合。 ❖ 这只是关于消费者偏好的三个基本假设，而本案例给大家提供了更多的关于偏好的假定和 理解，有利于我们更进一步认识消费者理论的基础，同时提供了一个平台使得我们可以开 始探讨消费者行为等复杂的经济现象。
• 价格 (p1,p2)=($2,$2) 时，选择 (x1,x2)
= (10,1).
• 价格 (p1,p2)=($2,$1)时，选择 (x1,x2) =
(5,5).
• 价格 (p1,p2)=($1,$2)时，选择 (x1,x2) =
(5,4).
每个商品束按各组价格计算的支出
Choices Prices
❖ 如果观察到的行为是最优化行为，那么 这种行为一定满足显示偏好强公理。
消费者效用最大化行为：消费者总是选择 他能够负担的最佳物品。
其最优选择一定满足显示偏好强公理。 总能找到选择的性状良好的偏好。这就是
最优化行为的偏好。
例题2 检验强显示偏好
❖ 消费者有如下选择:
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)
[案例评析]：
❖ 在初级微观经济学中，消费者偏好必须满足三个基本假设： ❖ 1．消费者能对任意两种物品的不同组合进行比较或排序。对于两个商品组合A和B，消费
者能确定对两个组合的喜欢程度的比较，如对A的偏好大于对B的偏好，对B的偏好大于对 A的偏好，对A、B的偏好相同，及A>B、A<B或者A=B，三者必居其一。 ❖ 2．费者偏好的可传递性，偏好在逻辑上是一致的。对于任何三个商品组合A、B、C，如 果消费者对A的偏好大于对B的偏好，对B的偏好大于对C的偏好，即若A>B、B>C，则必 有A>C。 ❖ 3．“多比少好”的原则或非饱和性。当全部商品都是值得拥有时，则消费者总是偏好数 量较多的商品组合。 ❖ 这只是关于消费者偏好的三个基本假设，而本案例给大家提供了更多的关于偏好的假定和 理解，有利于我们更进一步认识消费者理论的基础，同时提供了一个平台使得我们可以开 始探讨消费者行为等复杂的经济现象。
清华大学中级微观经济学讲义(清华 李稻葵)11-16页精选文档
to impatient people (borrowers) in exchange for a rate-of-return on the loaned funds. – both groups are better off.
Arbitrage
The price today of an asset is p0. Its price tomorrow will be p1. Should it be sold now?
The rate-of-return from holding the
asset is I.e.
R p1 p0 p0
( 1 R ) p 0 ( 1 r ) p 0 .
I.e. if the rate-or-return to holding the
asset Rr the interest rate, then
keep the asset.
And if Rr then ( 1 R ) p 0 ( 1 r lly asset values are uncertain. Incorporating uncertainty is difficult at this stage so we will instead study assets assuming that we can see the future with perfect certainty.
Assets with Consumption Returns
The example of house A=appreciation T=implicit rental rate P=initial investment h=(T+A)/P=total rate of return h=(T+A)/P=r
Arbitrage
The price today of an asset is p0. Its price tomorrow will be p1. Should it be sold now?
The rate-of-return from holding the
asset is I.e.
R p1 p0 p0
( 1 R ) p 0 ( 1 r ) p 0 .
I.e. if the rate-or-return to holding the
asset Rr the interest rate, then
keep the asset.
And if Rr then ( 1 R ) p 0 ( 1 r lly asset values are uncertain. Incorporating uncertainty is difficult at this stage so we will instead study assets assuming that we can see the future with perfect certainty.
Assets with Consumption Returns
The example of house A=appreciation T=implicit rental rate P=initial investment h=(T+A)/P=total rate of return h=(T+A)/P=r